A Method for Precise Bit-Error Probability Calculation of Asynchronous Multicode DS-CDMA Systems in Rayleigh Fading

A precise bit-error probability analysis method for multicode DS-CDMA systems in Rayleigh fading is derived. The proposed method applies to a multicode DS-CDMA system with an arbitrary number of multiple code sequences and any selection of multiple code sequences. The method gives accurate results for Rayleigh fading while requiring only a single numerical integration of an integrand involving the well-known Q-function. The solution discriminates the effect of the selection of different multiple code sequences on the bit-error probability, whereas Gaussian approximations do not. The numerical examples show that the differences between methods for a multicode DS-CDMA system operating over Rayleigh fading channels may be more significant than for a single code system in Rayleigh fading channels or a multicode system in AWGN channels when the spreading factor is not large compared to the number of multiple code sequences.