On joint power-delay double packet capture in an SSMA network with Rayleigh fading, shadowing, and propagation path loss

In this paper, joint power-delay double-capture probabilities of a spread-spectrum packet network are derived. What we mean in terms of "double-capture" is that a receiver can simultaneously capture the first two incoming packets (from different transmitters) encoded by the same spreading code. The power capture model concerned takes into account multiuser interference, multipath Rayleigh fading, shadowing, and propagation path loss. To derive delay capture probability with an arbitrary arrival delay, a discrete-time approximation is applied. The method of deriving double-capture probability can also be extended to calculating multiple-packet (more than two) capture probabilities. Performance of a common-code slotted ALOHA system is evaluated with the double-capture effect and the results are compared with those of a traditional ALOHA system. It is shown that the channel impairing factors can be greatly mitigated by exploiting joint power-delay double-capture effect.