[论文解读] Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts

Qingqing Wu, Rui Zhang|arXiv (Cornell University)|Jun 7, 2019

Advanced Wireless Communication Technologies参考文献 30被引用 43

一句话总结

该论文研究多天线接入点的联合主动预编码和离散相IRS波束赋形，在SINR约束下最小化AP发射功率，覆盖单用户和多用户下行。结果表明，在大N极限，离散相IRS在功率增益方面可达到同连续相IRS相同的O(N^2)级别，同时存在一个与比特相关的固定功率损失。

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.

研究动机与目标

• 通过使用离散相移而非理想的连续相移，推动IRS的实际部署。
• 在SINR约束下，通过主动预编码与IRS离散相位的联合优化来最小化AP发射功率。
• 提供单用户的最优与低复杂度算法，并拓展到多用户场景。
• 表征相位离散化的渐近功率损失并与连续相基准进行比较。

提出的方法

• 在SINR约束下，将联合AP预编码和IRS离散相位移的问题建模为MINLP。
• 使用SOS1和分支定界将单用户子问题转换为ILP以实现全局最优性。
• 开发一个低复杂度的逐次细化算法，一次分配一个离散相位。
• 证明随着N增大，离散相位移产生的功率损失仅依赖于相位等级，与N无关，呈现一个常数。
• 扩展到多用户场景，使用零强制预编码并与基准进行比较。

实验结果

研究问题

• RQ1 离散IRS相位移在大N范围内是否能够实现与连续相位位移相同的渐近功率增益？
• RQ2 在单用户和多用户下行中，联合设计AP预编码和IRS离散相位的最优或近似最优策略是什么？
• RQ3 相位离散化相对于连续相IRS对发射功率和系统性能有何影响？
• RQ4 在功率损失和成本方面，IRS单元数N与相移分辨率b之间的权衡是什么？

主要发现

Number of control bits b	Power loss (dB)	Notes
1	3.9	离散1位相位移相对于连续情况的损失约为3.9 dB。
2	0.9	2位相位移损耗约0.9 dB。
3	0.2	3位相位移损耗约0.2 dB。
∞	0	连续相位移（理论极限）

• 对于单用户，离散相位IRS优化可以通过ILP（分支定界）实现全局最优，或通过低复杂度的逐次细化近似得到接近最优的性能。
• 当N → ∞时，接收功率比P_r(b)/P_r(∞) 收敛到 η(b) = ((2^b/π) sin(π/2^b))^2，意味着功率损失仅取决于b，而与N无关。
• 在b=1、2、3时，对应的渐近功率损失分别为3.9 dB、0.9 dB和0.2 dB，随着b增大趋近于连续相性能。
• 在大N极限下，连续相移的O(N^2)渐近平方功率增益对离散相位移仍然成立。
• 对于多用户场景，所提出的设计优于基于量化和基于码本的方案，并且在较少活动天线的情况下能够达到大规模MIMO多用户SINR性能水平。
• 仿真结果验证了理论分析并证实离散相位IRS设计的有效性。