Comparison of the sum capacities of the m-O, PN/O and PN signature sequence sets

We make a comparison of the sum capacities, under equal input-energy constraint, of three signature sequence sets, labeled ´m-O´, ´PN/O´ and ´PN´. We consider each set containing K sequences of N chips with K>N, giving rise to channel oversaturation. It is found that with increasing load K/N and increasing SNR, all sequence sets have a sum capacity that comes closer to the upper bound on sum capacity, corresponding to the Gaussian multiple access channel (GMAC). As compared to the GMAC, the m-O set suffers from a reduction in sum capacity of at most only 2.4%. For a high spreading factor N, the maximum loss in sum capacity amounts to 4.6% and 21.4% for PN/O and PN respectively.