Performance of trellis coded direct-sequence spread-spectrum: multiple-access with noncoherent reception in a fading environment

The performance of different coding schemes for direct-sequence spread-spectrum (DS-SS) with multiple-access (MA) interference in a nonselective Rayleigh fading channel is considered. A conventional 64-ary orthogonal code (M₆₄) transmitting 6 bits of information is examined first. Each of the 64 code symbols in the M₆₄ code is assumed to be spread by a random sequence of length N, and the channel is assumed to be interleaved every N chips. We consider a M₆₄ DS-SS code concatenated with a (63, k) Reed-Solomon (RS) outer code and varying the amount of spreading and the code rate for a fixed data rate and bandwidth. Our analysis based on Gaussian approximation shows that when the number of users is reasonably large, an optimal value k* to achieve the minimum bit error probability of the (63, k) RS code can be found. Furthermore, we extend the results by substituting the M₆₄ code with the trellis coded Nordstrom-Robinson code (TCNR), and the trellis coded Reed-Muller code (TCRM), which have the same data rate as that of the M₆₄ code. An optimal value k* to achieve minimum bit error probability can also be found when the TCNR code or the TCRM code is concatenated with a (63, k) RS outer code