Waveform Design and Receive Processing for Nonrecurrent Nonlinear FMCW Radar

Transcription

1 Wavefor Design and Receive Processing for Nonrecurrent Nonlinear FMCW Radar John Jakabosky and Shannon D. Blunt Radar Systes Lab University of Kansas Lawrence, KS Braha Hied Sensors Directorate Air Force Research Laboratory Dayton, OH Abstract A spectral shaping optiization schee is used to design the autocorrelation response of individual segents of a nonrecurrent nonlinear FMCW wavefor denoted as Pseudo- Rando Optiized FMCW (or PRO-FMCW). Because each wavefor segent is unique, the range sidelobes do not cobine coherently during Doppler processing thereby providing further sidelobe suppression. The PRO-FMCW wavefor can be viewed as a specific instantiation of FM noise radar where the constant aplitude perits axiu power efficiency. A segented approach to processing the received data is used to reduce processing tie and coplexity. results fro hardware ipleentation are provided to deonstrate the efficacy of the proposed approach. I. INTRODUCTION The notion of changing the wavefor on a pulse-to-pulse basis during the coherent processing interval (CPI) can be traced back to stepped frequency wavefors to increase overall bandwidth and copleentary coding (see [1, Chap. 9] and references therein). With the eergence and continued advanceent of high-fidelity wavefor generation this concept of pulse agility or pulse diversity has also been exained as a way to increase the diensionality of the radar eission for diverse purposes such as the extension of the axiu abiguous range [2,3], ebedded counication on transit [4,5], and joint delay-doppler iaging [6], all being exaples of wavefor diversity [7-9]. One could likewise view noise radar as a continuous wave (CW) instantiation of this sae principle as the wavefor is always changing (see [1] and references therein). Because it iics rando noise, such a radar inherently possesses a low probability of intercept (LPI) and has no range abiguities, though the typical requireent for aplitude odulation tends to liit noise radar to short range applications. Alternatively, it has been shown [11] that randoly odulating phase or frequency has advantages over traditional coplex aplitude odulated noise radar in ters of range resolution as well as the ability to use power efficient aplifiers since the resulting phase/frequency odulated wavefor is constant odulus. An iportant iplication of this changing wavefor structure is that the range sidelobes likewise change on a pulseto-pulse basis (or processing segent-to-segent for CW). This sidelobe odulation effect produces a range sidelobe floor when perforing Doppler processing such that, in the presence of strong scatterers (e.g. clutter), these sidelobes can wash out the scene. Since traditional clutter filtering only reoves the ainlobe response of the scatterer, these This work was supported by a subcontract with Booz, Allen and Hailton for research sponsored by the Air Force Research Laboratory (AFRL) under Contract FA D-111. odulated sidelobes reain. Sophisticated adaptive filtering approaches ay address these odulated sidelobes [2,3,6], though at a high coputational cost. The alternative is to ebrace the large diensionality by axiizing the overall tie-bandwidth product and exploiting the lack of sidelobe coherence, which is essentially how noise radar operates. The approach proposed here eploys the rando FM structure, albeit with the inclusion of spectral shaping as suggested in [11] whereby the power spectral density is constrained to a Gaussian shape which likewise translates into a Gaussian-shaped autocorrelation with low range sidelobes. This spectral shaping procedure is inspired by the iterative approaches described in [12,13], though instead of avoiding spectral regions the goal here to atch to the Gaussian power spectral density. By initializing each FMCW segent with a rando phase signal followed by Gaussian spectral shaping, low range sidelobes can be achieved that likewise are not coherent over the segents used for Doppler processing. This nonrecurrent nonlinear FM continuous wavefor, denoted as Pseudo-Rando Optiized FMCW (PRO-FMCW), realizes a power efficient eission due to constant aplitude, good spectral containent due to the spectral shaping, is range unabiguous, and achieves very low sidelobe levels given a sufficiently long CPI for receive processing. The optiization process is aenable to real-tie operation given sufficient processing capability. Aside fro the need to account for the convolutional tails that arise for the CW wavefor structure, standard atched filter pulse copression and Doppler processing (including clutter cancellation) can be applied to the received data. Further, sliding window Doppler processing can be used to provide a rapid refresh of the range- Doppler response. II. SPECTRAL-SHAPING OPTIMIZATION The spectral shaping design developed here for the individual wavefor segents is the sae as that developed in [14], although here constant odulus is enforced and each wavefor segent is randoly (and independently) initialized prior to the spectral shaping optiization. The overall approach is as follows: a rando phase signal is generated, this signal is optiized to produce a segent of the wavefor with a prescribed power spectral density, and then the beginning of this segent is phase-aligned with the end of the previous segent. The nonrecurrent, nonlinear FMCW wavefor is thus constructed in piece-wise fashion where receive processing is likewise perfored on the individual segents.

