Orthogonal Time Frequency Space Channel Estimation Based on Model-driven Deep Learning
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摘要: 针对单输入单输出(SISO)的正交时频空间(OTFS)调制系统，该文利用一种模型驱动深度学习算法进行OTFS信道估计。该方案首先将去噪近似消息传递(DAMP)算法进行深度展开，利用去噪卷积神经网络代替传统的去噪器，对含噪的时延多普勒信道进行去噪估计，然后提供了状态演化方程来预测可学习去噪近似消息传递(LDAMP)算法的理论归一化均方误差性能。仿真结果表明，相比于其他估计方案，该方案不仅在低信噪比条件下具有优越的性能表现，而且还具有非常好的鲁棒性，在信道路径总数不变时，增加OTFS 2维网格点数量，可以有效提升信道估计精确度。Abstract: In this paper, a channel estimation scheme based on model-driven deep learning algorithm is proposed for Single Input Single Output (SISO) Orthogonal Time Frequency Space (OTFS) modulation systems. First, the Denoising Approximate Message Passing (DAMP) algorithm is considerably expanded. Then the traditional denoiser is replaced by the Denoising Convolutional Neural Network (DnCNN) to estimate the delay-Doppler channel with additive white Gaussian noise. The State Evolution (SE) equation is provided to predict the theoretical Normalized Mean Square Error (NMSE) performance of the Learned Denoising based Approximate Message Passing (LDAMP) algorithm. Simulation results show that the scheme performs well under a low Signal-to-Noise Ratio (SNR) and has great robustness compared with other estimation schemes. When the total number of channel paths is invariant, increasing the number of OTFS two-dimensional grid points can effectively improve channel estimation accuracy.
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算法1 基于OTFS系统的LDAMP算法 输入：测量矩阵：$ {\mathbf{X}} $；观测矢量：$ {\mathbf{y}} $；迭代次数：$ L $ 初始化：$ {{\mathbf{z}}^0} = {\mathbf{y}} $,$ {\hat \sigma ^0} = ||{{\mathbf{z}}^0}|{|_2}/\sqrt {MN} $, $ {\mathbf{\hat h}}_{{\text{eff}}}^0 = 0 $ for $ l = 0,1, \cdots ,L - 1 $ do (1) $ {\mathbf{\hat h}}_{{\text{eff}}}^{l + 1} = {D_{{{\hat \sigma }^l}}}({\mathbf{\hat h}}_{{\text{eff}}}^l + {{\mathbf{X}}^{\text{T}}}{{\mathbf{z}}^l}) $ (2) $ {{\mathbf{c}}^{l + 1}} = {{\mathbf{z}}^l}{\text{div}}{D_{{{\hat \sigma }^l}}}({\mathbf{\hat h}}_{{\text{eff}}}^l + {{\mathbf{X}}^{\text{T}}}{{\mathbf{z}}^l})/MN $ (3) $ {{\mathbf{z}}^{l{\text{ + }}1}} = {\mathbf{y}} - {\mathbf{X\hat h}}_{{\text{eff}}}^{l{\text{ + }}1} + {{\mathbf{c}}^{l + 1}} $ (4) $ {\hat \sigma ^{l{\text{ + }}1}} = ||{{\mathbf{z}}^{l{\text{ + }}1}}|{|_2}/\sqrt {MN} $ end for 输出：时延多普勒信道估计值$ {{\mathbf{\hat h}}_{{\text{eff}}}} = {\mathbf{\hat h}}_{{\text{eff}}}^L $ 
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表 2 主要仿真参数设置
参数名称 参数设置 载波数$ M $ $ 4,8,12 $ 符号数$ N $ $ 4,8,12 $ 子载波间隔$ \Delta f $ $15{\text{ kHz} }$ 载波频率$ {f_{\text{c}}} $ $ 4{\text{ GHz}} $ 带宽B 0.18 MHz 波长 75 mm 调制方式 4-QAM 信道模型 EVA
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