Distributed Cluster Formation and Power-Bandwidth Allocation for Imperfect NOMA in DL-HetNets

Abstract

In this paper, we consider an imperfect successive interference cancellation (SIC) receiver based non-orthogonal multiple access (NOMA) schemes. The achievable gain of exploited NOMA scheme herein is limited by two factors: 1) Power disparity \& sensitivity constraints (PDSCs) of SIC receivers and 2) Residual interference after the interference cancellations due to the error propagation. By quantifying the residual interference with a fractional error factor (FEF), we first show that NOMA cannot always perform better than orthogonal multiple access (OMA) especially under certain receiver sensitivity and FEF levels. Then, a distributed cluster formation (CF) and power-bandwidth allocation (PBA) approach are proposed for downlink (DL) heterogeneous networks (HetNets) operating on the imperfect NOMA. Contingent upon a mixed-integer nonlinear programming (MINLP) problem formulation, we develop a hierarchically distributed solution methodology where BSs independently form clusters and distributively determine the power-bandwidth allowance of each cluster. A generic CF scheme is obtained by creating a multi-partite graph (MPG) via partitioning user equipments (UEs) with respect to their channel gains since NOMA performance is primarily determined by the channel gain disparity of cluster members. A sequential weighted bi-partite matching (WBM) method is proposed for solving the resulted weighted multi-partite matching (WMM) problem. Thereafter, we present a hierarchically distributed PBA approach which consists of the primary master, secondary masters, and slave problems. For a given cluster power and bandwidth pair, optimal power allocations and Lagrange multipliers of slave problems are derived in closed-form. While power allowance of clusters is updated by the secondary masters based on dual variables of slave problems, bandwidth proportions of clusters are iteratively allocated by the primary master as per the utility achieved by the secondary masters at the previous iteration. Finally, the proposed CF and PBA approaches under the operation of imperfect NOMA are investigated and compared to OMA scheme by extensive simulations results in DL-HetNets.