Resource Allocation in Low Density Spreading 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 symbol over d k <; F sub-carriers. Given d k , ∀k as design parameters, we characterize the resource allocation solutions that closely maximize the ergodic mutual information (EMI) in a scenario where the BS assigns resources solely based on the UEs’ pathlosses. Conducting analysis in asymptotic limit where F, K, and d k , ∀k converge to +∞ at the same rate, we present EMI in terms of a deterministic equivalent plus a residual term. The deterministic equivalent is given in terms of pathloss values and LDS-codes, and the small residual term scales as O(1/d 2 ) where d = min{d k , ∀k}. We formulate an optimization problem to get the set C̅* of all spreading codes, irrespective of sparsity constraints, which maximize the deterministic equivalent of EMI. The spreading codes in C̅* with desired sparsity are obtained via a simple and efficient algorithmic solution. In the finite regime, the residual term is shown to be a small incremental gain for the sparse solutions in C̅*, which is dictated mainly by d k , ∀k values. Accordingly, we show that the solutions in C̅* with desired sparsity yield close to optimum values of EMI in the finite regime. Numerical simulation validates the attainable spectral efficiency enhancement as compared to regular, and random spreading.