The probability of multiple correct packet receptions in direct-sequence spread-spectrum networks

We provide methods to evaluate the probabilities P(l, m-l|K), l=0, 1, ..., m and m⩽K of exactly l correct packet receptions in a group of m receivers, given that K packets are transmitted simultaneously from users employing direct-sequence spread spectrum (DS/SS) signalling schemes. This quantity is useful for the design and performance evaluation of protocols for admission control and dynamic code allocation in multiple-access spread spectrum packet radio networks intended for terrestrial or satellite applications. The evaluations are carried out for DS/SS networks employing BPSK modulation with coherent demodulation and convolutional codes with Viterbi decoding. Systems with geographically dispersed receivers and systems with colocated receivers are considered. Approximations based on the independent receiver operation assumption (IROA) and the Gaussian multivariate distribution are developed, and their accuracy is checked against the exact expressions derived for synchronous systems. The joint first error event approximation (JFEEA) is also developed for coded systems and compared to the IROA