Strict parity symmetric prolate spheroidal wave functions signal construction and low complexity detection method

Abstract

Aiming at solving the problem of high signal processing and detection complexity of prolate spheroidal wave functions (PSWFs), we propose a time domain strict parity symmetry PSWFs signal construction method, based on the characteristics of PSWFs with the same parity symmetry after linear operation. According to the characteristics that the PSWFs of the same parity symmetry have the same orthogonality in the half-symbol period and the whole symbol period, we propose a PSWFs signal detection method based on the parity characteristics, which groups processing of odd symmetric and even symmetric signals and detects PSWFs signal in the half-symbol period signal to reduce the number of signal solutions for participating in the operation. Compared with the coherent detection method, theoretical and numerical analyses show that the proposed signal detection method can reduce the computational complexity from $O(NQ)$ to $O(NQ/2)$ (i.e., about 50%) without reducing the system error performance.