Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts (1906.03165v4)

Abstract: Intelligent reflecting surface (IRS) is a cost-effective solution for achieving high spectrum and energy efficiency in future wireless networks by leveraging massive low-cost passive elements that are able to reflect the signals with adjustable phase shifts. Prior works on IRS mainly consider continuous phase shifts at reflecting elements, which are practically difficult to implement due to the hardware limitation. In contrast, we study in this paper an IRS-aided wireless network, where an IRS with only a finite number of phase shifts at each element is deployed to assist in the communication from a multi-antenna access point (AP) to multiple single-antenna users. We aim to minimize the transmit power at the AP by jointly optimizing the continuous transmit precoding at the AP and the discrete reflect phase shifts at the IRS, subject to a given set of minimum signal-to-interference-plus-noise ratio (SINR) constraints at the user receivers. The considered problem is shown to be a mixed-integer non-linear program (MINLP) and thus is difficult to solve in general. To tackle this problem, we first study the single-user case with one user assisted by the IRS and propose both optimal and suboptimal algorithms for solving it. Besides, we analytically show that as compared to the ideal case with continuous phase shifts, the IRS with discrete phase shifts achieves the same squared power gain in terms of asymptotically large number of reflecting elements, while a constant proportional power loss is incurred that depends only on the number of phase-shift levels. The proposed designs for the single-user case are also extended to the general setup with multiple users among which some are aided by the IRS. Simulation results verify our performance analysis as well as the effectiveness of our proposed designs as compared to various benchmark schemes.

• The paper formulates the IRS-aided beamforming problem as a MINLP to minimize AP transmit power under SINR constraints with practical discrete phase shifts.
• It introduces optimal and suboptimal algorithms, using branch-and-bound and successive refinement for single-user cases and a ZF-based approach for multiuser scenarios.
• Analytical and simulation results confirm that IRS with discrete shifts achieves near-optimal power scaling, closely matching continuous phase shifts with a fixed power loss.

Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts

The paper addresses the critical problem of optimizing beamforming in multiuser wireless communication networks assisted by an intelligent reflecting surface (IRS). The IRS technology, comprising numerous passive elements capable of adjusting phase shifts, has emerged as a promising approach to enhance spectrum and energy efficiency in future wireless networks. Crucially, this paper explores the practical constraints imposed by discrete phase shifts on IRS elements, a significant deviation from prior works that predominantly assumed continuous phase shifts.

Key Contributions

The paper presents several key contributions and innovations:

1. Problem Formulation: The authors formulate the IRS-aided beamforming optimization problem as a mixed-integer non-linear program (MINLP). The objective is to minimize the transmit power at the access point (AP) while satisfying user-specific SINR constraints, considering the practical scenario where each IRS element can only assume a finite number of discrete phase shifts.
2. Algorithm Design:
   • Single-User Case: For the single-user scenario, both optimal and suboptimal algorithms are proposed. The optimal algorithm employs the branch-and-bound method to solve the ILP reformulation of the problem. Meanwhile, the suboptimal algorithm applies a successive refinement approach to iteratively adjust the phase shifts efficiently.
   • Multiuser Case: Extending the paper to multiuser scenarios, the authors propose a ZF-based successive refinement algorithm due to the intractability of directly applying the optimal approach. The ZF-based algorithm iteratively optimizes the discrete phase shifts while using zero-forcing (ZF) precoding at the AP to manage multiuser interference.
3. Performance Analysis: The paper provides an analytical characterization of the IRS with discrete phase shifts, showing that with asymptotically large $N$, the same squared power gain as that with continuous phase shifts is achieved, although with a constant power loss dependent on the resolution of the discrete phase shifters.

Numerical Validation and Results

Extensive simulations validate the proposed algorithms and analysis. Key findings include:

• Impact of IRS Elements: The numerical results confirm that as the number of IRS elements $N$ increases, both the proposed algorithms and theoretical analysis exhibit the expected power scaling behavior. The performance gap between IRS with discrete (e.g., 1-bit and 2-bit) and continuous phase shifts approaches a fixed value, in line with analytical predictions.
• Algorithm Efficiency: The successive refinement algorithm demonstrates near-optimal performance with significantly reduced computational complexity compared to the optimal exhaustive search. In multiuser scenarios, the ZF-based algorithm's performance closely matches that of the more complex MMSE-based approach.
• Comparative Analysis: When compared to existing benchmark schemes, including direct phase quantization and codebook-based strategies, the proposed algorithms achieve superior performance in terms of AP transmit power reduction. This is particularly evident in the high SINR regime where direct quantization schemes struggle due to severe multiuser interference.

Implications and Future Research

The paper provides several important implications and opens avenues for future research:

• Practical Feasibility: The results underscore the feasibility and efficacy of deploying IRS with low-resolution phase shifters, striking a balance between performance gains and implementation complexity/costs.
• Multi-AP and Large-Scale Systems: Future work could extend the optimization framework to multi-AP environments, considering the challenges of coordinating multiple IRSs and their potential interference.
• Joint Deployment Strategies: It would be beneficial to investigate joint deployment strategies of APs and IRSs in larger networks, optimizing both the spatial distribution and the number of elements/phase shifters to achieve desired performance outcomes cost-effectively.

Conclusion

This paper makes substantial contributions to the understanding and practical application of IRS technology in wireless networks. By tackling the challenge of discrete phase shifts, it bridges a crucial gap between theoretical models and real-world implementations, offering valuable insights and efficient algorithmic solutions for next-generation wireless communication systems.