Fast startup baseband amplifier

Abstract

A fast startup baseband amplifier includes an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit. The fast startup baseband amplifier can be used in a microwave passive sensor or system, and a method for passively detecting a movement of a target.

Description

FAST STARTUP BASEBAND AMPLIFIER CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 622,700 filed on January 19, 2022 and entitled “Fast Startup Baseband Amplifier”.

[0002] This application is related to U.S. Patent Application No. 18 / 728,142 filed on July 11, 2024 and entitled “Microwave Architecture for Passive Sensing Applications”, which claims priority to PCT Patent Application No. PCT / US23 / 06650 filed on January 13, 2023 and entitled “Microwave Architecture for Passive Sensing Applications”, which claims priority to U.S. Provisional Patent Application No.63 / 299,942 filed on January 15, 2022 and entitled “Microwave Architecture for Passive Sensing Applications”.

[0003] All of the foregoing patent applications are hereby incorporated by reference in their entirety. TECHNICAL FIELD OF THE INVENTION

[0004] The present invention relates in general to the field of radar systems, and more particularly, to a fast startup baseband amplifier and method of operation. STATEMENT OF FEDERALLY FUNDED RESEARCH

[0005] This invention was made with government support under Grant / Contract Nos. ECCS- 2030094 and ECCS-1808613 awarded by the National Science Foundation (NSF). The government has certain rights in the invention. BACKGROUND OF THE INVENTION

[0006] Without limiting the scope of the invention, its background is described in connection with passive radar systems.

[0007] Recent trends in smart-home and Internet of Things (IoT) technology have enabled a considerable amount of integration and access to information within a user’s home [1]. Advances in wearable and wireless health monitoring have also made users more aware of their own health [2]. With more wireless devices and sensors using IoT, spectrum allocation has become a concern [3]. As such, techniques to minimize the introduction of new frequencies is of paramountimportance. Doppler radar has long been used as a method of wirelessly detecting human motion such as heartbeat and respiration [4], and advanced techniques have been used to monitor target beat-to-beat blood pressure and synthesize an EKG [5], [6]. Typically, these methods require the radar to transmit its own carrier frequency, reducing the available bandwidth for other IoT devices and further cluttering the spectrum. Passive radar has been used as a method of detecting motions using existing wireless signals such as Wi-Fi [7]. Previous passive Doppler radar designs have used commercial RF building blocks, and as such have a large power consumption and relatively large size making it non-ideal for IoT applications.

[0008] In addition, biomedical radars are typically interested in low-frequency physiological signals such as heartbeat (~1 Hz) and respiration (~0.1 Hz). The output of a radar normally contains both the motion information as well as a DC component introduced by a variety of factors including stationary clutter and mixer bias. This DC component is typically much larger than the motion amplitude, limiting the ability to directly amplify the output of the radar without also amplifying the DC component and saturating the amplifier. As a result, AC-coupled amplifiers are used to remove the DC contribution and amplify only the signal of interest. AC-coupled amplifiers, however, have a tradeoff in traditional amplifier design. In order to achieve good low- frequency gain, a high value of resistance and capacitance is needed. This, however, also creates long time delays during power-on, creating the problem of long startup times as can be seen by the figures below. When low-frequency response is good, the startup time suffers proportionally.

[0009] Accordingly, there is a need for a fast startup baseband amplifier and method of operation. SUMMARY OF THE INVENTION

[0010] Various embodiments of the present disclosure provide a passive radar operating in the 5- GHz Wi-Fi band that detects small-amplitude motions. The radar is designed using discrete RF components to allow for maximum performance versus power consumption and utilizes an on- board fast startup baseband amplifier to quickly reach the desired operating point, while keeping cost and complexity low. In addition, the integration of all active electronics on-board reduces the overall size of the system considerably, making it an ideal candidate for future wireless sensing or IoT applications. As a result, the embodiments disclosed herein offer a compact, efficient method of detecting the Doppler information of a target.

[0011] One embodiment of the present disclosure provides a fast startup baseband amplifier having an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit.

[0012] In one aspect, the one or two diodes comprise a first diode that charges a first capacitor connected to the input, or the two MOSFETs charge the first capacitor when the two MOSFETs are ON. In another aspect, the one or two diodes comprise a first diode that charges the first capacitor connected to the input, and a second diode that discharges the first capacitor. In another aspect, the one or two diodes comprise one or two radio frequency Schottky diodes. In another aspect, the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs. In another aspect, the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier. In another aspect, the input buffer and DC offset circuit is configured to have unity gain. In another aspect, the input buffer and DC offset circuit has a startup time less than ten seconds. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, the one or two diodes further comprise a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor. In another aspect, a second capacitor is connected in parallel with the second resistor. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, a second capacitor is connected in parallel with the second resistor.

[0013] Another embodiment of the present disclosure provides a microwave passive sensor that includes a microwave receiver; a low noise amplifier coupled to the microwave receiver; a mixer coupled to the low noise amplifier; and a fast startup baseband amplifier coupled to the mixer, wherein the fast startup baseband amplifier comprises: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit.

[0014] In one aspect, the one or two diodes comprise a first diode that charges a first capacitor connected to the input, or the two MOSFETs charge the first capacitor when the two MOSFETs are ON. In another aspect, the one or two diodes comprise a first diode that charges the first capacitor connected to the input, and a second diode that discharges the first capacitor. In another aspect, the one or two diodes comprise one or two radio frequency Schottky diodes. In another aspect, the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs. In another aspect, the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier. In another aspect, the input buffer and DC offset circuit is configured to have unity gain. In another aspect, the input buffer and DC offset circuit has a startup time less than ten seconds. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, the one or two diodes further comprise a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor. In another aspect, a second capacitor is connected in parallel with the second resistor. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, a second capacitor is connected in parallel with the second resistor.

[0015] Another embodiment of the present disclosure provides a method for passively detecting a movement of a target, the method comprising: receiving signals using a microwave receiver; amplifying the received signals using a low noise amplifier coupled to the microwave receiver; producing baseband signals from the reflected signal and the direct signal using a mixer; amplifying the baseband signals using a fast startup baseband amplifier comprising: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit; and detecting the movement of the target using the amplified baseband signals.

[0016] In one aspect, the movement includes a heartbeat, a breath, a limb movement or the target moving as a whole. In another aspect, the one or two diodes comprise a first diode that charges a first capacitor connected to the input, or the two MOSFETs charge the first capacitor when the two MOSFETs are ON. In another aspect, the one or two diodes comprise a first diode that charges the first capacitor connected to the input, and a second diode that discharges the first capacitor. In another aspect, the one or two diodes comprise one or two radio frequency Schottky diodes. In another aspect, the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs. In another aspect, the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier. In another aspect, the input buffer and DC offset circuit is configured to have unity gain. In another aspect, the input buffer and DC offset circuit has a startup time less than ten seconds. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, the one or two diodes further comprise a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor. In another aspect, a second capacitor is connected in parallel with the second resistor. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, whereinthe two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, a second capacitor is connected in parallel with the second resistor.

[0017] Another embodiment of the present disclosure provides a system comprising: one or more microwave passive sensors, each microwave passive sensor comprising a microwave receiver, a low noise amplifier coupled to the microwave receiver, a mixer coupled to the low noise amplifier, and a fast startup baseband amplifier coupled to the mixer, wherein the fast startup baseband amplifier comprises: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit; one or more microwave sources; and a processor or computer coupled to the one or more microwave passive sensors.

[0018] In one aspect, the one or two diodes comprise a first diode that charges a first capacitor connected to the input, or the two MOSFETs charge the first capacitor when the two MOSFETs are ON. In another aspect, the one or two diodes comprise a first diode that charges the first capacitor connected to the input, and a second diode that discharges the first capacitor. In another aspect, the one or two diodes comprise one or two radio frequency Schottky diodes. In another aspect, the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs. In another aspect, the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier. In another aspect, the input buffer and DC offset circuit is configured to have unity gain. In another aspect, the input buffer and DC offset circuit has a startup time less than ten seconds. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, the one or two diodes further comprise a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor. In another aspect, a second capacitor is connected in parallel with the second resistor. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in seriesbetween the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, a second capacitor is connected in parallel with the second resistor.

[0019] Note that the invention is not limited to the embodiments described herein, instead it has the applicability beyond the embodiments described herein. The brief and detailed descriptions of this disclosure are given in the following. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] For a more complete understanding of the features and advantages of the present invention, reference is now made to the detailed description of the invention along with the accompanying figures and in which:

[0021] FIG. 1 is a block diagram of a radar system in accordance with one embodiment of the present disclosure;

[0022] FIG.2 is a photograph of a passive radar system in accordance with one embodiment of the present disclosure;

[0023] FIG. 3 depicts a fast startup baseband amplifier in accordance with one embodiment of the present disclosure.

[0024] FIG. 4A depicts the operation of an input buffer and DC offset circuit during startup in accordance with one embodiment of the present disclosure.

[0025] FIG. 4B depicts the operation of an input buffer and DC offset circuit after startup in accordance with one embodiment of the present disclosure.

[0026] FIG. 5 depicts an input buffer and DC offset circuit in accordance with another embodiment of the present disclosure.

[0027] FIG. 6 depicts the output voltage versus two-tone input power in accordance with one embodiment of the present disclosure.

[0028] FIG. 7 depicts an experimental test setup used to verify the passive radar’s motion detection capabilities in accordance with one embodiment of the present disclosure.

[0029] FIG.8 depicts the experimental results using passive radar to detect motion in accordance with one embodiment of the present disclosure.

[0030] FIGS. 9A and 9B depict a comparison of the low frequency performance of typical baseband amplifiers.

[0031] FIGS.9C and 9D depict a comparison of the startup times of typical baseband amplifiers.

[0032] FIG.10 depicts a comparison between amplifiers leveraging the fast start circuit (black) and without leveraging the fast start circuit (red) in accordance with one embodiment of the present disclosure.

[0033] FIG.11 depicts the design recovering from DC voltage level changes in accordance with one embodiment of the present disclosure.

[0034] FIG.12 depicts a flow chart of a method for passively detecting a movement of a target in accordance with one embodiment of the present disclosure.

[0035] FIG.13 depicts the use of beamforming to determine target direction in accordance with one embodiment of the present disclosure.

[0036] FIG.14 depicts collaborative sensing in accordance with one embodiment of the present disclosure.

[0037] FIGS. 15A-15B depict example applications leveraging the fast start amplifier: exercise monitoring (FIG.15A) and sleep studies (FIG.15B) in accordance with various embodiments of the present disclosure.

[0038] FIG.16 is a fast start amplifier block diagram in accordance with one embodiment of the present disclosure.

[0039] FIG.17 are graphs of time-domain simulation results (graph (a)) and frequency-domain simulation results (graph (b)) in accordance with one embodiment of the present disclosure.

[0040] FIG.18 is an image of an experimental circuit board and test setup in accordance with one embodiment of the present disclosure.

[0041] FIGS. 19A-19B are graphs showing the results using the experimental test system in accordance with one embodiment of the present disclosure.

[0042] FIG. 20 depicts an example passive sensor used to detect target angle in graph (a) and motion frequency in graph (b) simultaneously in accordance with one embodiment of the present disclosure.

[0043] FIG.21 depicts a passive radar beamforming setup in diagram (a), dependence on target position can be seen in graph (b), where a changing target position creates a varying response and dependence on transmitter position can be seen in graph (c), where a changing TX location changes the position of the “ghost” target, all in accordance with one embodiment of the present disclosure.

[0044] FIG.22 depicts a passive sensing noise and clutter simulation block diagram in accordance with one embodiment of the present disclosure.

[0045] FIGS 23A and 23B depict series patch antenna results with simulated and experimental S11 show a good match at the design frequency in FIG. 23A and radiation pattern shows the omnidirectional pattern in the H-plane and narrower beamwidth in the E-plane in FIG. 23B in accordance with one embodiment of the present disclosure.

[0046] FIG.24 depicts a RF front-end schematic and fast start amplifier circuit in each of the 16 receiving channels in accordance with one embodiment of the present disclosure.

[0047] FIG. 25 depicts RF front-end two-tone down conversion results in accordance with one embodiment of the present disclosure.

[0048] FIG.26 depicts a final beamforming passive radar block diagram and fabricated device in accordance with one embodiment of the present disclosure.

[0049] FIG. 27 depicts a controlled experimental setup in accordance with one embodiment of the present disclosure.

[0050] FIG.28 depicts cooperative microwave source experimental results in which results show good agreement with simulated results for a target in the same position in graphs (a)-(d), while phase errors that result in a low angle-of-arrival error compared to ideal values in graph (e) in accordance with one embodiment of the present disclosure.

[0051] FIG. 29 depicts the impact of Δ^^ on beamforming results in accordance with oneembodiment of the present disclosure.

[0052] FIG. 30 depicts a respiration detection experimental setup in accordance with one embodiment of the present disclosure.

[0053] FIG. 31 depicts experimental results with subject breathing normally in which target direction can be seen after beamforming in graph (a) and the subject’s respiration frequency can be found by calculating the FFT in the target’s direction in graph (b) in accordance with one embodiment of the present disclosure.

[0054] FIG. 32 depicts experimental results with subject breathing at an elevated rate in which once again, the target direction can be seen in graph (a) and the subject’s higher respiration rate can also be found in graph (b) in accordance with one embodiment of the present disclosure.

[0055] FIG. 33 depicts an externally timed fast startup schematic in accordance with one embodiment of the present disclosure.

[0056] FIG. 34 depicts externally timed MOSFET simulation results in accordance with one embodiment of the present disclosure

[0057] FIG 35 depicts a schematic of feedback based fast startup amplifier in accordance with one embodiment of the present disclosure

[0058] FIG. 36 depicts simulation results using the feedback based fast startup amplifier in accordance with one embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0059] While the making and using of various embodiments of the present invention are discussed in detail below, it should be appreciated that the present invention provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed herein are merely illustrative of specific ways to make and use the invention and do not delimit the scope of the invention.

[0060] To facilitate the understanding of this invention, a number of terms are defined below. Terms defined herein have meanings as commonly understood by a person of ordinary skill in the areas relevant to the present invention. Terms such as “a”, “an” and “the” are not intended to refer to only a singular entity but include the general class of which a specific example may beused for illustration. The terminology herein is used to describe specific embodiments of the invention, but their usage does not limit the invention, except as outlined in the claims.

