Minimax robust transmission waveform and receiving filter design for extended target detection with imprecise prior knowledge

It is well known that optimal extended target detection for wideband radar in the presence of colored Gaussian noise and signal-dependent interference can be implemented, based on the prior information of target impulse response, by transmit-receiver design via maximizing the output signal-to-interference plus noise ratio (SINR). However, the prior knowledge of the target is usually imprecise. The target impulse response is very sensitive to target-radar orientation, and the initial phase of target echo is a function of target-radar distance, namely, the exact target impulse response cannot be obtained in transmission waveform design. Additionally, the transmission waveform is desired to be of constant modulus for power efficiency. In this paper, we propose a robust method to jointly design the transmission waveform with constant modulus constraint and the receiving filters. The cost function is established by maximizing the worst-case output SINR and an iterative procedure is presented based on modified sequential quadratic programming. Numerical results show that the proposed method can increase the worst-case output SINR significantly. ► We propose a robust method of transmission waveform and receiving filters design. ► We analyze the effect of imprecise prior knowledge on waveform design. ► Target echo matrix is robust to random initial phase of target impulse response. ► Target-radar orientation region splitting will decrease uncertainty degree of target. ► Worst-case output SINR is a suitable principle in robust waveform design.