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. We aim to identify the LDS-code allocations that maximize the ergodic mutual information (EMI). The BS assigns resources solely based on pathlosses. Conducting analysis in the regime where $F$, $K$, and ${d_k,\forall k}$ converge to $+\infty$ at the same rate, we present EMI as a deterministic equivalent plus a residual term. The deterministic equivalent is a function of pathlosses and spreading codes, and the small residual term scales as $\mathcal{O}(\frac{1}{\min(d_k^2)})$. We formulate an optimization problem to get the set of all spreading codes, irrespective of sparsity constraints, which maximize the deterministic EMI. This yields a simple resource allocation rule that facilitates the construction of desired LDS-codes via an efficient partitioning algorithm. The acquired LDS-codes additionally harness the small incremental gain inherent in the residual term, and thus, attain near-optimal values of EMI in the finite regime. While regular LDS-NOMA is found to be asymptotically optimal in symmetric models, an irregular spreading arises in generic asymmetric cases. The spectral efficiency enhancement relative to regular and random spreading is validated numerically.

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