Signal-dependent Clutter Research Articles

MIMO DFRC Signal Design in Signal-Dependent Clutter

This paper deals with the Dual-Function Radar and Communication (DFRC) signal design for a Multiple-Input–Multiple-Output (MIMO) system, considering the presence of signal-dependent clutter. A modulation methodology called Spectral Position Index and Amplitude (SPIA) modulation is proposed, which involves selecting passband and stopband positions and applying amplitude modulation. Signal to Interference plus Noise Ratio (SINR) is maximized to enhance radar detectability. Meanwhile, variable modulus and communication modulation constraints are enforced to ensure compatibility with the current hardware techniques and communication demand, respectively. In addition, the mainlobe width and sidelobe level constraints used to concentrate energy in a specific area of space are enforced. To tackle the resulting nonconvex and NP-hard optimization problem, an Iterative Block Enhancement (IBE) framework that alternately updates each signal in each emitting antenna is exploited to monotonically increase SINR. Each block involves the Dinkelbach’s Iterative Procedure (DIP), Sequential Convex Approximation (SCA) and Alternating Direction Method of Multipliers (ADMM) to obtain a single signal. The computational complexity and convergence of the algorithm are analyzed. Finally, the numerical results highlight the effectiveness of the proposed dual-function scheme in sidelobe signal-dependent clutter.

QoS-Aware Precoder Optimization for Radar Sensing and Multiuser Communications Under Per-Antenna Power Constraints

In this work, we concentrate on designing the precoder for the multiple-input multiple-output (MIMO) dual functional radar-communication (DFRC) system, where the dual-functional waveform is designed for performing multiuser downlink transmission and radar sensing simultaneously. Specifically, considering the signal-independent interference and signal-dependent clutter, we investigate the optimization of transmit precoding for maximizing the sensing signal-to-interference-plus-noise ratio (SINR) at the radar receiver under the constraint of the minimum SINR received at multiple communication users and per-antenna power budget. The formulated problem is challenging to solve due to the nonconovex objective function and nonconvex per-antenna power constraint. In particular, for the signal-independent interference case, we propose a distance-majorization induced algorithm to approximate the nonconvex problem as a sequence of convex problems whose optima can be obtained in closed form. Subsequently, our complexity analysis shows that our proposed algorithm has a much lower computational complexity than the widely-adopted semidefinite relaxation (SDR)-based algorithm. For the signal-dependent clutter case, we employ the fractional programming to transform the nonconvex problem into a sequence of subproblems, and then we propose a distance-majorization based algorithm to obtain the solution of each subproblem in closed form. Finally, simulation results confirm the performance superiority of our proposed algorithms when compared with the SDR-based approach. In conclusion, the novelty of this work is to propose an efficient algorithm for handling the typical problem in designing the DFRC precoder, which achieves better performance with a much lower complexity than the state-of-the-art algorithm.

Multi-Spectrally Constrained Low-PAPR Waveform Optimization for MIMO Radar Space-Time Adaptive Processing

This paper focuses on the joint design of transmit waveforms and receive filters for airborne multiple-input-multiple-output (MIMO) radar systems in spectrally crowded environments. The purpose is to maximize the output signal-to-interference-plus-noise-ratio (SINR) in the presence of signal-dependent clutter. To improve the practicability of the radar waveforms, both a multi-spectral constraint and a peak-to-average-power ratio (PAPR) constraint are imposed. A cyclic method is derived to iteratively optimize the transmit waveforms and receive filters. In particular, to tackle the encountered non-convex constrained fractional programming in designing the waveforms (for fixed filters), we resort to the Dinkelbach's transform, minorization-maximization (MM), and leverage the alternating direction method of multipliers (ADMM). We highlight that the proposed algorithm can iterate from an infeasible initial point and the waveforms at convergence not only satisfy the stringent constraints, but also attain superior performance.

