An Exact Error Analysis for Hybrid DS/TH-CDMA in Nakagami Fading for UWB Communications

Exact bit error probabilities (BEP) are derived in closed-form for hybrid direct sequence time hopping code division multiple access (DS/TH-CDMA) systems that have been recently widely used for ultra-wideband (UWB) communications. Flat Nakagami fading channel is considered. The characteristic function (CF) method is adopted where an exact expression of the CF is obtained through a straight forward method. The method is simple and good for any arbitrary pulse shape. The results from exact analysis are then compared with those obtained from the standard Gaussian approximation (SGA), for which also a new expression is given for the error probability. It is shown that the shape of the CF depends considerably both on frames per bit and chips per frame and can be different even for the same processing gain (PG), since different combinations of the parameters may result into the same PG. In such a case, the BEP for a PG, however, though remains unchanged in a highly faded channel, may vary substantially in lightly faded channel. Irrespective of several system parameters, the SGA is found quite accurate for highly faded channel, which, however, becomes quite optimistic for low duty systems in lightly faded channels.