Sub-Nyquist Sampling and Measurement of MPSK Signal Based on Parameter Matching

Abstract

Accurate measurement of the M-ary Phase Shift Keying (MPSK) signal determined by finite parameters per unit of time is significant in engineering fields such as digital microwave and satellite communication. In this paper, we propose a sub-Nyquist sampling system with two channels for measuring characteristic parameters of MPSK signals based on the Finite Rate of Innovation (FRI) sampling theory. The carrier frequency parameter measurement process is modeled as a convex optimization problem, solvable using the parameter matching method on the estimated grid. The minimum harmonic frequency of the carrier is determined to build the exact grid, and the carrier frequency is estimated through a greedy search based on the given cost function. Even when the truth value of the carrier frequency is unknown, the discontinuity location parameters can be measured with high precision using the spectral estimation method on the Fourier coefficients of the MPSK signal. We propose an upper bound on the estimation error of this separable measurement method for signals with one segment. The amplitude and phase parameters can be measured by solving a least square problem. Our proposed measurement system, with lower hardware complexity, can accurately measure the MPSK signal with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> segments by sampling only 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> +5 points in a period, at a much lower sampling rate than the carrier frequency. Numerical simulations and hardware experiments demonstrate the superior performance of our state-of-the-art measurement method.