Multispectrally Compatible Transceiver Design for MIMO-STAP Radar and Communication Coexistence

Abstract

Designing multispectrally compatible transceiver with constant modulus (CM) constraints is essential for achieving radar and communications coexistence. The resulting problem, due to multispectral and CM constraints along with bivariate coupling, is nonconvex and nondeterministic polynomial (NP)-hard. Existing methods utilize either semidefinite relaxation (SDR) method of relaxing CM constraints, or alternating direction method of multipliers with matrix inversion, resulting in accuracy errors and high computational burden. We observe that multispectral constraints can be reformulated as continuous exact penalty functions, and bivariate transceivers under CM constraints can be projected onto product complex-circular-Euclidean manifold (P$\text{C}^{2}$EM) without relaxation. In light of these features, we propose an adaptive exact penalty product manifold (AE$\text{P}^{2}$M) method without relaxation and matrix inversion. First, we transform the multispectral constraints into penalty functions using the adaptive exact penalty technique. Then, we project the problem onto the P$\text{C}^{2}$EM to decouple bivariate and satisfy CM constraints. Finally, we employ a parallel simplified quasi-Newton method to design transceiver. Compared to current methods, the AE$\text{P}^{2}$M method bring benefits as: first, radar signal to interference plus noise ratio increased by 5.8 dB while energy distribution for communication reduced by $0.13$ dB; second computational burden reduced by approximately $89\%$.