2 The spectral shaping optiization is an iterative process involving the sequential application of and 1 k 1, k, r ( t) G( f ) exp j p ( t) (1) k1, k1, p ( t) w( t)exp j r ( t) (2) where p, ( t ) is the initial randoly generated phase signal for the th segent, w(t) is a rectangular window of length T, G(f) 2 1 is the desired power spectral density, and are the Fourier and inverse Fourier transfors, respectively, and () extracts the phase of the arguent. This process is repeated for K iterations to obtain the th optiized signal pk, () t. To prevent abrupt phase jups, the th optiized signal is phase rotated to yield the th wavefor segent as where end, 1 end, 1 K, s ( t) exp j p ( t) (3) is the ending phase for the ( 1)th segent. This optiization approach can be ipleented efficiently using FFTs and IFFTs. Leveraging general purpose GPU (GPGPU) coputation and parallel processing, it is possible to generate the optiized segents in real-tie. III. RECEIVE PROCESSING The receive echoes are organized for processing in the sae anner as the transitted wavefor segents. To account for the convolutional tails in the atched filtering of this CW signal, portions of the ( 1)th and (+1)th segents are included in the data to which the th atched filter is applied (Fig. 1). The th atched filter is the tie-reversed coplex conjugate of the wavefor segent defined in (3). This process is repeated for each segent. Doppler processing via FFT of M contiguous pulse copressed segents provides a range-doppler ap that can be updated in a sliding window anner as each new segent is pulse copressed. Standard clutter cancellation can also be incorporated into this sliding window Doppler processing. Pre 1 Received data segent Matched filter for segent Fig. 1. Pulse copression for the th segent Figure 1 shows that the atched filter is applied to the cobined pre, post, and current segents. Only a sall nuber of saples fro the previous segent are needed. The portion of the (+1)th segent that is required is deterined by the length of the desired range interval. For instance, to capture 75 eters of range data at a sapling rate of 2 Post +1 MS/s, 1 saples or 5 µs fro the (+1)th segent would be required. If the desired range interval is greater than the length of a segent, additional segents can be appended as required. Since the echoes generated by a segent also include the reflected responses fro previous segents, interference can be a proble. The cross-correlation sidelobe interference increases as ore saples fro the (+1)th segent are included. Thus the iniu required to iage the desired range should be used. IV. LABORATORY MEASUREMENTS To verify the perforance of the PRO-FMCW design, a wavefor with a length of T w = 2 illiseconds was produced coprising M = 1 4 segents of length T = 2 µs. This wavefor has a design bandwidth of B = 8 MHz and was sapled at 2 Mega-saples per second. Each segent possesses a tie-bandwidth product of 16 while the total processing gain is or 72. The optiization of each segent was perfored using a Gaussian power spectral density which produces both good spectral roll-off and low autocorrelation sidelobes. Each segent was optiized using (1) and (2) for K = 5 iterations. The initialization for each segent optiization was a rando sequence of 16 phase values drawn fro a unifor distribution on [ π, π] and subsequently ipleented using the polyphase-coded FM (PCFM) fraework fro [15]. The resulting wavefor was ipleented in a hardware testbed using a Tektronix AWG72 wavefor generator, a Rohde & Schwarz FSW spectru analyzer to capture the echo response, and a pair (one for TX, one for RX) of vertically polarized patch array antennas with effective gain of 14 i. The AWG was set to saple the wavefor at GS/s and the spectru analyzer captured coplex I and Q saples at 2 MS/s. A center frequency of 2.4 GHz was selected for the test. It was