Sample size required in error-rate measurement on fading channels

Abstract

This paper presents analytical and numerical results on the sample size required to achieve a specified root mean square (RMS) error in estimating the error rate for flat fading channels having complex Gaussian statistics. The analysis shows that for the large sample sizes normally used in estimating error rates, k, the required sample size normalized to the required sample size for independent symbol fading, can be expressed in the form k=1+d/spl beta/ where d is the symbol rate normalized to the Doppler spread of the channel. For a given modem, /spl beta/ is a function of the error probability and the order of diversity. It is shown that if the Doppler spread measure used is proportional to the RMS Doppler spread, P will be relatively insensitive to the shape of the Doppler power spectrum. Numerical results are presented for Lth order diversity reception of binary phase shift keying (PSK), differential PSK, and frequency shift keying (FSK) signals and for five different Doppler power spectra. Ideal maximal ratio combining is assumed for the PSK modem, and square law combining is assumed for the DPSK and FSK modems.