Systems and methods for pulse-mode interrogation of wireless backscatter communication nodes

Abstract

Systems and methods for interrogating a plurality of backscatter node devices in a wireless backscatter communication system are provided. The method may include transmitting one or more interrogator pulse signals from an interrogator device; for each of the one or more interrogator pulse signals, receiving at the interrogator device a raw backscatter signal including individual backscatter signals from each of the plurality of backscatter node devices, wherein each individual backscatter signal includes a reflection of the interrogator pulse signal modulated based on an input modulation signal of the respective backscatter node device; processing the one or more raw backscatter signals to determine a mapping model between the input modulation signal of each of the plurality of backscatter node devices and the one or more raw backscatter signals; and extracting one or more signals of interest based on the mapping model, wherein each signal of interest corresponds to an input modulation signal of a backscatter node device.

Description

SYSTEMS AND METHODS FOR PULSE-MODE INTERROGATION OF WIRELESSBACKSCATTER COMMUNICATION NODESCROSS-REFERENCE TO RELATED APPLICATION

[0001] Pursuant to 35 U.S.C. § 119(e), this application claims priority to the filing date of United States provisional patent application serial no. 63 / 495,987 filed April 13, 2023, the disclosures of which application is incorporated herein by reference in its entirety.BACKGROUND

[0002] The present disclosure provides systems and methods for pulse-mode interrogation of wireless backscatter communication nodes.

[0003] Prior work describes systems for backscatter communication with simple, batteryless, low power nodes. Those works opened opportunities for new types of wireless sensors, with the target application area being extremely small wireless implantable medical devices, specifically those used to sense electrical activity in nervous tissue such as neural interfaces. Neural interfaces include sensors and systems to observe and manipulate neural activity, such as electrophysiological recording and stimulation. Those prior works also opened opportunities for improvements to the capabilities of such systems and addressing some of the implementation challenges of such systems, such as: calibration of the wireless link, wireless node tracking, robustness to motion, signal-to-noise ratio, sensitivity of performance to orientation of the backscatter node, communication with multiple sensors simultaneously, and wireless communication through a scattering medium or reflecting surface, such as bone. Those challenges could be addressed by improving the capabilities and sophistication of the backscatter nodes and / or of the interrogator side of the link.

[0004] Channel -count, physical size, and recording longevity remain major barriers to greater adoption and performance of electrophysiological neural interfaces. Sensing from greater numbers of recording sites with lower risk could potentially yield a higher utility-to-risk ratio for these devices, driving higher adoption. Extremely small wireless neural sensors are one way of approaching the goals of high recording site count and low risk. One approach to address this is a transition to an ‘all wireless’ neural interface where each recording site is freely floating and transmits neural data wirelessly. One architecture for this is ultrasonic backscattercommunication between an external interrogator and implanted sensor wireless recording sites (see, Dongjin Seo et al. “Neural Dust: An Ultrasonic, Low Power Solution for Chronic Brain-Machine Interfaces”. In: arXiv.org q-bio.NC. April (July 2013), and Dongjin Seo et al. “Model validation of untethered, ultrasonic neural dust motes for cortical recording”. In: Journal of Neuroscience Methods 244 (Apr. 2015), pp. 114-122.). Achieving small size in a wireless sensor presents challenges. Using ultrasound for power and communication, rather than radio frequency electromagnetic (EM) waves, enables good antenna efficiency at small size because of the shorter wavelength of an acoustic wireless link versus an EM one for a given frequency, and reduced tissue heating for a given receiver power due to lower tissue absorption compared to EM.

[0005] Communicating using backscatter lends itself well to the asymmetric constraints on the sensor in the brain and the external transceiver (e.g., interrogator device(s)) outside the brain. Modulating information using impedance modulation (yielding a predominantly amplitude- modulated backscatter signal), as opposed to frequency modulation or phase modulation, enables very simple sensor devices, and lends itself to devices with relatively low transducer quality factor, as well as pulse-mode operation. Encoding information using analog rather than digital encoding allows reduced device complexity, and enables a small and low-power sensor. Additionally, this opens up new possibilities for sensor design outside of traditional CMOS (complementary metal oxide semiconductor) electronics. Pulse- mode analog-encoded amplitude-modulated backscatter communication has many desirable characteristics for a wireless system with asymmetric constraints, such as a neural interface or other body interface but there are many challenges with this approach that need fundamental advances in order to enable an effective overall system.

[0006] Some of the major remaining challenges include automatic calibration and adjustment of the wireless link, operation of the ultrasonic wireless link through and in the midst of bony reflectors such as the skull, simultaneous communication with multiple sensors, and separation of sensor modulation signals from motion artifact. Challenges with calibration include the need to manually isolate a region of interest of the backscatter to use for demodulation. This region of interest may need to be adjusted for motion of the sensor and may be sensitive to transmit-receive (Tx-Rx) timing variability. Furthermore, the transients inherent in pulse-mode operation cause modulation direction (sign) and amount to differ across the backscatter signal of the reflected pulse, thus leading to non-optimal demodulation extract signal-to-noise ratio (SNR) even with a manually tuned region of interest. Successfully operating a link despite the attenuation and scattering of ultrasound due to bone would enableultra-minimally invasive delivery of wireless sensors to the brain with subsequent wireless communication to the sensors from outside the skull and thus never requiring a large craniotomy. Challenges to enable simultaneous multi-sensor operation include de-mixing of potentially overlapping reflection signals and ensuring sufficient interrogation repetition frequency of each sensor to enable good reconstruction of a neural signal. Finally, low- sensitivity analog-encoded amplitude-modulation can be easily drowned out by motion artifact and transmit pulse variability.

[0007] To seize on these opportunities while overcoming the challenges, new methods are needed that make pulse-mode analog-encoded amplitude-modulated ultrasonic backscatter communication more capable and robust.SUMMARY

[0008] The systems and methods according to the present embodiments provide pulse-mode interrogation of wireless backscatter communication nodes that has desirable performance and robustness characteristics. In certain embodiments, asymmetric constraints are leveraged: additional signal processing complexity and computation abilities are added at the external side (e.g., interrogator system) of the wireless link to provide robustness without requiring additional complexity of the implanted sensors. For example, in certain embodiments, an array (e.g., 2-d array or 3-d array) of external transducer elements utilizes short ultrasound pulses and careful mapping of the mote modulation (sensor modulation) across each interrogator element to yield performant ultrasonic communication in the face of the various challenges identified above.

[0009] According to an embodiment, a wireless backscatter communication system is provided that includes a plurality of backscatter node devices, and at least one interrogator device, wherein the at least one interrogator device is configured to: transmit one or more interrogator pulse signals; for each of the one or more interrogator pulse signals, receive a raw backscatter signal including individual backscatter signals from each of the plurality of backscatter node devices, wherein each individual backscatter signal includes a reflection of the interrogator pulse signal modulated based on an input modulation signal of the respective backscatter node device; process the one or more raw backscatter signals using a machine learning algorithm to determine a mapping model between the input modulation signal of each of the plurality of backscatter node devices and the one or more raw backscatter signals; and extract one or more signals of interest based on the mapping model, wherein each signal of interest corresponds to an input modulation signal of a particular backscatter node device.

[0010] According to another embodiment, a method of interrogating a plurality of backscatter node devices in a wireless backscatter communication system is provided. The method includes transmitting one or more interrogator pulse signals from an interrogator device; for each of the one or more interrogator pulse signals, receiving at the interrogator device a raw backscatter signal including individual backscatter signals from each of the plurality of backscatter node devices, wherein each individual backscatter signal includes a reflection of the interrogator pulse signal modulated based on an input modulation signal of the respective backscatter node device; processing the one or more raw backscatter signals to determine a mapping model between the input modulation signal of each of the plurality of backscatter node devices and the one or more raw backscatter signals; and extracting one or more signals of interest based on the mapping model, wherein each signal of interest corresponds to an input modulation signal of a backscatter node device.

[0011] According to another embodiment, an interrogator device in a wireless backscatter system having a plurality of backscatter node devices is provided. The interrogator node device comprising a transducer, a processor and a memory storing code, which when executed by the processor configures the interrogator device to: emit, via the transducer, one or more interrogator pulse signals; for each of the one or more interrogator pulse signals, receive a raw backscatter signal including individual backscatter signals from each of the plurality of backscatter node devices, wherein each individual backscatter signal includes a reflection of the interrogator pulse signal modulated based on an input modulation signal of the respective backscatter node device; process the one or more raw backscatter signals using the processor to determine a mapping model between the input modulation signal of each of the plurality of backscatter node devices and the one or more raw backscatter signals; and extract one or more signals of interest based on the mapping model, wherein each signal of interest corresponds to an input modulation signal of a backscatter node device.

[0012] In certain aspects, the machine learning algorithm is based on one of: a linear regression algorithm, a weighted and flipped input data algorithm, a clustering algorithm, or a sparse dictionary learning algorithm.

[0013] In certain aspects, the interrogator device is further configured to, prior to processing the one or more raw backscatter signals using the machine learning algorithm, filter the one or more raw backscatter signals to isolate changes in instantaneous amplitude, phase and / or frequency across the one or more interrogator pulse signals.

