The effects of spatial diversity and imperfect channel estimation on multi-carrier CDMA systems

We previously compared the theoretical bit error rates of multi-carrier direct sequence code division multiple access (MC-DS-CDMA) and multi-carrier code division multiple access (MC-CDMA) for a single-input single-output (SISO) system. We constrained both multi-carrier schemes to the same bandwidth, information rate, and energy-per-bit, which resulted in a possible trade-off between diversity gain and channel estimation errors between the two schemes. In this paper, we incorporate spatial diversity into the comparison by considering a multiple-input multiple-output (MIMO) system employing Alamouti space-time block coding at each sub-carrier frequency. Since we only examine those cases where MC-CDMA has higher frequency diversity than MC-DS-CDMA, and since increases in diversity yield diminishing gains, the additional diversity benefits MC-DS-CDMA more than MCCDMA. To determine whether these gains for MC-DSCDMA are enough to offset the difference in frequency diversity between the two schemes, we derive closed-form expressions for the bit error probabilities of both schemes, and we compare the MIMO results against those of the SISO system for different information rates, number of users, and number of pilot symbols per channel estimate.