A Low Complexity Millimeter Wave Channel Estimation Algorithm in Reconfigurable Intelligent Surface
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摘要: 针对可重构智能表面(RIS)辅助的大规模多输入多输出(MIMO)毫米波系统中信道估计复杂度高的问题，该文提出一种低复杂度的信道估计算法。在该方案中，将RIS部分元素连接射频(RF)链，分离估计基站/用户和RIS之间的信道，分开获取信道有助于提升用户移动性场景下信道估计的灵活性。在所考虑系统中，首次使用低复杂度的2维快速傅里叶变换(2D-FFT)算法对角度进行估计，并考虑信号补零以获得更加精准的角度估计值，最后利用信号2维空间谱的谱峰和其对应的辐角得到路径增益估计。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，该算法具有压倒性的复杂度优势。Abstract: In this paper, a low complexity channel estimation algorithm is proposed, which is used to reduce the computational complexity of the millimeter wave channel estimation in the massive MIMO systems assisted by the Reconfigurable Intelligent Surfaces (RIS). In the proposed scheme, some elements of the RIS are connected to the Radio Frequency (RF) chain to estimate the channel between the base station/user and the RIS separately, which improves the flexibility of channel estimation. The zero-padding two-Dimensional Fast Fourier Transform (2D-FFT) algorithm is used for angle estimation in this scenario for the first time. The path gain estimation is obtained by using the spectral peak of the two-dimensional spatial spectrum of the signal and its corresponding argument. Simulation results show that the proposed algorithm achieves excellent channel estimation performance, and based on the system parameter setting to ensure the channel estimation performance, the proposed algorithm has a strong complexity advantage.
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表 1 本文算法流程表
算法：基于2D-FFT的RIS辅助通信系统信道估计 (1) 输入：RIS射频链接收信号：${\boldsymbol{Y}}_k^x$,${\boldsymbol{Y}}_k^y$；BS接收信号：${\boldsymbol{Y}}_{ {\text{BS} } }^x$ ,${\boldsymbol{Y}}_{ {\text{BS} } }^y$；导频： ${\boldsymbol{\varGamma}} _k^{}$,${\boldsymbol{\varGamma}} _{\text{R} }^x$,${\boldsymbol{\varGamma}} _{\text{R} }^y$；反射矩阵：${\boldsymbol{\varPhi}}$ (2) 所有接收信号与导频信号解相关，如${\boldsymbol{Y} }'^x_k = {\boldsymbol{Y} }_k^x{\boldsymbol{\varGamma} } _k^x = {\boldsymbol{H} }_k^x + {\boldsymbol{N} }'^x_k$ (3) 信号补0处理，并对其进行2D-FFT得到峰值点位置。如${\boldsymbol{Y} }'^x_k $补0得到${\boldsymbol{Y}}'^{x,{\text{pad} } }_k$，对其进行2D-FFT变换得到第$l_a $条路径峰值位置$ (m_{l_a}^x,n_{l_a}^x)$ (4) 得到链路对应角度估计值，如 $\hat \phi _{ { {\mathbf{H} }_k} }^{ {l_a} } = \arcsin \left(\dfrac{\lambda }{ { {d_{\text{R} } } } } \cdot \dfrac{ {m_{ {l_a} }^x} }{ {L'} }\right),{\text{ } }\hat \varphi _{ { {\mathbf{H} }_k} }^{ {l_a} } = \arcsin \left(\dfrac{\lambda }{ { {d_{\text{U} } } } } \cdot \dfrac{ {n_{ {l_a} }^x} }{ {M'} }\right)$ 并以相同思路分别得到RIS竖直RF链AOA的仰角估计值$\hat \theta _{{{\mathbf{H}}_k}}^{{l_a}}$，BS端的AoA估计值$\hat \psi_{l_b} $，RIS到BS的仰角和方位角的估计值$\gamma_{l_b} $, $ \hat\varphi_{l_b} $ (5) 依据补0后接收信号空间谱得到路径增益，如$ {\hat a_{{l_a}}}{\text{ = }}{\hat \beta _{{l_a}}}{{\text{e}}^{{\text{j}}{{\hat \alpha }_{{l_a}}}}} $其中 ${\hat \beta _{ {l_a},k} } \approx \dfrac{1}{ {LM} }{\text{|} }\tilde {\boldsymbol{Y}}'^{x,{\text{pad} } }_k(m_{ {l_a} }^x,n_{ {l_a} }^x){\text{|, } }{\hat \alpha _{ {l_a} } } \approx \arctan \dfrac{ { {\text{imag} }(\tilde {\boldsymbol{Y}}'^{x,{\text{pad} } }_k(m_{ {l_a} }^x,n_{ {l_a} }^x))} }{ { {\text{real} }(\tilde {\boldsymbol{Y}}'^{x,{\text{pad} } }_k(m_{ {l_a} }^x,n_{ {l_a} }^x))} }$ 并以相同思路得到RIS到BS端路径增益估计$\hat b_{l_b} $ (6) 输出：依据以上参数估计值，得到信道估计值
${\hat {\boldsymbol{H}}_k} = \displaystyle\sum\limits_{ {l_a} = 0}^{ {L_a} - 1} { { {\hat a}_{ {l_a} } }a_{ {\text{UR} } }^{}(\hat \theta _{ { {\mathbf{H} }_k} }^{ {l_a} },\hat \phi _{ { {\mathbf{H} }_k} }^{ {l_a} })a_{\text{U} }^{\text{H} }(\hat \varphi _{ { {\mathbf{H} }_k} }^{ {l_a} })} {\text{, } }\hat G{\text{ = } }\sum\limits_{ {l_b} = 0}^{ {L_b} - 1} { { {\hat b}_{ {l_b} } }{a_{\text{B} } }({ {\hat \psi }_{ {l_b} } })a_{ {\text{RB} } }^{\text{H} }({ {\hat \gamma }_{ {l_b} } },{ {\hat \varphi }_{ {l_b} } })}$
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表 2 不同算法计算复杂度对比
信道估计算法 计算复杂度 基于子空间的信道估计算法 $\begin{gathered} {\text{ } }O(\frac{ {32} }{3}({N^3} + {P^3}) + ({P^2} + {N^2})(2T + 2{L_a} - 2) + \\ +PM(2T + 2P - 2) + NP(2T + 2N - 2)) \\ \end{gathered}$ MUSIC+ML $\begin{gathered} {\text{ } }O(\frac{ {52} }{3}({(LT)^3} + {(NT)^3}) + 2({(NT)^2} + {(LT)^2}) + 2{L_a}{D_{ {\text{MUSIC} } } }(8MT - 4T \\ + 4({(LT)^2} + {(NT)^2}) - 4(L{L_a}T + N{L_a}T) + 2T(L + N) - 2) + 12L_a^3 \\ +{\text{2} }L_a^2(4(L + N) + 8T - 6) + 2{L_a}(2 - 2N + 2T(L + N) + 6T(M + L) - 8T)) \\ \end{gathered}$ Root-MUSIC+ML $\begin{gathered} {\text{ } }O(26({(LT)^3} + {(NT)^3}) + 3T({L^2} + {N^2}) + 18L_a^3 + {\text{3} }L_a^2(4(L + N) + 8T - 6) \\ + 3{L_a}(2 - L - N + 2T(N + L) + 6T(M + L) - 8T)) \\ \end{gathered}$ 本文算法 ${\text{ }}2({L^2}(M + N) + 3(M\log (M) + N\log (N)) + 6L\log (L) + 2L(2T - 1)(M + N)$
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