[0014] In certain aspects, the interrogator device includes at least three transducers configured to emit interrogator pulse signals and receive backscatter signals. In certain aspects,the interrogator device is further configured to track a position over time of at least a first one of the plurality of backscatter node devices relative to the at least one interrogator device. In certain aspects, the interrogator device is configured to track the position over time based on a change in time of flight between interrogator pulse signals and received individual backscatter signals for the first backscatter node device. For example, in certain aspects, the method of calculating a change in time of flight may include an averaged change over pulses of the tracked times of zero-crossings of the backscatter waveform, or a weighted- average of the change over pulses of the instantaneous phase offset between the backscatter waveform and a reference sinusoid. In certain aspects, the at least three transducers are arranged in a linear array or in a 2- dimensional array.

[0015] In certain aspects, the interrogator device is configured to: process the position over time information of the first backscatter node device to determine a second mapping model of the backscatter of the first backscatter node device and the backscatter modulation of the first backscatter node device as a function of the position of the first backscatter node device; and extract one or more signals of interest based on the second mapping model, wherein each signal of interest corresponds to an input modulation signal of the first backscatter node device independent from the position of the first backscatter node device or motion of the first backscatter node device.

[0016] In certain aspects, the interrogator device includes an ultrasonic transducer and the interrogator pulse signals include ultrasound pulse signals. In certain aspects, the interrogator device includes an electromagnetic transducer and the interrogator pulse signals include radio pulse signals.

[0017] In certain aspects, the plurality of backscatter node devices includes sensor devices and the input modulation signals include impedance modulation signals.

[0018] The present embodiments advantageously enable very simple backscatter sensors or node devices (backscatter nodes) in a way which scales to large numbers of nodes, and which find uses in scenarios where communication with large numbers of low-cost, low-power, or small-size devices is desirable, and high-bandwidth communication to any single node and extremely low error rate may not be critical. Moreover, the present embodiments enable backscatter communications systems with very simple low-cost wireless sensors nodes that do not require sophisticated modulation or coding techniques.

[0019] According to various embodiments, some or all of the following features may be used for the backscattering methods: (1 ) backscatter communications between sensor nodes and interrogator system; (2) ultrasound for wireless power and communication of sensor nodes; (3)using short interrogation pulses to enable temporal separation of sensor reflection from other motes and from other scatterers such as bone (e.g., the skull); (4) isolating the backscatter modulation signal separately on many external transceiver channels so that the detailed transducer system geometry does not need to be known a priori (unlike traditional beamforming which requires a known external transceiver array geometry); (5) at each sample point of the backscatter signal, isolating changes in instantaneous amplitude, phase, and frequency that occur across successive interrogation pulses; (6) learning a mapping between a sensor node input signal and the effect seen in backscatter ‘modulation space’ ; and (7) comparing backscatter data to this mapping to extract sensor input signals to improve SNR without explicit time-delay or phase-shift beamforming based on known geometry.BRIEF DESCRIPTION OF THE FIGURES

[0020] The invention may be best understood from the following detailed description when read in conjunction with the accompanying drawings. Included in the drawings are the following figures:

[0021] FIG. 1A illustrates beamforming according to prior art. FIG. IB illustrates transmission techniques according to an embodiment of the present invention.

[0022] FIG. 2 illustrates an example of backscatter signals according to an embodiment of the present invention.

[0023] FIGS. 3A-B depict results from a water tank calibration curve experiment according to an embodiment of the present invention.

[0024] FIG. 4 illustrates a clustering diagram of a clustering method according to an embodiment of the present invention.

[0025] FIGS. 5A-D illustrates an LCA Sparsification Diagram according to an embodiment of the present invention.

[0026] FIGS. 6A-B present experimental results obtained in connection with embodiments of the present invention.

[0027] FIG. 7 illustrates an analytical backscatter simulation diagram according to an embodiment.

[0028] FIGS. 8A-D illustrate an exemplary backscatter system, hardware, and processing diagram according to an embodiment.

[0029] FIGS. 9A-D present experimental results in connection with comparing embodiments.

[0030] FIGS. 10A-D present diagrams of an experimental configuration of an embodiment and results obtained from such configuration.

[0031] FIG. 11 illustrates processing steps for binary load-switched transcranial communication according to an embodiment.

[0032] FIG. 12 illustrates an experimental setup for multi-sensor transcranial communication.

[0033] FIG. 13 presents experimental results according to an embodiment.

[0034] FIG. 14 presents simulation and processing results according to an embodiment.DETAILED DESCRIPTION

[0035] One challenge is how to more accurately and robustly demodulate the impedancemodulation-encoded information in pulse-mode backscatter data. One embodiment includes system identification of the transfer function of the ultrasound field (from Tx pulse to Rx signal); this models all of the scatterers (i.e., nodes) in the field. This is highly computationally expensive, though, and may be under constrained. To simplify, instead of modeling the full transfer function of the ultrasound field, in an embodiment only the effect of the modulation itself is considered. Because the backscatter amplitude is (approximately) linearly related to the voltage across the piezo terminals (of the nodes) plus an offset, the system is designed to identify how features of the backscatter data linearly vary with input signal to the sensor. It is noted that the approximately linear relation is reasonable for many or most use cases, but is not necessarily generally true.

[0036] Furthermore, it is desirable to maintain the ability to use very simple and small sensors. While sophisticated digital modulation schemes, such as CDMA (code-division multiple access), could enable multi-mote operation, and continuous-wave digitally modulated backscatter could enable higher sampling rate, those require more sophisticated sensors with higher power requirements. This necessitates a relatively large CMOS circuit and more capable power harvesting and storage. To maintain the vision of very small and simple devices, pulsemode backscatter is utilized. In the spirit of backscatter communication, which enables asymmetric power constraints on the external transceiver and the internal sensor, the signal processing computational burden is advantageously shifted to the external transceiver (i.e. interrogator) to keep the internal sensor(s) simple.Signal model

[0037] According to an embodiment, a pulse-backscatter communication system includes a set of transceiver elements that generate a series of transmit pulse signals which traverse awireless medium and interact with one or more backscatter node devices (or “node device(s)” or “node(s)”). The nodes may include sensor nodes which modulate backscatter via impedance modulation, and may include any sensors for picking up and relaying a sensed biometric signal, e.g., neural voltage. In general, the backscatter nodes can transmit any information based on any modulation scheme, and could also be, for example, transponders which relay a preprogrammed unique identifier instead of a value sensed from the environment. Each node has an input signal which is assumed to be constant within the duration of a pulse and may vary across successive pulses. The reflection of each transmit pulse from each sensor is modulated, via impedance modulation or other method, by the input signal. Backscattered energy from the system is then captured by the transceiver elements (interrogator elements). Given backscatter data captured across multiple pulses, it is desirable to estimate the input signals into the nodes for each of those pulses. Embodiments herein advantageously address the problem of modeling the effect of the input signal on the received backscatter data with high enough fidelity to capture the phenomena of interest and extract the desired input signals, while also being tractable and practically implementable in a real-time system.

[0038] FIG. 1A illustrates delay-and-sum beamforming where a transceiver array applies phase-shifts to the transmit signal to create a transmit beam, 'illuminating' a narrow region of space, ideally hitting only one sensor at a time. Receive signals are also phase shifted and then summated, generating only one output backscatter signal per pulse. FIG. IB illustrates an embodiment wherein a transmit pulse is generated which 'illuminates' all sensors on each pulse. This could be a plane- wave, a hemispherical wave, or a holographic transmit signal which optimizes for, for example, maximizing the minimum power on a sensor. In this embodiment, receive signals at the transceiver elements are not summated prior to further processing; they are all digitized separately to allow further processing on this more information-rich dataset.

[0039] In the simplest case of a single sensor, one can consider the sensor input signal to linearly affect the average amplitude of each backscatter capture. In this case, the input signal can be extracted by computing the average amplitude of each backscatter capture (or a region of interest of the backscatter capture) and then filtering across pulses in the frequency band of interest. Alternatively, considering a much more complex model of the system, one could attempt to fit a model of the full transfer function of the wireless medium by parameterizing for the impedance at each point in the 3-dimensional medium, and then use backscatter from many pulses (possibly of varying transmit signals) to fit those parameters and determine changes in impedance at the sensor, or some other form of highly-parameterized system identification. This would be computationally demanding and would likely require many pulses to get one solutionto the model. Instead, in an embodiment, an intermediary approach is taken in which it is assumed that the sensor input signals linearly affect each sample of backscatter with some coefficient of modulation.

[0040] FIG. 2 illustrates an example of backscatter signals from a piezo transducer with varying resistive load (empirical backscatter from water-tank experiment). This system shows an approximately 17% change in amplitude between resistive loads of 10 and 10047

[0041] In the continuous-wave backscatter case, the reflection pressure amplitude can be thought of as the incident pressure amplitude times a reflection coefficient: Pr = PiT. As shown in Ghanbari et al., 2019 (Mohammad Meraj Ghanbari et al. “A Sub-mm 3 Ultrasonic Free- Floating Implant for Multi-Mote Neural Recording”. In: IEEE Journal of Solid-State Circuits 54.11(Nov. 2019), pp. 3017-3030.), the reflection coefficient T is approximately linear with the amplitude of the voltage at the piezo terminals. It is assumed that the modulator input signal linearly modulates that voltage. In this case, Pr = Pi(FOffset + ax), where x is the input signal value and a is a coefficient of modulation. In the short pulse-mode case, the ring-up and ringdown transients of the system dominate the reflection, so amplitude is not uniform throughout the receive signal from one pulse. In this case, the same notion of the input signal linearly affecting receive amplitude is used but it is applied to each sample of the receive waveform individually rather than the average amplitude. In this case: yraw =yo + x w +Z, where yrawis the backscatter signal across K samples, for one transceiver channel and one pulse. Each element of yo is an offset at each receive sample, and each element of w is a coefficient of modulation at each receive sample, z is a term which captures noise and other error.

