Micro-Doppler Processing for Ultra-Wideband Radar Data Graeme E. Smith*, Fauzia Ahmad# and Moeness G. Amin# * Dept. of Electrical & Computer Engineering, The Ohio State University, Dreese Labs, 2015 Neil Ave., Columbus, OH 43210 # Radar Imaging Lab, Center For Advanced Communications, Villanova University, 800 Lancaster Ave., Villanova, PA 19085 ABSTRACT In this paper, we describe an operational pulse Doppler radar imaging system for indoor target localization and classification, and show how a target’s micro-Doppler signature (µDS) can be processed when ultra-wideband (UWB) waveforms are employed. Unlike narrowband radars where time-frequency signal representations can be applied to reveal the target time-Doppler frequency signatures, the UWB system permits joint range-time-frequency representation (JRTFR). JRTFR outputs the data in a 3D domain representing range, frequency, and time, allowing both the µDS and high range resolution (HRR) signatures to be observed. We delineate the relationship between the µDS and the HRR signature, showing how they would form a complimentary joint feature for classification. We use real-data to demonstrate the effectiveness of the UWB pulse-Doppler radar, combined with nonstationary signal analyses, in gaining valuable insights into human positioning and motions.
1. INTRODUCTION Imaging of animate targets of interest, such as humans, behind walls and inside enclosed structures proves to be a challenging task due to clutter arising from reflections from exterior and interior walls as well as the interactions between the animate targets and the surroundings1-3. There exist two approaches that allow clutter removal and wall mitigation4-6. The first approach employs change detection and predicates on re-imaging the scene at different times, followed by subtraction of the complex or amplitude image values in two- or three-dimensional space. This approach is a special case of a first-order delay-line canceller where the delay may involve a long period of time and numerous pulses. The second approach uses Doppler radars and utilizes Doppler filters to capture the individual Doppler frequencies. This approach is effective in detecting motions and separating targets from the clutter in the Doppler domain; however, it fails to provide motion classifications where the movements of the limbs are considered vital to identifying an animate object7-9. However, signal processing techniques beyond conventional sub-band filtering or the Fourier transform can be employed to reveal such information about the moving target In this paper, we describe an operational pulse Doppler radar system for indoor target localization and classification, and show how a radar target’s micro-Doppler signature (µDS)8 can be processed when ultra-wideband (UWB) waveforms are employed. Unlike simple continuous wave (CW) radars where time-frequency signal representations can only be applied to reveal the target time-Doppler frequency signature, our system permits a joint range-time-frequency representation (JRTFR)10. The JRTFR outputs the data in a three-dimensional (3D) domain with axes representing range, frequency and time, allowing both the micro-Doppler signature (µDS) and high range resolution (HRR) signature to be observed. The µDS of a radar target arises due to the micro-motions associated with the target11,12 and has been shown to provide a good basis for target classification, particularly when the target set includes humans7-9,13. Typically, the processing employed to analyze the µDS utilizes a time-frequency representation (TFR)12. Although there are many such representations, the short-time Fourier transform (STFT) remains popular despite its coarser resolution relative to techniques, such as, the Wigner-Ville distribution, due to its lack of cross-terms. However, all micro-Doppler processing using TFRs relies on the radar signal being CW. If a pulse-Doppler system is employed, the pulses received while the target is in a single range bin can be considered as a sampled CW signal and a TFR is possible. Alternatively, when the target does traverse range bins, then a sampled CW signal can be reconstructed by coherently summing the range bins, although this will increase the power of any clutter return in the signal. In the event of ultra-wideband pulse-Doppler
radar, such processing is self-defeating since coherent summation of the range bins has the effect of reducing the bandwidth and the HRR information that was available is lost. Recently, preliminary research into combined µDS and HRR processing has been performed. Ghaleb, et al. demonstrated that, when used as an augmentation to inverse synthetic aperture radar (ISAR) imaging, the µDS could provide information about the position and orientation of wheels on vehicle target and help identify the limbs on a human target14. Lou, et al. also considered the relationship between the µDS and ISAR imagery and demonstrated that the Hough transform could be used to extract the µDS from the range-slow time plane, even in the presence of interference, for stepped frequency waveforms15. Fogle and Rigling developed a model of the µDS under an HRR assumption in which targets were considered comprising multiple point scatterers16. By using a combination of least squares fitting and expectation maximization, they were able to fit their model to real data and extract eight scattering centers and associated micro-motion parameters. The research reported in this paper differs from the aforementioned papers in that no attempt is made to extract the µDS from the HRR data. Instead, a data representation is developed in which the µDS can be seen alongside the scattering centers that become visible when UWB waveforms are used. The paper demonstrates, using real data, the effectiveness of an UWB pulse-Doppler radar, combined with nonstationary signal analyses, in gaining valuable insights into human positioning and motions. It delineates the relationship between the µDS and the HRR signature, showing how they would form a complimentary joint feature for classification. The remainder of the paper is organized as follows. Section 2 describes the joint range-time-frequency representation under UWB pulse-Doppler radar operation. The main components of the UWB pulse-Doppler radar system, which is based on a novel fast-time sample reconstruction technique to allow sub-Nyquist sampling rates on the analog-to-digital converters (ADCs) and was employed for real data collection experiments, are described in Section 3. The layout of the performed experiment involving a moving human in a realistic indoor environment is also provided in this section. Experimental results highlighting the benefits of the proposed JRTFR for gaining insights into motion of a human target are presented in Section 4. Finally, conclusions are drawn in Section 5.
