DS-CDMA with power control error using weighted despreading sequences over a multipath Rayleigh fading channel

Closed-form solutions for the average bit error rate (BER) performance of a direct-sequence code division multiple-access system with imperfect power control are derived for both coherent and noncoherent reception operating over a multipath Rayleigh fading channel. The RAKE structure receivers under consideration employ despreading sequences weighted by adjustable exponential chip waveforms optimized for multiple-access interference rejection. The chip-weighting waveforms employed are determined only by one parameter γ which leads to easy tuning of the waveforms in practice to achieve the best performance. The results indicate that the number of active users supported at a given BER for the case of γ tuned to maximize the average signal to interference plus noise ratio Hˆ is much larger than the case of γ=0 (fixed or rectangular despreading sequence). It is shown that imperfect power control affects the irreducible BER for the case of γ=0. On the other hand, the effect of imperfect power control on the BER performance for the case of γ tuned to maximize Hˆ is equivalent to a reduction in the average signal-to-noise ratio, and, hence, system performance can be compensated by increasing the transmitter power. It is further shown that the effect due to imperfect power control on BER performance is significant while that on the maximum value of Hˆ obtained by tuning γ is rather insignificant