[0042] Nomenclature as used herein includes: k, K samples in one Rx capture, for one transceiver channel: index, total number q, Q transceiver channels: index, total number p, P sensors: index, total number m, M pulses: index, total number n, N backscatter features: index, total number y, Y backscatter data for one pulse, multiple pulses x, X input signal for one sensor, multiple sensors w, W modulation profiles relating sensor modulation to backscatter z, Z noise and / or error terms® vector outer product

[0043] In an embodiment, a set of one or more optional ‘preprocessing’ steps prepares yraw. For example, a bandpass filter can be applied along the samples of yrawto isolate the transmit carrier frequency and reject some noise. Notably, because the system is pulse-mode, the receive signal is relatively wide-band and filter windows should be designed accordingly. It is also possible to filter for specific higher-order harmonics, such as second and third harmonics.

[0044] In an embodiment, the raw signal may be further processed to yield instantaneous amplitude, phase, and frequency. One method of performing this is via IQ demodulation at the carrier frequency. Alternatively, the Hilbert transform can be used, but that may be less stable because it does not assume a known frequency. If computational simplicity is desired, instantaneous amplitude may be computed via rectifying and filtering the signal, or squaring, filtering, and square-rooting the signal. Decimation or down sampling can be then applied along these versions of yraw- This is not required, but can reduce computational load for later processing stages. Embodiments of the present invention comprise code implementation for processing, including pre-processing, the backscatter data.

[0045] Due to the machine-learning nature of some of the later stages of the process and assumed small-signal linearity, any number features can be obtained from the raw backscatter (yraw) and fed into the learning algorithm(s) without changing the structure of the algorithm(s). The only downside to this may be increased computational load. One or more transformed versions of yraw are concatenated, and each of these results is concatenated across all transceiver channels to result in y G - , where N is considered a set of features across all transceiver channels which describe each pulse of backscatter. Each of these features is assumed to linearly vary with sensor input signal. Those features could include: raw Rx value, instantaneous amplitude, instantaneous phase, instantaneous frequency at each sample point for each transceiver channel for one pulse. Other featurization methods may include time- frequency estimation via a discrete wavelet transform, or other modeling methods.

[0046] Note: in each of these cases, noise terms corresponding to various sources of noise in the system, such as transmit signal inter-pulse variability, modulator noise, and receive amplification and digitization noise, could be explicitly considered and analyzed to design optimal noise-reduction filters.

[0047] Thus, the backscatter signal model for each backscatter sample n from 1 to N, for one transceiver channel, one sensor, and one pulse is: yraw = yo + x w +z,where: y G RNis the backscatter signal at feature n from 1 to N; scalar x is the input signal to the sensor; yo G RNis the ’nominal’ reflection of the mote when x is zero; w G RNis the ‘modulation profile’, which is the weighting of the sensor input signal on each backscatter sample n; z is term which captures additive noise and other error.

[0048] Extending this to multiple successive pulses of captured backscatter, each backscatter pulse y is included as a row in backscatter matrix Y.Y = 1<M) 0 yo + x 0 w +Z, where Y G RMxNcontains backscatter data at features n from 1 to N and pulses m from 1 to M. Note that along the sample dimension (n) the sampling period is typically on the order of 20 ns whereas along the pulse dimension (m) the sampling period is typically on the order of 100 ps. 1 G RMX1is a vector of ones which expands the unchanging ‘nominal backscatter’ yo across pulsetime. x G KMxlis the signal into the sensor across pulse-time (m). 0 is the outer product. It is useful to use backscatter Y to estimate the input signal x.

[0049] In a system with multiple sensors, with sensor p from 1 to P,Y = X [1(M) yo + x 0 w]p+ZP

[0050] This assumes linear superposition of the backscatter from each sensor. In a linear medium with sensors spread far apart, this is a reasonable assumption. For sensors that are closely packed, this assumption is more likely to break down. This can be rearranged to,Y = 1(]M) 0 X [yo] / > + X • W + ZY = X Y0; / > + X • W + Z where X;,[yo]p is the sum of all individual nominal sensor reflections, X G 1RMXPis the input signal across every pulse m and sensor p, and W GPXNis the modulation profile for each sensor.

[0051] In a system with other non-modulating ‘background scatterers’, such as the skull, a term ybackground describes those non-modulating scatterers. Because one does not need to solve for the background scatterers ybackground and the nominal reflection of each sensor yo, one can combine them into a ‘catch-all’ of non-modulating reflection called yofor ‘offset’, where yo=

[0052] This can be further simplified by highpass filtering Y along the pulse dimension (m) to remove the non-modulating reflection yoand isolate only the backscatter modulation across pulse m at each ultrasound sample n. Ymod = Y * / zpw, where hpv / is the discretized time-domain representation of a highpass filter applied along the pulse-time dimension. Note that X and W could be solved-for by considering yoto be one row of the W matrix. But, filtering out yosimplifies by requiring one fewer row of W to be solved for. Additionally, the non-modulating backscatter yois typically several orders of magnitude larger than any mote modulation profile (row of W), such that considering y0to be one row of the W matrix may have that row dominate any loss functions used to solve W, leading to poor solution of other rows of W. Any data whitening techniques used to help solve this would result in wildly varying noise levels in each row of W.Ymod = X W + Z

[0053] Rows of Ymod can be thought of as points in N-dimensional ‘modulation space’. Once in this simplified form, this becomes similar to many other matrix decomposition problems. It is desirable to solve for X. In the general sense, solving for X while only having access to backscatter data Ymod is under constrained. To overcome this, one of several methods may used to create an estimate of W, called W. Finally, an estimate of X, called X, can be found from Ymod and W. To help organize the implementation of these methods, the group of all processing steps up to and including pulsewise high pass filtering, to result in Ymod is called the ‘preprocessor’. The group of processing steps to find is called a ‘learner’ method. The group of processing steps to find X is called an ‘extractor’ method. Each of these methods steps can have several variations.

[0054] Before sending data from Ymod to a ‘learner’ step, it may be useful to lower the computational burden by only selecting pulses with high saliency. This is achieved, in an embodiment, with a processing step called the ‘discoverer’ , which selects pulses of data from Ymod whose L-2 norm crosses an automatically adjusting threshold, and sends those pulses to the learning algorithm.

[0055] Various Learner methods include the following:Learner : W via linear regression

[0056] In the case where ground truth data for the input signal X is known, a supervised fit can be utilized. Because it is assumed that YmOd is linear with X for small input signals, one canuse multiple linear regression on each feature n. Separately for each backscatter feature n, the equation can be set up as:es to take into account the offset is optional if filtering along pulses has been performed during the preprocessing stage.

[0057] can be estimated via the closed form solution to minimizing least squared error (i.e. ordinary least squares regression). This model is relatively simplistic and does not perfectly capture the effects of sensor impedance modulation on backscatter, but is advantageous in that it obviates the manual selection of a region of interest from which to extract the amplitude modulation signal.

[0058] As an example, data from a water tank calibration curve experiment was used to test this method (FIGS. 3A-B). Each trial of backscatter was broken into individual ramps of a sawtooth input signal. In one version of the analysis, hold-one-out validation was performed to obtain the extracted trace for each sawtooth ramp, where the model was fit on all other sawtooth ramps within that experiment, and then the model was used to extract the estimated input voltage for that sawtooth ramp. This method assumes that the parameters used to describe the backscatter do not change from ramp to ramp, i.e. that the sensor is in the same position for each ramp. In another version of the analysis, the ramps were broken into a ‘test’ group and a ‘train’ group. These two versions had similar results. FIGS. 3A-B depict ordinary least-squares regression fitting of modulation profiles for benchtop calibration curve experiment ‘AM’ . FIG. 3A depicts fit voltage and modulation profiles for separate ‘trials’ within one experiment (columns), where each trial corresponds to one ramp of the input voltage, ‘gt’ refers to ‘ground truth’; ‘lootw’ refers to ‘leave-one-out trial- wide’, where training is performed on all but one input ramp sweep, and test extraction performed on that input ramp, ‘hoew’ refers to ‘hold-out experiment- wi de’ , where training is performed on approximately 25% of input ramps, and test extraction performed on the rest. The 5th and 6th input ramps were used for training. FIG. 4B depicts the fit voltage data from FIG. 3A, overlaid and averaged for the ‘test’ trials of the holdout method.

