On Optimum Asymptotic Multiuser Efficiency of Randomly Spread CDMA
Mohammad Ali Sedaghat, Ralf R. Müller, Farokh Marvasti · IEEE Transactions on Information Theory · 2015
We extend the result by Tse and Verdú on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access (CDMA) with binary phase shift keying input. Random Gaussian and random binary antipodal spreading are considered. We obtain the optimum asymptotic multiuser efficiency of a K-user system with spreading gain N when K and N → ∞ and the loading factor, (K/N), grows logarithmically with K under some conditions. It is shown that the optimum detector in a Gaussian randomly spread CDMA system has a performance close to the single user system at high signal-to-noise ratio when K and N → ∞ and the loading factor, (K/N), is kept less than (log3K/2). Random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained. Furthermore, we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency. We obtain a condition such that for any binary input, an N × K random matrix, whose entries are chosen randomly from a finite set, is a detecting matrix as K and N → ∞.