[0061] Various methods are described below to provide an example of each claimed embodiment. They do not limit any claimed embodiment. Any claimed embodiment may cover methods that are different from those described above and below. The drawings and descriptions are for illustrative, rather than restrictive, purposes. First, a fast start up amplifier will be described. Second, a low cost fast start up amplifier will be described. Finally, a fast start passive radar will be described. Fast Start Up Amplifier

[0062] Various embodiments of the present disclosure provide a passive radar operating in the 5- GHz Wi-Fi band that detects small-amplitude motions. The radar is designed using discrete RF components to allow for maximum performance versus power consumption and utilizes an on- board fast startup baseband amplifier to quickly reach the desired operating point, while keeping cost and complexity low. In addition, the integration of all active electronics on-board reduces the overall size of the system considerably, making it an ideal candidate for future wireless sensing or IoT applications. As a result, the embodiments disclosed herein offer a compact, efficient method of detecting the Doppler information of a target. The radar is tested both in a controlled and experimental setting to verify its effectiveness in detecting small-amplitude motions. The results demonstrate that passive radar offers a low-power solution to detecting motion using ambient signals.

[0063] Traditionally, motion detection with Doppler radar uses a co-located transmitter and receiver. The transmitter illuminates the target, while the receiver chain detects and down- converts the signal reflected by the target [4]. So long as the target is not a perfect absorber, the target may be modeled as a source radiating at the frequency of interest. When the target is stationary, no Doppler shift is created. Living targets, however, create microscopic motions from heartbeat, respiration, and tremors that may be detected with a sensitive receiver. In passive radar, although the transmitter and receiver are no longer co-located, the theory of operation remains the same. Any displacement in line from the target to the receiver will create a Doppler shift that may be detected. One of the most beneficial features of passive radar is the ability to use third-party signals as a carrier frequency for Doppler information. If a simple example is considered, energy radiated by a third-party transmitter may take two paths to the receiver. The first path is the directpath to the receiver while the second has energy reflected from the target to the receiver. The unmodulated path carries no Doppler information but may act as the local oscillator (LO) for down-conversion. The energy reflected from the target carries the Doppler information and may be down-converted to baseband for digitization. It is worth noting, however, that the target may not always be radiating in the direction of the receiver. If, for example, the target is between the transmitter and receiver, very little of the reflected power will reach the receiver. In addition, since the geometry of this application is more complex compared to the monostatic case, new equations for received power must be derived. The two signals of interest are the unmodulated signal direct from the transmitter to receiver, and the modulated signal from the transmitter to target, then to receiver. The received power for the unmodulated path can be expressed simply as the received power using the well-known Friis transmission equation. For the modulated path, the equation for received power is more complex. Primarily, since the target may be located at any point, there are two distances that impact the received power, so the radar range equation may not be used. In addition, since the transmitter and receiver are no longer co-located, the radar cross section (RCS) should describe the relationship between the power density at the target and the power radiated in the direction of the receiver. The reflected power may then be given using the standard radar formula, where the target’s RCS is defined only for the specific arrangement of target, transmitter, and receiver locations. Finally, applying the Friis transmission equation to the equation for reflected power gives the final equation for received power, given in (1) where ^^்^and ^^்^are the transmitter power and gain, ^^ோ^is the receiver antenna gain, ^^ଶis the distance from transmitter to target and ^^ଷis the distance from the target to the receiver. ^ீ ீ మ^^^^ ^^ ೃ^ఙఒோ^ଶൌ (1)

[0064] Now referring to FIG. 1, aembodiment of the present disclosure is shown. The system 100 includes a microwave passive sensor 102, a microwave source 104, and a processor or computer 106 coupled to the microwave passive sensor 102. The microwave passive sensor 102 comprises a microwave receiver 108, a low noise amplifier (LNA) 110 coupled to the microwave receiver 108, a mixer 112 coupled to the low noise amplifier 110, and a fast startup baseband amplifier (FSBBA) 114 coupled to the mixer 112. The microwave passive sensor 102 provides Doppler information of a moving target 116 based on reflected signals 118 from the moving target 116 and direct-path signals 120 from the microwave source 104. As will be described in more detail below, the fast startup basebandamplifier includes an input buffer and DC offset circuit having one or two diodes, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit. Some non-limiting examples of low noise amplifiers 110, mixers 112 and another type of baseband amplifier can be found in PCT Patent Application No. PCT / US23 / 06650 filed on January 13, 2023 and entitled “Microwave Architecture for Passive Sensing Applications”, which is hereby incorporated by reference in its entirety. Note that the above system 100 can be modified to include any combination of one or more microwave passive sensors 102, one or more microwave sources 104, and one or more processors or computers 106.

[0065] The passive radar system is designed using discrete components to allow for optimization in the RF receiver chain while keeping the size and cost low. A non-limiting example of the system is shown in FIG. 2. A single transistor LNA is implemented using a wideband RF heterojunction bipolar transistor, such BFP740ESD by Infineon Technologies. Typically, the input and output of an LNA should be matched to 50Ω to minimize input / output reflection. However, since both the LNA and mixer design is performed as part of this work, the LNA output is not required to be matched to 50Ω, providing more versatility in the design. A single-diode mixer is implemented using a RF Schottky diode, such as BAT24-02LS by Infineon Technologies. The diode operating point must be chosen carefully to minimize the conversion loss, while also providing a reasonable impedance to the output of the LNA.

[0066] Before analysis of the baseband signal can be performed, the signal must first be digitized. In order to provide maximum resolution for the analog-digital converter (ADC), a baseband amplifier is needed to boost the baseband signal to an appropriate level. Typically, an AC-coupled amplifier is used to remove the DC voltage of the mixer and clutter reflections, giving the amplifier high-pass behavior. Since, however, the frequencies of human motion can be quite low, the cutoff frequency and startup times can be considerable. In order to alleviate this long startup time, a fast start circuit is used. To achieve fast startup, the amplifier should have a low resistance path to charge the first capacitor C1 when power is first applied and switch to a high resistance path once the first capacitor C1 is charged to an acceptable level. This condition can be satisfied with a single diode, shown in FIG.3.

[0067] Referring now to FIG. 3, a fast startup baseband amplifier 300 in accordance with one embodiment of the present disclosure is shown. The fast startup baseband amplifier 300 includes an input buffer and DC offset circuit 302 having a diode D1, and a baseband amplifier 304. Theinput 306 of the input buffer and DC offset circuit 302 is coupled to the mixer output 308. The input buffer and DC offset circuit 302 includes a first capacitor C1 connected in series with the input 306. A first resistor R1 is connected in series between the first capacitor C1 and a negative input (-) of the amplifier 310. The diode D1 is connected in series between the first capacitor C1 and a positive input (+) of the amplifier 310. A second resistor R2 is connected between the negative input of the amplifier and an output of the amplifier 310. A second capacitor C2 is connected in parallel with the second resistor R2. The output of the input buffer and DC offset circuit 302 is connected to the output of the amplifier 310. The output of the input buffer and DC offset circuit 302 is coupled to an input of the baseband amplifier 304, collectively referred to as 312.

[0068] As shown in FIG.4A, when forward biased, the diode D1 presents a low resistance path to quickly charge the first capacitor C1 to match Vbias (illustrated by arrow 402). As shown in FIG.4B, when the first capacitor C1 approaches its intended DC level, the diode D1 will cease conducting and will act as an open circuit, allowing the amplifier 310 to perform as designed (illustrated by arrow 404). This considerably reduces the amplifier’s startup time, allowing for accurate readings quickly after initially powering the device. The choice of diode D1 is quite important and comes with tradeoffs. A typical PN diode, for example, has a larger forward voltage drop and creates a longer startup time. A Schottky diode may shorten this startup time, but an increased reverse leakage current can unintentionally reduce the amplifier’s gain. The RB058LAM by ROHM Semiconductor was found to be an acceptable diode for the purposes of this work. Other Schottky diodes may be used depending on the specifications of the fast startup baseband amplifier. To further improve the startup time, the input stage is configured as unity gain to minimize the input capacitance. C1 and C2 control the high-pass and low-pass cutoff frequencies, respectively, after a value for R is chosen. The large capacitors present in the remaining amplifier stages 304 do not require a fast start diode since the DC outputs of the preceding stages are close to the desired voltage, making their startup time small. The baseband amplifier 304 has an overall gain of 60 dB with a passband from 0.2 Hz to 10 Hz.

[0069] Now referring to FIG. 5, an input buffer and DC offset circuit 500 in accordance with another embodiment of the present disclosure is shown. The input buffer and DC offset circuit 500 includes a first capacitor C1 connected in series with the input 306. A first resistor R1 is connected in series between the first capacitor C1 and a negative input (-) of the amplifier U1.The first diode D1 is connected in series between the first capacitor C1 and Vbias. The second diode D2 is connected in parallel with the first diode D1 in the opposite direction. The positive input (+) of the amplifier U1 is also connected to Vbias. A second resistor R2 is connected between the negative input of the amplifier U1 and an output of the amplifier U1, which is the output of the input buffer and DC offset circuit 500.

[0070] In this embodiment, a good low-frequency response and startup time can be achieved with the addition of two diodes. Intuitively, the diodes provide a low-resistance path to rapidly charge the first capacitor C1 via diode D1 or discharge the first capacitor C1 via D2, while during normal operation, the diodes have no effect on the circuit due to the negligibly small reverse current. This embodiment improves the operation in more scenarios.

[0071] An experimental setup is used to determine the passive radar’s effectiveness with known input powers. Two signal generators are used to create 5.5-GHz tones, one of which with a 5-Hz offset to simulate the RF energy modulated by motion. These tones are joined using a power combiner, then fed into a circulator to ensure that any reflections on the input of the radar do not damage the measurement devices. Each of the two tones are swept from -40 dBm to -10 dBm, and the corresponding output voltage is measured at the output of the baseband amplifier. The results from this input power sweep are shown in FIG. 6. From the results, a semi-linear relationship between input power and output voltage may be seen. Much like conventional mixer design, a strong LO drive is required to ensure optimal performance. In the case of passive radar, the LO would be the direct path from transmitter to receiver. Since the unmodulated path undergoes no reflection and is only attenuated by free-space path loss, it is expected to be higher power compared to the modulated signal, providing the required drive.

[0072] To determine the radar’s ability to detect physical motions, a realistic experimental setup is used. As shown in FIG.7, the experimental setup consists of a transmitter operating at 5.5-GHz, an actuator creating small periodic motions, and the passive radar. The transmitter is positioned such that both the passive radar and the target receive radiation. The transmitter’s output power is 5 dBm. The actuator creates 1.5 mm motion at user-defined frequencies. The output of the passive radar is digitized using an NI-6210 and a fast Fourier transform (FFT) is applied to the time-domain signal. The spectrum after applying FFT is shown in FIG.8 for various frequencies of motion created by the actuator: 1 Hz (black 802), 2 Hz (blue 804), 3 Hz (green 806), 4 Hz (magenta 808) and 5 Hz (red 810). The results of the FFT show the small motions created by theactuator can in fact be detected using ambient EM energy and the passive radar, all while only consuming 85 mW of power.

[0073] Current results have shown that the fast startup circuit has a major effect on startup performance for typical baseband amplifiers. FIGS.9A and 9B depict a comparison of the low- frequency performance of typical baseband amplifiers. FIGS.9C and 9D depict a comparison of the startup times of typical baseband amplifiers. A good low-frequency amplifier exhibits a long startup time (red lines in FIGS.9A and 9C), while an amplifier with a short startup time suffers from poor low-frequency performance (blue lines in FIGS.9B and 9D).

[0074] Now referring to FIG.10, a comparison between amplifiers leveraging the fast start circuit (black line 1002) and without leveraging the fast start circuit (red line 1004) is shown. This highlights the simulated impact on a novel radar system, where the long startup time (>100 s) can be reduced considerably (<10 s) to record useful data faster and save power. This considerable reduction in startup time is observed with no impact on amplifier performance. It is worth noting that the architecture has utility outside of interior or biomedical sensing and could be useful for many different radar applications. The design is also capable of recovering from DC voltage level changes, highlighted by FIG.11, where a disturbance in the radar output only interrupts operation momentarily. At 100 s, the DC level of the radar output changes by 1V (corresponding to a 100V change at the amplifier output). Despite this, the amplifier circuit quickly recovers and continues outputting signals of interest due to the adaptive nature of the fast start circuit.

[0075] Referring to FIG.12, a flow chart of a method 1200 for passively detecting a movement of a target in accordance with one embodiment of the present disclosure is shown. The method 1200 includes receiving signals using a microwave receiver in block 1202, amplifying the received signals using a low noise amplifier coupled to the microwave receiver in block 1204, producing baseband signals from the reflected signal and the direct signal using a mixer in block 1206, amplifying the baseband signals using a fast startup baseband amplifier as previously described or described below in block 1208, and detecting the movement of the target using the amplified baseband signals in block 1210.

[0076] In one aspect, the movement includes a heartbeat, a breath, a limb movement or the target moving as a whole. In another aspect, the one or two diodes comprise a first diode that charges a first capacitor connected to the input, or the two MOSFETs charge the first capacitor when the two MOSFETs are ON. In another aspect, the one or two diodes comprise a first diode thatcharges the first capacitor connected to the input, and a second diode that discharges the first capacitor. In another aspect, the one or two diodes comprise one or two radio frequency Schottky diodes. In another aspect, the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs. In another aspect, the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier. In another aspect, the input buffer and DC offset circuit is configured to have unity gain. In another aspect, the input buffer and DC offset circuit has a startup time less than ten seconds. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, the one or two diodes further comprise a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor. In another aspect, a second capacitor is connected in parallel with the second resistor. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, a second capacitor is connected in parallel with the second resistor.

[0077] The passive sensing technology used in tandem with the fast startup baseband amplifier has demonstrated the ability to use beamforming to determine the direction of targets. Fundamentally, beamforming uses the small difference in time of arrival when a target is off center from the radar to determine its angle of arrival. Scanning algorithms can then be used to visualize the target’s location, shown by FIG.13 in which an oblique incident wave (left) results in small time-of-arrival changes that can be used to determine target direction.

[0078] On its own, beamforming cannot fully localize a target, and can only determine its angle relative to the radar. Collaborative sensing, however, has recently been proposed as a method oflocalizing targets in 3D space. Intuitively, two collaborative passive beamforming radars can use spatial diversity to isolate a target’s location by finding the only point where the two radars “agree” that a target is present. This can be accomplished with simple triangulation, illustrated by FIG.14 where a single target is localized using two collaborative sensors.

