This paper deals with the NP-hard quadratic optimization problem under similarity and constant modulus constraints. A computationally efficient iterative algorithm based on the Alternating Direction Penalty Method (ADPM) framework is proposed for continuous and discrete phase cases. In each iteration, it converts the considered problem into two subproblems with closed-form solutions via an introduced auxiliary variable, while locally increasing the penalty factor involved in the ADPM framework. The proposed algorithm is proven to converge for any initialization under some mild conditions and avoids the non-convergence problem of the Alternating Direction Method of Multipliers (ADMM) when handling the NP-hard problems. It ensures that the obtained solution fulfills the Karush-Kuhn-Tucker (KKT) conditions for the continuous phase case. To further refine the ADPM solution, a joint approach involving both the ADPM and the coordinate descent frameworks is introduced. The extension that solves the quadratic optimization problem incorporating more complicated constraints is also developed. Finally, two radar waveform design examples are presented to demonstrate that the proposed algorithms can outperform their counterparts by providing better objective values with relatively low polynomial computational complexities.

Quadratic Optimization for Unimodular Sequence Design via an ADPM Framework

To ensure the proper functioning of active sensing systems in the presence of interferences from other electromagnetic equipment in a spectrally crowded environment, we devise four new solutions for spectrally compatible waveform design based on the min-max metric, namely, minimum modulus dynamic range, min-max spectral shape, minimum weighted peak sidelobe level, and minimum similarity. To address the resultant nonconvex and nonsmooth optimization problems, a unified algorithm framework is proposed. That is, we first approximate the min-max metric by using the “log-exponential smoothing” technique, then apply majorization-minimization to smooth and simplify the approximate optimization formulations, and finally use the Karush-Kuhn-Tucker theory to tackle the majorized problems. Besides, we develop an adaptive approximation parameter selection scheme, which monotonically decreases the approximation error at each iteration. The proposed algorithms are computationally efficient as they can be realized via fast Fourier transform. Finally, numerical examples are presented to demonstrate their excellent performance.

Min-Max Metric for Spectrally Compatible Waveform Design Via Log-Exponential Smoothing

This paper considers the phase-only sequence design problem for a cognitive radar in order to achieve both the desired autocorrelation and the stopband properties, which is useful to obtain good range compression as well as the spectral compatibility. We develop a new objective function accounting for the weighted integrated sidelobe level and the spectral power within specific stopbands. An iteration algorithm based on pattern search (PS) is proposed to minimize the nonconvex multidimensional objective function with the continuous phase case, which is split into multiple one-dimensional problems that are simplified and solved with closed-form solutions. In particular, the PS algorithm can be applied to the discrete phase case. Finally, we evaluate the effectiveness of the PS algorithm compared with the weighted-stopband cyclic algorithm new algorithm via numerical simulations in terms of the autocorrelation function, the spectral power function, and the convergence speed.

Cognitive Phase-Only Sequence Design With Desired Correlation and Stopband Properties

In this paper, under the peak-to-average power ratio (PAR) and energy constraints on the transmit waveforms, a new efficient weighted $\ell _p$ -norm metric (with $p\geq 2$ ) is introduced for colocated wideband/narrowband multiple-input multiple-output radar transmit beampattern matching design. The proposed metric can achieve quasi-equiripple beampattern, which is desirable to improve the robustness of radar systems with imprecise direction information of targets and reduce radar clutter. In addition, mainlobe ripple control, peak sidelobe suppression, and deep null/notch formation can be obtained. On the other hand, the PAR and energy constraints cause the radar waveform losing the degree of freedom to match arbitrary pattern shape, and the desired pattern usually lies in matching an appropriately scaled version of the shape. Thus, a scaling factor is introduced into the proposed metric to tackle the scaling ambiguity problem. The resultant optimization problems are difficult to solve due to the higher order polynomial objective function with coupled scaling factor and waveform matrix, and also the nonconvex PAR constraint. To develop a fast and efficient algorithm, by utilizing the majorization–minimization technique, we decouple the scaling factor and radar waveform matrix variables by a majorization step, derive a new quadratic majorizer to tackle the quadratic function with the matrix variable, and surrogate the nonsmooth nonconvex functions by convex functions. Numerical examples show that the devised approach can synthesize beampattern with lower peak sidelobe level and more flat mainlobe compared to the existing algorithms.