Transmit–Receive Design for Airborne Radar With Nonuniform Pulse Repetition Intervals

This article aims to the joint design of transmit waveform and receive filter to enhance the clutter suppression capability for airborne radar with nonuniform pulse repetition interval (NUPRI). Specifically, a multipulse echo model with NUPRI incorporating a moving point-like target and signal-dependent clutter is first established. Then the 2-D range-Doppler plane is acquired by performing pulse compression and the windowed pulse Doppler processing on the echo. Further, the signal to interference plus noise ratio (SINR) of the interested area in the range-Doppler plane is formulated as a figure of merit to maximize along with constant modulus constraint on the waveform. To solve the resultant nonconvex problem, the sequential greedy optimization algorithm through alternately updating the transmit waveform and receive filter is proposed. Each iteration of the developed algorithm invokes coordinate descent framework and a Lagrangian-based algorithm to obtain the transmit waveform and receive filter, respectively. The analytical guarantee of the monotonic SINR improvement is proved. Finally, the performance of the proposed algorithm is assessed through numerical simulations showing its capability to suppress signal-dependent clutter.

Information-Theoretic Radar Waveform Design under the SINR Constraint.

This study investigates the information–theoretic waveform design problem to improve radar performance in the presence of signal-dependent clutter environments. The goal was to study the waveform energy allocation strategies and provide guidance for radar waveform design through the trade-off relationship between the information theory criterion and the signal-to-interference-plus-noise ratio (SINR) criterion. To this end, a model of the constraint relationship among the mutual information (MI), the Kullback–Leibler divergence (KLD), and the SINR is established in the frequency domain. The effects of the SINR value range on maximizing the MI and KLD under the energy constraint are derived. Under the constraints of energy and the SINR, the optimal radar waveform method based on maximizing the MI is proposed for radar estimation, with another method based on maximizing the KLD proposed for radar detection. The maximum MI value range is bounded by SINR and the maximum KLD value range is between 0 and the Jenson–Shannon divergence (J-divergence) value. Simulation results show that under the SINR constraint, the MI-based optimal signal waveform can make full use of the transmitted energy to target information extraction and put the signal energy in the frequency bin where the target spectrum is larger than the clutter spectrum. The KLD-based optimal signal waveform can therefore make full use of the transmitted energy to detect the target and put the signal energy in the frequency bin with the maximum target spectrum.

Code Design for Moving Target-Detecting Radar in Nonhomogeneous Signal-Dependent Clutter

In this paper, we investigate the code design problem of improving the detection performance of a moving target in the presence of nonhomogeneous signal-dependent clutter for moving target-detecting (MTD) radar systems. The optimization metric is constructed based on the signal to clutter and noise ratio (SCNR) of interpulse matched filtering. Under the frameworks of cyclic and majorization-minimization algorithms, we propose a novel algorithm, named CMMCODE, to tackle the code design optimization problem in the case of unknown precise target Doppler information and nonhomogeneous clutter. In the white-noise case, the simplified algorithm is also given based on CMMCODE algorithm. The presented algorithm is computationally efficient and convergent. Numerical examples show the effectiveness of the proposed algorithms.

Robust cognitive transmit waveform and receive filter design for airborne MIMO radar in signal-dependent clutter environment

This paper investigates the robust cognitive joint design of transmit waveform and receive filter to improve the system performance of airborne multiple-input multiple-output (MIMO) radar. Considering the target Doppler frequency and spatial cone angle uncertainties are present, we formulate the averaged signal-to-clutter-plus-noise ratio (SCNR) as the optimization goal. Specifically, the averaged SCNR is maximized under only constant modulus constraint and that under constant modulus and similarity constraints. Four iterative optimization algorithms are developed to deal with the joint design problem. The first kind of iterative optimization algorithm is based on semidefinite programming (SDP) relaxation and randomization or rank-one decomposition techniques. The second kind of computational efficient iterative optimization algorithm utilizes the fractional programming and power method-like iteration. The proposed algorithms can achieve a monotonic output SCNR enhancement and are robust against the inaccuracies of target parameters. Several simulations results are implemented to validate the superiority of the proposed algorithms considering the output SCNR, space-time beampattern and computational complexity.

Hidden Convexity in Robust Waveform and Receive Filter Bank Optimization Under Range Unambiguous Clutter

This letter deals with the robust joint design of radar transmit waveform and receive filter bank in a background of range unambiguous signal-dependent clutter. Assuming an unknown Doppler shift for the target, the worst-case Signal-to-Interference-plus-Noise-Ratio (SINR) at the output of the receive filter bank is considered as the figure of merit. The transceiver design is pursued considering a max-min optimization problem with some constraints on the transmit energy, similarity, and signal dynamic range. Hidden convexity is shown and a procedure to derive optimal waveform and filters is given. Simulation results highlight the effectiveness of the devised method.