[0079] As described herein, a passive radar design operating in the 5-GHz Wi-Fi band is presented using discrete RF components in a board-level design. The design relies on ambient wireless signals to provide an unmodulated path acting as the LO, and a modulated path which contains the target’s Doppler information. In addition to the RF components, a fast startup baseband amplifier is implemented on-board. The fast startup circuit uses a single diode and a unity-gain buffer to provide the DC offset required for the amplifier to function as intended. Experimental results demonstrate the radar’s ability to accurately detect low-frequency, small-amplitude motion. Low Cost Fast Start Up Amplifier

[0080] With interest in the Internet of Things (IoT), smart home technology, smart cities, and wireless health monitoring continuing to grow, microwave radar sensors have seen commensurate growth as a method of monitoring microscopic motions or target position in a noncontact fashion, allowing for integration in a greater number of complex environments [8], [9],

[0010] . Especially when considering the privacy aspects of dense sensor networks, microwave radar can precisely measure target metrics without needing to perform imaging, allowing for privacy to be maintained when compared with camera-based sensors

[0011] . Many forms of radar have been explored as potential sensors, each of which reports unique performance in various sensing tasks compared with other architectures

[0012] . Interferometric radar, for example, can extract target motion with micrometers of resolution, allowing for the measurement of infrastructure motion for preventative maintenance

[0013] or monitoring of vital signs in home healthcare technologies

[0014] . Oftentimes, the output of the direct-conversion receiver is quite small in amplitude, and as such must be amplified before being digitized for signal processing. In many instances, however, the dc information can be orders of magnitude larger than the ac signals of interest, requiring ac-coupled amplifiers to prevent saturation and introducing high-pass frequency behavior that can attenuate low-frequency signals of interest

[0015] . This can be avoided by ensuring that the cutoff frequency of the amplifier is less than the lowest frequency signal of interest but creates a new limitation in the form of long startup times. These long startup times correspond to data loss and energy wasteduring the startup stage when the radar output cannot be measured, both of which are counterproductive to effective sensors. DC-coupled amplifiers with adaptive dc cancellation have been proposed but require several new components that further increase system complexity and cost

[0016] ,

[0017] ,

[0018] , preventing dense deployment of sensor networks. Simple low-cost fast start amplifiers have been previously developed but have so far not been rigorously analyzed

[0019] . Software-defined techniques have also been evaluated, but again require more advanced software capabilities and introduce the potential for loop instability caused by the iterative nature of software-controlled tuning

[0020] .

[0081] The following embodiment discloses a low-cost fast startup baseband amplifier that leverages two commercial diodes to achieve an optimal tradeoff between system complexity, startup time, and low-frequency amplifier performance. Non-limiting examples of applications using the architecture described herein are highlighted in FIGS. 15A-15B for both exercise monitoring (FIG. 15A - Application 1) and sleep studies (FIG. 15B – Application 2) in which respiration and heart rate data are received from sensor outputs. The addition of the fast start architecture (solid black line 1502) decreases the amplifier startup time considerably compared with traditional ac-coupled designs (red dashed line 1504) as shown in the graphs. The startup time with the traditional coupled designs suffers due to the low cutoff frequency. The theory of the fast start amplifier is first presented to provide an intuitive understanding of the amplifier’s operation and is then confirmed via a simulation study. The results are then evaluated in an experimental setting, with the results showing that the low-cost fast start baseband amplifier can achieve a faster startup time compared with traditional amplifiers while maintaining good low- frequency response.

[0082] In traditional ac-coupled amplifiers, dc information is removed using a coupling capacitor at the amplifier’s input. In this case, the combination of input capacitance and resistance creates a high-pass response with a cutoff frequency described by (1), where R1and C1, illustrated in FIG. 16, are the values of the input resistor and capacitor, respectively. Similarly, the values of R1 and C1 also dictate the time constant of the amplifier given in equation (2). As a result, there is a tradeoff between achieving a sufficiently low cutoff frequency and a fast startup time due to the inverse relationship between fC and τ ^^ ^^^ൌൌ(1)^^ ൌ ^^^^^^. (2)

[0083] As a result, leveraging traditional baseband amplifier designs for low-frequency signals can introduce limitations that reduce the operating efficiency of radar sensors. If a realistic case is considered, a cutoff frequency of 0.01 Hz could be used to monitor vital signs for sleep studies with little distortion. With traditional designs, however, the associated time constant would be approximately 16 s. In this case, it would take approximately 48 s for the capacitor voltage to reach 95% of its final value using capacitor charging formulas

[0021] , which presents a major limitation to the utility of the sensor if a long time is needed before data can be gathered.

[0084] To model the fast start baseband amplifier, a two-stage architecture is first considered. This architecture is illustrated in FIG.16. The first stage or input stage is responsible for removing the dc information from the radar’s output signal and accomplishing a fast start, whereas the second stage or amplifier stage(s) is used to provide gain to the ac-coupled signal. The input stage has a input voltage VIand a bias voltage VB. A first capacitor C1is series connected between the input voltage VI and a first resistor R1. A pair of Schottky diodes D1 and D2 are parallel connected in opposite directions from between the first capacitor C1 and the first resistor R1 to the bias voltage VB. The negative terminal (-) of the input stage amplifier is connected to first resistor R1and the positive terminal (+) of the input stage amplifier is connected to the bias voltage VB. A second resistor R2 is connected between the negative terminal (-) and the output of the input stage amplifier. A third resistor R3is connected between the output off the input stage amplifier and the negative terminal (-) of the amplifier stage amplifier. The positive terminal (+) of the amplifier stage amplifier is connected to the bias voltage VB. A fourth resistor R4 is connected between the negative terminal (-) and the output of the amplifier stage amplifier. The output of the amplifier stage amplifier is connected to the output voltage VO. The Schottky diode equivalent circuit is a series resistor RS connected in series with a circuit having an ideal diode Dideal and junction capacitance CJ both in parallel with a parallel resistance RP.

[0085] As was previously discussed, the long startup times associated with low-frequency baseband amplifiers are a result of the large resistances and capacitances used to reduce the lower cutoff frequency of the amplifier. As a result, when charging or discharging a large ac coupling capacitor, such as C1, the only route for the charge to flow is through proportionally large resistances. During this time, the dc offset introduced by the capacitor is mismatched to the dc bias of the amplifier, creating an error that is amplified and saturates the output. To minimize theimpact of this saturation, the input capacitor must be rapidly charged upon startup through a low- resistance path that is disabled during normal operation to ensure adequate low-frequency performance. This can be accomplished using two diodes to provide this low-resistance path when the voltage difference between the amplifier’s dc bias point and the ac-coupled radar output is greater than the diode’s forward voltage. It is worth noting that fast start diodes could be used in later stages if large capacitors are present. However, since the outputs of intermediate stages oscillate around the same bias level, including fast start diodes in the intermediate stages have little impact on startup times. Furthermore, adding fast start diodes after signal amplification can introduce nonidealities during normal operation as signal amplitude increases. Intuitively, the diodes clamp the ac-coupled input signal, preventing large dc voltage differences from being present at the capacitor’s output terminal. While for large signals, this would be detrimental due to clamping and distortion; for the very small amplitude signals at the radar front end’s output, the fast start diodes only have an impact during startup. Once the capacitor voltage is within the range set by the diodes, the diodes cease conducting and have little impact on the amplifier. As a result, the effect of large dc transients can be mitigated using inexpensive components and a simple amplifier architecture. In addition, since the ac component of a radar’s output is typically quite small, the effects of distortion and clamping are minimal on the final amplified signal.

[0086] Although the presented architecture is relatively simple, selecting the diodes to provide the fast start performance is nontrivial. Primarily, a low forward voltage is desired to maximize the fast start performance. In other words, it would be preferred to only charge the input capacitor via an RC circuit for 0.35 V in the case of a Schottky diode versus 0.7V in the case of a normal PN diode. Furthermore, the diode’s parasitics can also have a tremendous impact on the performance of the amplifier. If, for example, the diode presents a large capacitance, this will alter the low-frequency performance of the amplifier and negate any benefits afforded by the diode. The impacts of reverse leakage current can also change the amplifier’s frequency response if the value of RP is comparable to the values of R1 and R2. As a result, a diode with a low forward voltage, small CJ, and high RP is desired to minimize impacts after startup. While this can be accomplished using a theoretical assessment of diode characteristics, a simulation study is likely to provide a more intuitive understanding of the diode’s impact on fast start and low-frequency performance.

[0087] To evaluate the theoretical benefits of the fast start amplifier, a SPICE simulation is used along with commercial diode models. In addition, the impacts of amplifier gain are examined to demonstrate how the design adapts to meet the unique requirements of other sensors. Throughout the simulation study, the amplifier architecture in FIG.16 is used. Intuitively, the first stage can be thought to quickly remove the dc information via the diodes and ensure that the signal is centered at the optimal point. The second stage is a typical inverting amplifier design and can be used to determine the impacts of gain on the final performance of the amplifier. It is worth noting that while R2and R1in FIG.16 are chosen to provide unity gain, the first stage can provide gain. This, however, can have adverse impacts on practical systems due to the larger values of resistance and capacitance needed. As such, it is assumed here that the first stage is always unity gain, whereas the following stages are responsible for providing gain. A total gain of 40 dB is implemented for the initial simulation study.

[0088] As a first step, a Schottky diode is selected to find an acceptable combination of capacitance, leakage current, and forward voltage to provide a faster start without adversely impacting steady-state operation. To compare the performance of diodes, a figure of merit (FOM) is defined by (3), where IR is the leakage current in nA, CJ is the junction capacitance in pF, and VF is the forward voltage in V ^^^^^^ ൌ ^ூೃ^^^ಷ. (3) The RB520CM-60 Schottky diodewell in this simulation study, providing a highly accelerated startup time without impacting the low-frequency response after startup. The associated FOM of the RB520CM-60 diode is 2.22. The simulation is also performed using the RB400D Schottky diode with an associated FOM of 3.26 ൈ 10−4. The startup results both with and without the discussed diodes are shown in FIG.17 upper graph (a), where the RB520CM-60 diodes show improved startup times while maintaining low-frequency gain. The traditional diode is shown as the black line 1702, the RB400D diode is shown as the red dashed line 1704 and the RB520CM-60 are shown as the green dotted line 1706. The associated frequency-domain results are shown in FIG.17 lower graph (b), where only a 0.013-Hz bandwidth reduction can be seen with the addition of the RB520CM-60 diodes, whereas the RB400D diodes have a much greater impact on amplifier operation in the form of a 0.512-Hz bandwidth reduction and attenuation at frequencies of interest. Poor diode selection (dashed) can impact both time-domain and frequency-domain performances.

[0089] To evaluate the performance of the fast start architecture on low-frequency sensing, an experimental system is developed as shown in FIG.18 in which the input signal is routed to a fast start design amplifier and a traditional amplifier to evaluate the performance under matching conditions. The experimental system leverages the fast start architecture shown in FIG.16, with the AD8544 operational amplifier providing amplification and the RB520CM-60 Schottky diode used to provide the fast start path. Compared with FIG.16, the gain of the amplifier is distributed across two inverting amplifier stages each with a gain of 20 dB (40 dB total), with a final unity gain buffer stage used to decouple the experimental results from the impedance of the measurement equipment. A second baseband amplifier without fast start diodes is also implemented onboard to provide a direct comparison between fast start and traditional amplifier performance under similar input conditions. Both amplifiers were designed to have gain fluctuations of less than 1 dB from 0.1 to 10 Hz.

[0090] To quantify the impact on startup time, a time domain experiment is first conducted. These experiments leverage a low-distortion function generator to create a 0.1 Hz sinusoid with 20mVpp amplitude to mimic the low-frequency output of a radar sensor. The output signal of both the fast start and traditional baseband amplifier is recorded after startup to determine the impact on startup time. Before startup, both amplifier capacitors were allowed to discharge to simulate an unknown power-on event after a long period of no power. The results of this study are shown in FIG.19A in which the fast start baseband amplifier is shown in a solid black line 1902 and the traditional baseband amplifier is shown in the red dashed line 1904. From the results, an approximately 100 s startup time reduction is observed. If a commercial radar sensor is considered

[0022] , this startup reduction corresponds to an energy savings of over 57 J due to the ability to quickly collect meaningful data after startup. As such, the system provides experimental verification of the fast start amplifier’s ability to improve startup times and show sustained good low-frequency performance with little added cost and complexity.

[0091] To ensure that the inclusion of fast start diodes does not impact the low-frequency ac gain of the amplifier, experiments are also conducted in the frequency domain. The amplifiers are first powered ON and allowed to settle to their normal operating point, and then, the input signal frequency is varied from 0.01 to 100 Hz in logarithmic steps. The output voltage is measured at each step to quantify the amplifier gain versus frequency. The results of this study are shown in FIG.19B in which the experiment is shown in a solid black line 1912 and the simulation is shownin the red dashed line 1914. From the results, a modification of the low-frequency performance compared with the traditional baseband amplifier can be seen that closely follows the simulated results in FIG. 17 lower graph (b). Within the frequency range of interest, however, the ac performance of the fast start amplifier experiences little gain reduction. The Table below provides a comparison of the described circuit topology with previous works, where it is seen that the fast startup circuit can provide good performance improvements with a simple and low-cost ac- coupled amplifier architecture.

