In this report, we provide an accurate analysis of 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) signaling schemes. This quantity is essential for the design and performance evaluation of protocols for admission control, dynamic code allocation of multiple-access spread-spectrum packet radio networks; specific applications include networks of LEO satellites and multi-rate multi-media communications using CDMA (code-division multiple- access) techniques. 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.

First the exact multireception probabilities for synchronous uncoded systems are evaluated at the bit level; these results are essential for checking the accuracy of the other approximations used here. Our results establish that the Independent Receiver Operation Assumption (IROA) yields very good approximations whose accuracy increases as the number of chips per bit N increases. The IROA accuracy is not as satisfactory for colocated receivers when Eb/No is small; for this case we develop an approximation based on the Guassian multivariate distribution, which is ore accurate than the IROA. Extensive comparisons of the exact expressions with the Guassian and the IROA approximations are conducted. For convolutional code systems, we derive the multireception packet probabilities following a new approach, the Joint First Error Event Approximation (JFEEA), which is based on the lower bound of the probabilities of all-correct packet receptions and the moments of random variables. We compare this approximation with the IROA and observe good agreement between the two.