## Final Report Summary - CSFDA (Compressive Sensing Frequency Diverse Array With Applications to Two-Dimensional Localization of Targets)

Active phased-array has been widely utilized in many applications because it can steer the beam electronically with high effectiveness. The offered directional gain is useful for detecting weak targets. However, phased-array has the drawback of range-independent transmit beampattern. To overcome this disadvantage, Antonik et al. [1] proposed frequency diverse array (FDA). Different from conventional phased-arrays, the FDA employs a small frequency offset compared to the carrier frequency across the array elements. The use of frequency offset generates a beampattern that is a function of range, time and angle. Note that FDA radar is different from OFDM radar and MIMO radar. OFDM radar uses orthogonal subcarriers, but non-orthogonal carriers are employed in FDA radar. MIMO radar aims to provide non-coherent waveforms to obtain increased degrees-of-freedom [2], whereas FDA radar transmits overlapping signals with closely spaced frequencies to provide additional functionality. It is also different from traditional frequency scanning technique [3], which uses the same center frequency for each element at a given time. Another similar concept is the time modulated array [4], which weights each element using on/off switching operations.

Since FDA apparent scan angle is not equal to its nominal scan angle, precise beam steering depends on both the range and angle. Consequently, it is not sufficient to precisely steer the beam similar to traditional phased-arrays; nevertheless, it provides new degrees-of-freedom in the range, angle and time for controlling the array factor. This enables the array beam to scan without the need of phase shifters or mechanical steering. Due also to the frequency increments, FDA creates a range-angle-dependent beampattern whose amplitude and spatial distribution can be controlled by changing the frequency increments and the number of array elements [5,6]. This range-angle-time-dependent beampattern is of great importance because it provides local maxima at different ranges and/or angle cells in different time and can be exploited for suppressing range-dependent interferences or clutters, offering many promising applications [7-11]. This is the motivation of this project.

FDA provides a potential to suppress range-dependent clutter or interferences and two-dimensional (range and angle) localization of targets, but the range and angle of targets cannot be directly estimated from the FDA beamforming output due to the inherent ambiguity. In this project, we aim to develop practical two-dimensional localization of targets using FDA antenna. The investigations are summarized as follows:

1. We studied waveform optimization for FDA focusing on how the signal parameters impact the system performance. Using knowledge of the ambiguity function’s primary sidelobe locations, a optimization is designed to optimize the ambiguity function at those locations. In doing so, the waveform is determined by the optimization constraints including total bandwidth, number of subcarriers, number of transmit and receive elements, maximum signal amplitude and maximum peak-to-sidelobe ratio.

2. Since FDA beampattern is different from conventional phased-array, there is a fundamental question about what is the FDA manifold geometric and ambiguity properties. The researcher investigated the FDA manifold geometric and ambiguities properties through manifold geometry analysis. The FDA resolution and detection capabilities are derived as a function of the manifold length and first curvature for the sources with unequal power. The ambiguities inherent in a linear FDA manifold are investigated. The results show that, when compared to a phased-array, the FDA can resolve more sources.

3. FDA offers range-angle-dependent beampattern which has a potential application in range-angle localization of targets, but it cannot estimate directly both the range and angle of a target due to its coupling range and angle response. To resolve this problem, we divide the whole FDA array into subarrays which use distinct frequency increments. In doing so, the target’s range and angle are estimated directly from the transmit-receive beamforming output peak.

4. By jointly utilizing the advantages of cognitive radar with situational awareness by employing closed-loop control and FDA with range-angle-dependent beampattern, we propose a cognitive FDA radar. It can avoid undesired strong interferences and focus to the desired target through the presented closed-loop control algorithm. The algorithm aims to maximize the receiver output signal-to-interference-plus-noise ratio performance by iteratively optimizing the frequency increments in a closed-loop manner.

5. Inspired by the nested-array technique, we proposed a nested-FDA receiver by using diverse time-delayers and exploiting the second-order statistics of the received data for increased degrees-of-freedom via the difference co-array processing algorithm, which means that more sources can be resolved. The essence is to construct a new array structure by systematically nesting two uniform linear arrays through diverse time-delayers. This study is so far limited to one-dimensional array, but is being extended to multiple-dimensional case.