[0092] Comparison of Previous Works Reference

[0016]

[0020] This Embodiment

[0093] A low-frequency ac-coupled amplifier has been presented that leverages a passive fast start circuit to reduce the cost and improve the performance of practical baseband amplifiers. The fast start diodes provide a path for rapid charging of input capacitors and have little impact on circuit operation after startup. Guidelines on proper diode selection are provided to minimize the impacts on normal amplifier operation. The amplifier is analyzed theoretically and with simulation, with results being confirmed using an experimental system to directly compare the performance of traditional and fast start amplifiers. The overall results demonstrate that the disclosed architecture is a simple, low-cost solution to reduce the startup time of practical low- frequency amplifiers. Fast Start Passive Radar

[0094] Microwave radar sensing uses the phase delay and Doppler frequency shift of traveling electromagnetic (EM) waves to detect target parameters such as distance and motion wirelessly

[0023] . Many radars that are used today leverage active radar architectures, meaning that the sensor transmits a dedicated signal to illuminate a target and compares the reflected waves to the known reference. Based on these architectures, microwave radar has been used in many applications such as vital-sign detection [4],

[0016] ,

[0024] , gesture recognition

[0025] , automotive sensing

[0026] ,

[0027] ,

[0028] , and smart-infrastructure technologies

[0029] ,

[0013] . Furthermore, as the Internet of Things (IoT), autonomous vehicles, and smart healthcare technologies continue to advance, the number of deployed radar sensors continues increasing to address a variety of applications in day-to-day life

[0030] . As a result, active radar can experience difficulties when scaling due to interference issues among sensors within the same area. This becomes especially true as the EM spectrum becomes more congested, and engineers begin focusing on advanced techniques to share and minimize spectrum usage. In addition, active radar systems can create security concerns since the radar’s illumination signal can be detected and spoofed to confuse the radar sensor

[0031] .

[0095] Passive radar sensing, on the other hand, leverages ambient EM waves to accomplish target detection

[0032] . As a result, interference issues can be removed entirely while conserving power and cost due to the lack of transmitters in passive sensors. Traditionally, passive radars relied upon large, high-power illuminators of opportunity such as digital audio

[0033] or digital- video broadcast

[0034] ,

[0035] towers to detect the distance of targets with multichannel receivers to isolate the reference and surveillance signals. Enabled by trends in software-defined radio and the proliferation of ubiquitous wireless signals, however, recent years have seen considerable interest in using passive radar for close-range sensing. Existing techniques for passive radar sensing can be broken down into two primary approaches: software-enabled and hardware-enabled.

[0096] Software-enabled approaches leverage the capabilities of modern transceivers such as Wi- Fi access points or software defined radios to measure the motions and positions of targets. Some approaches leverage the Wi-Fi protocol’s signal metrics including channel state information (CSI)

[0036] ,

[0037] and received signal strength (RSS)

[0038] ,

[0039] to monitor small motions indoors for applications such as sleep studies

[0040] . Furthermore, Wi-Fi has been used to localize targets with centimeter-level precision by using a broad bandwidth and multiple access points

[0041] ,

[0042] . Other approaches have leveraged software-defined receivers to detect targets using advanced Wi-Fi signal processing in several applications including automotive

[0043] ,

[0044] , human and drone localization

[0045] ,

[0046] , and home healthcare

[0047] ,

[0048] ,

[0049] ,

[0050] . Reference-free approaches have been used to detect motions without a known reference

[0051] ,

[0052] . Beamforming techniques havealso been used to provide angular information

[0053] . These approaches, however, rely heavily on commercial Wi-Fi transceivers or signal demodulation to extract target metrics, increasing cost and size compared to bespoke hardware-enabled solutions and potentially introducing resource competition between sensing and communications hardware.

[0097] New hardware architectures have allowed for millimeter scale (mm-scale) motion detection leveraging noncooperative illuminators using architectures like those of traditional active radars. Injection-locked techniques have been shown to be able to extract target motion information using the injection-locking and injection-pulling effects in microwave oscillators

[0054] ,

[0055] ,

[0056] ,

[0057] . The results of these studies showed that human gestures

[0054] ,

[0056] and vital signs

[0055] ,

[0057] could be detected with custom systems. Other works have shown the ability to detect target motion without using an injection locked oscillator, instead leveraging a custom mixer to achieve down conversion [7],

[0058] ,

[0059] . The systems were shown to be able to detect mm-scale motions [7],

[0059] , human vital signs

[0058] , and gestures

[0058] using signals in the 2.4 [7],

[0058] and 5-GHz

[0059] Wi-Fi bands. In addition, a beamforming study using this architecture was conducted using two collocated 5-GHz passive radars

[0060] . However, the study in

[0060] did not leverage a high number of receiver channels to achieve a practically small angular resolution. Furthermore, the study did not use human targets to detect metrics such as respiration rate, instead adopting an ideal test setup. Finally, nonideal effects were not considered, which can impact the performance of a passive sensor since no signals originate onboard. A 16-channel beamforming passive radar sensor is presented herein that operates in the 5-GHz Wi-Fi band to detect small motions with a high degree of angular resolution. The sensor integrates all RF and baseband hardware onboard and leverages a USB link for data processing to determine target angle and motion frequency. This is illustrated in FIG.20 where the target angle is shown in graph (a) and the corresponding motion frequency is shown in graph (b). The 16-channel linear array of antennas allows for the detection of target direction while Doppler processing shows motion frequency in the target’s direction. In addition, the impacts of stationary clutter are analyzed to evaluate the impacts of clutter on passive radar motion sensing.

[0098] In contrast to traditional active radar techniques, passive sensing relies on ambient EM energy to extract the physical characteristics of targets, removing the need for a dedicated illumination signal. As a result, however, the signal models used in monostatic active radar setups must be modified to account for new effects introduced by the bistatic geometry. This is shownin FIG.20, where a Wi-Fi access point or transmitter 2002 generates EM energy that creates two paths for received energy: a direct path between the transmitter 2002 and radar 2004 shown by dTX (blue solid line), and an indirect path where energy is radiated to the target 2006 shown by dTX→T (red dotted line) then scattered in the direction of the radar 2004 shown by dT (red dotted line). The direct path can act as a constant reference since its distance is not modulated, while the indirect path encodes the target’s physiological movements, which is used to extract motion frequency.

[0099] Conventional beamforming techniques rely heavily on analog phase shifters in the transmit and receive signal paths, digital weighting of independent receiver channels, or a hybrid implementation of the two techniques to effectively isolate responses in a cluttered environment and estimate the angle of arrival for a reflected signal. In analog beamforming, a necessary requirement for the phased array is that the phase shifts should only be applied to the onboard reference to generate a relative phase shift between signals. In passive radar systems with no onboard oscillator, however, it is not feasible to apply a phase shift to only one of the two received signals as both originate off-board and occupy the same bandwidth. As such, analog beamforming cannot be reasonably performed in the described system as it is not possible to create a relative phase shift between the direct and modulated signal paths.

[0100] Digital beamforming removes the need for analog phase shifters by performing all relative phase shifts in the digital domain. The baseband output of an interferometry system is well-known and by the simple synthesis of an appropriate weighting vector, it is possible to perform beamforming in an entirely digital fashion

[0061] . Many techniques published in the literature, however, leverage onboard local oscillators (LOs) to provide a known reference signal that is independent of the receive channel (i.e., the LO signal is assumed to be equal in amplitude and phase at every receive channel). Passive sensing, on the other hand, does not use an oscillator and relies exclusively on the path length difference between the unmodulated and phase- modulated signals to produce a baseband response. As a result, the signal models for passive sensing are more complex. For a single passive sensing receiver, the normalized transmit and two received signals from an illuminator of opportunity and target can be represented as ^^^^^^ ൌ cos^2^^^^^^^^ (1)^^^^^^^ ∝ cos^2^^^^^^^ െ ^^^^^ଡ଼^ (2)^^ଶ^^^^ ∝ cos^2^^^^^^^ െ ^^^^^^ଡ଼→^^^^^ ^ ^^^^^^^^^ (3)respectively, where k = 2π / λ is the propagation phase constant, dTXis the distance from the transmitter to the radar, and dTX→T+ dTis the sum of distances between the transmitter and target and the target and radar

[0062] . Note that the received signals in equations (2) and (3) are shown in their normalized form to focus on the beamforming aspect of this work. In reality, R1 and R2 can differ significantly in amplitude and have large impacts on the design of the receiver, as shown in

[0058] and

[0059] . FIG.20 provides an illustration of the distances in equations (1)–(3) in the context of a motion-sensing application. In the passive sensing system, the received signals drive a nonlinear element such as a diode to accomplish frequency mixing. After Taylor series expansion of the nonlinear response and low-pass filtering, the baseband response can be written using the following equation: ^^^^^^^^ ∝ cos^^^^^^^ଡ଼→^^^^^ ^ ^^^^^^^ െ ^^^ଡ଼^^. (4)If, however, multiplethis baseband response is modified to account for the slight path differences between adjacent channels. Using the theory from

[0060] and assuming a sensor with N receive elements numbered from 0 to N − 1, the two received signals and corresponding baseband response at the nth element may be represented as ^^^^^^^ ൌ cos^2^^^^^^^ െ ^^^^^^ଡ଼ ^ ^^^^ cos^^^^^^ (5)^^ଶ^^^^ ൌ cos^2^^^^^^^ െ ^^^^^^ଡ଼→^^^^^ ^ ^^^^^^^ ^ ^^^^ cos^^^^^^ (6)^^^^^^^^ ∝ cos^^^^^^^ଡ଼→^ ^ ^^^ െ ^^^ଡ଼ െ ^^^^^cos^^^^ െ cos^^^^^^^ (7)ൌ cos^^^^^^^ଡ଼→^ ^ ^^^ െ ^^^ଡ଼^ െ ^^^^^where θ and β are theand target, respectively, d is thedistance between antenna elements, and ^^ ൌ ^^^^^cos^^^^ െ cos^^^^^ represents the impacts of thephase shifts of both the direct and modulated signals. An illustration of these angles and antenna distances is provided in FIG. 20 and FIG. 21 diagram (a), where it is seen that the direct and indirect signals both experience a phase shift between elements. When compared to the case of active radar, where it is assumed that an onboard oscillator provides a signal that is equal in phase to all receiver channels (i.e., θ = 90◦), equation (7) reduces to the well-known equation for the relative phase of baseband signals in a receiver array. A weighting vector can then be synthesized to compensate for the effects of ^^ and determine the response in a particular direction. Thisprocess can be repeated for multiple values of β (and therefore ^^) to visualize the angles that produce a maximum response, thereby providing a visualization of the target’s direction.

[0101] It is important to note that, if the location of the illuminator of opportunity is unknown, (7) contains two unknown variables θ and β and will induce a constant error in the angle-of-arrival estimation. As such, it is critical to the operation of the beamforming system to know the relative angle of the transmitter with respect to the radar

[0060] . In many cases, however, the transmitter position will remain in a fixed location. As a result, this error can be removed through a one-time calibration. Furthermore, since the system cannot employ quadrature demodulation, additional ambiguity is introduced in the baseband signal that ultimately creates a “ghost” target after beamforming. Beginning from equation (7), the baseband signal can be rewritten using Euler’s formula as ^^ ^^^^ ^ೕೖ^^^^షೕ^ഗି^షೕೖ^^^^శೕ^ഗ^^ ൌଶ (8) where d(t) represents the time-If a beamforming weight of ^^^^టis applied, the left component constructively interferes to produce a large response in the beamforming spectrum. If, however, a value of ^^ି^^టis applied during beamforming, the right component of equation (8) constructively interferes to produce a large response, creating the “ghost” target due to the lack of I / Q information. In addition, since the periodic motion d(t) induces positive and negative frequencies after beamforming, it is not possible to distinguish the real target based on the sign of the resulting motion frequency.

[0102] To visualize these effects, a simulation study was conducted where the target and transmitter position is varied. For the first study, the target angle β is simulated at 80◦, 125◦, and 30◦, with the transmitter at a fixed position of 90◦. The results of these effects are shown in FIG. 21 graph (b) along with the previously known target locations, where the true target position and “ghost” target positions are seen to move in the beamforming output proportional to the true position. The 80◦target angle β is shown as the red dashed line 2102, the 125◦target angle β is shown as the green dotted line 2104, and the 30◦target angle β is shown as the blue dash-dot line 2106. A second study was then conducted with a fixed target at 80◦and the transmitter angle θ set to 60◦, 90◦, and 110◦. The results of this study are shown in FIG.21 graph (c), where, to measure the target’s true position, the transmitter position must be known in each case. The 60◦transmitter angle θ is shown as the red dashed line 2112, the 90◦transmitter angle θ is shown as the greendotted line 2114, and the 110◦transmitter angle θ is shown as the blue dash-dot line 2116. In addition, it is also shown in FIG. 21 graph (c) that the position of the “ghost” target can be modified by changing the location of the transmitter, providing a route for accurate detection by selecting the location of the transmitter and radar such that the “ghost” target angle lies outside the boundaries of the sensing environment.

[0103] Compared to active monostatic radar systems, where the illumination signal originates onboard, the outputs of passive bistatic radar are inherently lower in magnitude due to several reasons. First, as was described in

[0059] , the radar cross section (RCS) of a target for bistatic passive radar is heavily dependent on the specific arrangement of the sensing environment. If, for example, a target is directly between the transmitter and passive radar receiver, very little of the signal encoding target motion is received by the sensor. Second, since a great majority of energy may be scattered away from the passive radar, large clutter could create strong responses during the angle-of-arrival estimation that obscure the true target due to multipath reflections. Finally, since the reference signal originates offboard and is subject to path loss described by the Friis equation, the magnitude of the reference signal may not be sufficient to drive the down conversion mixer, increasing the conversion loss. As a result of these effects, the inclusion of clutter (and thereby multipath) and noise effects is extremely important when modeling the performance of passive radar beamforming systems.

