Coding, processing gain, and modulation in frequency-hopped multiple access communications: tradeoff considerations

We consider a situation where K transmitter-receiver pairs communicate simultaneously over a channel of bandwidth B. Each transmitter sends one of the M possible signals in every 2 seconds over one of the p possible frequency slots, having a bandwidth of B/q. We assume the use of M-ary FSK orthogonal signaling with noncoherent detection. Each transmitter-receiver pair has a unique hopping pattern that selects the frequency slot. We model the hopping patterns as independent, identically distributed (i.i.d.) random sequences uniformly distributed over a set of q frequencies. We assume that each packet consists of a Reed-Solomon (RS) codeword, and one code symbol (M-ary) is transmitted per hop