Capacity Approaching Low Density Spreading in Uplink NOMA via Asymptotic Analysis

Low-density spreading non-orthogonal multiple-access (LDS-NOMA) is considered where K single-antenna user-equipments (UEs) communicate with a base-station (BS) over F fading sub-carriers. Each UE k spreads its data symbols over d _k <; <; F sub-carriers. The performance of LDS-NOMA system depends on the allocation of the non-zero elements in the LDS-codes. We aim to identify the LDS resource allocations, based solely on pathlosses, that maximize the ergodic mutual information (EMI). This problem can be solved only via an exhaustive search. Thus, relying on analysis in the regime where F, K, and d _k ,∀k converge to +∞ at the same rate, we present EMI as a deterministic equivalent plus a residual term. The deterministic equivalent is a function of pathloss values and LDS-codes, and the small residual term scales as O (1 / min(d _k ² )). First, we formulate an optimization problem to identify the resource allocations that maximize the deterministic equivalent of EMI. The Karush-Kuhn-Tucker conditions give a simple resource allocation rule that facilitates the construction of desired LDS-codes via an efficient partitioning algorithm. The finite-regime analysis shows that such sparse solutions additionally harness the small incremental gain inherent in the residual term, and thus, provides a near-optimal performance. The spectral efficiency enhancement relative to regular and random spreading is validated numerically.