[0104] To evaluate the impacts of nonidealities on passive sensing performance, noise and clutter models are introduced to previously develop passive sensing models, with an overall simulation diagram including key parameters is shown in FIG.22, which includes a transmitter 2202, a target 2204, a first stationary clutter 2206, a second stationary clutter 2208 and receiver 2210. The receiver 2210 is a passive radar model having an antenna 2212, a power calculation 2214, a signal model 2216 and a signal processor 2218. Environmental noise 2220 is modeled as white additive Gaussian noise occupying the frequency bands of interest and added in the RF front end and baseband circuitry with considerations of environmental, thermal, and flicker noise. Stationary clutter 2206 and 2208 creates strong dc outputs due to multipath reflections from the transmitter 2202 to the clutter 2206 and 2208 then to the receiver 2210 that must be mitigated in dc-coupled systems. In addition, the signal scattered by the target 2204 can also experience multipath effects, as illustrated in FIG.22. If an ac-coupled system is considered, however, the dc response produced by transmitter–clutter–receiver multipath is rejected before being digitized. The transmitter–target–clutter–receiver multipath (green paths 2222 and light blue paths 2224), on the other hand, includes ac information that will not be filtered before digitization and signal processing, which can impact beamforming if the multipath signal is stronger than the reflected signal. Coupled with the fact that a target 2204 may naturally scatter more energy in the direction of a strong clutter, the impacts of strong clutters and multipath can have a large impact on angle estimation, especially if the multipath signal is stronger in magnitude. In a similar case, the presence of multiple transmitters can introduce similar impacts after beamforming. Expressions for received power from targets and clutters are updated herein to account for the multipath effects in passive sensors. FIG.22 can be used as a reference to illustrate the distances mentioned in this derivation. In the case of power received from the ith target, the following expression is used to account for the bistatic geometry: ^^ ൌ^^^ீ^^ீ^^ఙ^^^^ఒమଡ଼^ସగ^యௗ^ మ^→^ ^^^ௗ^మ^^^(9) where PTX is the transmitrespectively, ^^^^^^^is the RCS of the ith target, λ is the free-space wavelength of the carrier, and dTX→T and dT are the ith target’s transmitter–target and target–radar distances. In the case of clutter, a second equation is developed as part of this work. In a similar derivation to the radar equation, the power reflected by the ith target in the direction of the jth clutter is represented as ^^ ൌ^^^ீ^^ఙ^→ి^^,^^^→େ ^^^^^^→େ ൌସగௗ^ మ^→^ ^^^(10) where ^^^→େis the RCS valueclutter. The value of ^^^→େin this equation is not equal to the value of ^^^in equation (9) since a target may naturally scatter more energy in one direction. Considering the RCS of the clutter, the free-space path loss from the clutter to the sensor, and the sensor’s antenna gain, the power received due to the clutter at the sensor is represented as ௌఙ^^,^మ^^େൌ^ ి^ఒൌ^^^ீ^^ఙ^→ి^^,^^ఙి^^,^^మమ(11) where ^^ iେ s the RCS that and dT→C and dC are the jth clutter’s target–clutter and clutter–radar distances. In the case of scenarios, this equation can be expanded to evaluate the impacts of multiple targets with multiple clutters. The angle of arrival may also be considered. The closed-form solution for the received signal at the nth channel is given as^^ୖଡ଼^^^^ ∝ ∑ே^^ୀ^ ^^^ ଡ଼^^^^ cos൫^^Δd^^^^^^^^^^^^^൯^∑ே^^ୀ^ ∑ே^^ୀ^^^^େ^^^, ^^^ cos൫^^Δdେ^^^, ^^^^^^^^^^^൯(12) Δ^^େ ൌ ^^^ଡ଼→^Δ^^^ ൌ ^^^ଡ଼→^ ^ ^^^ െ ^^^ଡ଼ (14)where Δ^^େis the path length difference between the transmitter–target–clutter–radar path and the direct path shown in equation (13), Δ^^^is the path length difference between the direct and transmitter–target–radar paths in equation (14), ^^^ଡ଼is the distance from the transmitter to the radar, and ψ is the phase shift between antenna elements. Note that both Δ^^େand Δ^^^encode target motion, highlighting the impact of static clutters if PCis close to or greater than the magnitude of PRX.

[0105] The impacts of stationary clutter on sensing a target moving with a 2-cm amplitude at 45◦can be observed in FIG.22. In the ideal case shown in FIG.22, only the target 2204 and “ghost” target produced by the lack of I / Q data can be seen. In the nonideal result in FIG.22 bottom graph (b), which includes a large clutter at 90◦and 20 evenly distributed clutters in the surrounding environment such as walls, furniture, and appliances, the ideal results in FIG.22 top graph (a) are modified considerably. Primarily, the impacts of the large clutter at 90◦creates an elevated noise level in that direction, while the distributed clutters raise the baseline noise levels outside the direction of the target.

[0106] It is worth noting that, in addition to the effects of clutter and noise detailed above, the presence of additional nonidealities such as multiple transmitters or varying data modulation techniques can have further impacts on the final beamforming results. As a result, the specific nature of a sensing environment should be evaluated to determine if the presence of multiple transmitters or severe multipath effects could have a negative impact on passive radar beamforming.

[0107] To verify the theory in a rigorous fashion, a 16-element 1-D beamforming passive sensor is developed based on the architecture first proposed in [7] to operate in the 5.8-GHz industrial, scientific, and medical (ISM) band. The system is developed on ISOLA FR4 substrate, which reports a dielectric constant of 4.3 and a loss tangent of 0.019. These metrics, however, are not measured in the band of interest and lead to inaccuracies in development. Ultimately, a dielectricconstant of 4.8 was used during development as this provided better agreement between simulated and experimental results.

[0108] To perform effective beamforming and angle-of-arrival estimation without introducing grating lobes, adjacent antenna elements in the linear receive array should be placed a maximum of λ / 2 m from each other. This is not a requirement as many works have demonstrated effective beamforming using nonuniform arrays where adjacent antenna elements can be separated with distances greater than λ / 2

[0044] ,

[0063] ,

[0064] . For this embodiment, however, the passive radar receiver array is designed with all antennas uniformly spaced with a pitch less than λ / 2. As was mentioned above, the beamforming passive radar is designed to operate in the 5.8-GHz ISM band with an associated free-space wavelength of 51.72 mm. As such, the passive radar receiver array is designed with an element pitch of 25 mm to provide a margin of error to support manufacturing tolerances.

[0109] To provide the maximum beamforming angular resolution while simultaneously ensuring a practical sensor size for experimentation, the beamforming passive radar developed in herein is designed with 16 independent receiver channels. Furthermore, to simplify the physical layout of the beamforming passive radar, all receiver components including the antenna, RF front end, and baseband amplifiers will be designed with a physical width of less than 25 mm. If this criterion is met, the physical layout can be accomplished by simply tiling each unit receiver with the appropriate spacing, without introducing the potential for inadvertent short circuits. Supporting electronics that are not repeated for every unit receiver such as power conditioning and analog-to digital converters (ADCs) are individually routed. In addition, several test structures are included onboard to allow testing of individual receiver elements without the effects of mutual coupling between adjacent array elements.

[0110] To measure the ambient EM energy, an onboard antenna element is developed and used for each element in the receiver array. The design of the antenna is nontrivial since many competing metrics introduce tradeoffs that must be considered during design. Primarily, the relationship between the antenna aperture and pitch must be considered, as an increase in the antenna aperture of an array element can improve the receiver sensitivity while also increasing the pitch between receiver elements. Furthermore, since the passive sensor is developed to accomplish 1-D beamforming, a wider beamwidth for array elements is desired in the beamforming plane to maximize the field-of-view (FOV) of the sensor. As a result, to preservethe half-wavelength spacing between elements and support a large FOV, a series patch antenna is used to increase the antenna aperture by adding more elements vertically, while maintaining a sufficiently small horizontal width that supports a half wavelength pitch between elements. The series patch antenna is designed using Applied Wave Research (AWR) Axiem to find dimensions that produce sufficiently low reflection at the desired operating frequency. Following this step, the antenna dimensions are then optimized to provide a good input match and an acceptable radiation pattern for 1-D beamforming. The simulated antenna characteristics (solid black line 2302) and measured antenna characteristics (dashed red line 2304) after this optimization are shown in FIGS.23A-23B. From the graph in FIG.23A, the reflection coefficient at the 5.8-GHz center frequency is seen to be sufficiently low for experimental testing while the radiation pattern in FIG.23B highlights the wide beamwidth in the H-plane (dashed red line 2314) and the narrower beamwidth in the E-plane (solid black line 2312) due to the series patch elements.

[0111] The RF signals detected by the antenna array are quite small in magnitude, and as such require amplification to drive the mixer into its nonlinear operating region. To highlight this, a bistatic case is considered with the transmitter, target, and radar at each vertex of an equilateral triangle with 2-m side length and a transmit power of 15 dBm, antenna gains of 8 dBi, and a target RCS of 0.1 m2. Using equation (9) and the free space path loss formula, the signal received directly from the transmitter is −22 dBm, while the signal encoding target motion is only −49 dBm. As a result, amplification is needed to ensure sufficient down conversion. To address this need, a discrete LNA is developed using the BFP740ESD transistor. The LNA is designed using AWR design environment to perform the input and output matching as well as find an optimal tradeoff between noise figure and gain. Intuitively, a low noise figure may be necessary if the received signals are sufficiently weak compared to environmental and electronic noise. Reducing the noise figure, however, can have the effect of reducing the transducer gain of the amplifier, which can create problems in the passive architecture when the signals are relatively weak in power. Primarily, since no RF signals originate onboard, the received signals must be sufficiently amplified to produce nonlinearity at the mixer. As a result, during the design of the RF front end, the transducer gain is prioritized over the noise figure of the LNA. Furthermore, the proximity of the transistor’s pins combined with the thick substrate introduces coupling effects that must be accounted for. As a result, the system is first simulated using closed form models for planar transmission lines, then extracted using AWR Axiem to account for coupling. After extraction, the stability of the amplifier decreased, requiring a gain reduction to prevent oscillation.

[0112] In addition to the LNA, a one-port mixer is developed to convert the two received signals into a single baseband output that can be used to detect motion and perform beamforming. Since the mixer does not require an LO and RF port, the design of the mixer is comparatively simple. The BAT2402-LS diode from Infineon, Neubiberg, Germany, is used to provide the nonlinearity needed for down conversion, along with passive components and transmission line structures to provide an improved match to the LNA output. Like the design of the LNA, closed-form models for input and output matching networks are first leveraged to obtain a first-order solution. EM extraction is then performed to account for second-order effects. During this process, the BAT2402-LS operating point is also swept to find a biasing point that provides an acceptable combination of low conversion loss at the power levels of interest and a good impedance match to the output of the LNA. It is worth noting that, since the RF front end is a custom design for this embodiment, the LNA output port and mixer input port do not necessarily need to be matched to 50 Ω. As a result, the output impedance of the LNA and the input impedance of the mixer can be modified to allow for improved power efficiency and performance in the RF front end. Furthermore, since none of the signals used in down conversion originate onboard and both occupy the same narrow bandwidth, I / Q demodulation is not possible with existing architectures. As a result, the output signal from the mixer, represented in equation (7), contains only the in phase component of the RF signal. This ultimately introduces ambiguities due to the symmetry of the cosine function and prevents perfect reconstruction of the target motion. The final RF front- end design is shown in FIG.24, with the LNA and single-diode mixer sections highlighted with accompanying passive components. The LNA amplifies the RF signals to drive the custom mixer to down convert the received signals to the baseband. The fast start circuit allows rapid charging of C1, shortening the startup time of the amplifier.

[0113] To characterize the ability of the RF front end to amplify the received signals and down convert to the baseband, a two tone test setup is used. An RF front-end test board consisting of the LNA and the single-diode mixer is fed with two 5.8-GHz signal generators that are offset in frequency. This frequency offset creates a constant IF output frequency after down conversion, allowing for rapid measurement of the output voltage amplitude. To improve the accuracy of the measurements, a simple baseband amplifier with a known gain is used to amplify the mixer output signal. The voltage of both tones at the RF front-end test board input port is swept, and the output peak-to-peak voltage is recorded after amplification. The results are then decoupled from the baseband amplifier’s gain to characterize the RF front-end’s ability to amplify and down convertsignals. The 2-D interpolation is then used to create FIG.25 the high output voltage is denoted as the red area 2502 and the low voltage is denoted as the blue area 2504. From the results, the output voltage shows a dependence on both input tone signal strengths, highlighting the importance of RF gain to drive the mixer for sufficient down conversion. If, for example, a lower received signal power is expected, more RF gain can be added to the system to ensure that enough conversion gain is provided at the mixer. Like traditional mixer design, a higher input voltage at the RF front- end input port creates more nonlinearity and improves the conversion gain of the RF front end.

[0114] After down conversion to the baseband, the radar output signal is on the order of mV. Direct sampling is feasible with modern ADCs but requires careful design to ensure low noise levels and effective sampling. Instead of relying on precision ADCs, a more effective solution would be to leverage baseband amplifier architectures to increase the amplitude of the radar’s output signal to acceptable levels. AC-coupled designs are typically leveraged since the radar’s dc output could be orders of magnitude larger than the signal of interest. Baseband amplifier design for low-frequency signals such as those produced by human activities comes with inherent tradeoffs, however, primarily between lower cutoff frequency and startup time. This is a result of the inverse relationship between the formulas for lower cutoff frequency and time constant, which are given in equations (15) and (16), respectively, where R1 and C1 are the values of the input capacitor and resistor, respectively, as shown in FIG.24. From the equations, it can be seen that a short-time constant correlates to a high cutoff frequency, which is detrimental when the frequencies of interest are less than 1 Hz ^^ ^^^ൌൌఛ (15)

[0115] Many previous works have leveraged modern software capabilities

[0020] or dc-coupled adaptive amplifier architectures

[0016] ,

[0017] to remove the dc component of the received signal while amplifying the ac signals of interest. These techniques, however, require many new hardware components to be added or require more advanced signal processing. Instead of leveraging these techniques, the fast start baseband amplifier architecture in

[0065] is used due to its simplicity and low cost compared to other designs. The architecture is shown in FIG.24, where the included fast start diodes provide a path for rapid charging upon startup. Using the architecture, the startup time of the radar’s baseband amplifiers can be shortened considerably. On the other hand, since accurate displacement reconstruction is not possible with the architecturedue to the lack of I / Q data, dc components created by target motion are not required to be preserved, making the employed fast start architecture an ideal solution for this radar. A pair of RB520CM-60 Schottky diodes are used to provide the desired fast start, and the proceeding amplifier stages are configured to provide 40-dB total baseband gain. The final stage of each baseband amplifier configured as a unity gain buffer to provide a low output impedance to the ADC.

[0116] After baseband amplification, the amplified signals are digitized using the ADS7953 ADC from Texas Instruments, Dallas, TX, USA. The ADS7953 was selected due to its high maximum sampling rate of 1 MS / s, 12-bit precision, and 16 input channels, which allows for the radar output signals to be digitized with sufficient precision and speed for future batch processing without needing multiple ADC chips in parallel. It is important to note during design that the ADC maximum sampling frequency is shared among all channels. As such, if each channel is sampled equally, the maximum per channel sampling rate is 62.5 kS / s. The ADC is programed via a serial peripheral interface to automatically step through each of the 16 radar outputs. The ADC output is then stored by an Espressif Systems ESP32-S2 microcontroller development board and sent to a computer through a universal asynchronous receiver-transmitter (UART) interface. The output data are then recorded by the computer for bulk processing. The final radar block diagram can be seen in FIG.26, with key components highlighted to show how the radar elements can be tiled if the unit widths are sufficiently small. The integrated circuit 2602 includes 16 radar units 2604 connected to a 16 channel ADC 2606 and a microcontroller unit (MCU) and power circuits (collectively 2608). The 1-D structure of the radar unit 2604 allows for tiling to be used to simplify the layout, so long as the unit element width is less than 25 mm. Each radar unit 2604 includes an antenna 2610 connected to a radio frequency (RF) front end 2612 and a baseband amplifier 2614. The RF front end 2612 and baseband amplifier 2614 have been previously described.

