Channel Estimation Algorithm for Reconfigurable Intelligent Surface Aided Millimeter Wave Systems
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摘要: 针对可重构智能表面(RIS)辅助的毫米波通信中信道状态信息难以获取问题，该文给RIS的部分器件配备射频链，以分开估计基站(BS)/用户(UE)到RIS之间的信道。根据该结构，提出一种低复杂度的信道估计算法。该算法首先采用解耦原子范数最小化(ANM)方法将信道的离开角和到达角的2维角度估计问题转化为两个1维的角度估计的半正定规划(SDP)问题；其次，利用交替方向乘子算法(ADMM)对该SDP问题进行求解，采用动量梯度下降法对信道矩阵参数进行更新以避免矩阵求逆运算，并通过对迭代步长和信道矩阵参数的联合优化以获得更加精准的信道估计值；最后利用信号的2维角度和信道矩阵参数得到路径增益估计。仿真结果表明，该算法达到了优良的信道估计性能，且在确保信道估计性能的系统参数设置下，该算法的复杂度较低。Abstract: As the channel status information is difficult to obtain in Reconfigurable Intelligent Surface(RIS) aided millimeter wave communication. The radio frequency chain is provided in some passive elements of RIS to assist channel estimation and estimate the channel between Base Station(BS)/User Equipment(UE) and RIS. Inspired by the structure, a low complexity channel estimation method is proposed. First, the two-dimensional angle estimation problem is transformed into two one-dimensional angle estimation Semi-positive definite programming (SDP) problem by the Atomic Norm Minimization(ANM) method.Second, an Alternating Direction Method of Multipliers(ADMM) algorithm is proposed to solve the Semi-Definite Programming (SDP) problem. Based on the ADMM algorithm, the algorithm applies momentum gradient descent method to avoid the inverse operation of the matrix, and improves the channel estimation accuracy by joint optimizing between a iteration step and channel parameters. Finally, the path gain estimation is obtained by using the signal angle and channel matrix. Simulation results show that the proposed algorithm has better channel estimation performance, and based on the system parameter set, the proposed algorithm has a low complexity.
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算法1 联合优化迭代步长和信道参数算法 输入：初始化$ {{\boldsymbol{H}}}_1^x $, $\beta = 0.5$, $\xi = 0.2$，容许误差$\varepsilon $, $t = 1$； (1)计算${ {\boldsymbol{g} } }_t^{} = {{\text{∇}} _{ { {({ {\boldsymbol{H} } }_{ {\rm{1} } }^x{ {\rm{)} } } }^t} } }{ {\boldsymbol{L} } }$，如果$ \left\| {{{{\boldsymbol{g}}}_t}} \right\| \le \varepsilon $，输出$ {({{\boldsymbol{H}}}_1^x)^t} $作为最优解； (2)令${{{\boldsymbol{d}}}_t}{{\boldsymbol{ = }}} - {{{\boldsymbol{g}}}_t}$； (3)根据式(14)确定迭代步长$ {\beta ^{{m_t}}} $； (4)计算式(15)，$t = t + 1$，转步骤(1)。 输出：$ {({{\boldsymbol{H}}}_1^x)^t} $, $ {\beta ^{{m_t}}} $。 
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算法2 D-ANM+改进ADMM信道估计算法 输入：BS, RIS, UE处的天线数目、导频信号、RIS射频链接收
的信号、噪声的功率，最大迭代次数${s_{\max }}$；计算UE-RIS的信道矩阵$ {{\boldsymbol{H}}}_1^{} $： (1)根据式(11)求解得到RIS水平射频链路接收信号的协方差矩阵； (2)根据解耦原子范数最小化方法，并采用改进的ADMM算法求
解式(17)，其信道参数的迭代过程如下：While $s \lt {s_{\max }}$ (a)根据算法1更新$ {({{\boldsymbol{H}}}_1^x)^t} $, $ {\beta ^{{m_t}}} $； (d)根据式(16)更新$({{{\boldsymbol{u}}}_x}, {{{\boldsymbol{u}}}_y})$； (e)根据式(17)更新${{\boldsymbol{U}}}$； (f)根据式(12c)更新${{\boldsymbol{\varLambda }}}$； (g)$s = s + 1$ End while (3)根据步骤(2)求解得到信道的估计值$ {{\boldsymbol{\tilde H}}}_1^x $, $ {{\boldsymbol{\tilde T}}}({{{\boldsymbol{u}}}_x}) $, $ {{\boldsymbol{\tilde T}}}({{{\boldsymbol{u}}}_y}) $； (4)采用Root-MUSIC算法求解角度和matrix pencil进行角度匹配
求解信道矩阵$ {{\boldsymbol{H}}}_1^{} $的UE端的离开角估计值$\tilde {{\boldsymbol{\varphi}}} $和RIS端的水平射频
链的AOA的方位角估计值$ {\boldsymbol{\tilde \theta}} $；并以相同的思路估计得到RIS端垂
直射频链的AOA的仰角估计值${{\boldsymbol{\tilde \phi}}} $；(5)根据式(19)，求解信道矩阵$ {{\boldsymbol{H}}}_1^{} $的路径增益${{\boldsymbol{\tilde \alpha}}} $； (6)根据以上得到的信道参数值$ ({\boldsymbol{\tilde \theta}} , {{\boldsymbol{\tilde \phi}}} , {{\boldsymbol{\tilde \varphi}}} , {{\boldsymbol{\tilde \alpha}}} ) $，得到估计的信道矩
阵$ {{\boldsymbol{\tilde H}}}_1^{} $；RIS-BS的信道矩阵${{{\boldsymbol{H}}}_2}$的估计参照步骤(1)～(6)的思路。 输出：UE-RIS估计的信道矩阵$ {{\boldsymbol{\tilde H}}}_1^{} $，RIS-BS估计的信道矩阵
${{{\boldsymbol{\tilde H}}}_2}$。
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