The effect of tap spacing on the performance of a RAKE receiver is analyzed analytically in a frequency-selective fading channel. A continuous time multipath fading channel model is used for the analysis, and the expression of the correlation between the desired signals, interference signals, and noise signals at the output of each branch of the RAKE receiver is derived for various chip waveforms. Since the noise components of each branch signal are correlated to each other, an optimum combining rule based on the maximum-likelihood criterion is derived to gain utmost performance. It is shown that the performance of the system can be improved by setting the tap spacing of the RARE receiver below the chip duration when the bandwidth of the transmitted signal is larger than the inverse of the chip duration. Also, it is shown that the normalized capacity of the system can be increased by using a chip waveform occupying wider bandwidth, which takes advantage of the increased diversity gain merits of a wide-band code-division multiple-access system at the same chip rate. It is noted that the derived combining rule gives diversity gain against the fading process as well as noise whitening processing gain against multiple-access interference at the same time.

In this letter, a timing control algorithm is described, which realizes timing synchronization on the direct sequence code-division multiple-access reverse link. In addition, the uncoded bit-error probability is analytically derived. Numerical results, confirmed by simulation, show that our synchronous transmission technique can offer better performance than conventional asynchronous transmission, especially for an exponentially decaying multipath intensity profile with a large decay factor.

The authors comment that the probability density function (PDF) of the signal-to-noise ratio (SNR) for third-order selection combining (SC3) given by Eng, Kong and Milstein (see ibid., vol.44, p.1117-29, 1996) is incorrect. A correction is given by presenting a more efficient method of deriving the generalized PDF of the SNR essential in the analysis of Nth-order selection combining.