[0117] To evaluate the system-level performance of the developed beamforming passive sensor, two experiment strategies were employed. First, to provide a controlled test that is decoupled from the scattering characteristics of a real target, two cooperative continuous wave (CW) microwave sources are used to induce a known and well-controlled response in the baseband signal. This controlled experiment will ultimately allow for an initial assessment of the beamforming model’s performance with a higher number of channels compared to previous works, while alsominimizing the impacts of noise, clutter, and target characteristics which may be cumbersome to measure otherwise. Following this first experiment, a second series of experiments was used to determine the passive radar’s performance in a respiration rate measurement scenario, where a real human target’s respiration rate can be measured along with the target’s angle relative to the radar sensor. Before experimental testing, the radar is characterized in situ to establish operating parameters. The antenna realized gain is found to be approximately 4 dBi, with a half-power beamwidth of 74◦in the H-plane and 30◦in the E-plane. The RF frontend gain is found to range from −20 to +2 dB in the operating region of interest, depending on the input signal strengths. The simulated noise figure of the LNA and mixer are found to be 2.6 and 15 dB, respectively.

[0118] For the initial experiment, two cooperative microwave sources along with accompanying antennas are leveraged to create a known baseband response. One source emulates the direct signal from a noncooperative transmitter to the passive radar receiver and will be called the “direct source.” The other transmitter is synchronized to the direct source and is offset in frequency to produce a known baseband response like that of a moving target. This transmitter can then be placed at different locations to assess the angle-of-arrival estimation performance. As such, the second transmitter will be called the “target source.” Both sources transmit signals in the 5.8-GHz ISM band at a power level of 10 dBm. The frequency offset for this experiment is 2 Hz. When enabling both the direct source and target source, the passive sensor will receive two signals that, after down conversion, produce a sinusoidal baseband response with a frequency equivalent to the frequency difference between the two sources. As the target source is physically moved in the sensing environment, the response after beamforming is expected to change due to the relative phase difference between adjacent elements. At each step, the passive radar collects and stores the corresponding baseband data for bulk processing. The data are then compared against simulation results to verify the accuracy of the models in a high angular resolution system and reveal nonidealities present in the sensor.

[0119] To reduce the impacts of human measurement error, a grid layout is used for this experiment, illustrated in FIG. 27 by a top–down illustration and an image of the experimental setup. The grid layout allows for precise angle measurements using trigonometric functions, reducing the impacts of human error on ground-truth angle measurement. In this layout, the passive sensor 2702 is the origin, while the direct source 2704 and target source 2706 maintain a constant y-coordinate of 1.5 m. The direct source 2704 is held at the 90◦direction for this case,and as such remains fixed at the (0 m, 1.5 m) coordinate. Due to the sizes of the transmitting antennas, the target source 2706 is first placed at a coordinate of (0.3 m, 1.5 m), and its x-value is increased by 0.1 m for each experiment until reaching 1.5 m. This corresponds to an angle-of- arrival sweep from 79◦to 45◦, with a total of 13 steps. A sample of angle-of-arrival measurements is given in FIG. 28 graphs (a)–(d), where it is seen that the measured results (solid black line 2802) show a high degree of agreement with the simulation results (dashed red line 2804). In all cases, the noise levels outside of the main lobe are at least 20 dB smaller in magnitude compared to the response induced by the target source. In addition, the phase error of the received signals is shown in FIG.28 graph (e) as a box and whisker plot. Although the recorded phase error reaches a maximum of 51◦, it can be shown that this corresponds to a relatively low angle error and can be explained by human error and the relatively low precision with which ground truth angles can be measured in the experimental environment. To provide a more useful and intuitive measure of the sensor’s accuracy, the maximum phase error can be converted to a corresponding target angle error. The phase error can be written as Δ^^ ൌ ^^^ െ 1^^^^^^cos^^^ᇱ^ െ cos^^^^^ (17)where θ is the measured target angle and θ′ is the target’s true angle. In equation (17), all values except θ′ are known or measurable. After algebraic manipulation, the angle error can be expressed as Δ^^ ൌ ^^ᇱ െ ^^ ൌ acos ^ ^థ^^ௗ^ cos^^^^^ െ ^^. (18)The angle error can also be found directly byto the target’s measured angle, allowing for a comparison between the calculated values in equation (18) with the experimental results. Both the measured angle error (dotted red line 2812) and calculated angle error (solid black line 2814) can be found in FIG.28 graph (e), where it is seen that despite the larger phase deviations present between receivers, the corresponding angle errors are quite low.

[0120] It is worth noting that, compared to previous works, the results in FIG.28 show no clear ambiguity or “ghost” targets compared to the results in FIGS.21 or 22. This is a byproduct of the use of cooperative sources, and the fact that the output in such an experiment is a perfect continuous sinusoid with a periodic phase delay between elements. Beginning from equation (8),the received baseband signal equations can be modified to account for the frequency difference between the two tones. The new baseband signal equation is then ^^ೕ^^^షೕ^ഗ షೕ^^^శೕ^^^^^^ ൌ ^ ି^^ഗଶ (19)where Δ^^ is the frequencythebeamforming weights ^^^^ట, only the positive frequency component remains. If, however, the beamforming ^^ି^^టare applied, only the negative frequency component remains.Coupled with the beamforming algorithm measures only positive frequencies whendetermining target the use of cooperative sources removes the previously seen ambiguities. Accurate angle measurement, however, relies upon knowing whether the frequency difference between two sources is positive or negative. If, for example, the Δ^^ is changed from +2 to −2 Hz, the measured angle would be mirrored around 90◦since the beamforming algorithm measures positive frequencies. This is shown in FIG.29, whereby simply changing the sign of Δ^^(solid black line ^Δ^^ 2902 and dashed red line െΔ^^ 2904), the beamforming results giveincorrect measurements for the target at 60◦using cooperative sources.

[0121] To evaluate the sensor’s performance in a practical application, the sensor is used to detect a breathing target’s direction relative to the radar sensor in a realistic environment. In this case, a human test subject is seated approximately 1.0 m to the passive radar sensor, with the radar aligned to the subject’s approximate chest level. A CW microwave source produces ambient EM energy at a frequency of 5.8 GHz at a power of 10 dBm, also aligned to the same height as the passive sensor and the subject’s chest. It is worth noting that the transmitter in this case does occupy spectrum resources. In a practical case, however, an “always-on” signal such as the pilot carrier in 802.11 Wi-Fi could be used to provide illumination. The subject is seated at approximately 150◦. Data are collected for approximately 12s. The experimental setup for respiration detection is shown in FIG.30 with the subject 30021.0 m from the passive radar 3004 and 1.0 m from the microwave source 3006. The passive radar 3004 is 1.2 m from the microwave source 3006.

[0122] The subject 3002 was first instructed to breathe at a normal rate, to assess the passive radar’s 3004 performance in both angle-of-arrival estimation and motion frequency measurement. The results of this study are shown in FIG.31. From the beamforming results in FIG.31 graph (a), it is seen that the passive sensor isolated the direction of the moving target. This is confirmedby calculating the fast Fourier transform (FFT) of the signal toward the peak of the beamforming results, as shown in FIG.31 graph (b), where the target’s respiration frequency of approximately 0.25 Hz can be seen. It can also be seen that the ambiguity previously discussed is present but is not perfectly symmetric about the 90◦point. This is due to the target’s unintentional motion toward or away from the sensor during the experiment, which creates an uneven response like that previously discussed.

[0123] A second experiment was also conducted in a similar manner, but with the target now instructed to breathe at an elevated rate. As a result, it is expected that the beamforming output of this experiment will be like the previous case, but with an increase in motion frequency measured at the peak angle. The results of this experiment are shown in FIG. 32. From the beamforming results in FIG.32 graph (a), a much clearer target can be seen because of the increased respiration rate. This is likely due to the increased chest wall motion that occurs when breathing is elevated. In addition, the frequency-domain results in FIG.32 graph (b) show that the increased respiration rate of approximately 1 Hz can be extracted, demonstrating the sensor’s ability to concurrently determine a target’s angle of arrival and motion frequency.

[0124] This embodiment provides a 16-channel beamforming passive radar that can be used in an indoor environment to detect a moving target’s angle and motion. The sensor leverages a single noncooperative transmitter in the 5-GHz Wi-Fi band and a digital beamforming approach to measure target characteristics. The theory of passive radar beamforming was presented and verified through an experimental setup, where a target’s respiration frequency and angle were measured. The experimental results demonstrate the passive radar’s ability to detect target motion using third-party illuminators of opportunity for a scalable approach to indoor sensing. MOSFET Based Fast Startup Baseband Amplifier

[0125] Diodes, while sufficient for a simple solution, have two primary drawbacks: (1) the available commercial diodes are limited and their parasitics can have major impacts on performance; and (2) after startup, diodes intrinsically present a resistance to the input stage of the amplifier, disallowing further improvements in frequency response. As such, the fast-startup baseband amplifier has been adapted to use MOSFET technology, which allows improved OFF performance (i.e., the MOSFETs conduct considerably less current when OFF). Two approaches have been considered for the MOSFET amplifier: externally-timed and feedback-based.

[0126] For an externally-timed fast-startup baseband amplifier, two MOSFETs (1 PMOS and 1 NMOS) are used as a substitute for the two diodes. Compared to diodes, MOSFETs have superior switching characteristics (lower on-resistance, higher off-resistance), and can be controlled electrically. A simplified schematic of the fast-startup circuit using externally timed MOSFETs M1 and M2 is shown in FIG.33. The operation mechanism is as follows: 1. After a power-on event, the large input capacitor to the baseband amplifier must be charged before the amplifier performs as needed. 2. Two resistors R3 and R4 and two capacitors C2 and C3 form an electrical timing network that turn the MOSFETs M1 and M2 ON after a power-on event for a tunable amount of time. 3. While the MOSFETs M1 and M2 are ON, the input capacitor rapidly charges. 4. Once the MOSFETs M1 and M2 are OFF, the amplifier resumes operation as normal.

[0127] Time-domain simulation results using the externally-timed MOSFET configuration are shown in FIG.34 graph (a), where the black curve is the output waveform using the fast-startup amplifier and the blue curve is the output waveform without the fast-start. From the results, a considerable improvement in startup time is seen (>300 s down to approximately 5 s). Furthermore, the timing circuit can be further configured by designers to meet the needs of their particular application. The frequency-domain results in FIG. 34 graph (b) highlight the highly improved frequency response using externally-timed MOSFETs, where very little frequency degradation is seen allowing accurate amplification of signals on the order of 0.1 Hz.

[0128] A second MOSFET-based architecture is also considered which uses a feedback network to dynamically turn ON and OFF the MOSFETs, allowing for improved response to disturbances in the input signal. A simplified schematic is shown in FIG.35. The feedback loop from amplifier out to M1 / M2 allow for dynamic correction of the input DC level, ensuring proper amplifier operation that is adaptable to a wide variety of applications. Intuitively, when the output of the amplifier is saturated (either VDD or 0V), the MOSFETs M1 and M2 turn ON in order to correct the input signal’s DC offset (charge of C1). When the output is near the ideal DC level, the MOSFETs turn OFF to allow the amplifier to operate normally.

[0129] Simulation results using the feedback-based fast-startup amplifier are shown in FIG.36. The time-domain results in FIG. 36 graph (a) once again show a vastly improved startup time compared to an amplifier without the fast-startup circuit. In addition, frequency-domain results inFIG. 36 graph (b) show near ideal performance and that very low frequency signals can be amplified with little distortion. Compared to the externally-timed approach, the feedback-based approach has the added benefit of being able to adapt to input disturbances, much like the diode- based approach. The feedback-based approach, however, has the potential to introduce nonidealities arising from the feedback loop itself. As a result, more study is needed to better quantify the benefits and drawbacks of each approach.

[0130] Based on the foregoing description, numerous embodiments are provided herein. Some non-limiting embodiments are described below.

[0131] One embodiment of the present disclosure provides a fast startup baseband amplifier having an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit.

[0132] In one aspect, the one or two diodes comprise a first diode that charges a first capacitor connected to the input, or the two MOSFETs charge the first capacitor when the two MOSFETs are ON. In another aspect, the one or two diodes comprise a first diode that charges the first capacitor connected to the input, and a second diode that discharges the first capacitor. In another aspect, the one or two diodes comprise one or two radio frequency Schottky diodes. In another aspect, the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs. In another aspect, the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier. In another aspect, the input buffer and DC offset circuit is configured to have unity gain. In another aspect, the input buffer and DC offset circuit has a startup time less than ten seconds. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, the one or two diodes further comprise a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor. In another aspect, a second capacitor is connected in parallel with the second resistor. In another aspect, the input buffer and DC offset circuitcomprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, a second capacitor is connected in parallel with the second resistor.

[0133] Another embodiment of the present disclosure provides a microwave passive sensor that includes a microwave receiver; a low noise amplifier coupled to the microwave receiver; a mixer coupled to the low noise amplifier; and a fast startup baseband amplifier coupled to the mixer, wherein the fast startup baseband amplifier comprises: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit.

[0134] In one aspect, the one or two diodes comprise a first diode that charges a first capacitor connected to the input, or the two MOSFETs charge the first capacitor when the two MOSFETs are ON. In another aspect, the one or two diodes comprise a first diode that charges the first capacitor connected to the input, and a second diode that discharges the first capacitor. In another aspect, the one or two diodes comprise one or two radio frequency Schottky diodes. In another aspect, the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs. In another aspect, the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier. In another aspect, the input buffer and DC offset circuit is configured to have unity gain. In another aspect, the input buffer and DC offset circuit has a startup time less than ten seconds. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, the one or two diodes further comprise a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor. In another aspect, a second capacitor is connected inparallel with the second resistor. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, a second capacitor is connected in parallel with the second resistor.

