The Influence of Adaptive Multicoding on Mutual Information and Channel Capacity for Uncertain Wideband CDMA Rayleigh Fading Channels

--We consider the problem of adaptive modulation for wideband DS-CDMA Rayleigh fading channels with imperfect channel state information (CSI). We assume a multidimensional signal subspace spanned by a collection of random spreading codes (multicoding) and study the effects of both the subspace dimension and the probability distribution of the transmitted symbols on the mutual information between the channel input and output in the presence of uncertainty regarding the true state of the channel. We develop approximations for the mutual information as well as both upper and lower bounds on the mutual information that are stated explicitly in terms of the dimension of the signal constellation, the number of resolvable fading paths on the channel, the current estimate of channel state, and the mean-squared-error of the channel estimate. We analyze these approximations and bounds in order to quantify the impact of signal dimension and symbol distribution on system performance. The results indicate that, as with space-time channels, higher signaling dimensions are always better, but the extent of the performance 1 This research was supported in part by NSF Grant Numbers CCR-9984462 and CCR-0196152. Resubmitted to IEEE Transactions on Information Theory, October 2003. 2 improvement depends on the relationship between the number of resolvable paths on the channel, the SNR, and the accuracy of the CSI estimates. Similarly, we show that the effect of the input symbol distribution on mutual information depends critically on the relationship between the SNR and the accuracy of the CSI estimates, and that adapting the distribution of the transmitted symbols in response to instantaneous changes in the channel state has the greatest impact when the CSI estimates are only partially accurate. Finally, we show that in the absence of any channel state information, the mutual information of the system for any constellation with a finite fourth moment decreases to zero at the same rate as the fourth moment of the fading process itself as the number of resolvable paths on the channel goes to infinity. Conversely, we show that if the distribution of the constellation is adapted in a particular manner so that both the dimension and the fourth moment of the constellation increase as the number of resolvable paths increases, the mutual information, and therefore channel capacity, can be made arbitrarily close to the capacity for a singleuser AWGN channel with the same SNR.