Simple MMSE equalizers for CDMA downlink to restore chip sequence: comparison to zero-forcing and RAKE

This work focuses on the forward link in a CDMA based multiuser communication system experiencing frequency dependent multipath fading. The mobile handset is assumed to have two antennas, either spatially separated or having diverse polarizations. Previous work on linear equalizers to restore orthogonality of the Walsh-Hadamard channel codes in this scenario led to a comparison of zero-forcing (ZF) equalizers and the RAKE receiver. A chip-rate MMSE equalizer is derived that minimizes the MSE between the synchronous “sum signal” of all the users from a given base station and the equalized chip sequence; this equalizer is followed by correlation with the desired user´s spreading code times the base-station´s long code. In this MMSE derivation, the sum of chip sequences of all the users is modeled as an i.i.d. random sequence. This leads to a “simple” MMSE equalizer that does not depend on the Walsh-Hadamard spreading codes, or the long code, currently employed at the base station. For further improvement, the “best” equalizer delay is chosen to minimize the MSE. Theoretically, the MMSE equalizer approaches the RAKE receiver at low SNR and the ZF equalizer at high SNR. Simulation results show that the ZF equalizer´s average performance is dominated by a very small percentage of “bad channels” with close to common zeroes, while the MMSE equalizer is resistant to this pathological noise gain problem. The end result is that the MMSE´s average BER performance is dramatically better than that of both ZF and RAKE (even though only moderately better than ZF for most well behaved channels)