[Paper Review] Joint Power Control and Beamforming for Uplink Non-Orthogonal Multiple Access in 5G Millimeter-Wave Communications

Lipeng Zhu, Jun Zhang+4 more|arXiv (Cornell University)|Nov 15, 2017

Advanced Wireless Communication Technologies25 references3 citations

TL;DR

This paper proposes a sub-optimal joint power control and analog beamforming scheme for uplink non-orthogonal multiple access (NOMA) in 5G millimeter-wave (mmWave) systems with a single RF chain and constant-modulus phase shifters. By decomposing the non-convex sum rate maximization problem into power control and beamforming sub-problems, the method achieves near-optimal sum rate performance while satisfying individual user rate constraints.

ABSTRACT

In this paper, we investigate the combination of two key enabling technologies for the fifth generation (5G) wireless mobile communication, namely millimeter-wave (mmWave) communications and non-orthogonal multiple access (NOMA). In particular, we consider a typical 2-user uplink mmWave-NOMA system, where the base station (BS) equips an analog beamforming structure with a single RF chain and serves 2 NOMA users. An optimization problem is formulated to maximize the achievable sum rate of the 2 users while ensuring a minimal rate constraint for each user. The problem turns to be a joint power control and beamforming problem, i.e., we need to find the beamforming vectors to steer to the two users simultaneously subject to an analog beamforming structure, and meanwhile control appropriate power on them. As direct search for the optimal solution of the non-convex problem is too complicated, we propose to decompose the original problem into two sub-problems that are relatively easy to solve: one is a power control and beam gain allocation problem, and the other is an analog beamforming problem under a constant-modulus constraint. The rational of the proposed solution is verified by extensive simulations, and the performance evaluation results show that the proposed sub-optimal solution achieve a close-to-bound uplink sum-rate performance.

Motivation & Objective

• Address the challenge of supporting more users than RF chains in mmWave systems by combining NOMA with beamforming.
• Formulate a non-convex optimization problem to maximize sum rate in a 2-user uplink mmWave-NOMA system under individual rate constraints.
• Overcome the complexity of joint power control and analog beamforming under constant-modulus constraints in mmWave systems.
• Develop a sub-optimal solution that decomposes the original problem into tractable sub-problems for practical implementation.
• Ensure feasibility and performance close to the theoretical sum rate upper bound under realistic hardware constraints.

Proposed method

• Decompose the joint power control and beamforming problem into two sub-problems: power control with beam gain allocation and analog beamforming under constant-modulus constraints.
• Use a constant-modulus (CM) phased array beamforming structure with a single RF chain to reduce hardware cost and complexity.
• Formulate the beamforming problem as a constrained optimization with amplitude and phase constraints on beamforming vectors.
• Apply successive interference cancellation (SIC) at the base station to decode users with different power levels in uplink NOMA.
• Optimize beamforming vectors to maximize beam gain for the stronger user while ensuring minimum rate for the weaker user.
• Verify the optimality of the solution by proving that the beamforming vector lies on the outer boundary of the feasible region, ensuring maximum gain under constraints.

Experimental results

Research questions

• RQ1 How can joint power control and analog beamforming be optimized in a 2-user uplink mmWave-NOMA system with a single RF chain?
• RQ2 What is the performance gain of the proposed sub-optimal solution compared to conventional beamforming or fixed power allocation?
• RQ3 Can the proposed method achieve a sum rate close to the theoretical upper bound under individual user rate constraints?
• RQ4 How does the constant-modulus constraint of analog beamforming affect the design and performance of the joint optimization?
• RQ5 What is the impact of user channel correlation and beam alignment on the achievable sum rate in mmWave-NOMA systems?

Key findings

• The proposed sub-optimal solution achieves a sum rate performance that is very close to the theoretical upper bound, demonstrating near-optimal efficiency.
• The beamforming vector for the stronger user is constrained to lie on the outer boundary of the feasible region, ensuring maximum beam gain under power and phase constraints.
• The method guarantees minimum rate requirements for both users by allocating sufficient beam gain and power, with the weaker user receiving just enough to meet its rate constraint.
• Simulation results confirm that the decomposition approach effectively balances sum rate maximization and individual rate constraints under hardware limitations.
• The solution is robust to channel correlation and maintains high spectral efficiency even when users are spatially close, thanks to directional beamforming and power domain multiplexing.
• Theoretical analysis proves that the optimal solution lies on the boundary of the feasible region, validating the design choice of constraining the beamformer amplitude to 1/√N.