Statistically Optimal Beamforming and Ergodic Capacity for RIS-Aided MISO Systems
Statistically Optimal Beamforming and Ergodic Capacity for RIS-Aided MISO Systems
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DOI：
10.1109/access.2023.3347925
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发表时间：
2023-07
期刊：
影响因子：
3.9
通讯作者：
Kali Krishna Kota;I. M. S. S. M. Student Member-I.-M.-S.-S.-M.-Student-Member-2280938857;I. P. D. M. Student Member;I. H. S. D. Member;Kali Krishna Kota
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作者：
Kali Krishna Kota;I. M. S. S. M. Student Member-I.-M.-S.-S.-M.-Student-Member-2280938857;I. P. D. M. Student Member;I. H. S. D. Member;Kali Krishna Kota
本文重点研究最佳波束成形，以最大化无源可重构智能表面（RIS）辅助多输入单输出（MISO）下行链路系统的平均信噪比（SNR）。我们考虑一个现实的设置，其中与用户设备 (UE) 的直接和间接（通过 RIS）链接都会经历相关的莱斯衰落。这种通用衰落模型对于捕捉视距 (LoS) 和相关多径衰落的影响尤其重要，这些影响可能由于大量 RIS 元件的紧凑放置而发生。无源RIS的假设施加了单位模量约束，这使得波束形成问题成为非凸的。为了解决这个问题，我们应用半定松弛（SDR）来获得最佳相移矩阵，并提出一种迭代算法来获得发射波束成形矢量和RIS相移矩阵的统计最优解。此外，为了测量所提出的波束成形方案的性能，我们分析了关键系统性能指标，例如中断概率（OP）和遍历容量（EC）。与现有工作类似，OP 和 EC 评估依赖于所提出的迭代算法的数值计算。然而，这不利于揭示系统性能对视距（LoS）分量、相关衰落、反射元件数量、基站（BS）天线数量和衰落因子等关键参数的功能依赖性。为了克服这一主要限制，我们针对上述一般衰落模型的各种特殊情况推导了最佳波束形成矢量和相移矩阵的封闭式表达式。这些定点解决方案有助于导出 OP 的封闭式解决方案，进一步提供 EC 的直接评估。然后使用这些数学表达式来获得对系统性能的有用见解。我们通过分析确定了这样一个事实：当视距分量被阻塞时，相关衰落比独立同分布 (i.i.d.) 情况更有利。此外，我们还分析证明，在独立同分布下，在不存在/存在 LoS 分量的情况下，最大平均 SNR 随 RIS 元件的数量线性/二次提高。褪色。
This paper focuses on optimal beamforming to maximize the mean signal-to-noise ratio (SNR) for a passive reconfigurable intelligent surface (RIS)-aided multiple-input single-output (MISO) downlink system. We consider a realistic setting where both the direct and indirect (through RIS) links to the user equipment (UE) experience correlated Rician fading. Such a general fading model is particularly important to capture the impact of line-of-sight (LoS) and correlated multipath fading that may occur due to the compact placement of a large number of RIS elements. The assumption of passive RIS imposes the unit modulus constraint, which makes the beamforming problem non-convex. To tackle this issue, we apply semidefinite relaxation (SDR) to obtain the optimal phase-shift matrix and propose an iterative algorithm to obtain a statistically optimal solution for the transmit beamforming vector and RIS-phase shift matrix. Further, to measure the performance of the proposed beamforming scheme, we analyze key system performance metrics such as outage probability (OP) and ergodic capacity (EC). Similar to the existing works, the OP and EC evaluations rely on the numerical computation of the proposed iterative algorithm. However, this is not conducive to revealing the functional dependence of system performance on key parameters such as line-of-sight (LoS) components, correlated fading, number of reflecting elements, number of antennas at the base station (BS), and fading factor. To overcome this major limitation, we derive closed-form expressions for the optimal beamforming vector and phase shift matrix for various special cases of the above general fading model. These fixed-point solutions aid in deriving a closed-form solution for OP that further provides a direct evaluation of EC. These mathematical expressions are then used to gain useful insights into the system’s performance. We analytically establish the fact that correlated fading is more beneficial than the independent and identically distributed (i.i.d.) case when the LoS components are blocked. Further, we also analytically demonstrate that the maximum mean SNR improves linearly/quadratically with the number of RIS elements in the absence/presence of LoS component under i.i.d. fading.