Acquisition based capacity of a synchronous direct sequence spread spectrum multiple access technique

In deriving the capacity of a direct sequence spread spectrum (DS/SS) multiple access system using the bit error rate (BER), it is assumed that the receiver has already achieved chip synchronisation with the spreading sequence used. In the absence of any other timing information the acquisition based capacity is also very important. It has been found that asymptotically, that is as the length N of the matched filter used to achieve the synchronization tends to infinity and pfa, the probability of acquisition failure tends to zero, the acquisition based capacity is upper bounded by N/2ln N, denoted as J_asymp. However, this bound J_asymp is not tight for finite N. In fact for a specified pfa, and N, the actual maximum number of users can be orders of magnitude lower than the predicted J _asymp. Thus, from a practical point of view the asymptotic bound is not very useful for a given problem at hand. We formulate the acquisition based capacity for a specified pfa and N