Random access channel assignment on a collision erasure channel

Channel assignment for wireless radios employing random access is found in several contexts, including low-power wide area network (LPWAN) protocols such as LoRaWAN. This paper considers the assignment of a set of N radios to M available channels with the objective of maximizing the sum throughput. The difficulty lies in the facts that i) the radios connect to the access point (or gateway) over independent erasure channels and ii) the radios are subject to collision, i.e., if two or more packets arrive at the access point on the same channel then all such packets "collide" and are lost. The problem is approached by defining lower and upper bounds on the throughput, and then extremizing the bounds. Initial numerical results for M = 2 channels suggest i) there is notable variation in sum throughput across problem instances, but ii) the impact of scheduling on the throughput for a given problem instance is relatively small.