[0059] FIGS. 3A-B depict least-squares regression fitting of modulation profiles for a water tank calibration curve experiment in which ground truth signals were estimated from the sawtooth-wave shape of the input signal. In practice, it is unlikely that ground truth signalswould be available for a wireless implanted device, but these results indicate that the method does generate modulation profiles useful for extraction.Learner : W via weighted and flipped input data

[0060] For a single sensor, a relatively simple method of determining the modulation profile is desired. Here, we discuss such a method that is similar to finding the direction in modulation space of maximum variance, but is done in such a way as to allow updates from online streamed data. The modulation profile w is randomly initialized. For each modulation space data point y, a ‘flipped’ version is computed as yniPPed = sign(y • w)y. This flips about the origin data points that are more than 180 degrees away from w. w is then updated with y in a weighted fashion. Weight is an update hyperparameter (in [0, 1.0]) multiplied by a saliency metric (in [0, 1.0]). The saliency metric may be, for example, the 12 norm of y divided by the all- time maximum 12 norm of y. w is updated as: wupdated = (1 - weight )w + (weight )ynipped. Or as Wupdated=(1—weight)w + weightyiiiP|>o<i / ||yiiiP|>o<i|| if it is desired that w be a unit vector.Learner : W via clustering

[0061] An adaptation of K-means clustering or variable-means clustering can be used to find individual centroids wpcorresponding to modulation profiles for each sensor node. The assumption here is that at any time, only one sensor will have a nonzero value in the highpass- filtered modulation space. If the input signal to each wireless device is sparse in the frequency band of interest (for example, neural spikes with good signal-to-noise ratio), this assumption is reasonable. Variations of the clustering algorithm include alternate distance metrics between points and cluster centroids, including euclidean distance, the angle between vectors, and the angle between vectors modulo 180 degrees, to account for a negative input signal into the backscatter node. A variation has a dynamic number of clusters, where a new cluster is created when a sample point is greater than a distance metric from all cluster centroids, and a cluster is removed if a sample within a distance metric of that cluster centroid is not seen for some duration. Embodiments of the present invention comprise backscatter clustering algorithms.FIG. 4 is a clustering diagram illustrating a clustering method using an angle metric to determine ‘closeness’ to each cluster and a thresholding routine to assign to an existing cluster or make a new one.Learner : W via sparse dictionary learning

[0062] Sparse dictionary learning finds dictionary elements, rows of WT, which linearly combine with some activation X to form each row of Ymod. Importantly, only a small number of the dictionary elements should be necessary to reconstruct any row of Ymod, hence the sparsityconstraint. This is a natural fit for backscatter data modulated by neural spikes (which are sparse in time) and for modulation profiles that are relatively sparse in space (localized to backscatter originating from a specific region in space, where motes are sparsely packed in space). This is a form of matrix decomposition where the LI norm of activations is incorporated into the loss function. Because the LI norm loss does not have a continuous derivative, (as opposed to the L2 norm loss), a direct gradient descent method is not readily available. Instead, a hierarchical numerical optimization routine is utilized.

[0063] Rozell et al. (2008) (Christopher J. Rozell et al. “Sparse Coding via Thresholding and Local Competition in Neural Circuits”. In: Neural Compulation 20.10 (Oct. 2008), pp. 2526- 2563.) presented a locally competitive algorithm for sparse dictionary learning. This algorithm can be adapted to this use case, and it is a natural fit that leverages spatiotemporal sparsity in the present datasets as well as the online nature of data collection, real-time calibration, and ongoing adjustment of profiles. This algorithm is like matching pursuit in that it has an inner loop which optimizes ‘activations’ of basis vectors and an outer loop which optimizes the basis vectors. In this case, though, it is unsupervised. Embodiments of the present invention comprise sparse dictionary learning algorithms. FIGS. 5A-D present LCA Sparsification Diagram according to an embodiment. Variations may include normalization of sparse dictionary elements and / or activations to a maximal value, injected random noise into the dictionary elements and / or activations during training to avoid stoppage in local minima, and automatically adjusting hyperparameters over the course of training. FIG. 5A presents an overview of an embodiment. FIG. 5B presents event detection according to an embodiment. FIG. 5C depicts an embodiment of an inner loop to find sparse activations of dictionary elements given a dictionary and input data. FIG. 5D presents an embodiment of an outer loop to update a dictionary. Embodiments shown in FIGS. 5A-D are adapted for backscatter communication from the original presentation in Rozell et al.Extractor : estimate X from Ymod and W

[0064] Once there is an estimate for the modulation profile matrix: W, one can solve for X. W is not, in general, invertible, so one must estimate X some other way. In an embodiment, the steps to calculate X from Ymod and W are called the ‘extractor’. In the simplest form of the ‘extractor’, one can project backscatter data against the basis of modulation profiles to extract input voltages. This works well when there is high spatial sparsity of motes in the system leading to sparsity along the sample-dimension (n) of Ymod.X = uYmod . ' WTwhere a is an arbitrary scaling factor, equal to 1 if the rows of W are normalized to unit vectors prior to extraction. Alternatively, the output of the ‘activations’ stage of a sparse dictionary learning algorithm can be used to calculate X.

[0065] This demodulation includes all backscatter signal captured in the pulse. Much of that backscatter signal has low SNR, so it degrades the overall SNR of the demodulated value. This can be helped somewhat with manual selection of a ‘region of interest’ (RO1), a down-selected region of backscatter that is used for norming.Methods for solving the motion artifact problem in the case of low-modulation-depth sensors.

[0066] Given the model of backscatter prior to high-pass filtering out the offset backscatter (ignoring the noise term Z):Y= 1(M) - <8> y0+ X • W

[0067] To solve the motion problem, we consider yoand W as dependent on the positions of the sensors. To capture this dependence, we denote Foas a map from R3P— > RNand Fw as a map from3I>— >PXN.Y= 1(M) ’ ® F0(p) + X ■ Fw o) where p is the position of each sensor in physical euclidean space (e.g. [xSensori, y'sensori, Zsensori, Xsensor2, yscnsor2, sensor2, VsensorP, VsensorP, sensorP ] ). In order to make this work, one should estimate p (different for each pulse), Fo, and Fw, all only from Y. Fo, and Fw are highly parameterized, which makes this challenging. To simplify this, one may focus on the case of only one sensor (P = 1).Sensor Position Extraction

[0068] It is desired that the position of the sensor be tracked over time. This position should be calculated only from backscatter data, should be robust to short pulses, noise, and low sampling rate relative to carrier. The precision should be sub-cycle, and there should be no drift over time. Position extraction is performed in two parts. In part 1, the change in time of flight (Ato / ) from the transmit pulse source to the sensor and back to each receive channel is estimated from tracking of phase of the backscatter. In part 2, this change in time of flight is used to triangulate the position in 3D physical space.

[0069] Part I: Tracking change in time of flight (Ato ): this may begin with each raw backscatter pulse receive signal (yraw) on each transceiver channel. yrawcan then optionally be filtered around the transmit carrier frequency and time-domain window.

[0070] To perform phase tracking, the data in each pulse of backscatter in a fixed region of interest (ROI) containing the backscatter signal from the sensor may be selected. This signal may be IQ-demodulated and instantaneous phase calculated at each point in the backscatter signal. To track the average phase-change-across-pulses of the whole region of backscatter from the sensor, the instantaneous phase may be unwrapped, then differentiated across successive pulses, then weighted-averaged over the ROI, then integrated across pulses. This phase tracking may be converted to an estimate of distance tracking with a known backscatter sampling rate and an assumed speed of wave propagation in the wireless medium. To perform zero-crossing tracking, for the first pulse, zero-crossings may be determined within an initial ROI containing the backscatter signal from the sensor. For pulse (n + 1), zero-crossings which are closest to the zero-crossings of pulse (n) can be found. The zero-crossings for each pulse may be averaged and converted from sample offset to A distance with a known backscatter sampling rate and an assumed speed of wave propagation in the wireless medium.

[0071] In an alternate version of phase tracking, the instantaneous amplitude of yrawmay be computed via I-Q demodulation. Next, the phase offset from the first sample to the sample of the peak amplitude may be found. This phase offset may be used to generate new in-phase and quadrature mixer signals. A new round of I-Q demodulation with these mixer signals may be performed to generate instantaneous phase offset between yrawand the in-phase mixer signal. This instantaneous samplewise phase offset signal is then unwrapped and then weighted- averaged over samples, where the weights come from the instantaneous amplitude of yraw- This yields a single value for phase offset of yraw relative to the mixer signal. This is then added to the phase offset used to generate the mixer signal. Assuming that the backscatter signal in yrawmoves with roughly ‘bulk motion’ (i.e. all points in the signal phase shift similarly due to motion), then this yields the wrapped phase offset of yrawrelative to zero phase. This phase is then unwrapped across successive pulses and the phase of the first pulse is subtracted. This yields the a relatively robust calculation of change in phase across pulses, which yields \t f when divided by 2^Carrier. Change in distance between a transducer and a sensor (called ‘A distance’), is the (Dtof times the speed of wave propagation in the wireless medium.

[0072] The output of these methods yielded the A distance trace, which is an estimate of the change in distance between the sensor and the external transducer across the trial. Note that this trace is the projection of the actual motion vector of the sensor onto the vector between the sensor and the external transducer. I.e. the sensor’s actual 1-dimensional motion is approximately this trace divided by the cosine of the angle between the motion vector of thesensor and the vector from the sensor to the external transducer. This angle is not easily ascertained from single-channel backscatter data.

[0073] In order to assess the limitations of the motion extraction, its susceptibility to backscatter additive noise and to sensor impedance modulation were investigated. A 1- dimensional simulation of backscatter was performed in 4 configurations: without motion and without additive noise, with motion and without additive noise, without motion and with additive noise, and with motion and with additive noise (FIG. 6A). Motion extraction from backscatter without motion and with noise showed a standard deviation of 4.05 pm over 198 pulses for phase tracking and standard deviation of 3.45 pm over 198 pulses for zero-crossing tracking. This indicated that motion extraction was relatively insensitive to backscatter additive noise.

