Golay complementary waveforms for sparse delay-Doppler radar imaging

Abstract

Abstract-We present a new approach to radar imaging that exploits sparsity in the matched filter domain to enable high resolution imaging of targets in delay and Doppler. We show that the vector of radar cross-ambiguity values at any fixed test delay cell has a sparse representation in a Vandermonde frame that is obtained by discretizing the Doppler axis. The expansion coefficients are given by the auto-correlation functions of the transmitted waveforms. We show that the orthogonal matching pursuit (OMP) algorithm can then be easily used to identify the locations of the radar targets in delay and Doppler. Unambiguous imaging in delay is enabled by alternating between a Golay pair of phase coded waveforms at the transmission to eliminate delay sidelobe effects. We then extend our work to multi-channel radar, by developing a sparse recovery approach for dually-polarimetric radar. We exploit sparsity in a bank of matched filters, each of which is matched to an entry of an Alamouti matrix of Golay waveforms to recover a co-polar or cross-polar polarization scattering component.Index Terms-Golay complementary waveforms, sparse representations, Vandermonde frame, orthogonal matching pursuit, delay-Doppler imaging.

Sub-Nyquist Radar Systems: Temporal, Spectral, and Spatial Compression

“…It is interesting to note that the considerations behind waveform design for CS recovery in the approaches [16], [17], [18] presented in the previous section are similar to traditional radar requirements. The well known ambiguity function (AF) impacts CS radar in a similar way as traditional radar systems.…”

“…In the works of [16], [17], [18], [21], the signal is still sampled at its Nyquist rate B h but the delay and Doppler resolutions are determined by the CS grid, containing N > τ B h grid points, rather than the signal's bandwidth and CPI, respectively. The key idea in [16], which adopts a pulse-Doppler radar model, is that the received signal x R (t) defined in (7) is generally a sparse superposition of time-shifted 6 COMPRESSED SENSING RECOVERY CS [12], [10] is a framework for simultaneous sensing and compression of finite-dimensional vectors, which relies on linear dimensionality reduction.…”

“…These rely on the compressed sensing (CS) [12], [10] framework, brought to the forefront by the works of Candes, Romberg and Tao [13], [14], and of Donoho [15]. Although the natural application of CS is typically the reduction of the required number of samples to perform a certain signal processing task, it was first used by the radar community to increase a target's parameter resolution [16], [17], [18], [19], [20], [21]. It was later applied to reduce the number of samples to be processed [22], [23], [24], [25], [26] and finally to reduce the sampling rate [27], [28] and number of antennas [29] required in radar systems, performing time and spatial compression and alleviating the burden on both the analog and digital sides.…”

Algorithms for Designing Unimodular Sequences with High Doppler Tolerance for Simultaneous Fully Polarimetric Radar

“…However, the AISO algorithm also does not consider the optimization of the cross-correlation properties of the sequences. In addition, Doppler tolerant complementary code sets are also developed these days because of their potential of making all the autocorrelation side-lobes sum to zero, at least in theory, but the orthogonality of the complementary sequences are not considered in most articles [21,22]. In addition, the Doppler frequency in [19,20] is considered to be a constant in one PRT, which means that the target is assumed to be in a uniform rectilinear motion state.…”

Golay Complementary Waveforms in Reed–Müller Sequences for Radar Detection of Nonzero Doppler Targets

“…These special designed waveforms have the property that the sum of their autocorrelation functions vanishes at all nonzero lags; thus, pairs of Golay complementary waveforms achieve an impulse autocorrelation output without any sidelobes, at least in theory. Numerous research publications have promoted this concept [ 23 , 25 , 26 , 27 , 28 , 29 , 30 ], but, as is widely understood, standard Golay complementary waveforms suffer two disadvantages; firstly, they have to be transmitted in pairs and those pairs have to completely separated on their return to the receiver and, secondly, they are sensitive to the mismatch of Doppler. Significant range sidelobes occur in nonzero Doppler lines in the AF.…”