Joint Design of Transmit Waveform and Receive Filter for Cross Ambiguity Function Synthesis

The cross-ambiguity function (CAF) is a crucial performance evaluation metric for transmit waveform. To improve the interference suppression performance in the wireless sensing field, we address the problem of synthesizing radar CAF by jointly designing the transmit waveform and receive filter in this letter. We first establish the joint design problem as a non-convex fractional problem by maximizing the signal-to-interference plus noise ratio (SINR) under practical constraints. To overcome the challenges posed by the peak-to-average ratio (PAR) constraint, we then propose an novel iterative optimization algorithm based on the Majorization-Minimization (MM) framework. This algorithm synthesizes the transmit waveform and receive filter alternately and efficiently. Finally, we conduct numerical simulations with different parameters to demonstrate the effectiveness of our proposed CAF synthesizing algorithm.