noted prior to testing that a nuber of interittent counications signals were operating within the bandwidth sapled by the spectru analyzer. The autocorrelation and cross-correlation of each of the 1 4 segents was first exained with the hardware in a loopback configuration. The cross-correlation was generated by correlating a given segent with the following segent. To provide an aggregated way in which to visualize the goodness of the wavefor, the RMS average is coputed across the set of segent autocorrelations and crosscorrelations. The RMS average autocorrelation is shown in Figs. 2 and 3. The RMS average peak sidelobe level over the set of initial rando segents is observed to be approxiately 33, which is iproved to 43 by the spectral shaping optiization. Further, Fig. 3 reveals the presence of slight shoulder lobes for the initialization segents that have subsequently been soothed out by a slight degradation in range resolution for the optiized segents. When the test set up was operated in a loopback configuration, the RMS average autocorrelation response of the captured wavefor closely resebles that of the optiized wavefor. The only nonconfority is an additional lower shoulder lobe present in positive delay (Fig. 3). This lobe was ost likely produced by the lack of gain flatness in the spectru analyzer s receive bandwidth.

3 -1 Optiized Optiized T -.5T.5T T Fig. 2. RMS average autocorrelation response T -.5T.5T T Fig. 4. RMS average cross-correlation response -1 Optiized -2 Optiized T -.5T.5T.1T Fig. 3. RMS average autocorrelation response (ainlobe detail) The RMS average cross-correlation of the segents is illustrated in Fig. 4. Copared to the initial segents, the spectral shaping optiization realizes a odest degradation for the cross-correlation axiu level fro 33 to The easured cross-correlation response was nearly identical to the optiized response. When perforing Doppler processing over a set of segents the ainlobe response of each segent cobines coherently while the sidelobe response does not, thereby producing sidelobe suppression in the autocorrelation as shown in Figs. 5 and 6. The ean sidelobe level for the coherently cobined response is approxiately 4 lower than the RMS average fro Figs. 2 and 3 when all 1 4 segents are cobined. The sidelobe response shown is only representative of that produced by a zero Doppler point scatterer. Any Doppler in the scatterer will produce a different sidelobe response, though it will still approxiate the shape in Figs. 5 and T -.5T.5T T Fig. 5. Integrated autocorrelation response Optiized -.1T -.5T.5T.1T Fig. 6. Integrated autocorrelation response (ainlobe detail)

4 The sidelobe level of the optiized wavefor is below 85 near the ainlobe and is below 75 towards the edge of the segent. A slight broadening of the ainlobe below 5 is evident when copared to the initial wavefor (Fig. 6). The response of the easured wavefor in loopback is very close to that of the optiized wavefor. There again exists a slight shoulder lobe around 3 in positive delay, with an additional lobe produced at approxiately 7, that is again believed to be an artifact of the receive channel equalization. The coherently cobined cross-correlation response is shown in Figs. 7 and 8. The cross-correlation level of the optiized wavefor is below 67, and drops below 8 at the edges of the segent. While this response is at a satisfactory level, it is still above the integrated autocorrelation sidelobe level fro Figs. 5 and 6. In this case, the crosscorrelation is a easure of the sidelobes produced fro range folded scatterers. PSD is shown in Fig. 9 for the initial wavefor, the optiized wavefor, and the easured loopback wavefor. Also shown in Fig. 9 is the spectral shape used in the optiization process. It is evident that the initial wavefor occupies a uch larger bandwidth and has a ore gradual spectral roll-off