Maximum Sum Rate of Slotted Aloha With Capture

Abstract

The sum rate performance of random-access networks crucially depends on the access protocol and receiver structure. Despite extensive studies, how to characterize the maximum sum rate of the simplest version of random access, Aloha, remains an open question. In this paper, a comprehensive study of the sum rate performance of slotted Aloha networks is presented. By extending the unified analytical framework proposed in [20], [21] from the classical collision model to the capture model, the network steady-state point in saturated conditions is derived as a function of the signal-to-interference-plusnoise ratio (SINR) threshold which determines a fundamental tradeoff between the information encoding rate and the network throughput. To maximize the sum rate, both the SINR threshold and backoff parameters of nodes should be properly selected. Explicit expressions of the maximum sum rate and the optimal setting are obtained, which show that similar to the sum capacity of the multiple access channel, the maximum sum rate of slotted Aloha also logarithmically increases with the mean received signal-to-noise ratio (SNR), but the high-SNR slope is only e −1 . Effects of backoff and power control on the sum rate performance of slotted Aloha networks are further discussed, which shed important light on the practical network design. .hk).1 Unless otherwise specified, throughout the paper we only consider synchronized slotted networks where the time is divided into multiple slots, and nodes transmit at the beginning of each time slot. was shown to be only e −1 with the collision model [3], which indicates that over 60% of the time is wasted when the network is either in collision or idle states. To improve the efficiency, Carrier Sense Multiple Access (CSMA) was further introduced in [4], with which the network throughput can approach 1 by reducing the sensing time. On the other hand, significant improvement in network throughput was also observed when the capture model is adopted [23]- [32]. Intuitively, with the capture model, more packets can be successfully decoded by reducing the SINR threshold. The network throughput is thus greatly improved, and may exceed 1 if the SINR threshold is sufficiently small.Despite extensive studies, how to maximize the network throughput has been an open question for a long time. In Abramson's landmark paper [3], by modeling the aggregate traffic as a Poisson random variable with parameter G, the network throughput of slotted Aloha with the collision model can be easily obtained as Ge −G , which is maximized at e −1 when G = 1. To enable the network to operate at the optimum point for maximum network throughput, nevertheless, it requires the connection between the mean traffic rate G and key system parameters such as transmission probabilities of nodes, which turns out to be a challenging issue. Various retransmission strategies were developed to adjust the transmission probability of each node according to the number of backlogged nodes to stabilize 2 the network [5]- [8]. Yet most of them ...

Maximum Sum Rate of Slotted Aloha With Successive Interference Cancellation

“…Both the maximum sum rate and the optimal setting including the SINR threshold and the transmission probabilities of nodes are obtained as functions of the mean received signal-to-noise ratio (SNR) and the number of nodes. The Additive-White-Gaussian-Noise (AWGN) channels were further considered in [9], and the comparison to [8] corroborates that the µ * ,collision into (61) and (60), respectively.…”

“…Let g k denote the channel gain from node k to the receiver, which can be written as It was shown in [8] that for Aloha networks with the capture model, nodes with higher mean received power would have better throughput performance, resulting in unfairness among nodes. Therefore, in this paper, we follow the assumption that the transmission power of each node is properly adjusted to overcome the effect of large-scale fading.…”

“…For given encoding rate R, if log 2 (1 + η) > R, then by random coding the error probability of the packet is exponentially reduced to zero as the codeword length goes to infinity. Similar to [6] and [8], we assume that the codeword length of each packet is sufficiently large such that a packet can be successfully decoded as long as η ≥ 2 R − 1. Denote…”

“…It is clear that r j i depends on the receiver design. In [8], it has been shown that with the capture model, all the packets have the same conditional probability of successful transmission of…”

“…3 illustrates how the steady-state point p A varies with the SINR threshold µ for the ordered SIC and unordered SIC cases. The result of the capture model [8] is also presented for the sake of comparison. Similar to the conditional probability of successful transmission illustrated in Fig.…”