Systems and methods for detecting pulses in a received signal in a streaming manner.

Abstract

This disclosure relates to systems and methods for stream-detecting pulses in a received signal. Threshold detection methods are combined with double-difference phase modulation detection methods to provide higher-performance pulse detection for any digital receiver. A first pulse detection technique uses a signal power threshold. The start of a pulse is declared and pulse processing begins when the square of the pulse amplitude exceeds the signal power threshold. A second pulse detection technique is model-based and uses a window detector that exceeds a phase difference threshold when the pulse has a consistent second-order (typically d-order) phase difference within the window. The first technique has low latency and is independent of pulse width, but operates well only when the SNR value is greater than 15 dB. The second technique has higher latency and requires a minimum pulse width, but operates with a lower (approximately 0 dB) SNR value.

Description

Technical Field

[0001] The techniques disclosed herein generally relate to radar pulse detection. In particular, they relate to radar pulse detection using digital radar receivers. Background Technology

[0002] A receiver system is any system configured to receive energy waves and process them to identify desired information carried in the energy waves. As used herein, an "energy wave" is interference that propagates through at least one medium while carrying energy. For example, energy waves can include electromagnetic waves, radio waves, microwaves, sound waves, or ultrasound.

[0003] Typically, a receiver system includes a transducer and a receiver. A transducer can be any device configured to convert one type of energy into another. Transducers used in receiver systems are generally configured to receive energy waves and convert them into electrical signals. An antenna is an example of a transducer. The receiver processes the electrical signals generated by the transducer to obtain desired information from the signals. The desired information includes information about the signals carried in the energy waves.

[0004] Energy waves are typically used to carry repetitive signals. A repetitive signal is a signal with a time period during which certain aspects of the signal repeat. Repetitive signals are used for timing operations, synchronization operations, radar operations, sonar operations, and other suitable operations. For example, the characteristics of a repetitive signal can be used to synchronize two or more devices. A repetitive signal will be referred to as a "pulse" below.

[0005] Digital radar receivers, which detect radar signals from other radars, have a front-end receiver that generates a pulse descriptor word (PDW) for each radar pulse they detect. They differ from radar systems in that they do not naturally generate range, and they must process unknown signals rather than searching for reflected forms of their transmitted signals. The digital versions of these receivers are typically designed as channelizers or filter banks; within each filter channel, the radar pulse is separated from other overlapping signals, and its noise is reduced relative to the total input bandwidth. These pulses, with their increased signal-to-noise ratio (SNR), are processed to generate data representing estimated signal characteristics of interest, such as phase modulation parameters, frequency, bandwidth, time of arrival, time of departure, pulse width, pulse amplitude, pulse repetition interval, and / or angle of arrival. While such channelizers offer many advantages, they also have critical disadvantages, such as large size, weight, and power consumption, stemming from the need for all the multipliers and adders required by the very large filter banks, which must operate continuously regardless of the presence of a signal. Furthermore, signals that do not match the bandwidth and frequency of each filter in the filter bank are processed suboptimally or split across filter channels, resulting in lost, erroneous, and inaccurate PDWs. Without channelizers, different methods must be used to accomplish the two main processing tasks of noise reduction and signal separation. In either case, for each received pulse, PDW information processing must be performed on the separated signal. Reliable pulse detection is essential for reliable PDW processing.

[0006] Existing pulse detection solutions rely on threshold crossing as the primary detection method. Therefore, this approach limits pulse processing to pulses with a relatively high signal-to-noise ratio (pulses easily distinguishable from noise). This, in turn, limits the detection range of any receiver using thresholding techniques (unless the transmitter signal power is increased). Summary of the Invention

[0007] The following detailed disclosure relates to systems and methods for better pulse detection through a combination of two different complementary approaches. One approach is a conventional approach using a threshold; the start of a pulse is declared and pulse processing begins when the pulse amplitude exceeds the threshold. The other approach is model-based and uses a window detector that detects pulses exceeding the threshold when the pulse has a consistent double (typically d-order) difference phase value within the window. The first approach has low latency and is independent of pulse width, but operates well only at “good” (greater than 15 dB) SNR values. Therefore, threshold detection techniques are limited to easily distinguishable pulses. The other approach has higher latency and requires a minimum pulse width, but operates at lower (approximately 0 dB) SNR values. The design proposed in this paper fuses these two approaches to produce a pulse detector that has lower latency for higher SNR pulses, but can also detect lower SNR pulses with additional latency.

[0008] More specifically, the threshold detection method is fused with the double-difference phase modulation detection method to provide a higher-performance signal detection method for any digital receiver processing pulse signals. The proposed method can accurately detect pulses under various conditions and therefore can be used to detect signals of any radar type. The fused pulse detector can be used as part of a conventional EW channel or a blind source separation-based EW receiver to continuously detect the input signal before pulse processing occurs. In practice, this approach can be used as part of any digital receiver architecture that processes pulse signals in a streaming manner.

[0009] According to some implementations, the system and method share the following features: (1) fusion of threshold-based and phase-based pulse detection methods; (2) ability to detect pulses with lower power and a wider range; (3) continuous threshold updates to handle varying noise conditions; and (4) continuous window updates in the phase modulation detection method to handle varying noise conditions.

[0010] The features described in the preceding paragraph offer advantages including higher quality signal detection and characterization using available hardware, and also enable digital receivers to be smaller, less expensive, and use less power. Therefore, these features can also enable higher-performance digital receivers by achieving more accurate signal detection in more challenging signal environments.

[0011] Although various implementations of systems and methods for detecting pulses using fusion threshold / phase modulation detection techniques will be described in detail below, one or more of those implementations can be characterized by one or more of the following aspects.

[0012] One aspect of the subject matter disclosed in more detail below is a method for detecting pulses in a received signal in a streaming manner, comprising: (a) sampling the received signal to generate samples in a digital format; (b) estimating the corresponding signal power of the received signal for each sample; (c) determining that the signal power estimated in step (b) is less than a signal power threshold; (d) estimating the corresponding instantaneous signal phase of the received signal for each of a plurality of signal samples within a window; (e) estimating the corresponding second-order difference of the signal phases of the plurality of samples within the window; (f) determining that the second-order difference estimated in step (e) is less than a phase difference threshold; and (g) processing the samples within the window to generate an information vector comprising a corresponding dataset of parameter values ​​of pulses in the received signal.