than the optiized wavefor. The easured wavefor has a sharp rolloff outside of twice the design bandwidth due to a axiu of 16 MHz analysis bandwidth for the spectru analyzer. The ainlobe shape is slightly distorted as well due to the lack of channel equalization. -5 Shape Optiized Optiized T -.5T.5T T Fig. 7. Integrated cross-correlation response Optiized -.1T -.5T.5T.1T Fig. 8. Integrated cross-correlation response (detail) The power spectral density (PSD) of each segent was coputed and averaged with all other segents. This average -B -.5B.5B B Noralized Frequency Fig. 9. Spectral content To validate the loopback easureents, a laboratory test was perfored in a roo contained any large etal panels of varying shapes. The previously exained wavefor was again used and was allowed to repeat continuously. The spectru analyzer was used to capture 2 seconds of continuous data at the full 2 MS/s rate. A person walked towards the antennas while the syste was operating. The last 5 nanoseconds of the previous segent and 2 icroseconds of the following segent were included for atched filtering to capture all scatterers in the scene. After atched filtering for each segent, the data was Doppler processed. A Blackan-Harris window was used to suppress Doppler sidelobes and a zero-doppler projection filter was used to reove stationary clutter. This process only reoved the ainlobe response of the clutter but left the sidelobe floor of the strongest scatterer intact. The range- Doppler ap was noralized so that corresponds to the strongest scatterer before clutter cancellation. The range-doppler ap for the laboratory easureent is shown in Fig. 1. Note that the person is within 2 eters of the transitter and that the roo diension is approxiately 7. The oving target response is ore than 6 above the surrounding sidelobe floor. There is also an abundance of reflections in the iage that extend out past 3 ties the roo length due to ultipath effects. A Doppler velocity versus tie plot is shown in Fig. 11. The range bin of the strongest scatterer fro Fig. 1 is shown. The tie axis has been interpolated with a sliding CPI window

5 Velocity (/s) Range () using 1 4 segents. In Fig. 11 the icro-doppler coponents of the walking person can be observed [16] for a range profile of up to 75 eters. The equipent setup is shown in Fig. 12. A ap of potential scatterers is shown in Fig. 13. The range profile generated by the test is shown in Fig. 14. The conjectured scatterers in Fig. 13 are again labeled in Fig. 14. The apparent dynaic range of the integrated range profile response is at least 7 below the direct path interference peak, thereby allowing for a nuber of sall scatterers to be observed Velocity (/s) Fig. 1. Range-doppler ap of a person walking Fig. 12. Equipent used for rooftop easureents Tie (s) Fig. 11. Doppler velocity versus tie V. FREE-SPACE MEASUREMENTS Finally, an open-air experient was perfored to verify the perforance of the PRO-FMCW wavefor. The sae equipent used in the laboratory experient was placed on the roof of a 3 story building located on the University of Kansas capus. Here the transit and receive antennas were the vertical channels of two quad-ridged horn antennas. Each antenna provided about 1 i of gain. The center frequency was 2.3 GHz. A wideband aplifier with 27 of gain was selected which provided approxiately 22 of transit power. The sae 1 4 segents were transitted and captured, yielding a total sapling tie of 2 s. For atch filtering, the last 5 ns of the previous segent and 5 µs of the following segent were appended to the current segent thus allowing Fig. 13. Annotated ap of radar scene