MIMO Radar Transmit–Receive Design for Moving Target Detection in Signal-Dependent Clutter

This paper deals with the joint design of Multiple-Input Multiple-Output (MIMO) Space-Time Transmit Code (STTC) and Space-Time Receive Filter (STRF) to improve the detectability of a moving target embedded in signal-dependent clutter in the presence of uncertainties on the target azimuth angle and Doppler frequency. The Signal to Interference plus Noise Ratio (SINR) is considered as a figure of merit to maximize and multiple restrictions on STTC are forced at the design stage, i.e., similarity and modulus constraints as well as a uniform power requirement among the transmit antennas. To deal with the resulting non-convex design problem, a novel polynomial-time iterative procedure based on Successive Greedy Optimization (SGO) framework ensuring that SINR monotonically increases and converges to a finite value, is developed. Each iteration of the proposed algorithm involves the generalized eigenvalue decomposition to design STRF and a nested iterative technique involving Dinkelbach's procedure and an Alternating Direction Penalty Method (ADPM) to obtain STTC. Numerical results are provided to assess the performance of the proposed algorithm against some counterparts in terms of the optimized SINR value and computational complexity.

Adaptive OFDM Waveform Design for Cognitive Radar in Signal-Dependent Clutter

The problem of adaptive orthogonal frequency division multiplexing (OFDM) waveform design in the case of stochastic extended targets in the presence of strong and nonstationary interferences is an essential part of a cognitive radar system. In this article, a new approach is developed based on maximizing the mutual information between the random target impulse response and the received echoes with respect to the transmitted waveform. We use the advantage of OFDM signals and present an adaptive structure to match the complex weights of OFDM signal with the radar scene for making complete use of the transmission power. The interference reflections are utilized rather than eliminating them to design the weights of the transmitted OFDM signal. The optimization algorithm for designing transmitted signals is based on adaptive learning whose essential information is obtained by a feedback between receiver and transmitter. This feedback includes essential target and interference characteristics which extracted from the reflected echoes. Based on changes in interference features, the weights of the transmitted OFDM signal on each subcarrier are designed and transmitted in the next coherent processing interval. Experimental results reveal that the proposed approach achieves a higher rate of performance compared to nonadaptive waveform design approaches.

Interference cancellation in co‐located MIMO radars using waveform optimisation in signal dependent clutter

In this study, two iterative design algorithms for multiple-input multiple-output (MIMO) radars with co-located antennas with point targets are proposed. In these algorithms, by joint design of the receiver filter and transmit waveform using linear combination of orthogonal waveforms, the authors aim to maximise the signal-to-interference plus-noise ratio (SINR) in the presence of signal dependent interference. In the first proposed algorithm, in each iteration, transmit waveforms and receive filter are designed in closed form to decrease the computational complexity. In the second method, by adding constant envelope criteria, the final waveform would be a linear combination of orthogonal waveforms and because of using a constant envelope, combining coefficients have equal magnitudes and different phases. Therefore, it is more practical for hardware implementation in comparison to the first proposed method. Simulation results show that both proposed methods have better SINR performances compared with other methods proposed in MIMO radar literature. The outperformance of the second proposed method with respect to phased arrays shows that by only using phase shifted combination of orthogonal waveforms, better performance in comparison to phased array radars can be achieved.

Low probability of intercept‐based distributed MIMO radar waveform design against barrage jamming in signal‐dependent clutter and coloured noise

This study investigates the problem of low probability of intercept (LPI)-based distributed multiple-input multiple-output (MIMO) radar waveform design against barrage jamming in signal-dependent clutter and coloured noise. Given the priori knowledge of the extended target impulse response, signal-dependent clutter, barrage jamming signals and coloured noise, the LPI-based scheme for optimal radar waveform design is proposed to minimise the total power consumption of the MIMO radar system by optimising the transmitted waveforms of different transmitters with a predetermined mutual information (MI) constraint for target characterisation performance. Firstly, the MI between the received echoes from the target at each receiver and the target impulse response is derived as a practical metric to characterise the parameter estimation performance of a target. Then, the LPI-based distributed MIMO radar waveform design strategy is developed. The resulting radar waveform optimisation problem is convex and solved analytically, whose solutions represent the optimum power allocation for each transmitter in the MIMO radar system. With the aid of numerical simulations, it is illustrated that to minimise the total transmission power, the optimal waveform should match with the target, clutter, jamming and coloured noise. In addition, it is also demonstrated that the LPI performance of the MIMO radar system can be significantly improved by employing the proposed radar waveform design scheme.