[0074] Motion extraction was also performed for the backscatter dataset from the 2019 reproduction calibration curve (FIG. 6B). This experiment was performed on a pneumatic vibration-isolation table to minimize any true motion between the external transducer and the sensor. The sensor input was driven by a 10.5 mV peak-peak sawtooth waveform. The backscatter modulation from sensor input (10.5 mV pkpk) showed up on the phase-tracking motion extraction as a signal with a peak-peak value of approximately 400 nm and on the zerocrossing motion tracking with a peak-peak value of approximately 0 m. This indicated that motion extraction was relatively insensitive to sensor impedance modulation. FIG. 6A presents results regarding motion extraction is relatively insensitive to backscatter additive noise: A simple simulation of backscatter was performed. In FIG. 6A, the top axes shows motion extraction from the simulated backscatter with no additive Rx noise, comparing a simulation with no sensor motion and a simulation with 0.425 mm peak-peak sinusoidal axial motion. In FIG. 6B, the bottom axes shows the motion extraction from the same simulations, but with additive noise included in the raw backscatter. (Blue lines are phase motion tracking, red lines are zero-crossings motion tracking.) FIG. 6B presents results regarding motion extraction is relatively insensitive to sensor impedance modulation: Both amplitude modulation extraction (top) and motion extraction (bottom) are performed on the backscatter dataset from the 2019 benchtop acoustic calibration curve replication experiment. (Blue lines are phase motion tracking, red lines are zero-crossings motion tracking.)

[0075] Changes in the instantaneous phase at various regions in the backscatter signal can be due to either sensor motion or sensor modulation of the backscatter. In the case of motion, the instantaneous phase of the entire backscatter region corresponding to the sensor shifts in a more or less uniform (‘rigid-body’) manner. In the case of the sensor modulation affecting the phasewithout sensor motion, recent experiments show that the ‘leading edge’ of the backscatter region corresponding to the sensor does not show any instantaneous phase shift, and only a very small portion (usually less than 1 cycle) of the ‘trailing edge’ of that region shows any significant instantaneous phase shift.

[0076] Part II: Estimate absolute position from xtof : here, one would like to estimate absolute position from changes in time of flight. This is similar to traditional triangulation, but instead of precise absolute time of flight information, there is precise change in time of flight information and imprecise absolute time of flight information (from peak of instantaneous amplitude). Furthermore, one predominantly cares about high precision of small changes in position (from motion) rather than high precision of the absolute position of the sensor.

[0077] Nomenclature used: u,, vq, wqthe cartesian position coordinates of each transceiver transducer x, y, z cartesian position of sensorX, Y, Z some fixed nominal offset of sensor position in cartesian coordinates Ax, Az / , Az small changes in position around X, Y, Z (changing across pulses) c speed of wave propagation (speed of sound in the case of ultrasound)Atofqchange in time of flight to sensor of pulse m relative to pulse 0 dqdistance from each transceiver channel to the sensor based on X. Y, Z, \tol' , dq distance from each transceiver channel to the sensor based on x, y, z

[0078] To do this estimation, the distance to each transducer may be described in two ways: one dependent on starting position and change in time of flight information, the other dependent on starting position and change in position. One then finds the sensor positions which minimizes the squared error between these two descriptions of distance. x = X + Ax y = Y + Ay z = Z + AzAdq = c(Atofq— (7 / 2)Atofo) dq = Dq+ Adq lf = (dq- dq)2

[0079] One seeks to find the X, Y, Z, Ax, Ay, Az which minimize the loss function / ’given known uq, vq, wqfor transceiver channel q from 1 to Q and estimated \tol'( / for many successivepulses. To do this, in an embodiment, one computes 3lf / 3Ax, 61f7<5Ay, 3lf / 3Az, 3lf / 3AX. 31J73AY, 31 / 3AZ to be able to perform gradient descent optimization steps and Newton-Raphson optimization steps to converge on a solution.Build a model of yoand W across sensor positions (Foand Fw)

[0080] To model Foand Fw, one first collects a large number of initial calibration backscatter pulses. From this, one selects a set of model points in p that capture all of the positions of the sensor. The value at each point in the model of Fois the average backscatter signal when the sensor is in the vicinity of that point. The value at each point in the model of Fw is determined using the “Learner : W via weighted and flipped input data” method described above, with the input being the difference between each backscatter pulse and a query of the Fomodel at that point (that difference being the modulation at that point). The ‘vicinity’ notion is achieved with a spatial gaussian weighting of input data to the model and query output of the model. Once the models are fit, the evaluation of Foand Fw can be achieved by querying each model in the vicinity of p. In order to reduce the fineness of discretization of the model over physical points in space necessary to achieve a given error, the backscatter signals used to fit the model are shifted to offset the delta time of flight signal associated with each pulse and transceiver channel. Then, when querying the model, the outputs are shifted back to undo the shifting present in the internals of the model.

[0081] Once p, Foand Fw are determined, for each pulse y0and W can be queried and then, Ymod = Y - 1(M) y<> = xw X can then be determined via the extraction methods described above.

[0082] Another way to think about this is that the motion model is a surface in R(2+3?), where the first two dimensions represent the index of the backscatter feature from 1 to N and the value of the model at that point, and the rest of the dimensions represent the Cartesian coordinates of P mote. In this case, the values of the surface at the feature indices and p is ‘querying’ the model to find either yoor W.

[0083] Code implementations of embodiments of the present invention have been adapted to operate on large data arrays using graphical processing units. Such code implementations may be abstracted into a processing pipeline which contains several processing steps. Each of those steps may be implemented as an instance of a python class which begins with "Step". Each processing step takes input data, processes it in some manner, and generates output data.

[0084] Some of the relevant processing steps are defined in the classes:"StepFilt" in file steps2_filt.py: Filtering a multidimensional ultrasound data array across the receive sample dimension and / or across the pulse dimension (the latter isolates backscatter modulation in a certain frequency band while keeping time-of-flight information intact)."StepIQDemod", "StepIQToAmp", "StepIQToPhase", and "StepInstFreq" in file steps2_iq_amp_phase.py: Preprocessing the raw ultrasound data into features relevant for identifying modulation."StepMetric" in file steps2_swmetrics.py: Computing statistical metrics of ultrasound data to help in identifying relevant regions of ultrasound."StepSingleProfile ", "StepDiscover", "StepCluster", "StepSparsify" in files steps2_learner.py: learning modulation profiles from ultrasound data. The "Clusterer" class in clusterer.py" and the "Sparsifier" class in sparsifier.py are implementations of the related clustering and sparse dictionary learning algorithms. Such code implementations may have additional implementation features not discussed above, including normalization, automatic hyperparameter adjustment, annealing, and optionally flipping some input data 180 degrees in feature space to handle the fact that the signal sent by the backscatter sensor can be negative."StepExtract" in file steps2_extractor.py: demodulating the signals of interest from preprocessed ultrasound data using modulation profiles. This is used for extraction when modulation profiles come from "StepSingleProfile" or "StepCluster", and sometimes for "StepSparsify"; when modulation profiles come from "StepSparisfy" or "StepMotionLeamer," the extraction may happen within those steps."StepDeltaTofFromPhase", "StepPosFromDeltaTof" in files steps2_position.py: estimating sensor position from backscatter position with very good sensitivity to small changes in position."StepMotionLearner" in file steps2_motion_learner.py: Modeling sensor backscatter and modulation profiles over the 3D spatial position of the sensor and use that to isolate backscatter modulation due sensor to input signal from backscatter modulation due to motion. Classes "MotionModelFixedGrid", "MotionModelStoredPoints," and "MotionModelFixedPoints" in file motion_model.py are alternate implementations of this model, with varying performance characteristics.

[0085] In general, backscatter communication is best utilized when there is an asymmetry in the performance requirements between two ends of a wireless link. Generally, the wireless backscatter node has more stringent requirements, such as low size, low cost, and / or low power;and the ‘interrogator’ side of the wireless link has less stringent requirements. The implemented interrogator system can be used as the ‘communication hub’ which communicates with multiple simple wireless devices. This could be a communication hub affixed to or in the body, in the case of implantable medical sensors, or this could be a communication hub in other settings, such as a factory industrial setting.

[0086] The systems and methods provided herein can be applied to any wireless communication energy or medium where backscattered signal can be acquired fast enough to utilize the time-of-flight information inherent in sequentially digitized samples. The demonstrated implementation digitally captures a raw time-domain waveform of the backscattered waves (sampled at a higher rate than the wave frequency). This is possible with sound waves and radio waves. The techniques could also be applied to lower wavelength electromagnetic radiation, such as infrared or visible light, but the implementation details would need to be slightly adjusted to account for sampling the intensity of reflected energy at a rate lower than the frequency of the radiation.

[0087] US Patent No. 10,682,530, US Patent No. 10,898,736, US Patent No. 10,765,865, US Patent No. 10,744,347, US Patent Application No. 2019 / 0150884 and US Patent Application No. 2019 / 0150883, which are hereby incorporated by reference in their entireties, describe various components (e.g., backscatter / sensor nodes including modulation circuits, interrogator transceiver components, etc.) of a backscatter communication system useful for embodiments herein.

