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In this paper, we consider the joint optimization of transmit waveform and receive filter in colocated multiple-input multiple-output (MIMO) radar to enhance target detection performance in the presence of signal-dependent interference. It is noticed that in the detection stage, the output energy is mainly concentrated in the mainlobe region. Therefore, we decompose the receive filter as the cascade of a receive beamformer and a temporal filter. Then, under the peak-to-average ratio (PAR) constraint, a problem is formulated to realize a trade-off between the signal-to-interference-plus-noise ratio (SINR) and the integrated sidelobe level (ISL) at the pulse compression output of mainlobe synthesized signal. A non-decreasing algorithm, which is the combination of sequential optimization algorithm and minorization-maximization (MM) method, is developed to solve this problem. Besides, in order to reduce computation burden, a special case is proposed, where we fix the temporal filter as the mainlobe synthesized signal. Then, another non-decreasing algorithm based on the MM method is proposed to solve the special case. Numerical experiments show that the proposed algorithms can obtain high output SINR and low output ISL efficiently.

By simultaneously transmitting multiple different waveform signals, a multiple-input multiple-output (MIMO) radar possesses higher degrees of freedom and potential in many aspects compared to a traditional phased-array radar. The spatial–temporal characteristics of waveforms are the key to determining their performance. In this paper, a transmitting waveform design method based on spatial–temporal joint (STJ) optimization for a MIMO radar is proposed, where waveforms are designed not only for beam-pattern matching (BPM) but also for minimizing the autocorrelation sidelobes (ACSLs) of the spatial synthesis signals (SSSs) in the directions of interest. Firstly, the STJ model is established, where the two-step strategy and least squares method are utilized for BPM, and the L2p-Norm of the ACSL is constructed as the criterion for temporal characteristics optimization. Secondly, by transforming it into an unconstrained optimization problem about the waveform phase and using the gradient descent (GD) algorithm, the hard, non-convex, high-dimensional, nonlinear optimization problem is solved efficiently. Finally, the method's effectiveness is verified through numerical simulation. The results show that our method is suitable for both orthogonal and partial-correlation MIMO waveform designs and efficiently achieves better spatial–temporal characteristic performances simultaneously in comparison with existing methods. [ABSTRACT FROM AUTHOR]

The water-filling (WF) algorithm is a widely used design strategy in the radar waveform design field to maximize the signal-to-interference-plus-noise ratio (SINR). To address the problem of the poor resolution performance of the waveform caused by the inability to effectively control the bandwidth, a novel waveform-related optimization model is established in this paper. Specifically, a corrected SINR expression is first derived to construct the objective function in our optimization model. Then, equivalent bandwidth and energy constraints are imposed on the waveform to formulate the waveform-related non-convex optimization model. Next, the optimal frequency spectrum is obtained using the Karush–Kuhn–Tucker condition of our non-convex model. Finally, the transmit waveform in the time domain is synthesized under the constant modulus constraint. Different experiments based on simulated and real-measured data are constructed to demonstrate the superior performance of the designed waveform on the SINR and equivalent bandwidth compared to the linear frequency modulated signal and waveform designed by the WF algorithm. In addition, to further evaluate the effectiveness of the proposed algorithm in the application of cognitive radar (CR), a closed-loop radar system design strategy is introduced based on our waveform design method. The experiments under real-measured data confirm the advantages of CR compared to the traditional open-loop radar structure. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A new strategy to optimise the waveform of multiple‐input multiple‐output (MIMO) radar under the relative entropy constraint and signal‐to‐noise ratio (SNR) constraint is presented. The Kullback–Leibler divergence (KLD) is exploited between the two probability density functions of binary hypothesis testing as the design metric. A particular analysis of detection performance is made here to illuminate the balance between the false alarm and missing alarm probabilities. The results of the simulation demonstrate that the waveform design process constrained by relative entropy outperforms the process employing an explicit SNR constraint when the SNR is relatively low (i.e., within the interval [−2 dB, 0.5 dB]). The enhanced performance is attributable to the capability of the proposed optimisation process to focus the energy of the transmission waveform onto components where the eigenvalues of the target signal are large and the eigenvalues of the noise are small. [ABSTRACT FROM AUTHOR]