[0013] According to some implementations, the method immediately following the preceding paragraph further includes: (h) calculating a real-time filtered estimate of a signal power threshold based on the signal power of the received signal for the sample, the initial noise power, and the desired false alarm probability; (i) sending the signal power threshold to a signal power threshold comparator performing step (c); (j) generating the desired false alarm probability and the desired detection curve probability; (k) constructing a lookup table including data values ​​representing the desired false alarm probability and the desired detection curve probability generated in step (j); and (i) retrieving a window length and a phase difference threshold from the lookup table based on the desired false alarm probability, the desired detection probability, and the measured signal-to-noise ratio.

[0014] According to one application, the method further includes: storing a dataset of parameter values ​​of an information vector in a non-transitory tangible computer-readable storage medium; identifying a signal transmitter based on the stored dataset of parameter values; locating the signal transmitter relative to a reference frame; and sending a control signal to the vehicle's actuator controller, the control signal guiding the movement of the vehicle based on the position of the signal transmitter.

[0015] Another aspect of the subject matter disclosed in more detail below is a method for detecting pulses in a received signal in a streaming manner, comprising: (a) sampling the received signal to generate samples in a digital format; (b) estimating the corresponding signal power of the received signal for each sample; (c) determining that the signal power estimated in step (b) is less than a signal power threshold; (d) estimating, after step (c), the corresponding d-order differences of phase of a plurality of samples within a window, wherein d is an integer greater than 1; (e) determining that the d-order differences estimated in step (d) are less than a phase difference threshold; and (f) processing the samples within the window to generate an information vector comprising a corresponding dataset of parameter values ​​of pulses in the received signal.

[0016] Another aspect of the subject matter disclosed in more detail below is a system for detecting pulses in a received signal in a streaming manner, comprising: a transducer for converting a received energy wave into a received signal in electrical form; a filter for allowing a portion of the received signal having frequencies within a selected frequency bandwidth to pass through; an analog-to-digital converter configured to sample the received signal output from the filter to generate signal samples; a pulse processing module configured to process the signal samples to generate an information vector including a corresponding dataset of parameter values ​​of pulses in the received signal; a buffer configured to store a window of signal samples; a threshold detector configured to direct signal samples to the pulse processing module if a signal power exceeding a signal power threshold is detected; or to direct signal samples to the buffer if the signal power does not exceed the signal power threshold; and a phase modulation detector connected to receive signal samples sent to the buffer, and the phase modulation detector being configured to direct signal samples from the buffer to the pulse processing module if the second-order difference of the phases of consecutive signal samples in the window is less than a phase difference.

[0017] According to some implementations, the threshold detector includes: a signal power estimation module configured to estimate the corresponding signal power of the received signal for each sample; and a signal power threshold comparator configured to determine whether the signal power estimated by the signal power estimation module is greater than a signal power threshold. Additionally, the phase modulation detector includes: a complex sample estimation module configured to calculate the phase of each sample; a phase difference estimation module configured to estimate the corresponding second-order difference of the phases of multiple samples within a window; and a second-order difference threshold comparator configured to determine whether the second-order difference estimated by the phase difference estimation module is less than a phase difference threshold.

[0018] According to one application, the system immediately following the preceding paragraph also includes: a non-transitory tangible computer-readable storage medium storing a dataset of parameter values ​​of an information vector generated by a pulse processing module; and a computer system configured to identify a signal transmitter based on the stored dataset of parameter values, locate the signal transmitter, and send control signals to the vehicle's actuator controller, the control signals guiding the movement of the vehicle based on the position of the signal transmitter.

[0019] According to some implementations, the system further includes a noise power estimation module configured to calculate a real-time filtered estimate of the signal power threshold based on the input sample power, the initial noise power, and the desired false alarm probability. Additionally, the system includes a false alarm probability / detection probability table configured to use the signal power threshold from the noise power estimation module to generate a window length and a phase difference threshold.

[0020] Other aspects of systems and methods for detecting pulses using fusion threshold / phase modulation detection techniques are disclosed below. Attached Figure Description

[0021] The features, functions, and advantages discussed in the preceding sections can be implemented independently in various embodiments, or can be combined in other embodiments. To illustrate the above and other objectives, various embodiments will be described below with reference to the accompanying drawings.

[0022] Figure 1 This is a block diagram identifying some components of a signal processing system used to generate pulse descriptor words (PDWs) using fusion threshold / pulse modulation detection.

[0023] Figure 2 This is a flowchart of the steps of a method for identifying second-order difference phase modulation detection for streaming linear chirp signals, according to one embodiment.

[0024] Figure 3 It is a graph showing the probability of detection curves for a window of 100 subsamples at a given false alarm rate setting.

[0025] Figure 4 This is a block diagram of the components and modules of a system 10 for identifying fusion pulse detection according to one embodiment.

[0026] Figures 5 to 9 This is a graph showing the false alarm probability (PFA) and detection probability (PD) curves represented by data stored in the corresponding PFA / PD tables for SNRs of 15dB, 10dB, 5dB, 0dB, and -5dB, respectively.

[0027] Reference will be made to the accompanying drawings below, wherein similar elements in different drawings have the same reference numerals. Detailed Implementation

[0028] The following describes in more detail illustrative embodiments of systems and methods for detecting pulses using fused threshold / phase modulation detection techniques. However, not all features of an actual implementation are described in this specification. Those skilled in the art will understand that in the development of any such actual implementation, numerous implementation-specific decisions must be made to achieve the developer's specific goals, such as complying with system-related and business-related constraints, which will differ from one implementation to another. Furthermore, it will be appreciated that such development work can be complex and time-consuming, but will still be routine work for those of ordinary skill in the art who will benefit from this disclosure.

[0029] According to the embodiments described in more detail below, a threshold detection method is fused with a double-difference phase modulation detection method to provide a higher-performance signal detection method for any digital receiver that processes pulse signals in a streaming manner. The proposed method can accurately detect pulses under a variety of conditions and can therefore be used to detect signals of any radar type. The fusion of the threshold- and phase-based pulse detection methods proposed in this paper enables the detection of pulses with lower power and a wider range. The threshold is continuously updated to handle varying noise conditions. In addition, the window in the phase modulation detection method is also continuously updated to handle varying noise conditions.