[0135] Another embodiment of the present disclosure provides a system comprising: one or more microwave passive sensors, each microwave passive sensor comprising a microwave receiver, a low noise amplifier coupled to the microwave receiver, a mixer coupled to the low noise amplifier, and a fast startup baseband amplifier coupled to the mixer, wherein the fast startup baseband amplifier comprises: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit; one or more microwave sources; and a processor or computer coupled to the one or more microwave passive sensors.

[0136] In one aspect, the one or two diodes comprise a first diode that charges a first capacitor connected to the input, or the two MOSFETs charge the first capacitor when the two MOSFETs are ON. In another aspect, the one or two diodes comprise a first diode that charges the first capacitor connected to the input, and a second diode that discharges the first capacitor. In another aspect, the one or two diodes comprise one or two radio frequency Schottky diodes. In another aspect, the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs. In another aspect, the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier. In another aspect, the input buffer and DC offset circuit is configured to have unity gain. In another aspect, the input buffer and DC offset circuit has a startup time less than ten seconds. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of theamplifier; and the output connected to the output of the amplifier. In another aspect, the one or two diodes further comprise a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor. In another aspect, a second capacitor is connected in parallel with the second resistor. In another aspect, the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier. In another aspect, a second capacitor is connected in parallel with the second resistor.

[0137] It is understood that particular embodiments described herein are shown by way of illustration and not as limitations of the invention. The principal features of this invention can be employed in various embodiments without departing from the scope of the invention. For example, the fast startup baseband amplifier can also be used in active radar systems such as conventional Doppler radar and interferometry radar for motion detection, vital signs sensing, and other Internet of Things applications. Those skilled in the art will recognize or be able to ascertain using no more than routine experimentation, numerous equivalents to the specific procedures described herein. Such equivalents are considered to be within the scope of this invention and are covered by the claims.

[0138] All publications and patent applications mentioned in the specification are indicative of the level of skill of those skilled in the art to which this invention pertains. All publications and patent applications are herein incorporated by reference to the same extent as if each individual publication or patent application was specifically and individually indicated to be incorporated by reference.

[0139] The use of the word “a” or “an” when used in conjunction with the term “comprising” in the claims and / or the specification may mean “one,” but it is also consistent with the meaning of “one or more,” “at least one,” and “one or more than one.” The use of the term “or” in the claims is used to mean “and / or” unless explicitly indicated to refer to alternatives only or the alternatives are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and / or.” Throughout this application, the term “about” is used to indicate that a valueincludes the inherent variation of error for the device, the method being employed to determine the value, or the variation that exists among the study subjects.

[0140] As used in this specification and claim(s), the words “comprising” (and any form of comprising, such as “comprise” and “comprises”), “having” (and any form of having, such as “have” and “has”), “including” (and any form of including, such as “includes” and “include”) or “containing” (and any form of containing, such as “contains” and “contain”) are inclusive or open- ended and do not exclude additional, unrecited features, elements, components, groups, integers, and / or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and / or steps. In embodiments of any of the compositions and methods provided herein, “comprising” may be replaced with “consisting essentially of” or “consisting of”. As used herein, the term “consisting” is used to indicate the presence of the recited integer (e.g., a feature, an element, a characteristic, a property, a method / process step or a limitation) or group of integers (e.g., feature(s), element(s), characteristic(s), property(ies), method / process steps or limitation(s)) only. As used herein, the phrase “consisting essentially of” requires the specified features, elements, components, groups, integers, and / or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and / or steps as well as those that do not materially affect the basic and novel characteristic(s) and / or function of the claimed invention.

[0141] The term “or combinations thereof” as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof” is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AB, BBC, AAABCCCC, CBBAAA, CABABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context.

[0142] As used herein, words of approximation such as, without limitation, “about”, “substantial” or “substantially” refers to a condition that when so modified is understood to not necessarily be absolute or perfect but would be considered close enough to those of ordinary skill in the art to warrant designating the condition as being present. The extent to which the description may vary will depend on how great a change can be instituted and still have one of ordinary skill in the art recognize the modified feature as still having the required characteristics and capabilitiesof the unmodified feature. In general, but subject to the preceding discussion, a numerical value herein that is modified by a word of approximation such as “about” may vary from the stated value by at least ±1, 2, 3, 4, 5, 6, 7, 10, 12 or 15%.

[0143] All of the compositions and / or methods disclosed and claimed herein can be made and executed without undue experimentation in light of the present disclosure. While the compositions and methods of this invention have been described in terms of preferred embodiments, it will be apparent to those of skill in the art that variations may be applied to the compositions and / or methods and in the steps or in the sequence of steps of the method described herein without departing from the concept, spirit and scope of the invention. All such similar substitutes and modifications apparent to those skilled in the art are deemed to be within the spirit, scope and concept of the invention as defined by the appended claims.

[0144] To aid the Patent Office, and any readers of any patent issued on this application in interpreting the claims appended hereto, applicants wish to note that they do not intend any of the appended claims to invoke paragraph 6 of 35 U.S.C. § 112, U.S.C. § 112 paragraph (f), or equivalent, as it exists on the date of filing hereof unless the words “means for” or “step for” are explicitly used in the particular claim.

[0145] For each of the claims, each dependent claim can depend both from the independent claim and from each of the prior dependent claims for each and every claim so long as the prior claim provides a proper antecedent basis for a claim term or element. REFERENCES

[0146] [1] S. Li, D. X. Li and S. Zhao, "The internet of things: a survey," Information Systems Frontiers, vol.17, no.2, pp.243-259, 2015.

[0147] [2] S. Majumder, T. Mondal and M. J. Deen, "Wearable Sensors for Remote Health Monitoring," Sensors, vol.17, no.1, p.130, 2017.

[0148] [3] D. Tarek, et. al., "Survey on spectrum sharing / allocation for cognitive radio networks Internet of Things," Egyptian Informatics Journal, vol.21, no.4, pp.231-239, 2020.

[0149] [4] C. Li, et. al., "A Review on Recent Advances in Doppler Radar Sensors for Noncontact Healthcare Monitoring," IEEE Transactions on Microwave Theory and Techniques, vol.61, no.5, pp.2046-2060, 2013.

[0150] [5] H. Zhao, et. al., "Non-contact Beat-to-beat Blood Pressure Measurement Using Continuous Wave Doppler Radar," in IEEE / MTT-S International Microwave Symposium, Philadelphia, 2018.

[0151] [6] S. Dong, et. al., "Doppler Cardiogram: A Remote Detection of Human Heart Activities," IEEE Transactions on Microwave Theory and Techniques, vol.68, no.3, 2020.

[0152] [7] D. V. Q. Rodrigues, D. Tang and C. Li, "A Novel Microwave Architecture for Passive Sensing Applications," in IEEE Radio and Wireless Symposium, Las Vegas, 2022.

[0153] [8] C. Gu and J. Lien, “A two-tone radar sensor for concurrent detection of absolute distance and relative movement for gesture sensing,” IEEE Sens. Lett., vol.1, no.3, Jun.2017, Art. no.3500504.

[0154] [9] J. Liu, C. Gu, Y. Zhang, and J.-F. Mao, “Analysis on a 77 GHz MIMO radar for touchless gesture sensing,” IEEE Sens. Lett., vol.4, no.5, May 2020, Art. no.3500804.

[0155]

[0010] P.Vaishnav and A. Santra, “Continuous Human activity classification with unscented Kalman filter tracking usingFMCWradar,” IEEE Sens. Lett., vol.4, no.5, May 2020, Art. no.7001704.

[0156]

[0011] E. L. Chuma, L. L. B. Roger, G. G. de Oliveira, Y. Iano, and D. Pajuelo, “Internet of Things (IoT) privacy–protected, fall-detection system for the elderly using the radar sensors and deep learning,” in Proc. IEEE Int. Smart Cities Conf. (ISC2), 2020, pp.1–4.

[0157]

[0012] J.-C. Chiao et al., “Applications of microwaves inmedicine,” IEEE J. Microw., vol. 3, no.1, pp.134–169, Jan.2023.

[0158]

[0013] D. V. Q. Rodrigues, D. Zuo, and C. Li, “Wind-induced displacement analysis for a traffic light structure based on a low-cost Doppler radar array,” IEEE Trans. Instrum. Meas., vol. 70, pp.1–9, 2021.

[0159]

[0014] C. Gu, Y. He, and J. Zhu, “Noncontact vital sensing with a miniaturized 2.4 GHz circularly polarized Doppler radar,” IEEE Sens. Lett., vol.3, no.7, Jul.2019, Art. no.3501204.

[0160]

[0015] A. Singh, S. U. Rehman, S. Yongchareon, and P. H. J. Chong, “Multi-resident noncontact vital sign monitoring using radar: A review,” IEEE Sens. J., vol.21, no.4, pp.4061– 4084, Feb.2021.

[0161]

[0016] D. Tang, J. Wang, W. Hu, Z. Peng, Y.-C. Chiang, and C. Li, “A DC-coupled high dynamic range biomedical radar sensor with fast-settling analog DC offset cancelation,” IEEE Trans. Instrum. Meas., vol.68, no.5, pp.1441–1450, May 2019.

[0162]

[0017] D. Tang, J. Wang, Z. Peng, Y.-C. Chiang, and C. Li, “A DC-coupled biomedical radar sensor with analog DC offset calibration circuit,” in Proc. IEEE Int. Instrum. Meas. Technol. Conf. (I2MTC), 2018, pp.1–6.

[0163]

[0018] Z. Peng, A. Mishra, J. R. Davis, J. A. Bridge, and C. Li, “Long-time non-contact water level measurement with a 5.8-GHz DC-coupled interferometry radar,” in Proc. IEEE Int. Instrum. Meas. Technol. Conf. (I2MTC), 2018, pp.1–5.

[0164]

[0019] A. B. Carman and C. Li, “Passive multistatic wireless sensing based on discrete LNA / Mixer Co-optimization and fast startup baseband amplifier,” in Proc. IEEE Topical Conf. Wirel. Sensors Sensor Netw., 2023, pp.43–45.

[0165]

[0020] Y. Yang, C. Gu, R. Gale, J. Chen, and C. Li, “DC-coupled Doppler radar sensor with software-configured fine-tuning architectures for precise monitoring of complex motion patterns,” in Proc. IEEE Wirel. Microw. Technol. Conf., 2012, pp.1–6.

[0166]

[0021] C. Alexander and M. Sadiku, Fundamentals of Electric Circuits, 6th ed., New York, NY, USA: McGraw-Hill Educ., 2017.

[0167]

[0022] Infineon Technologies, “BGT60UTR11AIP,” Accessed: Mar. 30, 2024. [Online]. Available: Webpage: www.infineon.com / cms / en / product / sensor / radarsensors / radar-sensors-for- iot / 60ghz-radar / bgt60utr11aip / .

[0168]

[0023] C. Li et al., “A review on recent progress of portable short-range noncontact microwave radar systems,” IEEE Trans. Microw. Theory Techn., vol.65, no.5, pp.1692–1706, May 2017.

[0169]

[0024] Z. Peng and C. Li, “Portable microwave radar systems for short-range localization and life tracking: A review,” Sensors, vol.19, no.5, p.1136, Mar.2019.

[0170]

[0025] C. Gu, J. Wang, and J. Lien, “Motion sensing using radar: Gesture interaction and beyond,” IEEE Microw. Mag., vol.20, no.8, pp.44–57, Aug.2019.

[0171]

[0026] J. Hasch, E. Topak, R. Schnabel, T. Zwick, R. Weigel, and C. Waldschmidt, “Millimeter-wave technology for automotive radar sensors in the 77 GHz frequency band,” IEEE Trans. Microw. Theory Techn., vol.60, no.3, pp.845–860, Mar.2012.

[0172]

[0027] R. Amar, M. Alaee-Kerahroodi, and P. Babu, “Optimized-slope FMCW waveform for automotive radars,” in Proc.23rd Int. Radar Symp., Gdansk, Poland, 2022, pp.110–115.

[0173]

[0028] T. T. Braun, J. Sch.pfel, P. Kwiatkowski, C. Schweer, K. Aufinger, and N. Pohl, “Expanding the capabilities of automotive radar for bicycle detection with harmonic RFID tags at 79 / 158 GHz,” IEEE Trans. Microw. Theory Techn., vol.71, no.1, pp.320–329, Jan.2023.

[0174]

[0029] S. Guan, J. A. Bridge, C. Li, and N. J. DeMello, “Smart radar sensor network for bridge displacement monitoring,” J. Bridge Eng., vol.24, no.1, Jan.2019, Art. no.04018102.

[0175]

[0030] O. B. Akan and M. Arik, “Internet of radars: Sensing versus sending with joint radar- communications,” IEEE Commun. Mag., vol.58, no.9, pp.13–19, Sep.2020.

[0176]

[0031] P. Nallabolu and C. Li, “A frequency-domain spoofing attack on FMCW radars and its mitigation technique based on a hybrid-chirp waveform,” IEEE Trans. Microw. Theory Techn., vol.69, no.11, pp.5086–5098, Nov.2021.

[0177]

[0032] H. Kuschel, D. Cristallini, and K. E. Olsen, “Tutorial: Passive radar tutorial,” IEEE Aerosp. Electron. Syst. Mag., vol.34, no.2, pp.2–19, Feb.2019.

[0178]

[0033] M. Wei., “Compressive sensing for passive surveillance radar using DAB signals,” in Proc. Int. Radar Conf., Oct.2014, pp.1–6.

[0179]

[0034] D. Gromek, P. Samczynski, K. Kulpa, P. Krysik, and M. Malanowski, “Initial results of passive SAR imaging using a DVB-T based airborne radar receiver,” in Proc.11th Eur. Radar Conf., Oct.2014, pp.137–140.

[0180]

[0035] M. Ummenhofer, J. Schell, J. Heckenbach, H. Kuschel, and D. W. D’O Hagan, “Doppler estimation for DVB-T based passive radar systems on moving maritime platforms,” in Proc. IEEE Radar Conf. (RadarCon), May 2015, pp.1687–1691.

[0181]

[0036] B. Tan and B. Sun, “Using Wi-Fi signal as sensing medium: Passive radar, channel state information and followups,” 2022, arXiv:2201.03005.

[0182]

[0037] B. Tan, Q. Chen, K. Chetty, K. Woodbridge, W. Li, and R. Piechocki, “Exploiting WiFi channel state information for residential healthcare informatics,” IEEE Commun. Mag., vol. 56, no.5, pp.130–137, May 2018.

