Ergodic capacity and outage properties of CDMA in multiple-access fading channels


Markus Gärtner and Helmut Bölcskei


Proc. of International Symposium on Information Theory and its Applications (ISITA), Parma, Italy, pp. 722-727, Oct. 2004.

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The purpose of this paper is to conduct an analysis similar to the one by Rupf and Massey in [1] for frequency-selective fading multiple-access channels (MACs) with perfect channel state information (CSI) at the receiver and no CSI at the transmitters. For fixed spreading gain N and the number of users K going to infinity, we show that spreading does not incur a loss in ergodic sum capacity. The corresponding optimum spreading sequences are precisely those that achieve the Welch-bound-equality (WBE). For N>=KL, where L denotes the length of the channel impulse response, we find that shift-orthogonal sequence sets maximize the ergodic sum capacity of the fading CDMA channel. For N>K, we show that the ergodic sum capacity achieved by CDMA is strictly smaller than the ergodic sum capacity of the fading MAC. In the high-SNR regime, assuming N>=KL, shift-orthogonal sequence sets are shown to also yield full sum diversity gain. In the low-SNR regime, CDMA is capable of achieving the same sum outage performance as the fading MAC, independently of the spreading gain. However, neither WBE sequences nor shift-orthogonal sequences turn out to be optimal in this case.

[1] M. Rupf and J. L. Massey, "Optimum sequence multisets for synchronous code-division multiple-access channels", IEEE Trans. Inform. Theory, Vol. 40, No. 4, pp. 1261-1266, July 1994.


CDMA, multiple-access channel, ergodic capacity, outage probability

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