6. Since conventional high-gain active transmit array beam is often highly visible to intercept receivers, the researcher proposed to replace traditional high-gain array transmit beam by a series of low-gain FDA transmit beam with nonlinear frequency increments to reduce the system visibility. In receiver, these basis beampatterns are coherently combined via beamforming to synthesize an ensemble of the original high-gain beampatterns scanned across the prescribed surveillance field with unaffected moving-target tracking performance. In doing so, the radar can effectively track the moving-target while limiting the area detectable for intercept receivers. Moreover, inspired also by that cognitive radar is a transmitter-centric closed-loop radar system, where it can real-time exploit its environment to update current probabilistic understanding of the channel, we further applied cognitive feedback to the RF stealth beamforming to formulate cognitive RF stealth radar for improved moving-target tracking performance.

7. We applied FDA to develop directional modulation (DM) technique for physical-layer security wireless communications. DM is promising technique for physical-layer secure communications, which has received much attention in recent years. However, up to now, all published DM techniques are based on phased-array. Although the DM techniques using phased-array can steer the beam to an arbitrary direction, they cannot steer to a range-dependent only position. This is because phased-array produces fixed steering direction at an angle for all the ranges. As compared to phased-array approaches, FDA provides new opportunities to realize DM. Thus, we proposed a range and angle dependent DM scheme using FDA with symmetrical frequency increments for secure point-to-point communications. The choice of symmetrical frequency increments, instead of linearly increasing frequency increments as a standard FDA, is proposed to decouple FDA range and angle dependent transmit beampattern. In doing so, we can significantly reduce the signal-to-noise ratio (SNR) of the signals arriving at undesired positions.

8. We are investigating the applications of FDA in millimeter-wave wireless communications, which is a key technique in future 5G wireless communications. Our focus is placed to resolve non-line-of-sight propagation problem by fully exploiting the advantages of FDA in range-angle-dependent propagation.

One potential application of FDA is joint range and angle estimation of targets [10-12]. The essence is to divide the FDA into multiple subarrays where each subarray uses a distinct frequency increment and a unique waveform. In doing so, the ranges and angles can be estimated by transmit beamspace-based subspace algorithms. Another FDA application is for cognitive radar. Cognitive radar is considered as an intelligent active sensing system that utilizes adaptive radar waveforms and machine learning techniques to achieve improved performance for radar tasks such as target recognition, sensor scheduling and scene analysis. Since FDA creates a range-dependent beampattern whose amplitude and spatial distribution can be controlled by the frequency increments, the researcher proposed a cognitive FDA radar by iteratively adjusting the frequency increments in a closed-loop way to control the transmitted energy distribution to suppress undesired interferences [13]. FDA can also be used to develop low probability of identification (LPI) radar [14]. The essence is to reduce the instantaneous transmit peak power with spoiled frequency increments and weights. These basis patterns are combined at the receiver using complex weights to synthesize the original high-gain beampattern for unaffected array detection performance.

Certainly, FDA also has several remaining technical challenges:

1) Waveform Optimization: Waveform optimization is required to further understand how the signal parameters affect the system performance. The ambiguity function may provide a useful optimization metric. Using the knowledge of the ambiguity function’s primary sidelobe locations, an optimization algorithm could be designed to optimize the ambiguity function at those locations. The waveform can be designed by the optimization constraints, including the total bandwidth, the number of subcarriers, the number of transmit and receive elements, the maximum chirp rate, the maximum transmit signal amplitude, and the maximum peak sidelobe levels. This constrained optimization problem should be further investigated.

2) Array Optimization Design: Linear array geometry is exclusively used in literature because it allows the relationship between the temporal, spatial, and spectral aspects of the FDA to be clearly visualized. However, a linear FDA does not perform well in target localization and 3-D imaging. The FDA with constant element spacing may not be an ideal configuration due to the frequency diversity. Larger inter-element spacing may be utilized to reduce the array complexity. Furthermore, we may consider nonlinear frequency increments. Optimal FDA geometric configuration is thus a necessary future research work.

3) Optimal Array Signal Processing: It is necessary to reduce the computation complexity in FDA receiver signal processing. Relaxing the weighting function’s frequency offset dependence would allow the spatial weighting to be factored out from the summation and applied once to the entire signal. This can significantly reduce the computation complexity. Subspace processing is a typical array processing approach, but it is difficult to obtain the required covariance matrix of noise and interference in FDA radar due to its range, angle and time dependent response. Additionally, Doppler effects should also be considered in future FDA signal processing algorithms.