[0030] The system disclosed in this article will receive the signal {z} n The sample form of |z| is used as input, and the presence of a pulse signal is detected based on two different but fused detectors. The threshold detector uses only the sample |z|. n | 2 The square of the magnitude of the difference is calculated, and it is detected when the difference exceeds a threshold T. A double-difference phase modulation detector detects the presence of a second-order polynomial phase modulation signal by measuring the variance of the second-order difference and detecting when that variance is less than a phase threshold D. The second-order polynomial phase modulation signal (e.g., linear frequency modulation) is given by the following formula:

[0031]

[0032] Among them, t n This is the sampling time, and a, b, and c are constant parameters controlling the frequency modulation. Such signals have many applications in radar used for range and range rate measurements. It typically consists of a parameter set {a...} up b up c up} (e.g., for up-modulation per cycle) or a cycle pair definition, namely, up-modulation for increasing frequency and down-modulation for decreasing frequency. These cycle pairs will then have a pair of parameter sets {a} associated with them. up b up c up} and {a down b down c down}

[0033] To detect such signals, the present invention continuously generates two thresholds, T and D, as well as a window size W. These control the detection process and are based on two parameters (the desired false alarm probability PFA and the desired detection probability PD). These thresholds are continuously updated by circuitry that tracks (potentially) changing noise levels so that the detector remains optimal relative to the noise level.

[0034] Note that in the case of general polynomial phase signals (not just linear frequency modulation), the phase-modulated signal is defined as:

[0035] s(t)=e 2πif(t) (2)

[0036] Where f(t) is a parameter vector of length d f d f -1st order real-valued polynomial. In this case, d f The phase difference will be used for detection.

[0037] For the sake of illustration, an implementation will now be described in which incoming radar pulses are separated and then a pulse descriptor word (PDW) is generated for vehicle control. However, it should be understood that the system disclosed herein can be used in applications other than vehicle control.

[0038] Figure 1 This is a block diagram of the components of a signal processing system 100 for generating PDW fusion threshold / pulse modulation detection, according to an example embodiment. Figure 1 An example system for an EW receiver is shown. (Note that the techniques described herein can also be used with conventional channelized receivers.)

[0039] exist Figure 1 In the exemplary embodiment shown, the signal processing system 100 includes a signal data processor 102 communicatively coupled to a transducer, such as an antenna 118, via a signal preconditioning circuit. In this example, the signal preconditioning circuit includes a low-noise amplifier 108, a bandpass filter 110, and an analog-to-digital converter (ADC) 112. The antenna 118 may be configured to monitor at least one radar signal transmitter. Figure 1 The diagram illustrates a wide-area sensor with two radar signal transmitters (106 and 107). In operation, a signal pre-conditioning circuit converts the sensor output signal received from antenna 118 into a conditioned signal. Each conditioned signal is derived from a time-varying signal received at antenna 118. The time-varying signal may include a mixture of signals received from radar signal transmitters 106 and 107. For example, the time-varying signal may include a first radar signal 114 generated by radar signal transmitter 106 or a second radar signal 116 generated by radar signal transmitter 107, which is received by antenna 118.

[0040] The signal data processor 102 includes a preprocessor 104 and a postprocessor 106. The regulated signal is transmitted to the preprocessor 104. The preprocessor 104 includes multiple signal denoising modules 113 (in...). Figure 1 Only one of them is shown in the image) and the corresponding multiple pulse processing modules 124 (in Figure 1(Only one is shown in the image). The regulated signal is denoised by the signal denoising module 113 before pulse detection to determine whether the denoised signal sample should be sent to the associated pulse processing module 124. The post-processor 106 is communicatively coupled to receive the output from the pulse processing module 124.

[0041] For example, radar signal 114 is initially received at antenna 118 as a pulse with signal characteristics including, but not limited to, frequency and bandwidth. In this example, after processing by pre-conditioning circuitry, the single pulse of the first radar signal 114 is subsequently received at signal denoising module 113 as a mixed signal (i.e., the conditioned signal represents the signal pulse of the first radar signal 114 and has various characteristics, including, but not limited to, noise and information other than the desired information of interest). Signal denoising module 113 denoises the mixed input signal and outputs a denoised signal with frequency and bandwidth (or a regular pattern of frequency and bandwidth).

[0042] The denoised signal sample undergoes pulse processing only when a pulse is detected by the fusion threshold / phase modulation detector system disclosed herein. The preprocessor 104 includes a corresponding fusion pulse detector for each pulse processing module 124. Figure 1 In the illustrated embodiment, the fusion pulse detector includes a threshold detector 120 and a phase modulation detector 126. The threshold detector 120 is connected to receive denoised signal samples from the signal denoising module 113. The preprocessor 104 also includes a first selector 122 with an input port that also receives denoised signal samples from the signal denoising module 113. The first selector 122 has a first output port and a second output port that can be switched to the input port. The state of the first selector 122 is controlled by the threshold detector 120. If the threshold detector 120 detects a signal with a power exceeding a specified signal power threshold, the threshold detector 120 outputs a first selector state control signal that causes the first selector 122 to pass the denoised signal samples to the pulse processing module 124. This is achieved by switching the first output port of the first selector 122 to the input port of the first selector 122.

[0043] The preprocessor 104 also includes a phase modulation detector 126 and a first-in-first-out (FIFO) buffer 128 (hereinafter referred to as "FIFO buffer 128"), both having input ports connected to the second output port of the first selector 122; and a second selector 130, which has an input port connected to the output port of the FIFO buffer 128. If the threshold detector 120 detects a signal that does not have power exceeding a specified threshold, the threshold detector 120 outputs a second selector state control signal, which causes the first selector 122 to pass the denoised signal sample to the phase modulation detector 126 and the FIFO buffer 128 instead of to the pulse processing module 124. This is achieved by switching the second output port of the first selector 122 to the input port of the first selector 122.

[0044] The state of the second selector 130 is controlled by the phase modulation detector 126. If the phase modulation detector 126 detects a signal with a second-order difference less than a specified phase difference threshold (meaning a pulse has been detected), the phase modulation detector 126 outputs a third selector state control signal, which causes the second selector 130 to pass the output of the FIFO buffer 128 to the pulse processing module 124. This is achieved by switching the first output port of the second selector 130 to its input port. If the phase modulation detector 126 detects a signal with a second-order difference greater than the specified phase difference threshold (meaning a pulse has not yet been detected), the phase modulation detector 126 outputs a fourth selector state control signal, which prevents the second selector 130 from passing the output of the FIFO buffer 128 to the pulse processing module 124. This is achieved by switching the second output port of the second selector 130 to its input port.

