Performance analysis of a linear MMSE receiver for bandlimited random-CDMA using quadriphase spreading over multipath channels

This paper analyzes the bit-error-rate (P_e) performance of a linear minimum mean-square error (LMMSE) receiver for bandlimited direct-sequence code-division multiple-access systems which use quadriphase spreading with aperiodic pseudonoise (PN) sequences. The analysis is based on the improved Gaussian approximation (IGA) with focus on chip pulse shaping. It shows that the IGA reduces to the standard Gaussian approximation (SGA) if 1) random quadriphase spreading is employed, 2) the spreading factor takes moderate to large values, and 3) the chip pulse excess bandwidth (BW) is zero. Hence, the SGA, known for its inaccuracy in low regions of P_e, remains an accurate approximation even when the number of active users in the system is small as long as the aforementioned conditions are met. The analysis holds for either matched or different transmit and receive filters. Consequently, closed form conditional P_e expressions are derived for the coherent selective RAKE and the LMMSE receivers and verified with Monte Carlo simulations. Numerical results are presented to illustrate the performance improvement achieved by the LMMSE receiver which, in contrast to the coherent selective RAKE receiver, not only suppresses interference when the excess BW of chip pulse is nonzero, but also harnesses the energy of all paths of the desired user. Under the examined scenarios tailored toward current narrowband system settings, the LMMSE receiver achieves 60% gain in capacity over the selective RAKE receiver. A third of the gain is due to interference suppression capability of the receiver while the rest is credited to its ability to collect the energy of the desired user diversified to many paths. Future wideband systems will yield an ever larger gain.