[Paper Review] Joint Beamforming Design in Multi-Cluster MISO NOMA Intelligent Reflecting Surface-Aided Downlink Communication Networks

Yiqing Li, Miao Jiang+2 more|arXiv (Cornell University)|Sep 16, 2019

Advanced Wireless Communication TechnologiesEngineering24 references47 citations

TL;DR

This paper proposes a SOCP-ADMM based joint beamforming design for a multi-cluster MISO NOMA system aided by an IRS, with a low-complexity ZF alternative, to minimize total transmit power under rate constraints.

ABSTRACT

Considering intelligent reflecting surface (IRS), we study a multi-cluster multiple-input-single-output (MISO) non-orthogonal multiple access (NOMA) downlink communication network. In the network, an IRS assists the communication from the base station (BS) to all users by passive beamforming. Our goal is to minimize the total transmit power by jointly optimizing the transmit beamforming vectors at the BS and the reflection coefficient vector at the IRS. Because of the restrictions on the IRS reflection amplitudes and phase shifts, the formulated quadratically constrained quadratic problem is highly non-convex. For the aforementioned problem, the conventional semidefinite programming (SDP) based algorithm has prohibitively high computational complexity and deteriorating performance. Here, we propose an effective second-order cone programming (SOCP)-alternating direction method of multipliers (ADMM) based algorithm to obtain the locally optimal solution. To reduce the computational complexity, we also propose a low-complexity zero-forcing (ZF) based suboptimal algorithm. It is shown through simulation results that our proposed SOCP-ADMM based algorithm achieves significant performance gain over the conventional SDP based algorithm. Furthermore, when the number of passive reflection elements is relatively high, our proposed ZF-based suboptimal algorithm also outperforms the SDP based algorithm.

Motivation & Objective

• Motivate power-efficient downlink transmission in IRS-aided multi-cluster MISO-NOMA networks.
• Formulate and solve a non-convex QCQP that jointly optimizes BS transmit beams and IRS reflection coefficients under rate constraints.
• Develop a scalable optimization framework that yields a locally optimal solution with manageable complexity.
• Provide a low-complexity alternative (ZF-based) that performs well as the number of IRS elements grows.

Proposed method

• Formulate the transmit signal model with a multi-cluster MISO-NOMA setup and IRS reflection; define SINRs for cell-edge and central users under NOMA with SIC.
• Transform the non-convex QCQP into an SOCP-ADMM friendly form using auxiliary variables and QoS constraints.
• Apply ADMM to decompose the problem into tractable SOCP subproblems for the BS beamformers and IRS coefficients, including a projection step for the IRS update.
• Propose a low-complexity ZF-based suboptimal algorithm by enforcing inter-cluster interference nulling through an SVD-based null-space design.
• Derive closed-form updates for the auxiliary variables and dual variables, and analyze computational complexity of the proposed schemes.

Experimental results

Research questions

• RQ1 Can joint optimization of BS beamformers and IRS reflection coefficients minimize the total transmit power under per-user rate requirements in a multi-cluster MISO-NOMA IRS-aided downlink?
• RQ2 How does an SOCP-ADMM solution compare to an SDP-based approach in terms of performance and complexity?
• RQ3 Does a zero-forcing based suboptimal algorithm provide competitive power efficiency, particularly when the IRS has many elements?
• RQ4 How do different IRS reflection coefficient models (continuous amplitude/phase, unit-modulus phase, and quantized phase) impact the optimal design and power consumption?

Key findings

• The SOCP-ADMM algorithm yields significant power savings compared to the conventional SDP-based method.
• With a larger number of passive IRS elements, the ZF-based suboptimal algorithm outperforms the SDP-based approach in some scenarios.
• The proposed framework accommodates Case I (continuous amplitude/phase), Case II (unit-modulus phase), and Case III (quantized phase) IRS models.
• The approach provides a locally optimal solution with feasible computational complexity for practical IRS sizes.