References:

[1] P. Antonik, M.C. Wicks, H.D. Griffiths, et al. “Frequency diverse array radar,” Proc. of IEEE Radar Conference, Verona, NY, April 2006, pp. 215—217.

[2] J. Li, P. Stoica. “MIMO radar with collocated antennas,” IEEE Signal Processing Magazine, 2007, 24(5): 106—114.

[3] F.S. Johnsson, L.G. Josefsson, T. Lorentzon. “A novel frequency-scanned reflector antenna,” IEEE Transactions on Antennas and Propagation, 1989, 37(7): 984—989.

[4] W.H. Kummer, A. T. Villeneuve, T.S. Fong, F. G. Terrio. “Ultra-low sidelobes from time-modulation arrays,” IEEE Transactions on Antennas and Propagation, 1963, 11(6): 633—639.

[5] P.F. Sammartino, J. Baker, H.D. Griffiths. “Frequency diverse MIMO technique for radar,” IEEE Transactions on Aerospace and Electronic Systems, 2013, 49(1): 201—222.

[6] W.-Q. Wang. “Frequency diverse array antenna: New opportunities,” IEEE Antennas and Propagation Magazine, 2015, 57(2): 145—152.

[7] W.-Q. Wang. “Overview of frequency diverse array in radar and navigation applications,” IET Radar, Sonar and Navigation, 2015, in press

[8] F. Jawad, M.A. Temple, M.A. Saville. “Exploiting frequency diverse array processing to improve SAR image resolution,” Proc. of IEEE Radar Conference, May 2008, pp. 1—5.

[9] W.-Q. Wang, H.Z. Shao. “Range-angle localization of targets by a double-pulse frequency diverse array radar,” IEEE Journal of Selected Topics in Signal Processing, 2014, 8(1): 106—114.

[10] W.-Q. Wang, H.C. So. “Transmit subaperturing for range and angle estimation in frequency diverse array radar,” IEEE Transactions on Signal Processing, 2014, 62(8): 2000—2011.

[11] J. Xu, G.S. Liao, S.Q. Zhu, et al. “Joint range and angle estimation using MIMO radar with frequency diverse array,” IEEE Transactions on Signal Processing, 2015, 63(13): 3396—3410.

[12] W.-Q. Wang. “Subarray-based frequency diverse array radar for target range-angle estimation,” IEEE Transactions on Aerospace and Electronic Systems, 2014, 50(4): 3057—3067.

[13] W.-Q. Wang. “Cognitive frequency diverse array radar with situational awareness,” IET Radar, Sonar and Navigation, 2016, 10(2): 359—369.

[14] W.-Q. Wang. “Moving-target tracking by adaptive RF stealth radar using frequency diverse array antenna,” IEEE Transactions on Geoscience and Remote Sensing, 2016, in press.

Since FDA apparent scan angle is not equal to its nominal scan angle, precise beam steering depends on both the range and angle. Consequently, it is not sufficient to precisely steer the beam similar to traditional phased-arrays; nevertheless, it provides new degrees-of-freedom in the range, angle and time for controlling the array factor. This enables the array beam to scan without the need of phase shifters or mechanical steering. Due also to the frequency increments, FDA creates a range-angle-dependent beampattern whose amplitude and spatial distribution can be controlled by changing the frequency increments and the number of array elements [5,6]. This range-angle-time-dependent beampattern is of great importance because it provides local maxima at different ranges and/or angle cells in different time and can be exploited for suppressing range-dependent interferences or clutters, offering many promising applications [7-11]. This is the motivation of this project.

FDA provides a potential to suppress range-dependent clutter or interferences and two-dimensional (range and angle) localization of targets, but the range and angle of targets cannot be directly estimated from the FDA beamforming output due to the inherent ambiguity. In this project, we aim to develop practical two-dimensional localization of targets using FDA antenna. The investigations are summarized as follows:

1. We studied waveform optimization for FDA focusing on how the signal parameters impact the system performance. Using knowledge of the ambiguity function’s primary sidelobe locations, a optimization is designed to optimize the ambiguity function at those locations. In doing so, the waveform is determined by the optimization constraints including total bandwidth, number of subcarriers, number of transmit and receive elements, maximum signal amplitude and maximum peak-to-sidelobe ratio.