[0088] The following is offered by way of illustration and not by way of limitation.EXPERIMENTALEmbodiments of the present invention were applied in connection with obtaining experimental simulations and results described below.Analytical backscatter simulation

[0089] A simulation of ultrasound backscatter was developed to enable flexible and rapid testing of backscatter processing techniques without requiring the creation of a multitude of empirical experimental setups. The simulation analytically computes the effects of a disturbance as it propagates through a one-dimensional domain. This is simple compared to a three- dimensional time-domain-solved finite-element model, but has vastly superior computational efficiency in simulating backscatter. In connection with this description of experimental results,FIG. 7 illustrates an analytical backscatter simulation diagram according to an embodiment, and FIGS. 8A-D illustrate an exemplary backscatter system, hardware, and processing diagram according to an embodiment. FIG. 7 presents an analytical backscatter simulation diagram. In FIG. 7, subdomain transmission properties depicted in blue arrows, boundary reflection properties depicted with orange arrow, boundary transmission properties depicted with green arrow. Reflections can be analytically computed with known input signal properties and these transmission and boundary properties. FIGS. 8A-D present a backscatter system, hardware, and processing diagram according to an embodiment. FIG. 8A presents an overview of an embodiment. FIG. 8B presents a sensor architecture according to an embodiment. FIG. 8C presents Cephasonics ultrasound transceiver system diagram according to an embodiment.FIG. 8D presents a preprocessing system running in software according to an embodiment.

[0090] The implementation of the simulation consists of several components. A onedimensional domain contains several abutting subdomains, each corresponding to a type of material. For example, a domain may consist of subdomains with materials: scalp, skull, brain, pary-lene, PZT, parylene, brain, skull. Each subdomain contains some number of driven sources (disturbances). When the simulation is initialized, the driven sources are propagated until hitting a boundary, at which point two propagated sources are created, one for the reflected wave and one for the transmitted wave. This process continues until the amplitude of any propagated source falls below a small threshold. The displacement u or pressure p imparted by a source is an analytical function of time and space and several source-defining parameters. In order to compute the displacement u or pressure p at any point in time and space in the domain, computed values for all sources are superimposed.

[0091] The advantage of this analytical approach is that once all sources are parameterized, u can be computed for any arbitrary time or point in space without simulating the intervening points in time and space. This not possible with an explicit time-domain solved finite element model. Furthermore, when initializing the simulation, each propagated source keeps track of the number of times that, relative to the originating driven source, each subdomain has been transited and each boundary has been interacted with. In this way, multiple versions of the simulation can be run with differing subdomain properties without reinitializing the sources. Instead, the effects of transiting each subdomain and interacting with each boundary are recomputed, and then source parameters are updated. This enables very computationally efficient simulations where the impedance or lengths of subdomains change across successive transmit pulses. Additionally, the independence of computation across time points and change in subdomain properties lends itself to highly parallel computation. The simulation wasimplemented in python, using the ‘c py’ numerical package to perform very high throughput simulation computation on relatively inexpensive consumer graphics processing unit hardware (NVIDIA RTX 2080 Ti).

[0092] This simulation does not capture nonlinearities, near-field and surface effects, Poisson effects, dispersion, and complex 3-dimensional reflective surfaces. Nonetheless, it does capture to a first order the effects of impedance modulation, transmission through nonmodulating layers, attenuation and geometric spreading losses, and all of those effects for arbitrary positions of sensors and transceiver elements in 3 dimensions. This is sufficient for exploring methods of transcranial communication, multi-sensor extraction, and separation of motion artifact from sensor modulation. An example simulation consisted of 1 Tx element, 9 Rx elements, and 2 motes, where the simulated domains consisted of brain-parylene-PZTparylene- brain subdomains. Each ‘run’ of the simulation corresponded to successive pulses of a pulsemode backscatter system, for which the simulation used differing subdomain thicknesses to simulate motion of a sensor and differing acoustic impedance of the PZT subdomain to simulate sensor modulation. Simulated backscatter Rx was computed for 880 samples per pulse. This simulation computed at approximately 60,000 pulses per second, fast enough for the simulation to be considered ‘real time’ in relation to a notional backscatter communication system for recording neural signals. This is roughly 7 to 8 orders of magnitude faster than a similar simulation using an explicit time-domain-solved finite element model. Such a speed-up was critically enabling in the development of backscatter processing methods which rely on copious amount of backscatter data to fit extraction models.Empirical water-tank setup

[0093] A water-tank experimental setup was employed to perform controlled experiments on backscatter sensors. The external interrogator utilized transmit-receive hardware from Cephasonics (Santa Clara, CA, USA), a 1.5D transducer array probe (GE M5Sc-RS), and a custom signal processing pipeline. In some experiments, the experimental setup was placed in a Faraday cage and on a pneumatic vibration isolation table to reduce EMI and vibrational noise sources. Sensors consisted of a piezoelectric crystal (750 pm x 750 pm x 750 pm), ‘piezo’, epoxied to a steel rod and encapsulated in parylene. Two silver wires connected to metallized surfaces of the piezo served as electrical access to the transducer, and the assembly was placed through a hole in the water tank so that it was exposed to the acoustic field. The electrical terminals of the piezo, accessible from outside the water tank, were connected to one of: 2-state relay to perform binary modulation, 3 -state relay and resistor bridge to perform low-depthtrinary modulation, a passive resistor to sweep across passive impedance loading, or a modulator circuit.Processing package

[0094] A backscatter processing software package was developed to enable the rapid and reconfigurable exploration backscatter processing methods. The package was organized around a processing ‘pipeline’ which consisted of multiple processing ‘steps’. Each step took data from one or more previous steps in the pipeline, performed some operation on the data, such as IQ demodulation, and produced output data for that step.Methods SNR Comparison

[0095] In order to compare methods, we selected one benchtop backscatter dataset (id: AN135) and ran a variety of methods on it to compare signal-to-noise performance of the extract across methods. In this trial, four sensors were set up in the water tank. One had an simulated spiketrain input signal and the other three had zeroed-out input signal. The simulated input spiketrain had a time dilation of 72x relative to a biologically accurate spiketrain, so that the frequency content of each spike was centered at approximately 12.5 Hz instead of the approximate 900 Hz of biological spikes. The peak-peak amplitude of the input spikes was 40 mV. The transceiver system operated at approximately 874 Hz pulse repetition frequency, with 40 MHz sampling rate and approximately 1.775 MHz carrier frequency. A transmit pulse of four cycles in duration was utilized.

[0096] In processing, the ultrasound data was looped three times to allow the fitting process to settle and allow for filter delays. The output from the middle loop of ultrasound data was used for post-processing.

[0097] In order to quantify signal-to-noise ratio, extracted signals were compared with known input simulated spiketrain signals. The transceiver hardware suffered from a small amount of sampling period imprecision and jitter owing to having software in the loop. Due to this, a direct and precise comparison of the extracted signal to the known input signal at an exact point in time could not be reliably made. Instead, when comparing signals in post-processing the sampling rate of the extracted signal was manually adjusted from the nominal rate of 900 Hz to 874 Hz to line up the extracted signal with the known input signal. The signal plus noise power was then computed as the average power of the extracted signal in the regions where the known input signal was nonzero, and the noise power was computed as the average power of the extracted signal in the regions where the known input signal was zero. Signal to noise ratio(SNR*, with * to denote the caveat of this particular formulation) was computed as signal plus noise power minus noise power, quantity divided by noise power. Note that with this particular calculation for SNR, it is possible for the value to be negative, which is not possible for true SNR measurements. In the plots in FIGS. 9A-D, such a case is represented by a NaN value, which is not plotted.

[0098] The methods were compared across three categories: the method and features of extraction, the set of channels used, and the metric used for scaling, ‘feat’ refers to the method and features of extraction: in the ‘flat’ case, no modulation profile learning was performed, and the extracted signal corresponded to the LI norm of the entire filtered input signal. In the ‘roi’ case, no modulation profile learning was performed, and the extracted signal corresponded to the LI norm of a manually tuned region of interest of the filtered input signal. In the ‘raw’, ‘amp’, ‘phase’ and ‘freq’ cases, modulation profile learning was performed with the weighted and flipped data method. The features of the input signal used corresponded to the raw filtered signal, the instantaneous amplitude, the instantaneous phase relative to a reference wave, and the instantaneous frequency, respectively, or a combination of those features. The channels used were either an individual channel from 0 to 39, the channel corresponding to the median extraction SNR of all channels, the channel corresponding to the best extraction SNR of all channels, a manual selection of channels with good noise properties, or all channels. Several different metrics were used for scaling the features before learning and extraction. This was done so that one feature or channel did not dominate the learning or extraction, similar to ‘data whitening’ techniques. These metrics were computed pulsewise, with a decay over recent pulses. In terms of metrics used for scaling, ‘None’ refers to no metric, ‘inv nlp5’ refers to the inverse of the normalized L-0.5 norm, ‘inv nil’ refers to the inverse of the normalized L-l norm, ‘inv nl2’ refers to the inverse of the normalized L-2 norm, ‘inv nl3’ refers to the inverse of the normalized L-3 norm, ‘inv variance’ refers to the inverse of the variance, ‘12ol 1 ’ refers to the L-2 norm divided by the L-l norm, ‘13oll ’ refers to the L-3 norm divided by the L-l norm, ‘12olls’ refers to the L-2 norm divided by the squared L-l norm, ‘13olls’ refers to the L-3 norm divided by the squared L-l norm. Measures of sparsity were also considered, ‘hoyer’ refers to Hoyer sparsity , and ‘hoyer3oll’ refers to Hoyer sparsity cubed divided by the L-l norm.

