New bounds for the sum capacity of binary and nonbinary synchronous CDMA systems

Lower and upper bounds are derived for the sum capacity of synchronous CDMA where the signature matrix and input alphabets are binary or (2p + 1)-ary, in two cases of noiseless and noisy channels. The bounds are very tight in some regions. Interestingly, simulations show that the formulas for noisy systems tend to the ones for noiseless system as noise tends to 0 while it cannot be deduced easily from the formulas. The results give good insights about the extent of the number of users in which errorless communication is possible for a system with a given chip rate.