Performance of RAKE reception in dense multipath channels: implications of spreading bandwidth and selection diversity order

We develop an analytical framework to quantify the effects of the spreading bandwidth (BW) on spread spectrum systems operating in dense multipath environments in terms of the receiver performance, the receiver complexity, and the multipath channel parameters. The focus of the paper is to characterize the symbol error probability (SEP) performance of a RAKE receiver tracking the L strongest multipath components in wide-sense stationary uncorrelated scattering (WSSUS) Gaussian channels with frequency-selective fading. Analytical SEP expressions of the RAKE receiver are derived in terms of the number of combined paths, the spreading BW and the multipath spread of the channel. The proposed problem is made analytically tractable by transforming the physical RAKE paths, which are correlated and ordered, into the domain of a "virtual RAKE" receiver with independent virtual paths. This results in a simple derivation of the SEP for a given spreading BW and an arbitrary number of combined paths.