[0099] FIGS. 9A-D show the results of this comparative work. FIG. 9A shows SNR* across individual channels and extraction methods. From this, we can see that ‘raw’ and ‘amp’ features performed the best and that the extraction utilizing these learned profiles yielded superior SNR* to the ‘flat’ and ‘roi’ cases without learned profiles. Furthermore, this shows that extraction with respectable SNR can be achieved from single channels using only phase or frequencyinformation. The ‘phase’ feature experienced some glitches on some channels, throwing off the performance. For this reason, the all-channel extraction from phase (Panel D, 3rd column, 6th row) failed. For this reason, phase extraction methodology for signals which sometimes have very low amplitude should be improved. FIG. 9B shows SNR* across scaling metrics and channel selections. When using more than one channel, normalizing by the L-l norm, L-2 norm, or scaling by L-2 norm divided by squared L- 1 norm or L-3 norm divided by squared L- 1 norm produced superior SNR* to no scaling. FIG. 9C shows that the best combination of methods is achieved when extracting simultaneously across the 'raw', 'amp', and 'freq' features across all channels, while using the L-l norm to normalize the features.

[0100] Time-domain representations of the known input signal and the extracted signals are shown in FIG. 9D. The ‘flat’ feature on the ‘median’ channel, with 3.59 dB SNR*, corresponds roughly to the performance one could expect with a single channel and no calibration. The best case method, ‘raw’ + ‘amp’ + ‘freq’ features normalized, shows 19.47 dB SNR*, all with automated calibration. We can also see that adding data from additional channels beyond the ‘best’ channel decreases the SNR* for the ‘flat’ and ‘roi’ cases without learned modulation profiles, but for all learned modulation profiles methods, it improves SNR*. This shows that the automated calibration or learning of modulation profiles improves SNR* over other methods, and substantially lessens the need for manual calibration of the system. FIGS. 9A-D present methods of SNR Comparison according to embodiments. FIG. 9A presents SNR* vs single channels for extraction methods / features. FIG. 9B presents SNR* vs scaling metric for combinations of channels and features. FIG. 9C presents methods SNR* summary. FIG. 9D presents extracted signal for methods and features combinations (rows) and channels combinations (columns), 'input' is known input signal. In each of FIGS. 9A-D, top left number is SNR*, bottom left number is Hoyer sparsity.Water tank: Binary amplitude- shift keyed transcranial backscatter communication

[0101] An ultrasonic wireless micro implantable device, with architecture and modulator implementation previously reported was suspended in a water tank (FIG. 10B), and a backscatter communication link was established between it and an external interrogator. FIGS. 10A-D present diagrams of an experimental configuration of an embodiment and results obtained from such configuration. The placeholder sensor consisted of a piezoelectric crystal (750 pm x 750 pm x 750 pm) electrically connected to a resistor bridge and relay. An input signal to the mote, a binary pulse with 10% duty cycle, drove the relay to toggle the load on the piezo and change the mote backscatter state. The water tank contained the superior portion of a formalin-preservednon-human primate cranium specimen (Macaca mulatta, male, 14 years of age at death) placed between the mote and the external interrogator. The ultrasonic path passed through portions of the parietal and temporal bones, where the bone thickness varied from 2.0 mm to 3.5 mm.

[0102] The raw backscatter signal (FIG. 10A) shows spatially separated backscatter regions from the skull and from the mote, which were able to be resolved due to the short 2 ps transmit pulse. This separation enabled isolation of the mote backscatter from the saturated skull backscatter by mapping regions which corresponded to mote modulation. This mapping process was automated, which allowed simultaneous mote signal isolation across all 40 transmit-receive channels of the external interrogator. A mote input signal which spanned the full modulation range of the mote had a demodulated signal ratio of maximal modulation to standard deviation in the nonmodualating times 662. This result indicates that the skull is not an insurmountable problem for ultrasonic wireless communication, and that short pulses are particularly helpful in addressing this challenge. FIG. 10A presents a schematic of transcranial ultrasonic pulsebackscatter communication of an embodiment. FIG. 10BB presents an experimental setup of an embodiment: (top) external transducer; (center) skull; (center) mote and mote suspension. FIG. 10C presents raw time-domain backscatter signal from an interrogation pulse with (i) ringdown from the external transducer transmit pulse; (ii) saturated skull reflection skull; (iii) backscatter from the mote. Red and blue regions depict the backscatter signal for two mote signal states. FIG. 10D presents demodulated binary pulse test signal of an embodiment.Water tank: multi-sensor transcranial communication

[0103] A multi-mote transcranial benchtop experiment was performed to demonstrate feasibility of separation of backscatter signals from multiple sensors while traversing the skull. FIG. 11 illustrates processing steps for binary load-switched transcranial communication according to an embodiment. In FIG. 11, the top row: raw receive signal for one pulse and two transceiver channels. In FIG. 11, the second row: modulation space Ymod for many backscatter instantaneous amplitude features (columns of image) and pulses (rows of image), for two channels. In FIG. 11, the third row: modulation profile W for one sensor (shown separately for each channel). In FIG. 11, the bottom plot: result of projecting Ymod along W. FIG. 12 illustrates experimental setup (i.e., benchtop multi-sensor transcranial), which consisted of four sensors with their piezo components in a water tank and electrical modulator components outside the water tank. Two of the sensors experienced modulator failures prior to the commencement of this experiment, but the two remaining sensors successfully were modulated by a simulated spiketrain signal applied by a digital to analog converter to the input terminals ofthe sensor. An ex- vivo non-human primate cranium specimen (Formalin-preserved, Macaca mulatta, male, 14 years of age at death) was placed between the external transceiver and the sensor piezos.

[0104] FIG. 13 shows the results of this experiment. These results show that utilizing very short pulses of ultrasound can enable time-of-fight separation of the reflection from different motes and from the skull. That time-domain separation is important so that high-gain digitization can be applied to the mote reflection without saturating the transceiver frontend with the high-amplitude skull reflection. While the results are preliminary, they show that separation of signals from individual sensors can be done with acceptably-low levels of crosstalk (given these input signal magnitudes). FIG. 13 relates to benchtop multi-sensor transcranial backscatter communication of an embodiment. This experiment utilized artificially generated 'spike' signals with 40 mV peak-peak values. Furthermore, due to the pulse repetition frequency limitations of the experimental setup, the spikes were 'time-dilated' by 72x to allow greater oversampling of the spike waveform with backscatter pulses. In FIG. 13, top row: backscatter signals across 20 selected receive channels. These data were time-domain windowed to only show the backscatter corresponding to the region of space past the skull. In FIG. 13, second row: modulation space Ymod for many backscatter instantaneous amplitude features (columns of image) and pulses (rows of image). In FIG. 13, third and fourth rows: modulation profiles W for two sensors, where each profile is for all features across all channels. In FIG. 13, fifth and sixth rows: extracted signals for two sensors, showing readily discernible spikes.Simulation: disambiguation of sensor impedance modulation from sensor motion

[0105] A simulation was performed to generate simulated backscatter data for demonstrating separation of modulation signal from motion confound. The simulation consisted of 1 mote moving along a straight line with 30 pm RMS (root-mean-squared) displacement and frequency power spectral density proportional to the piecewise linear function defined by points: [(1 Hz, 0), (10 Hz, 0.5), (50 Hz, 2), (100 Hz, 1.5), (500 Hz, 1), (1000 Hz, 0.25), (1500 Hz, 0.25)]. The input signal was simulated neural spikes with a 2 mV pk-pk deflection and 300 Hz firing rate. The sensor consisted of subdomains: ‘brain’ with nominal 60 mm thickness, ‘polyimide’ with nominal 250 pm thickness, ‘mote’ with nominal lambda over two thickness, ‘polyimide’ with nominal 250 pm thickness, and ‘brain’ with infinite effective thickness (no reflection off of far side). The mote had a modulation sensitivity of approximately 0.18 % / mV. The external transceiver consisted of a 3 x 3 array of elements. The central element emitted a transmit pulse at30 kHz pulse repetition frequency, with 1.8 MHz carrier frequency and 3 cycles per pulse. Simulated Rx was computed for all 9 transceiver elements, with 40 MHz sampling rate.

[0106] FIG. 14 shows the results of this simulation and processing. The naive L-l norm extraction (third row) shows a signal that is dominated by motion artifact. The extraction with separation of motion artifact from impedance modulation (fifth row) shows readily discernible simulated spikes which align with the known simulated input signal. While this simulation is limited in its modeling of real-world phenomena, for example the lack of a true 3D representation of the interaction of the transmit pulse and the sensor, in a limited sense, this result shows that backscatter modulation from sensor modulation and from motion artifact can be separated even when the motion artifact is of much higher magnitude than sensor modulation. In FIG. 14, the top row: input signal into sensor (simulated spikes with poisson firing pattern and 2 mV pk-pk amplitude.). In FIG. 14, the second row: raw backscatter signals across 9 transceiver channels. Simulated backscatter implements motion of the sensor along a line in 3D space with root-mean-square of position offset of 30 pm. Modulation sensitivity is simulated to be approximately 0.18% / mV; (third row) demodulation without the motion model, via LI norm of the backscatter pulse across all channels is dominated by motion artifact. In FIG. 14, the fourth row: plots showing slices of the models for F G> and F ">W. In FIG. 14, the fifth row: extraction using the motion model to separate sensor modulation from motion artifact shows relatively good match between extracted and input signal, with readily distinguishable spikes.

