Maximum Sum Rate Anlysis

　

In random access networks where each node accesses the channel in an uncoordinated manner, the number of successfully decoded packets in each time slot is a random variable. Therefore, the average number of successfully decoded packets per time slot, which is referred to as the network throughput, has been widely adopted in the literature as an important performance metric. When the collision model is adopted, the network throughput also reflects the access efficiency, that is, the percentage of time that the network has a successful transmission. In practice, nevertheless, the network sum rate, i.e., the average number of successfully received information bits of the network per unit time, could be of more interest. To characterize the network sum rate, the information encoding rate of each packet needs to be further considered.

When the information encoding rate of each node is given, the network sum rate can be obtained as a weighted sum of each node’s throughput, i.e., weighted by its information encoding rate. The sum rate performance of a multi-rate CSMA network with the collision model was characterized in [Sun-Dai'17], and optimized by properly tuning the transmission probabilities of nodes. Both the optimal transmission probability and the corresponding network sum rate were derived as functions of the information encoding rates of nodes.

Note that the information encoding rate could be further tuned to maximize the network sum rate. Intuitively, with a larger information encoding rate, the chance that a packet is successfully decoded is reduced, which leads to a lower network throughput. Such a tradeoff between the network throughput and the information encoding rate of packets was first revealed in [Li-Dai'16], which shows that there exists an optimal information encoding rate of packets that maximizes the sum rate of Aloha networks. The analysis was further extended to Aloha networks with successive interference cancellation (SIC) in [Li-Dai'18], and CSMA networks with both collision and capture models in [Sun-Dai'19].