[0183]

[0038] X. Li, Z. Deng, F. Yang, X. Zheng, L. Zhang, and Z. Zhou, “WiFi indoor location method based on RSSI,” in Proc. 11th IEEE Int. Conf. Intell. Data Acquisition Adv. Comput. Syst., Technol. Appl. (IDAACS), vol.2, Cracow, Poland, Sep.2021, pp.1036–1040.

[0184]

[0039] S. Sigg, S. Shi, F. Buesching, Y. Ji, and L. Wolf, “Leveraging RFchannel fluctuation for activity recognition: Active and passive systems, continuous and RSSI-based signal features,” in Proc. Int. Conf. Adv. Mobile Comput. Multimedia. New York, NY, USA: Association for Computing Machinery, 2013, pp.43–52.

[0185]

[0040] J. Liu, Y. Wang, Y. Chen, J. Yang, X. Chen, and J. Cheng, “Tracking vital signs during sleep leveraging off-the-shelf WiFi,” in Proc.16th ACM Int. Symp. Mobile Ad Hoc Netw. Comput. New York, NY, USA: Association for Computing Machinery, Jun.2015, pp.267–276.

[0186]

[0041] C. Chen, Y. Chen, H.-Q. Lai, Y. Han, and K. J. R. Liu, “High accuracy indoor localization: A WiFi-based approach,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Mar.2016, pp.6245–6249.

[0187]

[0042] C. Chen, Y. Chen, Y. Han, H.-Q. Lai, and K. J. R. Liu, “Achieving centimeter- accuracy indoor localization on WiFi platforms: A frequency hopping approach,” IEEE Internet Things J., vol.4, no.1, pp.111–121, Feb.2017.

[0188]

[0043] G. P. Blasone, F. Colone, and P. Lombardo, “Passive radar concept for automotive applications,” in Proc. IEEE Radar Conf. (RadarConf), Mar.2022, pp.1–5.

[0189]

[0044] A. Quirini, G. P. Blasone, F. Colone, and P. Lombardo, “A simple NULA design strategy for target detection and DoA estimation in mobile passive radar,” in Proc. Int. Conf. Radar Syst. (RADAR), Oct.2022, pp.570–575.

[0190]

[0045] M. Di Seglio, F. Filippini, C. Bongioanni, and F. Colone, “Human and drone surveillance via RpF-based WiFi passive radar: Experimental validation,” in Proc.23rd Int. Radar Symp. (IRS), Sep.2022, pp.402–407.

[0191]

[0046] H. Sun, L. G. Chia, and S. G. Razul, “Through-wall human sensing with WiFi passive radar,” IEEE Trans. Aerosp. Electron. Syst., vol.57, no.4, pp.2135–2148, Aug.2021.

[0192]

[0047] B. Tan et al., “Wi-Fi based passive human motion sensing for in-home healthcare applications,” in Proc. IEEE 2nd World Forum Internet Things (WF-IoT), Dec. 2015, pp. 609– 614.

[0193]

[0048] Q. Chen, Y. Liu, B. Tan, K. Woodbridge, and K. Chetty, “Respiration and activity detection based on passive radio sensing in home environments,” IEEE Access, vol.8, pp.12426– 12437, 2020.

[0194]

[0049] W. Li, B. Tan, and R. Piechocki, “Passive radar for opportunistic monitoring in e- Health applications,” IEEE J. Transl. Eng. Health Med., vol.6, pp.1–10, 2018.

[0195]

[0050] W. Li, B. Tan, and R. J. Piechocki, “Non-contact breathing detection using passive radar,” in Proc. IEEE Int. Conf. Commun. (ICC), May 2016, pp.1–6.

[0196]

[0051] F. Colone, F. Filippini, M. D. Seglio, P. V. Brennan, R. Du, and T. X. Han, “Reference-free amplitude-based WiFi passive sensing,” IEEE Trans. Aerosp. Electron. Syst., vol.59, no.5, pp.6432–6451, Oct.2023.

[0197]

[0052] M. D. Seglio, F. Filippini, C. Bongioanni, and F. Colone, “Reference free WiFi PHY preamble based passive radar for human sensing,” in Proc. Int. Conf. Radar Syst. (RADAR), Oct. 2022, pp.119–124.

[0198]

[0053] J. M. Nu.ez-Ortu.o, J. P. Gonz.lez-Coma, R. N. L.pez, F. Troncoso-Pastoriza, and M..lvarez-Hern.ndez, “Beamforming techniques for passive radar: An overview,” Sensors, vol. 23, no.7, p.3435, Mar.2023.

[0199]

[0054] Y.-C. Lai, C.-C. Chou, M.-C. Tang, T.-S. Horng, and F.-K. Wang, “Finger gesture sensing and recognition using a Wi-Fi-based passive radar,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun.2019, pp.293–296.

[0200]

[0055] M.-C. Tang, F.-K. Wang, and T.-S. Horng, “Vital-sign detection based on a passive WiFi radar,” in IEEE MTT-S Int. Microw. Symp. Dig., Sep.2015, pp.74–75.

[0201]

[0056] M.-C. Tang, F.-K. Wang, and T.-S. Horng, “Human gesture sensor using ambient wireless signals based on passive radar technology,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp.1–4.

[0202]

[0057] D. V. Q. Rodrigues and C. Li, “A microwave passive topology based on simultaneous injection-locking and injection-pulling for passive indoor sensing applications,” in Proc. Int. Microw. Antenna Symp. (IMAS), Feb.2023, pp.107–110.

[0203]

[0058] D. Tang, V. G. R. Varela, D. V. Q. Rodrigues, D. Rodriguez, and C. Li, “A Wi-Fi frequency band passive biomedical Doppler radar sensor,” IEEE Trans. Microw. Theory Techn., vol.71, no.1, pp.93–101, Jan.2023.

[0204]

[0059] A. B. Carman and C. Li, “Passive multistatic wireless sensing based on discrete LNA / Mixer co-optimization and fast startup baseband amplifier,” in Proc. IEEE Topical Conf. Wireless Sensors Sensor Netw., Jan.2023, pp.43–45.

[0205]

[0060] A. B. Carman and C. Li, “A digital beamforming approach for indoor passive sensing,” in Proc. IEEE Top. Conf. Wireless Sensors Sensor Netw., Jan.2024, pp.12–14.

[0206]

[0061] C. Feng et al., “Multitarget vital signs measurement with chest motion imaging based on MIMO radar,” IEEE Trans. Microw. Theory Techn., vol. 69, no. 11, pp. 4735–4747, Nov. 2021.

[0207]

[0062] A. B. Carman and C. Li, “Null / optimum point optimization for indoor passive radar motion sensing,” in Proc. IEEE Radar Conf. (RadarConf), San Antonio, TX, USA, May 2023, pp. 1–5.

[0208]

[0063] S. P. Hehenberger, A. Yarovoy, and A. Stelzer, “A 77-GHz FMCW MIMO radar employing a non-uniform 2D antenna array and substrate integrated waveguides,” in IEEE MTT- S Int. Microw. Symp. Dig., Nov.2020, pp.1–4.

[0209]

[0064] Z. Peng and C. Li, “A portable K-band 3-D MIMO radar with nonuniformly spaced array for short-range localization,” IEEE Trans. Microw. Theory Techn., vol. 66, no. 11, pp. 5075–5086, Nov.2018.

[0210]

[0065] A. B. Carman and C. Li, “Low-cost fast start amplifier architecture for AC-coupled measurement of low-frequency signals,” IEEE Sensors Lett., vol.8, no.5, pp.1–4, May 2024.

Claims

CLAIMS What is claimed is:

1. A fast startup baseband amplifier comprising: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output; and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit.

2. The fast startup baseband amplifier of claim 1, wherein: the one or two diodes comprise a first diode that charges a first capacitor connected to the input; or the two MOSFETs charge the first capacitor when the two MOSFETs are ON.

3. The fast startup baseband amplifier of claim 1, wherein the one or two diodes comprise: a first diode that charges the first capacitor connected to the input; and a second diode that discharges the first capacitor.

4. The fast startup baseband amplifier of claim 1, wherein the one or two diodes comprise one or two radio frequency Schottky diodes.

5. The fast startup baseband amplifier of claim 1, wherein the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs.

6. The fast startup baseband amplifier of claim 1, wherein the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier.

7. The fast startup baseband amplifier of claim 1, wherein the input buffer and DC offset circuit has a startup time less than ten seconds.

8. The fast startup baseband amplifier of claim 1, wherein the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier.

9. The fast startup baseband amplifier of claim 8, further comprising a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor.

10. The fast startup baseband amplifier of claim 8, further comprising a second capacitor connected in parallel with the second resistor.

11. The fast startup baseband amplifier of claim 1, wherein the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier.

12. The fast startup baseband amplifier of claim 11, further comprising a second capacitor connected in parallel with the second resistor.

13. A microwave passive sensor, comprising: a microwave receiver; a low noise amplifier coupled to the microwave receiver; a mixer coupled to the low noise amplifier; and a fast startup baseband amplifier coupled to the mixer, wherein the fast startup baseband amplifier comprises: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit.

14. The microwave passive sensor of claim 13, wherein: the one or two diodes comprise a first diode that charges a first capacitor connected to the input; or the two MOSFETs charge the first capacitor.

15. The microwave passive sensor of claim 13, wherein the one or two diodes comprise: a first diode that charges the first capacitor connected to the input; and a second diode that discharges the first capacitor.

16. The microwave passive sensor of claim 13, wherein the one or two diodes comprise one or two radio frequency Schottky diodes.

17. The microwave passive sensor of claim 13, wherein the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs.

18. The microwave passive sensor of claim 13, wherein the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier.

19. The microwave passive sensor of claim 13, wherein the input buffer and DC offset circuit is configured to have unity gain.

20. The microwave passive sensor of claim 13, wherein the input buffer and DC offset circuit has a startup time less than ten seconds.

21. The microwave passive sensor of claim 13, wherein the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier.

22. The microwave passive sensor of claim 21, further comprising a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor.

23. The microwave passive sensor of claim 21, further comprising a second capacitor connected in parallel with the second resistor.

24. The microwave passive sensor of claim 13, wherein the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor;a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier.

25. The microwave passive sensor of claim 24, further comprising a second capacitor connected in parallel with the second resistor.

26. A method for passively detecting a movement of a target, the method comprising: receiving signals using a microwave receiver; amplifying the received signals using a low noise amplifier coupled to the microwave receiver; producing baseband signals from the reflected signal and the direct signal using a mixer; amplifying the baseband signals using a fast startup baseband amplifier comprising: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit; and detecting the movement of the target using the amplified baseband signals.

27. The method of claim 26, wherein the movement comprises a heartbeat, a breath, a limb movement or the target moving as a whole.

28. The method of claim 26, wherein: the one or two diodes comprise a first diode that charges a first capacitor connected to the input; or the two MOSFETs charge the first capacitor when the two MOSFETs are ON.

29. The method of claim 26, wherein the one or two diodes comprise: a first diode that charges the first capacitor connected to the input; and a second diode that discharges the first capacitor.

30. The method of claim 26, wherein the one or two diodes comprise one or two radio frequency Schottky diodes.

31. The method of claim 26, wherein the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs.

32. The method of claim 26, wherein the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier.

33. The method of claim 26, wherein the input buffer and DC offset circuit has a startup time less than ten seconds.

34. The method of claim 26, wherein the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier.

35. The method of claim 34, further comprising a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor.

36. The method of claim 34, further comprising a second capacitor connected in parallel with the second resistor.

37. The method of claim 26, wherein the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier;the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier.

38. The method of claim 37, further comprising a second capacitor connected in parallel with the second resistor.

39. A system comprising: one or more microwave passive sensors, each microwave passive sensor comprising a microwave receiver, a low noise amplifier coupled to the microwave receiver, a mixer coupled to the low noise amplifier, and a fast startup baseband amplifier coupled to the mixer, wherein the fast startup baseband amplifier comprises: an input buffer and DC offset circuit having either one or two diodes or two MOSFETs, an input and an output, and a baseband amplifier having an input coupled to the output of the input buffer and DC offset circuit; one or more microwave sources; and a processor or computer coupled to the one or more microwave passive sensors.

40. The system of claim 39, wherein: the one or more microwave passive sensors comprise two or more microwave passive sensors; the one or more microwave sources comprise two or more microwave sources; and the processor or computer uses beamforming to determine a direction of one or more targets.

41. The system of claim 39, wherein: the one or two diodes comprise a first diode that charges a first capacitor connected to the input; orthe two MOSFETs charge the first capacitor when the two MOSFETs are ON.

42. The system of claim 39, wherein the one or two diodes comprise: a first diode that charges the first capacitor connected to the input; and a second diode that discharges the first capacitor.

43. The system of claim 39, wherein the one or two diodes comprise one or two radio frequency Schottky diodes.

44. The system of claim 39, wherein the two MOSFETs are externally timed using a third resistor, a fourth resistor, a third capacitor and a fourth capacitor connected to the two MOSFETs.

45. The system of claim 39, wherein the two MOSFETs are feedback timed based on a feedback loop from an output of the baseband amplifier.

46. The system of claim 39, wherein the input buffer and DC offset circuit is configured to have unity gain.

47. The system of claim 39, wherein the input buffer and DC offset circuit has a startup time less than ten seconds.

48. The system of claim 39, wherein the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the one or two diodes comprise a first diode connected in series between the first capacitor and a positive input of the amplifier, wherein the first diode charges the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier.

49. The system of claim 48, further comprising a second diode connected in parallel with the first diode, wherein the second diode discharges the first capacitor.

50. The system of claim 48, further comprising a second capacitor connected in parallel with the second resistor.

51. The system of claim 39, wherein the input buffer and DC offset circuit comprises: a first capacitor connected in series with the input; a first resistor connected in series between the first capacitor and a negative input of an amplifier; the two MOSFETs comprise a first MOSFET connected in series between the first capacitor and a positive input of the amplifier, a second MOSFET connected in parallel with the first MOSFET, wherein the two MOSFET charge the first capacitor; a second resistor connected between the negative input of the amplifier and an output of the amplifier; and the output connected to the output of the amplifier.

52. The system of claim 51, further comprising a second capacitor connected in parallel with the second resistor.

Images