6 Range () Rel Power () Direct Path Lied Center Tree Shed Sign Car? Dole Institute VI. CONCLUSIONS The design of a nonrecurrent, nonlinear FMCW wavefor denoted as pseudo-rando optiized (PRO-FMCW) was proposed that eploys spectral shaping optiization. The wavefor is divided into segents for optiization and range- Doppler receive processing. This wavefor exhibits good spectral containent and was capable of producing range sidelobes below 75. Following ipleentation using an arbitrary wavefor generator and spectru analyzer, physical easureents of a oving target (walking person) indicate sidelobe levels in the easured data that agree well with expectations. This perforance was also verified using openair easureents Range () Fig. 14. Annotated range profile The open-air test equipent was oved to the opposite side of the roof, and aied at a road intersection about 1 k away. A dataset of 1 4 segents spanning 2 s was again collected. Since the dynaic range of the data captured was liited by the large near-in scattering, the nearby scatterers were estiated using a least-squares forulation and subsequently subtracted fro the easured data. The resulting range-doppler ap is shown in Fig. 15. The values depicted are noralized to the peak scatterer in the data without cancellation. Three oving targets with SINR greater than 1 were observed and are highlighted in red. All of the detected targets were below the 75 range-doppler sidelobe level produced by the peak scatterer, which is why the cancellation stage was necessary. These oving targets are cars accelerating after a stoplight. Note that the speed liit of the road is 4 ph (approxiately 18 /s) Velocity (/s) Fig. 15. Range-Doppler ap of oving cars ( scale) REFERENCES [1] N. Levanon and E. Mozeson, Radar Signals, Wiley-IEEE Press, 24. [2] T. Higgins, K. Gerlach, A.K. Shackelford, and S.D. Blunt, Aspects of non-identical ultiple pulse copression, IEEE Radar Conf., Kansas City, MO, pp , May 211. [3] D.P. Scholnik, Range-abiguous clutter suppression with pulse-diverse wavefors, IEEE Radar Conf., Kansas City, MO, pp , May 211. [4] M. Cook, S.D. Blunt, J. Jakabosky, "Optiization of wavefor diversity and perforance for pulse-agile radar," IEEE Radar Conf., Kansas City, MO, pp , May 211. [5] S.D. Blunt, M.R. Cook, and J. Stiles, Ebedding inforation into radar eissions via wavefor ipleentation, Intl. Wavefor Diversity & Design Conf., Niagara Falls, Canada, pp , 8-13 Aug. 21. [6] T. Higgins, S.D. Blunt, and A.K. Shackelford, Tie-range adaptive processing for pulse agile radar, Intl. Wavefor Diversity & Design Conf., Niagara Falls, Canada, pp , 8-13 Aug. 21. [7] M. Wicks, E. Mokole, S. Blunt, R. Schneible, and V. Auso, eds., Principles of Wavefor Diversity and Design, SciTech, 21. [8] U. Pillai, K.Y. Li, I. Selesnick, and B. Hied, Wavefor Diversity: Theory & Applications, McGraw-Hill, 211. [9] F. Gini, A. De Maio, and L.K. Patton, eds., Wavefor Design and Diversity for Advanced Radar Systes, IET, 212. [1] Special issue on Signal Processing in Noise Radar Technology, IET Radar, Sonar & Navigation, vol. 2, no. 4, Aug. 28. [11] S.R.J. Axelsson, Noise radar using rando phase and frequency odulation, IEEE Trans. Geoscience & Reote Sensing, vol. 42, no. 11, pp , Nov. 24. [12] T. Higgins, T. Webster, and A.K. Shackelford, "Mitigating interference via spatial and spectral nulls," IET Intl. Radar Conf., Oct. 212 [13] W. Rowe, P. Stoica, and J. Li, "Spectrally constrained wavefor design," IEEE Signal Processing Magazine, vol. 31, no. 3, pp , May 214. [14] J. Jakabosky, S.D. Blunt, and T. Higgins, Ultra-low sidelobe wavefor design via spectral shaping and LINC transit architecture IEEE Intl. Radar Conf., Washington, DC, May 215. [15] S.D. Blunt, M. Cook, J. Jakabosky, J. de Graaf, and E. Perrins, Polyphase-coded FM (PCFM) radar wavefors, part I: ipleentation, IEEE Trans. Aerospace & Electronic Systes, vol. 5, no. 3, pp , July 214. [16] V.C. Chen, F. Li, S.-S. Ho, and H. Wechsler, Micro-Doppler effect in radar: phenoenon, odel, and siulation study, IEEE Trans. Aerospace & Electronic Systes, vol. 42, no. 1, pp. 2-21, Jan. 26.