[0045] Each pulse processing module 124 includes a PDW generation module configured to generate PDW parameter vector signals. Each PDW parameter vector signal includes data representing a characteristic of interest of one of radar signals 114 and 116 (e.g., frequency, bandwidth, time of arrival, time of departure, pulse width, pulse amplitude, pulse repetition interval, and / or angle of arrival). The PDW parameter vector signals are transmitted to a post-processor 106. The post-processor 106 includes a computing device 132 and a memory 134. The computing device 132 is configured to perform operations based on the data included in the PDW parameter vector signals. Such operations include, but are not limited to, detection, processing, and quantization. The result data from the operations performed by the computing device 132 is stored in the memory 134. The memory 134 includes one or more non-transitory tangible computer-readable storage media. According to one embodiment, the computing device 132 is a processor configured to execute instructions in software form.

[0046] According to one implementation, the PDW generation module sends each PDW as a PDW parameter vector signal similar to (amplitude, time of arrival, center frequency, pulse width, and bandwidth) = (amp, toa, cf, pw, bw) to the computing device 132. The PDW for each intercepted signal is stored in a pulse buffer for further processing by the computing device 132. As part of this processing, the PDWs are classified and deinterlaced by clustering the input radar pulses into groups. In principle, each group should have characteristics representing a single radar source or radar source category, thereby allowing the identification of that radar source or radar source category. Typically, the identification of a particular signal is inferred by correlating the observed characteristics of the signal with characteristics stored in a list that also includes the identification of known radars. In addition to a deinterlacer that includes identification of radar transmitters, the computing device 132 also includes a geolocation engine for determining the coordinates of the identified radar transmitter's location.

[0047] In addition, Figure 1 In the exemplary embodiment shown, computing device 132 causes post-processor 106 to transmit human-readable data signal 136 to a human-machine interface to facilitate interaction, modification, visualization, at least one further operation, and visualization of at least one of the following by a user of signal processing system 100 regarding information about at least one radar signal 114 and 116: the human-readable data signal 136. The human-machine interface may be, for example, a display device 140 that receives the human-readable data signal 136 from post-processor 106. In one example, characteristics of radar signal transmitters 106 and 107 determined by signal processing system 100 are displayed on display device 140 as a map having a grid representing a physical spatial domain including the monitored space, wherein the location and identification information of radar signal transmitters 106 and 107 are displayed and plotted substantially in real time. The human-readable data signal 136 may also be transmitted from post-processor 106 to at least one device and / or system associated with signal processing system 100 (e.g., an airborne or ground-based vehicle 142). Furthermore, the computing device 132 enables the post-processor 106 to transmit actuator control signals 138 substantially in real time to the actuator controller 144 included in the vehicle 142 to guide or control its movement. For example, the vehicle 142 may be a remotely and / or autonomously operated land vehicle or an unmanned aerial vehicle.

[0048] In one operating mode, at least one of the frequency and bandwidth information included in the respective PDW, along with the positions of the respective radar transmitters 106 and 107, is plotted on a map on the display device 140 to facilitate accurate position tracking and association with those specific radar transmitters. If at least one radar transmitter is moving, the map on the display device 140 is updated substantially in real time with the position information of at least one corresponding moving radar transmitter. Furthermore, the computing device 132 determines at least one of the velocity, acceleration, trajectory, and orbit (i.e., including current and previous positions) of one or more moving radar transmitters (e.g., radar transmitters 106 and 107). In another operating mode, characteristics determined by the signal data processing method implemented by the signal data processor 102 can trigger various substantially real-time physical actions in physical devices and systems communicating with the signal processing system 100. For example, the characteristics of various radar signal transmitters (including the frequencies and bandwidths determined by the signal data processing method implemented by the signal processing system 100) can be transmitted as data substantially in real time to the actuator controller 144 in the vehicle 142 (e.g., the rudder and flaps of an unmanned aerial vehicle) to guide its movement or facilitate its maneuvering, for example, to avoid the operating area of ​​an unauthorized radar signal transmitter identified as a threat, or to move toward the unauthorized transmitter to eliminate the threat. As another example, the characteristics of radar signal transmitters 106 and 107 determined by the signal data processing method described herein can be transmitted in control signals substantially in real time to at least one of the electronic support measures (ESM) devices and electronic warfare (EW) systems associated with the signal processing system 100 to, for example, direct radar jamming signals to a specific radar signal transmitter operating in a monitored environment in the event of unauthorized interference.

[0049] The phase modulation detector 126 continuously generates a representation of the detected value based on a window of signal samples. The signal. Phase modulation detection requires knowing the instantaneous phase of the input signal at each sample. Therefore, this phase must be estimated in any of a number of ways.

[0050] Figure 2 The identification, according to one embodiment, is performed by phase modulation detector 126 (see [link]). Figure 2 A flowchart of the execution steps. The notation is as follows: Z -1 Represents a register or storage element (i.e.) Figure 4Registers 32 and 34 in the table are also used to delay a value by one clock cycle; the circled "+" sign indicates summation (i.e., summers 36, 38, 40, and 46); MOD(1) indicates the corresponding modulo-1 circuits 42 and 44, which are configured to perform standard digital modulo-1 calculations for each normalized value between -1 and 1 (which occurs naturally in digital arithmetic circuits); and RV(W D ) represents the corresponding variance estimation circuits 48 and 50, which are configured to perform real-time window variance estimation in parallel based on the corresponding signals output by the summer 46 and the modulo operation 1 circuit 44 (where W D (This is the length of the window). (Variance is the expected value of the squared deviation of a random variable from its mean, and it informally measures the distance between a set of (random) numbers and their mean.) These two variance calculations are based on two possible phase path offsets of π / 2. This ensures that the variance calculation works correctly even when the angles are close to the extremes of +1 and -1. The minimum variance circuit 52 receives the outputs from the variance estimation circuits 48 and 50, selects the minimum of the two inputs, and then outputs the detected value.

[0051] Figure 2 The phase modulation detection process shown includes: (1) a novel real-time window variance estimation method that uses few resources, has no division, and is suitable for hardware implementation; and (2) the use of parallel streaming computation, which selects the optimal modulus value within a window of samples. This reduces the overall detection latency compared to other methods.

