Content area
The random access radio to channel assignment problem concerns the assignment of N homogeneous radios, operating in a common collision domain and with a fixed and common contention probability p, to M homogeneous channels so as to maximize the channel-average throughput.
The throughput on each channel is the expected number of received transmissions in a time slot. Two cases are considered. The first case, termed collision loss, assumes that multiple transmissions in a time slot on a channel collide and are not received, i.e., a transmission is received when it is the sole transmission in the time slot on its channel; this is a classical model known as the collision channel. The second case, termed collision resistance, assumes the receiver is capable of multi-packet reception (MPR) in that it can receive up to K transmissions in a time slot on a channel but all such transmissions are lost when that number exceeds K. Evidently, the second case generalizes the first case, which corresponds to K = 1. The single channel throughput is nonlinear in the number of assigned radios — it is initially increasing in the “underloaded” regime, reaches its global maximum, and then is subsequently decreasing in the “overloaded” regime.
The assignment problem is a nonlinear combinatorial optimization problem. The problem is approached by integer relaxation: instead of assigning discrete radios to channels, the relaxed problem considers the assignment of a continuous quantity called load across the channels. This relaxation permits the use of classic techniques for the nonlinear optimization over continuous variables, e.g., Karush-Kuhn-Tucker (KKT) conditions. Numerical investigation of the accuracy of the solution of the relaxed problem to the solution of the combinatorial problem is limited by the combinatorial explosion of the search space for even moderate size problem instances, i.e., M and N, but the investigation suggests the solution of the relaxed problem yields channel-average throughputs that are close to those of the solution of the combinatorial problem.
The assignment problem is of relevance in random access multi-channel wireless systems. Specifically, the proliferation of the Internet of Things (IoT) and the advent of massive machine-type communication (MMTC) have ushered in a new focus in wireless communication on enabling Low Power Wide Area Networks (LPWANs). LPWANs are specifically engineered to support a large number of low-power wireless devices operating over vast geographical ranges with low duty cycles. Among the LPWAN protocols, Long Range Wide Area Network (LoRaWAN) has emerged as a prominent solution, leveraging a multi-channel random access protocol to facilitate efficient communication.
