Capacity Approaching Low Density Spreading in Uplink NOMA via Asymptotic Analysis

Abstract

Low density spreading multiple-access is considered where K single-antenna user equipments (UEs) communicate with a base station (BS) over F sub-carriers. Each UE k spreads its data symbol over d k < F sub-carriers, while d k = 1 corresponds to a power domain non-orthogonal multiple-access (NOMA). For given design parameters d k , we provide an analytical framework for characterizing resource allocations that closely maximize the ergodic sum-rate in the considered NOMA schemes.In particular, we are interested in a scenario where the BS assigns resources solely based on the UEs pathloss values. To this end, we let F , K, and d k to grow into mF , mK, and md k , respectively, such that the overlap of UEs on sub-carriers remain intact. In asymptotic regime where m → ∞, we derive a deterministic expression for the ergodic sum-rate in terms of pathloss values and spreading codes. This is incorporated into an optimization problem to characterize the set of all asymptotically optimal spreading codes irrespective of sparsity constraints. Then, algorithmic solutions are proposed to find the asymptotic codes with desired number of non-zero elements in each of the spreading codes, and the number of UEs transmitting on each sub-carrier. We show that the attained codes get the maximum of ergodic sum-rate in finite regime up to a small gap. Numerical simulation validates the attainable spectral efficiency enhancement as compared to the random assignment of spreading codes. I. INTRODUCTION Consider a scenario where K single-antenna user equipments (UEs) communicate with a base station (BS) over F sub-carriers. Given an overloaded setting with K > F , inevitable multiple access interference (MAI) occurs that needs to be dealt via non-orthogonal multiple access (NOMA) techniques. In order to distinguish UEs at the BS, one can add redundancy by spreading UEs symbol over d k sub-carriers. The NOMA scenario where d k values are much smaller than F is dubbed as multi-carrier low density spreading multiple access (MC-LDSMA) in H. Asgharimoghaddam and A. Tölli are with the Centre for Wireless Communications