[0107] All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein.

[0108] The use of the terms “a” and “an” and “the” and “at least one” and similar referents in the context of describing the disclosed subject matter (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The use of the term “at least one” followed by a list of one or more items (for example, “at least one of A and B”) is to be construed to mean one item selected from the listed items (A or B) or any combination of two or more of the listed items (A and B), unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually toeach separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or example language (e.g., “such as”) provided herein, is intended merely to better illuminate the disclosed subject matter and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.

[0109] Certain embodiments are described herein. Variations of those embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the embodiments to be practiced otherwise than as specifically described herein. Accordingly, this disclosure includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the disclosure unless otherwise indicated herein or otherwise clearly contradicted by context.

Claims

CLAIMS:

1. A wireless backscatter communication system comprising: a plurality of backscatter node devices; and at least one interrogator device, wherein the at least one interrogator device is configured to: transmit one or more interrogator pulse signals, for each of the one or more interrogator pulse signals, receive a raw backscatter signal including individual backscatter signals from each of the plurality of backscatter node devices, wherein each individual backscatter signal includes a reflection of the interrogator pulse signal modulated based on an input modulation signal of the respective backscatter node device; process the one or more raw backscatter signals using a machine learning algorithm to determine a mapping model between the input modulation signal of each of the plurality of backscatter node devices and the one or more raw backscatter signals; and extract one or more signals of interest based on the mapping model, wherein each signal of interest corresponds to an input modulation signal of a particular backscatter node device.

2. The system of claim 1, wherein the machine learning algorithm is based on one of: a linear regression algorithm; a weighted and flipped input data algorithm, a clustering algorithm, or a sparse dictionary learning algorithm.

3. The system of claim 1, wherein the at least one interrogator device is further configured to, prior to processing the one or more raw backscatter signals using the machine learning algorithm, filter the one or more raw backscatter signals to isolate changes in instantaneous amplitude, phase and / or frequency across the one or more interrogator pulse signals.

4. The system of claim 1, wherein the at least one interrogator device includes at least three transducers configured to emit interrogator pulse signals and receive backscatter signals.

5. The system of claim 4, wherein the at least one interrogator device is further configured to track a position over time of at least a first one of the plurality of backscatter node devices relative to the at least one interrogator device.

6. The system of claim 5, wherein the at least one interrogator device is configured to track the position over time based on a change in time of flight between interrogator pulse signals and received individual backscatter signals for the first backscatter node device.

7. The system of claim 4, wherein the at least three transducers are arranged in a linear array or in a 2-dimensional array.

8. The system of claim 1, wherein the interrogator device includes an ultrasonic transducer and wherein the interrogator pulse signals include ultrasound pulse signals.

9. The system of claim 1, wherein the interrogator device includes an electromagnetic transducer and wherein the interrogator pulse signals include radio pulse signals.

10. The system of claim 1, wherein the plurality of backscatter node devices includes sensor devices and wherein the input modulation signals comprise impedance modulation signals.

11. A method of interrogating a plurality of backscatter node devices in a wireless backscatter communication system, wherein the method comprises: transmitting one or more interrogator pulse signals from an interrogator device, for each of the one or more interrogator pulse signals, receiving at the interrogator device a raw backscatter signal including individual backscatter signals from each of the plurality of backscatter node devices, wherein each individual backscatter signal includes a reflection of the interrogator pulse signal modulated based on an input modulation signal of the respective backscatter node device; processing the one or more raw backscatter signals to determine a mapping model between the input modulation signal of each of the plurality of backscatter node devices and the one or more raw backscatter signals; andextracting one or more signals of interest based on the mapping model, wherein each signal of interest corresponds to an input modulation signal of a backscatter node device.

12. The method of claim 11, wherein the interrogator device includes an ultrasonic transducer and wherein the interrogator pulse signals include ultrasound pulse signals.

13. The method of claim 11, wherein the interrogator device includes an electromagnetic transducer and wherein the interrogator pulse signals include radio pulse signals.

14. The method of claim 11, wherein the plurality of backscatter node devices includes sensor devices and wherein the input modulation signals comprise impedance modulation signals.

15. The method of claim 11, wherein the processing the one or more raw backscatter signals includes processing the one or more raw backscatter signals with a machine learning algorithm to determine the mapping model, wherein the machine learning algorithm comprises a machine learning algorithm based on one of: a linear regression algorithm; a weighted and flipped input data algorithm, a clustering algorithm, or a sparse dictionary learning algorithm.

16. The method of claim 11, further including, prior to processing the one or more raw backscatter signals, filter the one or more raw backscatter signals to isolate changes in instantaneous amplitude, phase and / or frequency across the one or more interrogator pulse signals.

17. The method of claim 11, wherein the interrogator device includes at least three transducers configured to emit interrogator pulse signals and receive backscatter signals.

18. The method of claim 17, wherein the method further includes tracking a position over time of at least a first one of the plurality of backscatter node devices relative to the interrogator device.

19. The method of claim 18, wherein the tracking the position over time is based on a change in time of flight between interrogator pulse signals and received individual backscatter signals for the first backscatter node device.

20. The method of claim 17, wherein the at least three transducers are arranged in a linear array or in a 2-dimensional array.

21. An interrogator device in a wireless backscatter system having a plurality of backscatter node devices, the interrogator node device comprising a transducer, a processor and a memory storing code, which when executed by the processor configures the interrogator device to: emit, via the transducer, one or more interrogator pulse signals, for each of the one or more interrogator pulse signals, receive a raw backscatter signal including individual backscatter signals from each of the plurality of backscatter node devices, wherein each individual backscatter signal includes a reflection of the interrogator pulse signal modulated based on an input modulation signal of the respective backscatter node device; process the one or more raw backscatter signals using the processor to determine a mapping model between the input modulation signal of each of the plurality of backscatter node devices and the one or more raw backscatter signals; and extract one or more signals of interest based on the mapping model, wherein each signal of interest corresponds to an input modulation signal of a backscatter node device.

22. The interrogator device of claim 21 , wherein the processing the one or more raw backscatter signals includes processing the one or more raw backscatter signals with a machine learning algorithm to determine the mapping model, wherein the machine learning algorithm comprises a machine learning algorithm based on one of: a linear regression algorithm; a weighted and flipped input data algorithm, a clustering algorithm, or a sparse dictionary learning algorithm.

23. The interrogator device of claim 21 , wherein the code, when executed by the processor further configures the interrogator device to, prior to processing the one or more rawbackscatter signals using the machine learning algorithm, filter the one or more raw backscatter signals to isolate changes in instantaneous amplitude, phase and / or frequency across the one or more interrogator pulse signals.

24. The interrogator device of claim 21, wherein the interrogator device includes at least three transducers configured to emit interrogator pulse signals and receive backscatter signals.

25. The interrogator device of claim 24, wherein the code, when executed by the processor further configures the interrogator device to track a position over time of at least a first one of the plurality of backscatter node devices relative to the at least one interrogator device.

26. The interrogator device of claim 25, wherein the code to track the position over time is based on a change in time of flight between interrogator pulse signals and received individual backscatter signals for the first backscatter node devices.

27. The interrogator device of claim 24, wherein the at least three transducers are arranged in a linear array or in a 2-dimensional array.

28. The interrogator device of claim 21, wherein the interrogator device includes an ultrasonic transducer and wherein the interrogator pulse signals include ultrasound pulse signals.

29. The interrogator device of claim 21, wherein the interrogator device includes an electromagnetic transducer and wherein the interrogator pulse signals include radio pulse signals.

30. The interrogator device of claim 21, wherein the plurality of backscatter node devices includes sensor devices and wherein the input modulation signals comprise impedance modulation signals.

31. The system of claim 5, wherein the at least one interrogator device is configured to: process the position over time information of the first backscatter node device to determine a second mapping model of the backscatter of the first backscatter node device andthe backscatter modulation of the first backscatter node device as a function of the position of the first backscatter node device; and extract one or more signals of interest based on the second mapping model, wherein each signal of interest corresponds to an input modulation signal of the first backscatter node device independent from the position of the first backscatter node device or motion of the first backscatter node device.

32. The method of claim 18, further comprising: processing the position over time information of the first backscatter node device to determine a second mapping model of the backscatter of the first backscatter node device and the backscatter modulation of the first backscatter node device as a function of the position of the first backscatter node device; and extracting one or more signals of interest based on the second mapping model, wherein each signal of interest corresponds to an input modulation signal of the first backscatter node device independent from the position of the first backscatter node device or motion of the first backscatter node device.

33. The interrogator device of claim 28, wherein the code, when executed by the processor further configures the interrogator device to: process the position over time information of the first backscatter node device to determine a second mapping model of the backscatter of the first backscatter node device and the backscatter modulation of the first backscatter node device as a function of the position of the first backscatter node device; and extract one or more signals of interest based on the second mapping model, wherein each signal of interest corresponds to an input modulation signal of the first backscatter node device independent from the position of the first backscatter node device or motion of the first backscatter node device.

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