Fundamentals of RIS-Aided Localization in the Far-Field
Fundamentals of RIS-Aided Localization in the Far-Field
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DOI：
10.1109/twc.2023.3307818
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发表时间：
2022-06
影响因子：
10.4
通讯作者：
Student Member Ieee Don-Roberts Emenonye;S. M. I. Harpreet S. Dhillon-S.-M.-I.-Harpreet-S.-Dhillon-2226656304;F. I. R. Michael Buehrer
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文献类型：
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作者：
Student Member Ieee Don-Roberts Emenonye;S. M. I. Harpreet S. Dhillon-S.-M.-I.-Harpreet-S.-Dhillon-2226656304;F. I. R. Michael Buehrer
本文在可重构智能表面 (RIS) 的帮助下，开发了正交频分复用 (OFDM) 系统定位的基本界限。具体来说，我们从假设 RIS 的位置和方向可以被视为无线系统中 RIS 辅助定位的先验信息开始，并推导出用户设备 (UE) 定位的贝叶斯界限。为此，我们首先导出通道参数的贝叶斯费舍尔信息矩阵 (FIM)，以导出贝叶斯定位边界。然后，为了关注几何信道参数，我们推导了等效Fisher信息矩阵（EFIM）并表明它具有确定的结构。随后，我们通过与 EFIM 相关的信息损失表明，当 RIS 反射系数在所有 OFDM 符号上保持恒定，并且没有有关干扰参数的先验信息时，EFIM 中与 RIS 角度参数相关的相应子矩阵是零矩阵。由于 EFIM 是零矩阵，当 RIS 反射系数在所有 OFDM 符号上保持恒定时，不可能估计 RIS 相关的角度信道参数。这一观察对于 RIS 相关角度参数的估计至关重要。它规定要估计与 RIS 相关的角度参数，必须有多个具有不同 RIS 反射系数的 OFDM 传输。此外，由于这一观察，我们注意到，当 RIS 反射系数在所有 OFDM 符号上保持恒定时，通过从单个 RIS 到 UE 的反射接收到的信号来定位单个天线 UE 在远场中是不可行的。我们还表明，RIS 相关通道参数的 FIM 可以分解为 i）接收器提供的信息，ii）发射器提供的信息，以及 iii）RIS 组件提供的信息。然后，我们将几何通道参数的贝叶斯 EFIM 转换为 UE 位置和方向参数的贝叶斯 FIM，并检查其在特定类别 RIS 反射系数下的具体结构。
This paper develops fundamental bounds for localization in orthogonal frequency division multiplexing (OFDM) systems aided by reconfigurable intelligent surfaces (RISs). Specifically, we start from the assumption that the position and orientation of a RIS can be viewed as prior information for RIS-aided localization in wireless systems and derive Bayesian bounds for the localization of a user equipment (UE). To do this, we first derive the Bayesian Fisher information matrix (FIM) for channel parameters to derive the Bayesian localization bounds. Then, to focus on the geometric channel parameters, we derive the equivalent Fisher information matrix (EFIM) and show that it has a definite structure. Subsequently, we show through the information loss associated with the EFIM that when the RIS reflection coefficients remain constant across all OFDM symbols, and there is no prior information about the nuisance parameters, the corresponding submatrix in the EFIM related to the RIS angle parameters is a zero matrix. As a result of the EFIM being a zero matrix, estimating the RIS-related angle channel parameters is not possible when the RIS reflection coefficients remain constant across all OFDM symbols. This observation is crucial for the estimation of the RIS-related angle parameters. It dictates that to estimate the RIS-related angle parameters, there must be more than one OFDM transmission with differing RIS reflection coefficients. Furthermore, due to this observation, we note that localization of a single antenna UE through the signals received from reflections from a single RIS to the UE is not feasible in the far-field when the RIS reflection coefficients remain constant across all OFDM symbols. We also show that the FIM for the RIS-related channel parameters can be decomposed into i) information provided by the receiver, ii) information provided by the transmitter, and iii) information provided by the RIS components. We then transform the Bayesian EFIM for geometric channel parameters to the Bayesian FIM for the UE position and orientation parameters and examine its specific structure under a particular class of RIS reflection coefficients.