Optimum spreading bandwidth for selective RAKE reception over Rayleigh fading channels

Building on the recent developments in the performance analysis of generali zed selection combining (GSC), this paper examines the optimum spreading ba ndwidth for a fixed-complexity GSC diversity receiver operating over indepe ndent identically distributed Rayleigh paths. For this purpose, the study c onsiders three performance criteria: 1) average combined signal-to-noise ra tio (SNR) at the GSC output; 2) average bit error probability (BEP); and 3) outage probability of the instantaneous combined SNR at the GSC output. Fo r the average BEP criterion, results are presented for both coherent and no ncoherent 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 transendental equation is provided. In other cases, where the optimization is not easily tractable i n an analytic fashion, a numeric-search procedure is used to find this opti mum bandwidth for different performance criteria and system parameters of i nterest, Finally, simplified rule-of-thumb-type formulas are also presented as a good reference for picking the optimum spreading bandwidth given a se t of system parameters and a particular performance criterion of interest.