As the problem of spectral congestion is becoming severe, the coexistence between two primary spectrum users, radar and communications, has spurred extensive research interest. To reduce the mutual interferences between the two functions, MIMO radar waveform design needs to consider the compatibility in both spectral and spatial domains, where the former is achieved by null forming in the frequency domain and the latter is achieved by shaped beampattern synthesis. Additionally, high power efficiency and low system overhead are two desirable characteristics for MIMO radar system design. To this end, we first introduce a new realistic waveform constraint, peak-to-valley-power-ratio (PVPR) constraint per antenna to improve the power efficiency. Then, combined with PVPR constraint, we propose a switchable individual antenna power control scheme to jointly optimize waveforms and antenna locations. We adopt a max–min beampattern matching criterion and impose the ℓ 2 , 1 -norm penalty on the waveform matrix to promote the sparsity of the array. To solve the resultant non-smooth and non-convex problem, we develop a modified alternating directions method of multipliers, where a surrogate subproblem over primal variables is solved instead of the original problem, and its local convergence is analyzed. Finally, numerical experiments demonstrate the effectiveness and superiority of the proposed method over counterparts, especially obtaining the lowest sidelobe level and deeper spectral nulls using much fewer antennas. [ABSTRACT FROM AUTHOR]

The problem of data-driven joint design of transmitted waveform and detector in a radar system is addressed in this article. We propose two novel learning-based approaches to waveform and detector design based on end-to-end training of the radar system. The first approach consists of alternating supervised training of the detector for a fixed waveform and reinforcement learning of the transmitter for a fixed detector. In the second approach, the transmitter and the detector are trained simultaneously. Various operational waveform constraints, such as peak-to-average-power ratio and spectral compatibility, are incorporated into the design. Unlike traditional radar design methods that rely on rigid mathematical models, it is shown that radar learning can be robustified to uncertainties about environment by training the detector with synthetic data generated from multiple statistical models of the environment. Theoretical considerations and results show that the proposed methods are capable of adapting the transmitted waveform to environmental conditions while satisfying design constraints. [ABSTRACT FROM AUTHOR]

To improve the detection performance of the radar transmit waveform while enabling the transmitter to perform at its maximal efficiency, a joint design method is proposed for the transmit and receive filter in the presence of signal-dependent clutter with a Peak-to-Average-power Ratio (PAR) constraint of the transmit waveform. First, an optimized model of the radar’s output Signal-to-Interference-plus-Noise Ratio (SINR) for range-extended target detection is established. Second, the analytic expression of the receiver is obtained by converting the optimization problem into the Rayleigh quotient model. The optimal matrix solution is then obtained by transforming the non-convex problem into a convex problem via the semi-definite matrix of the waveform. Finally, the optimal vector solution of the waveform is extracted from the optimal matrix solution by combining the rank-one approximation method combined with the nearest neighbor method. An optimal waveform with a maximal output SINR for a given PAR range is obtained using the proposed method. The SINR value of the waveform when PAR = 2 is the same as the SINR value of the optimized waveform under the energy constraint and is about 0.5 dB higher than the waveform when PAR = 1. Simulation results demonstrate the effectiveness of the proposed method.

We address the problem of designing a transmit beampattern for multiple-input multiple-output (MIMO) radar considering coexistence with wireless communication systems. The designed beampattern is able to manage the transmit energy in spatial directions as well as in spectral frequency bands of interest by minimizing the deviation of the designed beampattern versus a desired one under a spectral constraint as well as the constant modulus constraint. While unconstrained beampattern design is straightforward, a key open challenge is jointly enforcing the spectral constraint in addition to the constant modulus constraint on the radar waveform. A new approach is proposed in this paper, which involves solving a sequence of constrained quadratic programs such that constant modulus is achieved at convergence. Furthermore, we show that each problem in the sequence has a closed form solution leading to analytical tractability. We evaluate the proposed beampattern with interference control (BIC) algorithm against the state-of-the-art MIMO beampattern design techniques and show that BIC achieves closeness to an idealized beampattern along with desired spectral shaping. [ABSTRACT FROM AUTHOR]

Waveform design is essential to unleash the performance advantages promised by multiple-input multiple-output (MIMO) radar, and this topic has attracted a lot of attention in the recent years. Revisiting an earlier examined MIMO radar waveform design problem that optimizes both minimum mean-square error estimation (MMSE) and mutual information (MI), in this correspondence we formulate a new waveform design problem and provide some further results, which complement the previous study. More specifically, we present an iterative optimization algorithm based on the alternating projection method to determine waveform solutions that can simultaneously satisfy a structure constraint and optimize the design criteria. Numerical examples are provided, which illustrate the effectiveness of the proposed approach. In particular, we find that the waveform solutions obtained through our proposed algorithm can achieve very close and virtually indistinguishable performance from that predicted in the previous study. [ABSTRACT FROM AUTHOR]