Quartic Optimization for Ambiguity Function Shaping via RTR Algorithm under ADPM Framework

Abstract

The construction of an efficient framework to syn-thesize the required ambiguity functions (AF) is essential for cognitive radar (CR) to improve its ability to adapt to its environment. It is equivalent to minimizing the expectation of the slow-time ambiguity function (STAF) over the range-Doppler bins. This is to optimize a non-convex quartic function with the constant modulus constraint (CMC). In this paper, we developed the Riemannian trust region (RTR) algorithm under the alternating direction penalty method (ADPM) framework to deal with this problem. Utilizing the ADPM framework, we split the original problem into two sub-problems for iteration. In the first sub-problem, we derived the closed-form solution directly, then proposed the RTR algorithm in the second sub-problem. Simulation results show that our proposed algorithm outperforms other state-of-the-art algorithms with a higher signal-to-interference ratio (SIR) value.