Efficient Low-PAR Waveform Design Method for Extended Target Estimation Based on Information Theory in Cognitive Radar.

This paper addresses the waveform design problem of cognitive radar for extended target estimation in the presence of signal-dependent clutter, subject to a peak-to-average power ratio (PAR) constraint. Owing to this kind of constraint and the convolution operation of the waveform in the time domain, the formulated optimization problem for maximizing the mutual information (MI) between the target and the received signal is a complex non-convex problem. To this end, an efficient waveform design method based on minimization–maximization (MM) technique is proposed. First, by using the MM approach, the original non-convex problem is converted to a convex problem concerning the matrix variable. Then a trick is used for replacing the matrix variable with the vector variable by utilizing the properties of the Toeplitz matrix. Based on this, the optimization problem can be solved efficiently combined with the nearest neighbor method. Finally, an acceleration scheme is used to improve the convergence speed of the proposed method. The simulation results illustrate that the proposed method is superior to the existing methods in terms of estimation performance when designing the constrained waveform.

Efficient low‐PAR radar waveform design method based on the alternating direction method of multipliers for multiple missions

This study addresses the low-peak-to-average power ratio (PAR) radar waveform design problem to optimise the detection and estimation performance simultaneously in the presence of signal-dependent clutter. The aim is to realise an effective trade-off between maximising the output signal-to-interference-plus-noise ratio (SINR) and mutual information (MI) under a low-PAR constraint. In the existing method, this problem is solved via convex optimisation, but the high computational complexity of this method limits its application. Motivated by the decomposability and superior convergence of the alternating direction method of multipliers, the authors propose an efficient method to obtain the optimal waveform by converting the original non-convex problem into simpler convex sub-problems that can be solved efficiently. The simulation results illustrate that the optimal waveform can be obtained efficiently within the given low-PAR range and that the synthesised waveform can provide a reasonable trade-off between the detection and estimation performances. Compared with the existing method, the proposed method has reduced computational complexity without SINR and MI performance degradations.

Comments on “Waveform Design for Radar STAP in Signal Dependent Interference”

We read with great interest the recently published paper [1] (together with some additional technical details in [2]) dealing with an important topic for the radar signal processing Community.With regret, we noticed that the mentioned reference [1] provides some claims which do not agree with what we proved in paper [3]; contains some technical inconsistencies from the optimization theory point of view. Thus, respectfully, we feel obliged to provide the necessary clarifications and corrections. Specifically, this comments paper has the following technical purposes: a) to rectify some untrue claims by the Authors of [1] about reference [3]; b) to show that the optimization problem arising in [1] (eq. (17)) is a special instance of the more general optimization problem addressed in [3] (eq. (13)); c) to prove that the solution of the waveform design problem in [1] (eq. (25)) given by eq. (36) is not generally correct. [1] P. Setlur and M. Rangaswamy, Design for Radar STAP in Signal Dependent IEEE Transactions on Signal Processing, vol. 64, no. 1, pp. 19-34, Jan. 2016. [2] P. Setlur and M. Rangaswamy, Joint Filter and Waveform Design for Radar STAP in Signal Dependent Interference, Tech. Rep. DTIC, available at : https: // arxiv.org/abs/ 1510. 00055, US Air Force Res. Lab., Sensors Directorate, WPAFB, Dayton, OH, 2014. [3] A. Aubry, A. De Maio, A. Farina, and M. Wicks, Knowledge-Aided (Potentially Cognitive) Transmit Signal and Receive Filter Design in Signal-Dependent Clutter, IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 1, pp. 93-117, Jan. 2013.

