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The problem of designing optimal spreading sequences for the symbol synchronous fading CDMA channel is considered for arbitrary channel fading distributions. A numerical algorithm is developed to compute optimal spreading sequences when the channel distribution information is available. The optimal signature sequences for a flat fading CDMA channel are characterized completely using numerical optimization algorithms. From the numerical results it can be seen that the generalized Welch bound equality signals (GWBE) achieve the sum capacity without any loss of optimality for a broad class of flat fading channels. It is also shown that under low SNR conditions, the GWBE Signals are precisely the sequences that maximize the sum capacity in the flat fading Rayleigh multiple access channel.