Asymptotical analysis of the optimal spreading sequence allocation in flat fading channels

Using a result from extreme value theory, we characterize the sum capacity of optimally allocated sequences in flat fading channels in a large system model, i.e., when both the number of users and the processing gain increase without bounds while their ratio remains fixed. Thus we are able to evaluate explicitly possible gains of using optimal sequences compared to random sequences. Since optimization of sequences requires perfect knowledge of channel state information at the transmitter, there is usually no need to constrain the problem of finding optimal sequences while not simultaneously allowing power control, as was done by P. Viswanath and V. Anantharam (see IEEE Trans. on Inform. Theory, vol.45, p.1984-92, 1999). Therefore, we address the problem of joint power control law/signature optimization, and show that it can be solved as a determinant optimization problem (see Witshenusen, H.S., SIAM J. Appl. Math,. p.515-22, 1975). The sum capacity of optimal signature sequences with power control is derived for the general case and then extended for the asymptotic large system model.