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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.

We propose a novel robust design method to jointly optimize the radar transmit code and receive filter, exploiting the signal-to-interference-plus-noise ratio (SINR) at the receiver end as design figure of merit. We confer robustness to our method against uncertainties on the target impulse response (TIR) using a worst-case optimization approach. Precisely, we model the uncertainty set as a finite collection of TIRs, obtained sampling the actual TIR at some aspect angles. We further enforce a peak-to-average power ratio (PAR) constraint to the transmit code, which is very important for radar applications, where the transmitter operates close to saturation. The design problem is tackled using a sequential optimization procedure alternating between two semi-definite programming (SDP) problems, followed by randomization steps. Our numerical results highlight the robustness and applicability of the proposed method.

We propose a novel robust design method to jointly optimize the radar transmit code and receive filter, exploiting the Signal-to-Interference plus Noise Ratio (SINR) at the receiver end as design figure of merit. We confer robustness to our method against uncertainties on the target impulse response (TIR) using a worst-case optimization approach based on two different uncertainty sets. The former is composed of a finite collection of TIRs, obtained by sampling the actual TIR at some aspect angles; the latter is a spherical uncertainty set. We further enforce a peak-to-average power ratio (PAR) constraint to the transmit code, which is very important for radar applications where the transmitter operates close to saturation. The design problem is tackled using a sequential optimization procedure alternating between two semi-definite programming (SDP) problems, followed by randomization steps. Our numerical results highlight the robustness and applicability of the proposed method in different scenarios.