[Paper Review] On User Pairing in NOMA Uplink

Mohammad Ali Sedaghat, Ralf R. Müller|arXiv (Cornell University)|Jul 6, 2017

Advanced Wireless Communication Technologies28 references3 citations

TL;DR

This paper proposes optimal and suboptimal user pairing algorithms for uplink Non-Orthogonal Multiple Access (NOMA) with single- and multi-antenna base stations, leveraging channel state information to maximize sum rate. It analytically demonstrates that optimal pairing significantly outperforms random pairing in finite dimensions, while both converge in the large-system limit, and shows the proposed NOMA scheme surpasses existing signal alignment-based approaches.

ABSTRACT

User pairing in Non-Orthogonal Multiple-Access (NOMA) uplink based on channel state information is investigated considering some predefined power allocation schemes. The base station divides the set of users into disjunct pairs and assigns the available resources to these pairs. The combinatorial problem of user pairing to achieve the maximum sum rate is analyzed in the large system limit for various scenarios, and some optimum and sub-optimum algorithms with a polynomial-time complexity are proposed. In the first scenario, $2M$ users and the base station have a single-antenna and communicate over $M$ subcarriers. The performance of optimum pairing is derived for $M ightarrow \infty$ and shown to be superior to random pairing and orthogonal multiple access techniques. In the second setting, a novel NOMA scheme for a multi-antenna base station and single carrier communication is proposed. In this case, the users need not be aware of the pairing strategy. Furthermore, the proposed NOMA scheme is generalized to multi-antenna users. It is shown that random and optimum user pairing perform similarly in the large system limit, but optimum pairing is significantly better in finite dimensions. It is shown that the proposed NOMA scheme outperforms a previously proposed NOMA scheme with signal alignment.

Motivation & Objective

• To analytically evaluate the performance gain of optimal user pairing in uplink NOMA compared to random pairing.
• To design low-complexity, polynomial-time algorithms for optimal and suboptimal user pairing under various system configurations.
• To propose a novel multi-antenna NOMA uplink scheme where users need not know the pairing strategy, enhancing practicality.
• To compare the proposed NOMA scheme with existing signal alignment-based NOMA and orthogonal multiple access (OMA) techniques.
• To derive the asymptotic sum rate performance in the large-system limit (M→∞) for both single- and multi-antenna scenarios.

Proposed method

• The paper models uplink NOMA with M subcarriers and 2M single-antenna users, forming M disjoint user pairs, and derives the sum rate under successive interference cancellation (SIC).
• It employs large random matrix theory to analyze the asymptotic sum rate in the limit M→∞, deriving the Stieltjes transform of the eigenvalue distribution of the effective channel matrix.
• For multi-antenna base stations, the paper proposes a novel NOMA scheme using beamforming and precoding, where users are paired based on channel quality without requiring knowledge of the pairing strategy.
• The method includes a suboptimal pairing algorithm based on user channel gain ordering, with complexity O(M²), and a near-optimal algorithm with O(M³) complexity using combinatorial optimization.
• The performance is evaluated via analytical derivation of the limiting sum rate and comparison with random pairing and OMA, using the ergodic sum rate as the metric.
• The paper derives the asymptotic eigenvalue distribution of the effective channel matrix Ω, showing convergence to a deterministic limit under i.i.d. fading.

Experimental results

Research questions

• RQ1 How much performance gain does optimal user pairing provide over random pairing in uplink NOMA for finite system dimensions?
• RQ2 What is the asymptotic sum rate performance of optimal user pairing in uplink NOMA as the number of subcarriers M→∞?
• RQ3 Can a low-complexity, suboptimal user pairing algorithm achieve near-optimal performance in practical systems?
• RQ4 How does the proposed multi-antenna NOMA uplink scheme compare to existing signal alignment-based NOMA and OMA in terms of sum rate and fairness?
• RQ5 Does the performance gap between optimal and random pairing diminish in the large-system limit, or is it significant even asymptotically?

Key findings

• Optimal user pairing achieves a significantly higher sum rate than random pairing in finite-dimensional systems, with the gain being most pronounced when the number of users is small.
• In the large-system limit (M→∞), the sum rate performance of optimal and random pairing converges, indicating that the performance gap vanishes asymptotically.
• The proposed NOMA scheme for multi-antenna base stations outperforms a previously proposed signal alignment-based NOMA scheme, particularly in high-SNR regimes.
• The asymptotic sum rate for optimal pairing is analytically derived as M→∞, showing a closed-form expression involving the Stieltjes transform of the channel matrix eigenvalue distribution.
• The two nonzero eigenvalues of the effective channel matrix Ω converge in probability to the same value, given by a function of the SNR γ and power allocation ratio α.
• The derived asymptotic sum rate expression confirms that NOMA with optimal pairing achieves a higher sum rate than OMA, even in the large-system limit.