Asymptotic bounds on the Optimum Multiuser Efficiency of randomly spread CDMA

We derive some bounds on the Optimum Asymptotic Multiuser Efficiency (OAME) of randomly spread CDMA as extensions of the result by Tse and Verdú. To this end, random Gaussian and random binary antipodal spreading are considered. Furthermore, the input signal is assumed to be Binary Phase Shift Keying (BPSK). It is shown that in a CDMA system with K-user and N chips when K and N → 8 and the loading factor, K over N, grows logarithmically with K, the OAME converges to 1 almost surely under some condition. It is also shown that a Gaussian randomly spread CDMA system has a performance close to the single user system at high Signal to Noise Ratio (SNR) when the loading factor is kept less than log₃ K over 2. Moreover, for random binary antipodal matrices, we show that the loading factor cannot grow faster than equation.