2. Since FDA beampattern is different from conventional phased-array, there is a fundamental question about what is the FDA manifold geometric and ambiguity properties. The researcher investigated the FDA manifold geometric and ambiguities properties through manifold geometry analysis. The FDA resolution and detection capabilities are derived as a function of the manifold length and first curvature for the sources with unequal power. The ambiguities inherent in a linear FDA manifold are investigated. The results show that, when compared to a phased-array, the FDA can resolve more sources.

3. FDA offers range-angle-dependent beampattern which has a potential application in range-angle localization of targets, but it cannot estimate directly both the range and angle of a target due to its coupling range and angle response. To resolve this problem, we divide the whole FDA array into subarrays which use distinct frequency increments. In doing so, the target’s range and angle are estimated directly from the transmit-receive beamforming output peak.

4. By jointly utilizing the advantages of cognitive radar with situational awareness by employing closed-loop control and FDA with range-angle-dependent beampattern, we propose a cognitive FDA radar. It can avoid undesired strong interferences and focus to the desired target through the presented closed-loop control algorithm. The algorithm aims to maximize the receiver output signal-to-interference-plus-noise ratio performance by iteratively optimizing the frequency increments in a closed-loop manner.

5. Inspired by the nested-array technique, we proposed a nested-FDA receiver by using diverse time-delayers and exploiting the second-order statistics of the received data for increased degrees-of-freedom via the difference co-array processing algorithm, which means that more sources can be resolved. The essence is to construct a new array structure by systematically nesting two uniform linear arrays through diverse time-delayers. This study is so far limited to one-dimensional array, but is being extended to multiple-dimensional case.

6. Since conventional high-gain active transmit array beam is often highly visible to intercept receivers, the researcher proposed to replace traditional high-gain array transmit beam by a series of low-gain FDA transmit beam with nonlinear frequency increments to reduce the system visibility. In receiver, these basis beampatterns are coherently combined via beamforming to synthesize an ensemble of the original high-gain beampatterns scanned across the prescribed surveillance field with unaffected moving-target tracking performance. In doing so, the radar can effectively track the moving-target while limiting the area detectable for intercept receivers. Moreover, inspired also by that cognitive radar is a transmitter-centric closed-loop radar system, where it can real-time exploit its environment to update current probabilistic understanding of the channel, we further applied cognitive feedback to the RF stealth beamforming to formulate cognitive RF stealth radar for improved moving-target tracking performance.

7. We applied FDA to develop directional modulation (DM) technique for physical-layer security wireless communications. DM is promising technique for physical-layer secure communications, which has received much attention in recent years. However, up to now, all published DM techniques are based on phased-array. Although the DM techniques using phased-array can steer the beam to an arbitrary direction, they cannot steer to a range-dependent only position. This is because phased-array produces fixed steering direction at an angle for all the ranges. As compared to phased-array approaches, FDA provides new opportunities to realize DM. Thus, we proposed a range and angle dependent DM scheme using FDA with symmetrical frequency increments for secure point-to-point communications. The choice of symmetrical frequency increments, instead of linearly increasing frequency increments as a standard FDA, is proposed to decouple FDA range and angle dependent transmit beampattern. In doing so, we can significantly reduce the signal-to-noise ratio (SNR) of the signals arriving at undesired positions.

8. We are investigating the applications of FDA in millimeter-wave wireless communications, which is a key technique in future 5G wireless communications. Our focus is placed to resolve non-line-of-sight propagation problem by fully exploiting the advantages of FDA in range-angle-dependent propagation.

One potential application of FDA is joint range and angle estimation of targets [10-12]. The essence is to divide the FDA into multiple subarrays where each subarray uses a distinct frequency increment and a unique waveform. In doing so, the ranges and angles can be estimated by transmit beamspace-based subspace algorithms. Another FDA application is for cognitive radar. Cognitive radar is considered as an intelligent active sensing system that utilizes adaptive radar waveforms and machine learning techniques to achieve improved performance for radar tasks such as target recognition, sensor scheduling and scene analysis. Since FDA creates a range-dependent beampattern whose amplitude and spatial distribution can be controlled by the frequency increments, the researcher proposed a cognitive FDA radar by iteratively adjusting the frequency increments in a closed-loop way to control the transmitted energy distribution to suppress undesired interferences [13]. FDA can also be used to develop low probability of identification (LPI) radar [14]. The essence is to reduce the instantaneous transmit peak power with spoiled frequency increments and weights. These basis patterns are combined at the receiver using complex weights to synthesize the original high-gain beampattern for unaffected array detection performance.