MIMO Radar Waveform Design for Quasi-Equiripple Transmit Beampattern Synthesis via Weighted $l_p$ -Minimization

This paper deals with the problem of local ambiguity function shaping in the presence of narrow-band spectral interferences (e.g., the communication signal and jamming), which has significant applications in the radar detection field. An objective function involving the weighted integrated sidelobe level and the spectral stopband energy is developed as a figure of merit to minimize. Besides, the energy and the peak-to-average ratio restrictions are forced on the probing waveform. To handle the resulting non-convex quartic optimization problem, an iterative sequential quartic optimization algorithm sharing polynomial time complexity is proposed. In each iteration, it decomposes the original problem into two alternately tractable quadratic subproblems both of which can be converted to linear optimization problems with closed-form solutions. Finally, the numerical simulations are provided to assess the effectiveness of the proposed algorithm. The results show that the proposed algorithm outperforms some available counterparts in the aspect of the convergence speed and the capability to prohibit the narrow-band spectral interferences and the sidelobes of a strong return from masking weak targets.

Cognitive Local Ambiguity Function Shaping With Spectral Coexistence

This paper considers an effective electronic counter-countermeasures (ECCM) technique against velocity deception jamming in multi-target scenario for radar system. The essence of the technique is outlined based on the variations of initial phases of the transmitted pulses in pulse repetition interval (PRI) domain. With the optimized waveform, the false targets generate notches around the true targets in frequency domain. We formulate the multi-target, multi-jamming signal model and derive the cost function for the optimizing waveform design. In addition, we propose a modified Newton method to solve the optimizing problem. Simulations are presented to demonstrate the effectiveness of the proposed method in solving the ECCM optimizing problem for multi-target scenarios.

Optimized phase-coded waveform design against velocity deception

This paper considers an effective signaling scheme to combat the range repeat jammer for radar system. Robustness against jammer is achieved by designing different phase-coded pulses with weighted auto- and cross- correlation in a coherent processing interval (CPI). In this way, the matched filter output forms notches around the true target so that the true target can be indicated clearly. In the same time the jammer is suppressed for the good cross-correlation property between pulses. To obtain the desired waveforms, we formulate the penalty function and propose the pattern search (PS) method to optimize it. Finally, we present simulations to demonstrate the effectiveness of the proposed method.

Optimized phase-coded waveforms design against range repeat jamming

We consider the suppression problem of rangevelocity deception jamming based on adaptive iterative filtering algorithm for pulse Doppler (PD) radar. First, we present the real target signal and false target signal model based on digital radio frequency memory (DRFM). Then, we suppress rangevelocity jamming by adaptive iterative filtering algorithm in range dimension processing and Doppler dimension processing for target signal and jamming respectively. At the stage of analysis, we consider multiple real targets and false targets in range-Doppler plane, and evaluate the suppression performance of the proposed algorithm by simulation. The results highlight that the proposed algorithm will converge fast and yield an excellent suppression performance.

Range-velocity jamming suppression algorithm based on adaptive iterative filtering

The adaptive multi-pulse compression (AMPC) has been shown to successfully suppress the range-doppler sidelobes at the cost of heavy computation load. The fast adaptive multi-pulse compression (FAMPC) algorithm reduces the computation complexity of the AMPC via dimensionality reduction while it suffers noticeable performance degradation. This paper proposes a modified adaptive multi-pulse compression (MAMPC) algorithm that uses a two-stage processing scheme and implements with the gain-constraint-APC (GCAPC). The proposed method has almost identical estimation performance to the AMPC while maintains the same order of computation load as that of the FAMPC.

Ya Yang

Papers

Cognitive Phase-Only Sequence Design With Desired Correlation and Stopband Properties

Optimized phase-coded waveform design against velocity deception

Optimized phase-coded waveforms design against range repeat jamming

Range-velocity jamming suppression algorithm based on adaptive iterative filtering

A modified adaptive multi-pulse compression algorithm for fast implementation