2. JOINT RANGE-TIME-FREQUENCY REPRESENTATION A majority of radar signals are recorded in the time domain. Conversion to the frequency domain is commonly achieved using the Fourier transform as !
ℱ 𝑢 𝑡
𝑢 𝑡 𝑒 !!"# d𝑡
𝜔 =
(1)
!!
where 𝑢 𝑡 is the signal of interest, 𝑡 represents time and 𝜔 denotes the angular frequency. Despite its popularity, (1) is limited because it assumes that the signal is stationary, i.e. there is no variation in the frequency content with time. Many common signals, such as a linear frequency modulation (LFM) chirp, are nonstationary and as such, cannot be adequately analyzed using the Fourier transform. A time-frequency transform, on the other hand, represents a signal in a two-dimensional domain—with time and frequency as the axes—and the stationary signal assumption is significantly relaxed. The most straightforward timefrequency representation (TFR) is the short-time Fourier transform (STFT) that takes the Fourier transform of the signal in short segments12, i.e. !
𝑆𝑇𝐹𝑇 𝑢 𝑡
𝑢 𝑡 ℎ 𝑡 − 𝜏 𝑒 !!"# d𝑡
𝜔, 𝜏 =
(2)
!!
where ℎ 𝑡 is a window function that selects a short segment of the signal and may also apply a weighting to reduce sidelobes. The signal is still assumed to be stationary over the duration of the window function, but so long as the duration of ℎ 𝑡 is short compared to the various frequency components that make up 𝑢 𝑡 , (2) is adequate for analysis. The square modulus of (2), 𝑆𝑇𝐹𝑇 𝑢 𝑡 𝜔, 𝜏 ! , is referred to as the spectrogram of the signal. The frequency resolution of (2) will depend on the duration of ℎ 𝑡 that is typically required to be short so that transient components may be observed resulting in a coarse frequency resolution. More sophisticated TFRs are available, such as the WignerVille distribution, but these commonly result in cross-terms—spurious components that are artifacts of the transform and
Fig. 1: Calculation of the joint range-time-frequency data cube.
not the signal—that make them unsuitable for µDS analysis, since the cross-term power may well exceed the relatively weak signature components. In a pulse-Doppler radar, the signal 𝑢 𝑡 will be sampled at the pulse repetition frequency (PRF) and would typically represent the backscatter signal received from the target over a coherent processing interval (CPI). During the CPI, it would be assumed that the target remains within a single range bin and a signal is obtained for each bin, i.e. a set of signals, 𝑢! 𝑡 with 𝑖 being the range bin index, is available for processing. A particular signal 𝑢! 𝑡 may then be processed using Fourier processing or a TFR as needed by the application, with TFR being the analysis method of choice for µDS applications. Such an approach is successful if the range bin length is large compared with the distance a target may be expected to travel during the CPI, however, it fails if it is not the case since the target leaves the range bin and the backscatter signal is split over multiple 𝑢! 𝑡 . Such failure may be compensated for by constructing a single signal from data in multiple range bins, i.e. 𝑢 𝑡 = ! 𝑢! 𝑡 , but this has the effect of increasing the range bin size—which increases the clutter power in the signal—and can be considered self-defeating as the UWB waveform was used to provide fine range resolution and this is now lost. An alternative is to use the joint range-time-frequency representation10. The JRTFR results from performing a TFR of the data in each range bin and collecting the results into a data cube. It may be thought of as the time-frequency analogue of a range-Doppler surface that would be obtained by taking the Fourier transform of the data in each range bin. The process by which the JRTFR is calculated is illustrated in Fig. 1. The data is collected with the radar and arranged into a matrix with slow time, or pulse index, along one axis and range bin, or fast time, along the other. A TFR is then performed at each range bin along the slow time axis. The TRF employed should be selected based on the situation: the STFT was used in this paper. The output TFRs are then “stacked” as indicated in Fig. 1 to create a data cube with axes slow time, frequency, and range. The data cube is the JRTFR. The JRTFR represents a generalization of the other signal representations mentioned above. The individual elements within the data cube are complex valued and as such, coherent summation may be performed across them. Summation along the range axis results in a two-dimensional matrix with frequency and slow time as axes—this is the TFR of the signal. Alternatively, summing along the slow time axis leads to another two-dimensional matrix, this time containing the range-Doppler surface. Summation over both the slow time and range axes would result in a one-dimensional vector representing the Fourier transform of the signal obtained by coherently summing all of the range bins. Likewise, summing over the slow time and frequency axes would provide an average range profile. That the other possible signal representations are all contained within the JRTFR makes a persuasive argument for its use, since it must contain all the information from these representations.