Certainly, FDA also has several remaining technical challenges:

1) Waveform Optimization: Waveform optimization is required to further understand how the signal parameters affect the system performance. The ambiguity function may provide a useful optimization metric. Using the knowledge of the ambiguity function’s primary sidelobe locations, an optimization algorithm could be designed to optimize the ambiguity function at those locations. The waveform can be designed by the optimization constraints, including the total bandwidth, the number of subcarriers, the number of transmit and receive elements, the maximum chirp rate, the maximum transmit signal amplitude, and the maximum peak sidelobe levels. This constrained optimization problem should be further investigated.

2) Array Optimization Design: Linear array geometry is exclusively used in literature because it allows the relationship between the temporal, spatial, and spectral aspects of the FDA to be clearly visualized. However, a linear FDA does not perform well in target localization and 3-D imaging. The FDA with constant element spacing may not be an ideal configuration due to the frequency diversity. Larger inter-element spacing may be utilized to reduce the array complexity. Furthermore, we may consider nonlinear frequency increments. Optimal FDA geometric configuration is thus a necessary future research work.

3) Optimal Array Signal Processing: It is necessary to reduce the computation complexity in FDA receiver signal processing. Relaxing the weighting function’s frequency offset dependence would allow the spatial weighting to be factored out from the summation and applied once to the entire signal. This can significantly reduce the computation complexity. Subspace processing is a typical array processing approach, but it is difficult to obtain the required covariance matrix of noise and interference in FDA radar due to its range, angle and time dependent response. Additionally, Doppler effects should also be considered in future FDA signal processing algorithms.

References:

[1] P. Antonik, M.C. Wicks, H.D. Griffiths, et al. “Frequency diverse array radar,” Proc. of IEEE Radar Conference, Verona, NY, April 2006, pp. 215—217.

[2] J. Li, P. Stoica. “MIMO radar with collocated antennas,” IEEE Signal Processing Magazine, 2007, 24(5): 106—114.

[3] F.S. Johnsson, L.G. Josefsson, T. Lorentzon. “A novel frequency-scanned reflector antenna,” IEEE Transactions on Antennas and Propagation, 1989, 37(7): 984—989.

[4] W.H. Kummer, A. T. Villeneuve, T.S. Fong, F. G. Terrio. “Ultra-low sidelobes from time-modulation arrays,” IEEE Transactions on Antennas and Propagation, 1963, 11(6): 633—639.

[5] P.F. Sammartino, J. Baker, H.D. Griffiths. “Frequency diverse MIMO technique for radar,” IEEE Transactions on Aerospace and Electronic Systems, 2013, 49(1): 201—222.

[6] W.-Q. Wang. “Frequency diverse array antenna: New opportunities,” IEEE Antennas and Propagation Magazine, 2015, 57(2): 145—152.

[7] W.-Q. Wang. “Overview of frequency diverse array in radar and navigation applications,” IET Radar, Sonar and Navigation, 2015, in press

[8] F. Jawad, M.A. Temple, M.A. Saville. “Exploiting frequency diverse array processing to improve SAR image resolution,” Proc. of IEEE Radar Conference, May 2008, pp. 1—5.

[9] W.-Q. Wang, H.Z. Shao. “Range-angle localization of targets by a double-pulse frequency diverse array radar,” IEEE Journal of Selected Topics in Signal Processing, 2014, 8(1): 106—114.

[10] W.-Q. Wang, H.C. So. “Transmit subaperturing for range and angle estimation in frequency diverse array radar,” IEEE Transactions on Signal Processing, 2014, 62(8): 2000—2011.

[11] J. Xu, G.S. Liao, S.Q. Zhu, et al. “Joint range and angle estimation using MIMO radar with frequency diverse array,” IEEE Transactions on Signal Processing, 2015, 63(13): 3396—3410.

[12] W.-Q. Wang. “Subarray-based frequency diverse array radar for target range-angle estimation,” IEEE Transactions on Aerospace and Electronic Systems, 2014, 50(4): 3057—3067.

[13] W.-Q. Wang. “Cognitive frequency diverse array radar with situational awareness,” IET Radar, Sonar and Navigation, 2016, 10(2): 359—369.

[14] W.-Q. Wang. “Moving-target tracking by adaptive RF stealth radar using frequency diverse array antenna,” IEEE Transactions on Geoscience and Remote Sensing, 2016, in press.