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.

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This paper addresses the waveform design problem to estimate the target impulse response (TIR) of the temporally correlated extended target in a cognitive radar, subject to a detection constraint and a peak-to-average power ratio constraint. Owing to these types of constraints and the convolution operation of the waveform in the time domain, the formulated optimization problem for minimizing the mean square error of the estimated TIR based on Kalman filtering is a complex non-convex problem. To this end, an auxiliary variable is first introduced to modify the original problem, and the non-convex problem is converted to a convex problem with respect to 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. Moreover, the convex problem is further decomposed into three simple sub-problems which can be solved efficiently. Finally, the optimal waveform can be obtained efficiently through cognitive iteration combined with the nearest neighbor method. The simulation results illustrate that the proposed method is superior to the existing method in terms of the estimation performance and computational complexity when designing the constrained waveform. INDEX TERMSWaveform design, cognitive radar, extended target, estimation performance, peak-to-average power ratio, Kalman filtering.