A combinatorial model for the analysis of digital matched filter receivers for direct sequence signals

The validity range of the performance analysis methods of direct sequence spread spectrum (DS-SS) receivers, using digital correlators for baseband matched filtering, is exceeded if data decision is based on samples of both autocorrelation and crosscorrelation functions, which may be dictated by timing errors due to oscillator uncertainties and code Doppler. In the present work, a combinatorial model with general applicability to the calculation of the statistics at the digital matched filter output, considering the correlation properties of the spread spectrum codes used, is presented. The model provides exact results not only for the case of mainlobe processing but also for the processing of sidelobes of the correlation functions of pseudonoise waveforms. The model has been used to analyze a direct sequence spread spectrum receiver, employing a novel sampling-window technique in order to combat sampling errors. Theoretical bit error rate calculations are presented along with measurements on a hardware realization