Optimal Joint Subcarrier and Power Allocation in NOMA is Strongly NP-Hard

TL;DR

This paper proves that the problem of jointly allocating subcarriers and power in multi-carrier NOMA systems is strongly NP-hard for many common utility functions, indicating no efficient solution exists in general.

Contribution

It establishes the computational complexity of joint subcarrier and power allocation in NOMA, proving NP-hardness for a broad class of utility functions, and identifies some special cases that are tractable.

Findings

Joint subcarrier and power allocation in NOMA is strongly NP-hard.

The NP-hardness applies to popular utility functions like sum-rate and fairness.

Some special cases of the problem can be solved efficiently.

Abstract

Non-orthogonal multiple access (NOMA) is a promising radio access technology for 5G. It allows several users to transmit on the same frequency and time resource by performing power-domain multiplexing. At the receiver side, successive interference cancellation (SIC) is applied to mitigate interference among the multiplexed signals. In this way, NOMA can outperform orthogonal multiple access schemes used in conventional cellular networks in terms of spectral efficiency and allows more simultaneous users. This paper investigates the computational complexity of joint subcarrier and power allocation problems in multi-carrier NOMA systems. We prove that these problems are strongly NP-hard for a large class of objective functions, namely the weighted generalized means of the individual data rates. This class covers the popular weighted sum-rate, proportional fairness, harmonic mean and max-min fairness utilities. Our results show that the optimal power and subcarrier allocation cannot be computed in polynomial time in the general case, unless P = NP. Nevertheless, we present some tractable special cases and we show that they can be solved efficiently.