ALOHA with capture over slow and fast fading radio channels with coding and diversity

A multiqueue service room MAC protocol for wireless networks with multipacket reception

“…If we relabel users in each group at the beginning of each slot, starting from the service room to the end of the th queue, we have (13) Let be the state of the th ( ) user in the th ( ) group at the beginning of slot (after new packet generation), where we define the state of a user as the number of packets it, if enabled, can transmit in slot . Specifically, when the th user in the th group is inside the service room at the beginning of slot , is the number of packets generated before its entering the service room.…”

“…As a commonly seen form of MPR, the capture effect first drew the attention of researchers. The impact of capture on the performance of slotted ALOHA is studied in [2], [9], [13], [19], [24], [27], [28], and references therein. The performance of the FCFS algorithm in channels with capture is analyzed in [23].…”

Modulation and coding for the Gaussian collision channel

“…Then, a signal burst may survive to a collision provided that the interference signal is sufficiently faded. This so-called "capture effect" has been investigated for S-ALOHA [39], [40] and should be taken into account in an extension of this work.…”

“…Proof of (36) and (38) Proof of (39) and (41) By summing over all and dividing by we immediately obtain (42). The convergence in probability of to given in (44) follows immediately from Corollary 1 of Appendix A, since is a continuous (linear) function of the probabilities for .…”

“…With the channel model (4) and perfect CSI, the instantaneous mutual information is given by (39) where and is the number of collisions in the pattern . Since is a nonincreasing function of , and is binomially distributed, the outage probability can be computed as (40) where is the largest such that .…”