[0052] The aforementioned method is based on the following fact: the quadratic polynomial sample function {Q} i} has a constant second difference, i.e., Δ 2 {Q i}=Q i+2 -2Q i+1 +Q i It is constant and noise-free. (A quadratic polynomial is a polynomial function containing at most second-order terms.) Therefore, measuring the variance of a noisy quadratic sample function gives a measure of the degree of non-constancy that a noisy second-order difference will exhibit. Since the polynomial function measuring the phase (normalized between 1 and -1) is being used, the phase will wrap around at these endpoints, which complicates the problem. For example, a phase of 0.9 advancing 0.2 on the next sample will become 1.1, i.e., changed to -0.9. Therefore, the phase near the endpoints will jump values, and this will cause a jump in the second-order difference, even though it should be constant. To eliminate this problem, two computational channels are provided that measure the phase and the phase offset by 1 / 2. Therefore, one of the two computational channels should have little or no jumps, and thus the minimum of the variance is used as a measure of the determination of the detection. By calculating the d-order difference Δ dThis can be easily generalized to nonlinear frequency modulation, i.e., polynomials of arbitrary order d. In the following example, a second-order difference is used. The second-order difference phase modulation detection process is referred to as Δ in this paper. 2 Phase representation, while window W D W is usually used to represent it in the following text.

[0053] Note that, in addition to the real-time variance method mentioned above, an optional approximate variance method that does not require any division is also described (but does require looking up 1 / W from the PFA / PD table). D (The table). For the input sequence {x n The iteration of this real-time approximate variance is given in the following formula:

[0054] u n =u n-1 +(1 / W)x n -(1 / W)x n-W

[0055] v n =v n-1 +(x n -u n ) 2 -(x n-W -u n-W ) 2

[0056] Besides detecting phase modulation, this method can also be used to estimate SNR. Specifically, the minimum variance value can be used by interpolation from a lookup table. To estimate the SNR value. Specifically, this can be done through simulation to create a model that will... A table mapping SNR (dB) values. If needed, for example, the SNR values ​​can be made available to the pulse processing module 124 (see...). Figure 1 This is because other signal processing methods can greatly benefit from having SNR estimation. The SNR value can also be added to the PDW to generate the output vector.

[0057] Therefore, the pulse detection method proposed in this paper combines two complementary pulse detection techniques. A threshold detector 120 detects a pulse when its power (amplitude squared) exceeds a specified signal power threshold. Using this technique, the start of a pulse can be accurately declared with virtually no delay, and this determination is independent of the pulse width. However, the threshold method only works reliably for SNRs above 15 dB. The phase modulation detector 126 is a window detector, where a specified phase difference threshold is exceeded when the detected signal has a consistent phase value (indicating pulse) within the window. The fused pulse detector (the threshold detector 120 supported by the phase modulation detector 126) has lower delay for higher SNR pulses, but can also detect lower SNR pulses with additional delay. The input denoised signal samples are initially filtered by the threshold detector 120, which directs the signal to the pulse processing module 124 if a pulse is detected, or to the phase modulation detector 126 and the FIFO buffer 128 if no pulse is detected. The signals received by the FIFO buffer 128 are also filtered by the phase modulation detector 126. If a pulse is detected, the phase modulation detector 126 directs the signal from the FIFO buffer 128 to the pulse processing module 124, or if no pulse is detected, the phase modulation detector 126 does not direct these signals to the pulse processing module 124.

[0058] Standard threshold detection performance can be captured in a receiver operating characteristic curve, which includes a set of SNR curves for a given false alarm probability (PFA) and detection probability (PD). For example, an ROC curve indicates that an SNR of approximately 15 dB would be required for a PFA of 0.2% and a PD of 99%. Typical systems make trade-offs to determine both the benefits and costs of losing present pulses and correspondingly detecting non-existent pulses. For example, threat radar detectors have a high cost of losing detected pulses but tolerate false detections, while surveillance sensors have a high processing cost of handling many false detections but can tolerate a lower detection rate.

[0059] In contrast, Figure 2 The phase modulation detection method shown has better detection at lower SNR levels. Figure 3 This is a graph showing the probability of the detection curve (SNR vs. PD) for a window of 100 subsamples at a given false alarm rate setting. Therefore, Figure 2 The method shown yields good results even at SNRs below 9dB, far below the typical SNR required for reliable signal detection (usually 12dB or 15dB). The cost of this method is some delay (given by the window length) and limitations on the pulse width.

[0060] Figure 4 This is a block diagram of the components and modules of a system 10 using fused pulse detection according to one embodiment. The basic operation of system 10 is as follows. As shown, a complex set of samples (potentially including received sample signal pulses at any given time) flows into the fused pulse detection system. Parameter inputs include initial noise power N. init The desired PFA and desired PD. The threshold detector includes: a signal power estimation module 12, which is configured to calculate the power |z| of the input signal z. n | 2 ; and a signal power threshold comparator 14, which compares the calculated power with the signal power threshold T. Power |z n | 2 It is also output to the third selector 16.

[0061] On the one hand, if the signal power threshold comparator 14 determines |z n | 2 If the value is greater than T, then the first selector state control signal ( Figure 4 The "yes" option is sent to the first selector 122 and the third selector 16. On the other hand, if |z is determined... n | 2 If not greater than T, then the second selector state control signal ( Figure 4 The "No" option is sent to the first selector 122 and the third selector 16.

[0062] In response to receiving a first selector state control signal, the first selector 122 transmits signal z to the pulse processing module 124 and the pulse end processing module 30. The pulse is processed to generate a PDW output. Conversely, in response to receiving a second selector state control signal, the first selector 122 does not transmit signal z to the pulse processing module 124 and the pulse end processing module 30. Instead, the first selector 122 transmits signal z to the FIFO buffer 128 and the complex sample phase estimation module 24, which is part of the phase modulation detector.

[0063] In response to receiving the second selector state control signal ( Figure 4 (No) in the text, the third selector 16 will select the power |z n | 2 The signal is transmitted to the noise power estimation module 20. Conversely, in response to receiving the first selector state control signal ( Figure 4 (The "yes" in the text), the third selector 16 does not transfer power |z n | 2 The signal is transmitted to the noise power estimation module 20.

[0064] The noise power estimation module 20 is configured to estimate the noise power based on the input sample power and the initial noise power N. init The expected PFA is used to calculate the real-time filtered estimate of the signal power threshold T. This is done by calculating the running average and variance |z|. n | 2 This is achieved by μ at time i. i and σ i 2 Represent, and then calculate

[0065] T i =μ i +kσ i

[0066] Where k is determined by the cumulative distribution function of the standard normal distribution. A value of k=3 gives a PFA of 99.73%. Then...

