Exact Error Rate Analysis for Pulsed DS- and Hybrid DS/TH-CDMA in Nakagami Fading

Abstract

Exact bit error probabilities (BEP) are derived in closed-form for binary pulsed direct sequence (DS-) and hybrid direct sequence time hopping code division multiple access (DS/TH-CDMA) systems that have potential applications in ultra-wideband (UWB) communications. Flat Nakagami fading channel is considered and the characteristic function (CF) method is adopted. An exact expression of the CF is obtained through a straightforward method, which is simple and good for any arbitrary pulse shape. The CF is then used to obtain the exact BEP that requires less computational complexity than the method based on improved Gaussian approximation (IGA). It is shown under identical operating conditions that the shape of the CF, as well as, the BEP differs considerably for the two systems. While both the systems perform comparably in heavily faded channel, the hybrid system shows better BEP performance in lightly-faded channel. The CF and BEP also strongly depend on chip length and chip-duty that constitute the processing gain (PG). Different combinations of the parameters may result into the same PG and the BEP of a particular system for a constant PG, though remains nearly constant in a highly faded channel, may vary substantially in lightly-faded channel. A comparison of the results from the exact method with those from the standard Gaussian approximation (SGA) reveals that the SGA, though accurate for both the systems in highly-faded channel, becomes extremely optimistic for low-duty systems in lightly-faded channel. The SGA also fails to track several other system trade-offs.