Maximum Sum Rate of Slotted Aloha With Successive Interference Cancellation

Abstract

This is a sequel of our previous work [8] on characterization of maximum sum rate of slotted Aloha networks.By extending the analysis to incorporate the capacity-achieving receiver structure, Successive Interference Cancellation (SIC), this paper aims to identify the rate loss due to random access. Specifically, two representative SIC receivers are considered, i.e, ordered SIC where packets are decoded in a descending order of their received power, and unordered SIC where packets are decoded in a random order. The maximum sum rate and the corresponding optimal parameter setting including the transmission probability and the information encoding rate in both cases are obtained as functions of the mean received signal-to-noise ratio (SNR). The comparison to the capture model shows that the gains are significant only with the ordered SIC at moderate values of the mean received SNR ρ.With a large ρ, the rate gap diminishes, and they all have the same high-SNR slope of e −1 , which is far below that of the ergodic sum capacity of fading channels. The effect of multipacket reception (MPR) on the sum rate performance is also studied by comparing the MPR receivers including SIC and the capture model to the classical collision model. 2 Let us start by summarizing two basic features that are shared by most random-access schemes. 1) Independent Encoding and Uncoordinated Transmissions:Each node independently encodes its information, and decides when to transmit. As the subset of active nodes is random and timevarying, it is normally assumed to be unknown at the transmitter side.2) Time-Slotted and Packet-Based: Though it may not seem to be essential or necessary for random access, a time-slotted and packet-based network has been assumed in the literature since Abramson's Aloha was proposed [5]. Due to the uncoordinated transmissions of nodes, not all the transmitted packets can be successfully decoded in each time slot.With the above features of random access, the number of successfully decoded packets would be varying from time to time. As a result, most studies have focused on the average number of successfully decoded packets per time slot, which is referred to as the network throughput. To analyze the information-theoretic sum rate of a time-slotted packet-based random-access network, a key assumption was further made in [6] that each packet consists of one codeword, and the codeword length is long enough such that a packet can be successfully decoded as long as its information encoding rate does not exceed its single-user capacity, i.e., log 2 (1 + η), where η is the signal-to-interference-plus-noise ratio (SINR) of the packet. Moreover, it is commonly assumed that all the nodes have a uniform information encoding rate if their channel statistics are identical and they are unaware of the instantaneous realization of the channel gains [4], [6], [7]. Under these assumptions, the sum rate of a random-access network is determined by both the encoding rate of each packet and the network throughput.As demonstrated in our rec...

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