[0067] T = (1-α)T + αT i

[0068] Use a standard exponential filter with parameter α.

[0069] During pulse processing, samples are not sent to any of the noise power estimation module 20, FIFO buffer 128, and complex sample phase estimation module 24. If the pulse is not processed, the noise power estimation module 20 estimates what the signal power threshold T should be to obtain the desired PFA rate for the threshold detection method. The signal power threshold T is sent to the signal power threshold comparator 14 and the pulse end processing module 30. This signal power threshold is also used by the PFA / PD table to generate the window length W for the second-order phase difference estimation module 26, which is part of the phase modulation detector; and to generate a phase difference threshold D for use by the phase difference threshold comparator 28, which is also part of the phase modulation detector. The FIFO buffer 128 provides a time delay that aligns the samples with the delay of the second-order phase difference estimation module 26.

[0070] As previously described, in response to receiving the second selector state control signal, the first selector 122 passes signal z to the FIFO buffer 128 and the complex sample phase estimation module 24. The FIFO buffer 128 acquires samples at the sampling clock rate and after a sampling time of W, delivering them to the output, thus operating as a normal "first-in, first-out" circuit.

[0071] The complex sample estimation module 24 is configured to calculate the phase of each sample. The second-order phase difference estimation module 26 receives the phase estimate from the complex sample estimation module 24. According to one embodiment, the second-order phase difference estimation module 26 is configured as follows: Figure 2As shown. The second-order phase difference estimation module 26 generates values. This value It is compared with the phase difference threshold D in the phase difference threshold comparator 28.

[0072] On the one hand, if the phase difference threshold comparator 28 determines... If the value is less than D (indicating that a phase modulation pulse signal has been detected), then the third selector state control signal is sent to the second selector 130, which switchesably connects its first output port to its input port. On the other hand, if it is determined... If the value is not less than D, then the fourth selector status control signal is sent to the second selector 130, which switchesably connects its second output port to its input port. The first output port of the second selector 130 is connected to the pulse processing module 124 and the pulse end processing module 30; the second output port of the second selector 130 is not connected.

[0073] In response to receiving the third selector status control signal, the second selector 130 transmits signal z from the FIFO buffer 128 to the pulse processing module 124 and the pulse end processing module 30. The pulse is processed to generate a PDW output. According to one embodiment, the value... It is also sent to the pulse processing module for SNR estimation. In contrast, in response to receiving the fourth selector state control signal, the second selector 130 does not pass signal z to the pulse processing module 124 and the pulse end processing module 30.

[0074] The pulse termination processing module 30 has the following noteworthy aspects. When pulse processing is initialized by a threshold detector, the pulse termination processing module 30 uses a standard method such as the following for pulse termination processing: when a preset number of consecutive samples with a signal power less than T have been detected (both values ​​EOP and T are input to the pulse termination processing module 30), a "complete" signal is sent by the pulse termination processing module 30 to the pulse processing module 124 and the third selector 16; otherwise, a "not complete" signal is sent. This allows pulse processing to end in a more reliable manner. However, if pulse processing is initialized by a phase modulation detector, it responds to an indication from the phase difference threshold comparator 28. A signal not less than D is sent as a "complete" signal (meaning no more pulses are detected).

[0075] The false alarm probability / detection probability table 22 (hereinafter referred to as "PFA / PD table 22") is a predefined table that generates the preferred window length and detection threshold for a second-order difference phase modulation detector based on the desired false alarm probability, the desired detection probability, and the measured signal-to-noise ratio. To construct an example of PFA / PD table 22, simulations were performed and PFA and PD curves were generated. Figures 5 to 9 This is a graph showing the PFA and PD curves, represented by data stored in the corresponding PFA / PD tables, for SNRs of 15dB, 10dB, 5dB, 0dB, and -5dB, respectively. The PD curve is the lower bound of the threshold for achieving a given PD performance, while the PFA curve is the upper bound of the threshold for achieving a given PFA performance. More specifically, the lower curve is used for PD equal to 0.6847 (-·-·-), 0.9545 (...), and 0.9973 (-··-·-), while the upper curve is used for PFA equal to 0.3173 (--), 0.0455 (---), and 0.9973 (----). Figure 9 The results show that the second-order difference phase modulation detector is useless when the SNR is -5dB, but when the SNR is above 0dB, the second-order difference phase modulation detector can be used as a detector with a larger window for lower SNR.

[0076] A larger window provides better performance at the cost of more delay, and also means that short pulses may be lost if their pulse width is less than the window length. Therefore, Table 22 of the PFA / PD table will produce the minimum window length that gives the desired performance. This is determined at the intersection of the two curves, which also determines the corresponding second-order phase difference threshold D. For example, Figure 7 The diagram shows that for a 5dB SNR, a window length W of 50 samples and a normalized second-order phase difference threshold D of 0.48 will give a PD of 99.73% and a PFA of 0.27%. Here, the threshold is normalized to a noise power level of 1.

[0077] The normalized threshold from the PFA / PD table is multiplied by T to give the final phase difference threshold D, which is used in conjunction with the output of the second-order phase difference estimation module 26. Compare (see) Figure 4 ).

[0078] In addition to storing the value W of a given PFA and PD, its inverse 1 / W can also be stored in the PFA / PD table 22. This eliminates the need to perform division (which is typically very hardware-intensive).

[0079] Methods and means for improving pulse detection through a combination (fusion) of two different complementary methods have been described. The first pulse detection technique uses a signal power threshold. The start of a pulse is declared and pulse processing begins when the square of the pulse amplitude exceeds the signal power threshold. The second pulse detection technique is model-based and uses a window detector that exceeds a phase difference threshold when the pulse has a consistent second-order phase difference value within the window.

[0080] This document describes certain systems, devices, applications, or processes as comprising multiple modules. A module can be a unit with different functions that can be implemented in software, hardware, or a combination thereof. When the functionality of a module is performed by software in any part, the module may include a non-transitory tangible computer-readable storage medium. The methods disclosed above use streaming (or dynamic) computation, and are therefore configured such that modules performing those computations are suitable for FPGA or ASIC or other hardware-based implementations.

[0081] Although systems and methods for detecting pulses using fusion threshold / phase modulation detection techniques have been described with reference to various embodiments, those skilled in the art will understand that various changes can be made and equivalents can be substituted for elements therein without departing from the teachings herein. Furthermore, many modifications can be made to adapt the concepts disclosed herein and reductions in practice to particular situations. Therefore, the subject matter intended to be covered by the claims is not limited to the disclosed embodiments.