3. DATA COLLECTION 3.1. System Description
A block diagram of the UWB pulse-Doppler radar system is provided in Fig. 2. The transmitted waveform is a 700 ps impulse with approximately Gaussian shape (see Fig 3), which is upconverted by 3 GHz for transmission. As direct upand down-conversion are employed only a single local oscillator is required, and there is no IF stage. The receiver comprises both inphase and quadrature ( I & Q) channels. The operational bandwidth of the system is 1.5 – 4.5 GHz, which provides a 5cm range resolution. The peak transmit power is 25dBm. A single horn antenna, model BAE-H1479, is used for transmission, while an 8-element array of Vivaldi elements with an inter-element spacing of 6 cm is used as the receiver. The pulse repetition frequency is 10MHz, providing a maximum unambiguous range of 15m. Despite the high PRF, the system refresh rate is 100Hz. This is because a) equivalent time sampling is used, b) instead of simultaneous reception, the receive array elements are accessed sequentially through a multiplexer, and c) multiple range profiles are coherently summed to compensate for the low transmit power. The Xilinx FPGA controls the equivalent time sampling and range profile summation. The range profiles produced for each receive array element have a fast time sampling rate of 76.8 GSamples/s. The output of the FPGA is connected to a computer by a USB 2.0 link and data is streamed off of the board. The system is capable of recording for an extended duration, limited only by the amount of storage space available on the computer hard drive. The output of each test run is a set of eight binary files that include the I & Q channel ADC samples from each of the receive array elements. This data can then be post-processed in Matlab. A detailed description of the system is provided by Wang and Fathy17. 3.2. Experimental Trial Overview
Fig. 2: Block diagram of the UWB pulse-Doppler radar system.
Fig. 3: The baseband impulse signal transmitted by the system.
An indoor experiment was conducted to obtain the µDS of a male human target. The test range was a corridor within the Center for Engineering Education and Research (CEER) Building at Villanova University, and its layout is shown in Fig. 4. No attempts were made to reduce clutter through inclusion of RF absorbers. As a result, the recorded dataset is highly realistic. The view along the test range is shown in Fig. 5(a) where clutter objects are clearly visible—the windows to the left of the photo are centered at ≈ 3 m downrange, the fire extinguisher is located at ≈ 6 m downrange, and, as indicated on the schematic in Fig. 4, there were furniture items behind the system. A photograph showing the radar positioned within the trial space is presented in Fig. 5(b). During the trial, the test subject was asked to walk back and forth between two markers on the corridor floor, the first of which was at 2 m range and the second at 10 m. Two test cases were considered: first, walking with arms held behind the back; second, walking with a natural arm swing. Data was recorded for 30 s allowing the target to complete multiple lengths of the test range. In addition to the target trials, reference data was collected for the test area with no test subject present.
4. DATA ANALYSES 4.1. Data Processing Following subtraction of the reference data to remove clutter, the first stage of the data processing was to combine the data from each receive array element. With eight elements, it is possible to produce a beamformed image1, but this approach was not taken for this preliminary investigation. Instead, the data from the eight elements was coherently summed. Summation was performed after appropriate delays were applied to each element to allow for the slightly 80cm Tx 40cm
70cm
Rx Array
30cm Tables & Chairs
Targets walked back & forth between 2m and 10m along the centre line.
Fig. 4: The layout of the experimental test range. (a)
(b)
Fig. 5: Photographs of the trials range (a) the view along the range showing clutter environment and (b) the radar in position.
