A slotted ALOHA with multiple common receivers over AWGN Rayleigh-fading channels

The capture probability for an inbound radio channel in a radio LAN (local area network) is formulated in a closed form by taking into account both AWGN (additive white Gaussian noise) and Rayleigh fading. The received power ratio between a packet signal with minimum received power and an interference signal is considered as a criterion for the capture effect. It is revealed that, though the maximum overall throughput for a slotted ALOHA over Rayleigh fading channels is very vulnerable to AWGN for a single common-receiver case, pluralizing common receivers dramatically improves the overall throughput. Surprisingly, it has also been found that, even if the signal-to-noise ratio is as bad as 2.5 (dB), the instability of a slotted ALOHA over Rayleigh-fading channels is still much less serious than that over channels without capture. This means that the capture effect overwhelms AWGN regarding stability