Robust Transmitter–Receiver Design in the Presence of Signal-Dependent Clutter

This paper considers the robust transmit–receive design for the detection of a moving point-like target embedded in signal-dependent clutter. In particular, we focus on the phase-only waveforms, sharing either the continuous or the finite alphabet phases and present iterative sequential optimization (ISO) algorithms to sequentially improve the worst-case signal-to-interference-plus-noise ratio (SINR) over clutter statistics. At each iteration, ISO involves multiple fractional programming problems that can be efficiently solved by either Dinkelbach's procedure with closed-form solutions for the continuous phases or the one-dimensional searching method for the discrete phases case. The ISO algorithms enjoy a polynomial complexity in terms of computational burdens. The effectiveness of ISO is confirmed experimentally in terms of the achieved SINR and computational efficiency. Our results also highlight that the design is robust against possible inaccuracies in the prior knowledge of the signal-dependent clutter and even velocity deceptive jamming.

Robust Waveform Design for Multistatic Cognitive Radars

In this paper, we propose robust waveform techniques for multistatic cognitive radars in a signal-dependent clutter environment. In cognitive radar design, certain second order statistics such as the covariance matrix of the clutter, are assumed to be known. However, exact knowledge of the clutter parameters is difficult to obtain in practical scenarios. Hence, we consider the case of waveform design in the presence of uncertainty on the knowledge of the clutter environment and propose both worst-case and probabilistic robust waveform design techniques. Initially, we tested our multistatic, signal-dependent model against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered scenario. We therefore derived a new approach where we assume uncertainty directly on the radar cross-section and Doppler parameters of the clutters. Accordingly, we propose a clutter-specific stochastic optimization that, by using Taylor series approximations, is able to determine robust waveforms with specific signal to interference and noise ratio outage constraints.

Adaptive Detection of a Subspace Signal in Signal-Dependent Interference

This paper deals with the problem of adaptive detection of subspace signals embedded in thermal noise and clutter that depends on the transmitted signal. To this end, at the design stage, we assume that the signal-dependent (SD) clutter shares the same subspace as the target signals. As customary, a set of secondary data, free of signal components, is also assumed available. Two adaptive detectors, referred to as the SD Rao and SD Wald, are proposed by resorting to the Rao test and Wald test design criteria. Unlike the classical Rao and Wald tests, which are derived by dividing the complex parameter into the real and imaginary parts, the proposed detectors treat the complex parameter as a single quantity to reduce the computational burden. Moreover, we derive the theoretical false alarm probabilities and detection probabilities and show that both the two proposed detectors exhibit the constant false alarm rate property. Numerical results show that the proposed detectors achieve a detection performance improvement over the conventional multidimensional detectors.

Low probability of intercept-based adaptive radar waveform optimization in signal-dependent clutter for joint radar and cellular communication systems.

In this paper, we investigate the problem of low probability of intercept (LPI)-based adaptive radar waveform optimization in signal-dependent clutter for joint radar and cellular communication systems, where the radar system optimizes the transmitted waveform such that the interference caused to the cellular communication systems is strictly controlled. Assuming that the precise knowledge of the target spectra, the power spectral densities (PSDs) of signal-dependent clutters, the propagation losses of corresponding channels and the communication signals is known by the radar, three different LPI based criteria for radar waveform optimization are proposed to minimize the total transmitted power of the radar system by optimizing the multicarrier radar waveform with a predefined signal-to-interference-plus-noise ratio (SINR) constraint and a minimum required capacity for the cellular communication systems. These criteria differ in the way the communication signals scattered off the target are considered in the radar waveform design: (1) as useful energy, (2) as interference or (3) ignored altogether. The resulting problems are solved analytically and their solutions represent the optimum power allocation for each subcarrier in the multicarrier radar waveform. We show with numerical results that the LPI performance of the radar system can be significantly improved by exploiting the scattered echoes off the target due to cellular communication signals received at the radar receiver.

LFM-based waveform design for cognitive MIMO radar with constrained bandwidth

Abstract Waveform design is studied for a cognitive multiple-input multiple-output (MIMO) radar system faced with a combination of additive Gaussian noise and signal dependent clutter. The linear frequency modulation (LFM) signals are employed as transmitted waveforms. Based on the sensed statistics of the target and clutter-plus-noise, assuming the LFM waveforms transmitted at different transmitters can have different starting frequencies and bandwidths, these waveform parameters are designed to maximize the signal-to-clutter-plus-noise ratio at the receiver of the cognitive MIMO radar system. The constraints of the allowable range of operating frequency and total transmit energy are considered. We show that in the tested examples, the designed waveforms are nonorthogonal which leads to superior performance compared with that of the frequency spread LFM waveforms commonly used in the traditional MIMO radar systems.