[0082] The embodiments disclosed above use one or more processing or computing devices. Such devices typically include processors, processing means, or controllers, such as general-purpose central processing units, microcontrollers, reduced instruction set computer processors, ASICs, programmable logic circuits, FPGAs, digital signal processors, and / or any other circuitry or processing means capable of performing the functions described herein. The methods described herein may be encoded as executable instructions embodied in a non-transitory tangible computer-readable storage medium, including but not limited to storage devices and / or memory devices. When such instructions are executed by a processing means, the processing means performs at least a portion of the methods described herein. The examples above are merely exemplary and are therefore not intended to limit the definitions and / or meanings of the terms "processor" and "computing means" in any way.

[0083] Furthermore, this disclosure includes embodiments according to the following:

[0084] Item 1. A method for detecting pulses in a received signal in a streaming manner, comprising:

[0085] (a) Sample the received signal to produce a digital sample;

[0086] (b) Estimate the corresponding signal power of the received signal for each sample;

[0087] (c) Determine that the signal power estimated in step (b) is less than the signal power threshold;

[0088] (d) After step (c), estimate the corresponding second-order differences of the phases of multiple samples within the window;

[0089] (e) Determine that the second-order difference estimated in step (d) is less than the phase difference threshold; and

[0090] (f) Process the samples within the window to generate an information vector that includes a corresponding dataset of parameter values ​​of the pulses in the received signal.

[0091] Item 2. The method according to Item 1 further includes storing the samples in the window in a first-in-first-out buffer during step (c) and before step (f).

[0092] Item 3. The method according to Item 2 further includes transferring samples within the window from the first-in-first-out buffer to the pulse processing module, the pulse processing module being configured to perform step (f) in response to step (e).

[0093] Item 4. The method according to item 1 further includes:

[0094] (g) Estimate the corresponding instantaneous signal phase of the received signal for each signal sample after step (c) and before step (d).

[0095] Item 5. The method according to Item 3, wherein step (f) is performed with a time delay that is a function of the delay inherent in the sequential execution of steps (g), (d) and (e).

[0096] Item 6. The method according to Item 5, wherein steps (g), (d) and (e) are not performed when step (f) is performed.

[0097] Item 7. The method according to item 1 further includes:

[0098] (g) A real-time filtered estimate of the signal power threshold is calculated based on the signal power of the received signal used for the sample, the initial noise power, and the expected false alarm probability; and

[0099] (h) Send the signal power threshold to the signal power threshold comparator that performs step (c).

[0100] Item 8. The method according to item 7 further includes:

[0101] (i) Generate the expected false alarm probability and the expected detection curve probability;

[0102] (j) Construct a lookup table comprising data values ​​representing the expected false alarm probability and the expected detection curve probability generated in step (i); and

[0103] (k) Based on the expected false alarm probability, the expected detection probability and the measured signal-to-noise ratio, retrieve the window length and phase difference threshold from the lookup table.

[0104] Item 9. The method according to item 1 further includes:

[0105] (g) Store the dataset of parameter values ​​of the information vector in a non-transitory tangible computer-readable storage medium;

[0106] (h) Identify the signal transmitter based on the dataset of stored parameter values;

[0107] (i) Positioning signal transmitter relative to a reference frame; and

[0108] (j) A control signal is sent to the vehicle's actuator controller, which guides the movement of the vehicle based on the position of the signal transmitter determined in step (i).

[0109] Item 10. The method according to item 1 further includes:

[0110] (g) Determine that the second-order difference estimated in step (d) is no longer less than the phase difference threshold; and

[0111] (h) In response to step (g), step (f) ends.

[0112] Item 11. A method for detecting pulses in a received signal in a streaming manner, comprising:

[0113] (a) Sample the received signal to produce a digital sample;

[0114] (b) Estimate the corresponding signal power of the received signal for each sample;

[0115] (c) Determine that the signal power estimated in step (b) is less than the signal power threshold;

[0116] (d) Estimate the corresponding d-order difference of phase for multiple samples within the window following step (c), where d is an integer greater than 1;

[0117] (e) Determine that the d-order difference estimated in step (d) is less than the phase difference threshold; and

[0118] (f) Process the samples within the window to generate an information vector that includes a corresponding dataset of parameter values ​​of the pulses in the received signal.

[0119] Item 12. The method according to item 11 further includes:

[0120] (g) Estimate the corresponding instantaneous signal phase of the received signal for each signal sample after step (c) and before step (d).

[0121] Item 13. The method according to Item 12, wherein step (f) is performed with a time delay that is a function of the delay inherent in the successive execution of steps (g), (d) and (e).

[0122] Item 14. The method according to Item 13, wherein steps (g), (d) and (e) are not performed when step (f) is performed.

[0123] Item 15. The method according to item 11 further includes:

[0124] (g) Determine that the second-order difference estimated in step (d) is no longer less than the phase difference threshold; and

[0125] (h) In response to step (g), step (f) ends.

[0126] Item 16. A system for detecting pulses in a received signal in a streaming manner, comprising:

[0127] A transducer is used to convert received energy waves into received signals in electrical form.

[0128] A filter is used to allow a portion of the frequencies of a received signal within a selected frequency bandwidth to pass through.

[0129] An analog-to-digital converter is configured to sample the received signal output from a filter to generate signal samples;

[0130] The pulse processing module is configured to process signal samples to generate an information vector, which includes a corresponding dataset of parameter values ​​of the pulses in the received signal.

[0131] A buffer is configured as a window to store signal samples;

[0132] A threshold detector is configured to: guide a signal sample to a pulse processing module if the detected signal power exceeds a signal power threshold; or guide a signal sample to a buffer if the signal power does not exceed the signal power threshold; and

[0133] A phase modulation detector is connected to receive signal samples, which are sent to a buffer, and the phase modulation detector is configured to guide the signal samples from the buffer to the pulse processing module if the second-order difference of the phases of consecutive signal samples in the window is less than the phase difference.

[0134] Item 17. The system according to item 16, wherein the threshold detector comprises:

[0135] A signal power estimation module is configured to estimate the corresponding signal power of the received signal for each sample; and

[0136] A signal power threshold comparator is configured to determine whether the signal power estimated by the signal power estimation module is greater than a signal power threshold.

