Marvin K. Simon

Optimum spreading bandwidth for selective RAKE reception over Rayleigh fading channels

Building on the developments in the performance analysis of generalized selection combining (GSC), this paper examines the optimum spreading bandwidth for a fixed-complexity GSC diversity receiver operating over independent identically distributed Rayleigh paths. For this purpose, the study considers three performance criteria: (1) average combined signal-to-noise ratio (SNR) at the GSC output; (2) average bit error probability (BEP); and (3) outage probability of the instantaneous combined SNR at the GSC output. For the average BEP criterion, results are presented for both coherent and noncoherent combining. For the average combined SNR and some instances of the average BEP optimization problem, an accurate approximate estimate of this optimum bandwidth in the form of a solution of a transcendental equation is provided. In other cases, where the optimization is not easily tractable in an analytic fashion, a numeric-search procedure is used to find this optimum bandwidth for different performance criteria and system parameters of interest. Finally, simplified rule-of-thumb-type formulas are also presented as a good reference for picking the optimum spreading bandwidth given a set of system parameters and a particular performance criterion of interest.

An MGF-based numerical technique for the outage probability evaluation of diversity systems

Relying on a simple algorithm for the Laplace transform inversion of cumulative distribution functions, we develop a moment generating function-based numerical technique for the outage probability evaluation of maximal-ratio and equal-gain combining over generalized fading channels.

Error rate analysis of M-PSK with equal gain combining over Nakagami fading channels

We present a new analytical approach to determine the exact average symbol error rate (SER) of M-ary phase-shift-keying signals with coherent equal gain combining (EGC) reception. The analysis assumes independent Nakagami-m fading paths which are not necessarily identically distributed. The proposed approach takes advantage of an alternate integral representation of the conditional SER along with Gauss-Hermite quadrature integration, to derive the final average SER expression in the form of a single finite-range integral and an integrand composed of tabulated functions. We also present a simpler but approximate approach for the closed-form evaluation of the SER of these signals over independent identically distributed Nakagami-m fading paths.

Performance of SingleChannel Receivers

As alluded to in Chapters 4, 5, and 6, the alternative representations of the Gaussian and Marcum Q -functions and other related functions expressed in the so-called desired form are the key mathematical tools to unifying the evaluation of the average error probability performance of digital communication systems over the generalized fading channel. Before discussing the specific details of these performance evaluations later in this chapter and the ones that follow, we first present the appropriate expressions for evaluating the performance of these systems over the AWGN.