(a)
(b)
(c)
Fig. 6: Compensating for target motion (a) the full dataset, (b) a single walk with peaks and best fit indicated and (c) the motion compensated profiles.
different path lengths to the target. An alternative would have been to take the signal from a single element. However, summation across the aperture provides a 9 dB gain in signal-to-noise ratio (SNR). Even with background subtraction, there was still some residual clutter present in the data, particularly at the range of the metal fire extinguisher cabinet visible in Fig. 5(a). Application of a 2.1 Hz wide notch filter, centered at DC, was sufficient to remove the residual clutter. As the fast time sample rate is much greater than required, the range-bins were collapsed to reduce the size of the dataset. The sampling rate of 76.8 GSamples/s provides a sample bin length of 4 mm, which is much finer than the range resolution of 5 cm. Contiguous groups of ten range bins were summed to give a sample bin length of 4 cm. This downsampling brought the amount of data to be processed to a more manageable level. To perform µDS analysis, the gross motion of the target had to be compensated. Fig. 6(a) shows the full 30 s of data for the male target walking in the test range. The paths away from and toward the radar are clearly visible with the peak power in range having a saw tooth pattern over time. A single path was selected for further processing—the first towards the radar path—and this is shown in Fig. 6(b) with the peak power in each range profile indicated by a black dot. Clearly, some of the peak powers were away from the true target position, so a straight line was fitted to the data, indicated by the white line. The fitted line was taken to indicate the center of the target and a fixed number of range bins were extracted in front of (towards the radar) and behind the target—the precise number depended on the test case. This extraction provided the aligned profiles shown in Fig. 6(c). The 0 m aligned range is equivalent to the downrange of the white line in Fig. 6(b) and, in this case, the range bins for 23 cm in front to 78 cm behind the target were extracted. The aligned range profiles, centered on the target, were then used for micro-Doppler analysis. 4.2. UWB Micro-Doppler Signatures Prior to analysis with the JRTFR, the range-Doppler surface and spectrogram of each dataset were calculated. The range-Doppler surface was obtained by taking the discrete Fourier transform of each range bin in the aligned profiles and the spectrogram was obtained by coherently summing the aligned range bins to form a sampled CW signal and then performing a STFT. In both cases, a Kaiser-Bessel window with shape parameter 6 was used. For the range-Doppler surface, the window duration matched the full extent of the slow time axis; for the STFT, the window duration was chosen to be 330 ms. The conventional analysis is presented in Fig. 7. Fig. 7(a) and (c) show the range-Doppler surface and spectrogram, respectively, for the case where the target held his arms behind his back while walking, while Fig. 7(b) and (d) are for the case with the arms swinging. The results are consistent with published literature on µDS for humans. The rangeDoppler surface shows a spread of frequencies ranging from DC to over 45Hz. This spread is a result of the swinging of the limbs. The maximum frequency observed equates to a speed of 2.5 ms-1. This speed is over twice the average human walking speed, approximately 1 ms-1, and arises due to the kicking action of the leg swing13. The spectrograms show the signature to be comprised of multiple components that have approximately sinusoidal natures. This is again consistent with the literature, although as always, the real data is not as clear as the simulations presented in13,16.
Certain features visible in the range-Doppler surface in Fig. 7(a) may be attributed to the experimental setup. Between 0 and 5 m of range, there are limited low frequency components in the data. This is not part of the signature, but a result of the elevation beamwidth being too narrow to illuminate the feet of the target at close ranges. Beyond 8 m, limited high frequency signature is seen, although the bright flashes at DC, attributed to corner reflector effects of the feet falling on the floor, are still visible. This is due to the short ranges employed in the trial. Between 2 and 10 m, the received power falls by 28 dB and the dynamic range of the plot is 30 dB. Increasing the plot dynamic range has little impact, since the radar power is low and beyond ≈ 8 m, the human target return is obscured by noise. Considering the range-Doppler surface and the spectrogram together highlights their limitations. The spectrogram makes clear that only certain frequencies are present at a given time, but there is no indication as to what range they originate from. Conversely, the range-Doppler surface informs on the relationship between frequency and range, but the entire 6 s observation interval is presented at once and time details are lost. The JRTFR allows us to overcome these limitations. The alternative analysis using the JRTFR for the swinging arm case is presented in Fig. 8. A series of contiguous slow time slices from the data cube are presented. The first slice is for a slow time of 3 s and the subsequent slices are spaced by 0.1s. The intensity scale of each image is power in dB normalized by the peak power of the entire JRTFR data cube. The dynamic range on each plot is from -20 to 0 dB. The first observation is that the Doppler shift of the highest power response in each slice varies with time. This is attributed to the forward and backward sway in the person’s torso and is visible in the oscillation of the highest power response in the spectrograms of Fig. 7. Second, it is observed that the range extent of the target varies in the different slow time slices. For example, at a slow time of 3 s there are several scattering centers visible with the same frequency as the highest power response. However, in slices such as this the spread in frequency is low. Conversely, in the slice for slow time 3.4 s there is a large spread in frequency, with two distinct scatterers visible at target centered range 0 m. But in slices such as these the range extent is reduced compared to the slice at 3 s.
