Abstract
In this work, the issue of robust waveform optimization is addressed in the presence of clutter to improve the worst-case estimation accuracy for collocated multiple-input multiple- output (MIMO) radar. Robust design is necessary due to the fact that waveform design may be sensitive to uncertainties in the initial parameter estimates. Following the min-max approach, the robust waveform covariance matrix design is formulated here on the basis of Cramer-Rao Bound to ease this sensitivity systematically for improving the worst-case accuracy. To tackle the resultant complicated and nonlinear problem, a new diagonal loading (DL)-based iterative approach is developed, in which the inner optimization problem can first be decomposed to some independent subproblems by using the Hadamard's inequality, and then these subproblems can be reformulated into convex issues by using DL method, as well as the outer optimization problem can also be relaxed to a convex issue by translating the nonlinear function into a linear one, and, hence, both of them can be solved very effectively. An optimal solution to the original problem can be obtained via the least-squares fitting of the solution acquired by the iterative approach. Numerical simulations show the efficiency of the proposed method. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or repro- duction of this work in whole or in part requires full attribution of the original publication, including its DOI. (DOI: 10.1117/1.JRS.10.035005)
Highlights
Several numerical simulations are given to demonstrate the benefits of the proposed method, compared to the nonrobust method proposed in Ref. 22, the robust minimum mean-squared error (MMSE)-based method developed in Ref. 21, and uncorrelated waveforms, which can be illustrated from the following perspectives: the improvement of the worst-case parameter estimation performance, the robustness of the three methods, and the effect of the bound of uncertainties of h~ k and h_ ̃ k on the worst-case Cramér–Rao Bound (CRB)
The worst-case CRBs obtained by the proposed method, the robust MMSE-based algorithm proposed in Ref. 21, and that of uncorrelated waveforms against array signal-to-noise ratio (ASNR) are compared in Fig. 2 to verify the improvement of the worst-case parameter estimation performance with the CRB acquired by the nonrobust method with perfect knowledge of hand h_ ̃ as a benchmark
The worst-case CRB The worst-case CRB regardless of ASNR. The reason for these can be illustrated as following: the optimized waveforms generated by the proposed method that aims at lowering the worst-case CRB focus the transmitted energy on the uncertainty set of the initial parameter estimates while uncorrelated waveforms emit omnidirectionally; the robust MMSE-based algorithm is to reduce the worstcase MMSE rather than CRB by designing the transmitted waveforms, yet the variance obtained by the MMSE estimator is lower than CRB considerably.[37]
Summary
Inspired by the achievement in multiple-input multiple-output (MIMO) communication,[1] the MIMO concept was introduced into the radar field, which has rapidly drawn more and more attention.[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] Compared with phased array, MIMO radar has the capability of transmitting arbitrary waveforms, which is regarded as waveform diversity.[2]. In Ref. 12, the transmitted waveforms are designed to acquire the improvement in the detection probability for MIMO space–time adaptive processing (STAP) with perfect target and clutter prior knowledge These parameters must be estimated with error in application. 8 and 9), and this problem was tackled in Ref. 28 based on the assumption proposed in Ref. 22 that is reasonable only under some certain conditions (see Ref. 22 for more details) Focusing on these issues, partially on the basis of our previous works,[28] following the min–max approach, the problem of robust WCM optimization in the context of clutter is considered in this paper aiming to systematically ease the sensitivity of parameter estimation performance to the uncertainty in the initial parameter estimates by including the parameter estimation error model into the design issue, which is based on minimizing the trace of the worst-case CRB matrix.
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