Bit error probability approximation for short-time Fourier transform based nonstationary interference excision in DS-SS systems

Abstract

The problem addressed in this paper is bit error probability (BEP) approximation in direct sequence spread-spectrum (DS-SS) systems that implement the short-time Fourier transform (STFT) as a means of nonstationary jammer excision. The jammer, previously concentrated in the time–frequency ( t– f) plane, it is suppressed by removing its t– f signature via a binary mask. The applied binary mask gives rise to odd higher-order central moments of the decision variable d, i.e., introduces a deviation in the probability density function of d, f d ( x ) , from a Gaussian law. Two analytical approximations to f d ( x ) are proposed, Gaussian approximation (GA) and Hermite–Gaussian approximation (HGA). The HGA takes advantage of the Hermite polynomials and central moments of d thus reducing the approximation error introduced by the GA. Analytical expressions for the mean, variance and third central moment of d, when the STFT of the received signal is modified by an arbitrary two-dimensional function, are derived and numerically confirmed. The HGA outperforms the GA for various types of monocomponent and multicomponent jammers, which was verified by simulations.