[0137] Item 18. The system according to item 17, wherein the phase modulation detector comprises:

[0138] The complex sample phase estimation module is configured to calculate the phase of each sample;

[0139] The second-order phase difference estimation module is configured to estimate the corresponding second-order differences of the phases of multiple samples within a window; and

[0140] A phase difference threshold comparator is configured to determine whether the second-order difference estimated by the phase difference estimation module is less than a phase difference threshold.

[0141] Item 19. The system according to Item 16 further includes a first selector connected to receive signal samples and to pass the signal samples to a pulse processing module or a phase modulation detector according to a selector state control signal output by a threshold detector.

[0142] Item 20. The system according to Item 19 further includes a second selector connected to receive signal samples from the buffer and to pass or not pass the signal samples from the buffer to the pulse processing module according to a selector state control signal output by the phase modulation detector.

[0143] Item 21. The system according to item 16 further includes:

[0144] A non-transitory tangible computer-readable storage medium storing a dataset of parameter values ​​for an information vector generated by a pulse processing module; and

[0145] The computer system is configured to identify the signal transmitter based on a dataset of stored parameter values, locate the signal transmitter, and send control signals to the vehicle's actuator controller, which guide the vehicle's movement based on the position of the signal transmitter.

[0146] Item 22. The system according to Item 16 further includes a noise power estimation module configured to calculate a real-time filtered estimate of the signal power threshold based on the input sample power, the initial noise power, and the desired false alarm probability.

[0147] Item 23. The system according to Item 12 further includes a false alarm probability / detection probability table configured to use a signal power threshold from the noise power estimation module to generate a window length and a phase difference threshold.

[0148] Unless the language of the claims expressly specifies or indicates a condition instructing the performance of some or all of those steps, the method claims set forth below should not be construed as requiring that the steps described herein be performed in alphabetical order (any alphabetical order in the claims is for reference only for the purposes of referring to the previously described steps) or in the order in which they are stated. Nor should the method claims be construed as excluding any portion of two or more steps that are performed simultaneously or alternately, unless the language of the claims expressly indicates a condition excluding such an interpretation.

Claims

1. A method for detecting pulses in a received signal in a streaming manner, comprising: (a) Sample the received signal to produce a digital sample; (b) Estimate the corresponding signal power of the received signal for each sample; (c) Compare the signal power estimated in step (b) with the signal power threshold; If it is determined that the signal power estimated in step (b) exceeds the signal power threshold, then the start of a pulse is determined and pulse processing begins; and if it is determined that the signal power estimated in step (b) is less than the signal power threshold, then step (d) is executed. (d) Estimate the corresponding second-order difference of the phase of multiple samples within the window following step (c); (e) Compare the second-order difference estimated in step (d) with the phase difference threshold; as well as If it is determined that the second-order difference estimated in step (d) is less than the phase difference threshold, then step (f) is executed; and if it is determined that the second-order difference estimated in step (d) is greater than the phase difference threshold, then step (f) is not executed. (f) Process the samples within the window to generate an information vector, the information vector including a corresponding dataset of parameter values ​​of pulses in the received signal.

2. The method according to claim 1 further includes storing the samples in the window in a first-in-first-out buffer (128) during step (c) and before step (f).

3. The method of claim 2 further includes transferring samples within the window from the first-in-first-out buffer (128) to a pulse processing module (124), the pulse processing module being configured to perform step (f) in response to step (e).

4. The method according to claim 1, further comprising: (g) A real-time filtered estimate of the signal power threshold is calculated based on the signal power, initial noise power, and expected false alarm probability of the received signal for the sample; and (h) The signal power threshold is sent to the signal power threshold comparator (14) that performs step (c).

5. The method according to claim 1, further comprising: (i) Generate the expected false alarm probability and the expected detection curve probability; (j) Construct a lookup table, the lookup table including data values ​​representing the expected false alarm probability and the expected detection curve probability generated in step (i); as well as (k) Based on the expected false alarm probability, the expected detection probability and the measured signal-to-noise ratio, retrieve the window length and the phase difference threshold from the lookup table.

6. The method according to claim 1, further comprising: (g) Store the dataset of parameter values ​​of the information vector in a non-transitory tangible computer-readable storage medium; (h) Identify the signal transmitter (106, 107) based on the dataset of stored parameter values. (i) Positioning the signal transmitters (106, 107) relative to a reference frame; and (j) A control signal is sent to the vehicle's actuator controller, the control signal guiding the movement of the vehicle based on the position of the signal transmitter determined in step (i).

7. A system (10) for detecting pulses in a received signal in a streaming manner, comprising: A transducer (118) is used to convert the received energy wave into an electrical signal. A filter (110) is used to allow a portion of the frequency of the received signal within a selected frequency bandwidth to pass through; An analog-to-digital converter (112) is configured to sample the received signal output by the filter (110) to generate a signal sample; A pulse processing module (124) is configured to process the signal samples to generate an information vector, the information vector including a corresponding dataset of parameter values ​​of the pulses in the received signal; A buffer (128) is configured as a window to store the signal samples; The threshold detector (120) is configured to: if the detected signal power exceeds the signal power threshold, guide the signal sample to the pulse processing module (124), and if the signal power does not exceed the signal power threshold, guide the signal sample to the buffer (128). as well as A phase modulation detector (126) is connected to receive the signal samples sent to the buffer (128), and the phase modulation detector (126) is configured to: guide the signal sample from the buffer (128) to the pulse processing module (124) if the second-order difference of the phases of consecutive signal samples in the window is less than the phase difference threshold, and not guide the signal sample from the buffer (128) to the pulse processing module (124) if the second-order difference of the phases of consecutive signal samples in the window is greater than the phase difference threshold.

8. The system (10) according to claim 7, wherein, The threshold detector (120) includes: The signal power estimation module (12) is configured to estimate the corresponding signal power of the received signal for each sample; and The signal power threshold comparator (14) is configured to determine whether the signal power estimated by the signal power estimation module (12) is greater than the signal power threshold.

9. The system (10) according to claim 7, wherein, The phase modulation detector (126) includes: The complex sample phase estimation module (24) is configured to calculate the phase of each sample; The second-order phase difference estimation module (26) is configured to estimate the corresponding second-order difference of the phases of multiple samples within the window; and A phase difference threshold comparator (28) is configured to determine whether the second-order difference estimated by the phase difference estimation module is less than a phase difference threshold.

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