(a)
(b)
(c)
(d)
Fig. 7: The range-Doppler surfaces (a) and (b) and spectrograms (c) and (d) for a human target walking with arms behind the back (a) and (c) and swinging freely (b) and (d).
Fig. 8: 12 contiguous slices, spaced by 0.1 s, from the JRTFR data cube for a person walking with swinging arms. All subplots are normalized by the peak power in the data cube and have a dynamic range ranging from -20 dB to 0 dB.
It was postulated that the changes in range and frequency extent observed in the JRTFR data cube related to specific stages of the human walking gate. The human gate cycle has been successfully modeled with the limbs swinging according to sinusoidal motions13. The arms swing approximately in phase with the legs but on opposite sides of the body, e.g. the left arm swings with the right leg. During walking, at the start of the gate cycle both feet are on the ground one in front of the torso, the other behind. The foot of the leg to the rear is lifted and swung forward, so that it may be placed on the ground ahead of the foot that remained in contact with the ground. During this swing the torso moves forward as the supporting leg, whose foot remained in contact with the ground, pivots forward at the ankle. Once both feet are back on the ground the process starts again, now with the leg that had been supporting becoming the once that swings. When both feet are on the ground, the person has maximum range extent, but since the limbs are not moving a minimum Doppler spread would be expected—the condition in Fig. 8 at slow time 3 s. Conversely, when the swinging leg is passing the leg whose foot is on the floor, the range extent will be reduced, but the Doppler spread high as many parts of the body exhibit micro-motions—the condition in Fig. 8 at slow time 3.4 s. Comparable results were obtained for the case where the arms were held behind the back, Fig. 9. In this case, fewer scattering centers were visible in the slices of the JRTFR data cube because the arms no longer exhibit micro-motions to separate them from the torso. However, the slow time slices in which there is large range extent, but narrow frequency spread and vice versa are still visible. The preliminary results serve to highlight the advantages of using an UWB waveform combined with µDS processing. Considering the columns of Fig. 6(c), each of which is an HRR profile, it is apparent that a human target’s profile changes rapidly with time. The range-Dopper surfaces and spectrograms of Fig. 7 go some way to capturing these variations, but in the case of the range-Doppler surface, the temporal information is lost, while for the spectrogram, the range information and hence, the advantage of using an UWB waveform are lost. It is only through the use of a JRTFR that frequency, range, and time information can be retained simultaneously as in Fig. 8 and Fig. 4.
5. CONCLUSIONS
Fig. 9: 12 contiguous slices, spaced by 0.1 s, from the JRTFR data cube for a person walking with their arms behind their back. All subplots are normalized by the peak power in the data cube and have a dynamic range ranging from -20 dB to 0 dB.
In this paper, we presented a joint range-time-frequency representation for combining the HRR signatures provided by UWB waveforms with the µDS of moving indoor targets. In the JRTFR, the µDS is considered as existing in a threedimensional space with axes of range, slow time, and frequency. A unique UWB pulse-Doppler radar system, which operates coherently with a 5 cm range resolution, was used to gather a novel dataset in which a human target is observed walking back and forth. The HRR capabilities of the radar allow the multiple scattering centers of the target to be resolved, while the coherency facilitates µDS analysis. It was shown using real data that, while conventional TFR methods for analyzing the µDS resulted in a loss of the HRR capability, the JRTFR allowed association of the Doppler frequencies appearing at a particular time with a range. This allowed an association of the range and frequency information at a given slow time with particular stages of the human walking gate. JRTFR analysis of the µDS of the human targets revealed that regions of low frequency extent in the TFR are associated with maxima in the target range extent and those of high frequency spread in the TFR were associated with minima in the target range extent. From these preliminary results, it is apparent that adding this extra degree of freedom to µDS increases the features that may be observed. As such, it is postulated that working in the range-time-frequency space will be beneficial for target classification.
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