An Asymptotically MSE-Optimal Estimator Based on Gaussian Mixture Models
An Asymptotically MSE-Optimal Estimator Based on Gaussian Mixture Models
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DOI：
10.1109/tsp.2022.3194348
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发表时间：
2021-12
影响因子：
5.4
通讯作者：
M. Koller;B. Fesl;N. Turan;W. Utschick
中科院分区：
文献类型：
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作者：
M. Koller;B. Fesl;N. Turan;W. Utschick
针对加性高斯噪声背景下的线性逆问题，研究了一种基于高斯混合模型的信道估计器。我们将GMM与给定的信道样本进行拟合，得到近似真实信道概率密度函数的解析概率密度函数。然后，以封闭形式计算对应于该近似PDF的条件均值估计器(CME)，并将其用作基于真实信道PDF的最优CME的近似值。该最优CME不能解析地计算，因为真实的通道PDF通常是未知的。我们给出了一些温和的条件，使我们能够证明随着GMM分量的增加，基于GMM的CME收敛到最优CME。此外，我们研究了估计器的计算复杂性，并基于常见的基于模型的见解提出了简化方案。进一步，我们研究了估计器在多输入多输出(MIMO)和宽带系统的数值实验中的行为。
This paper investigates a channel estimator based on Gaussian mixture models (GMMs) in the context of linear inverse problems with additive Gaussian noise. We fit a GMM to given channel samples to obtain an analytic probability density function (PDF) which approximates the true channel PDF. Then, a conditional mean estimator (CME) corresponding to this approximating PDF is computed in closed form and used as an approximation of the optimal CME based on the true channel PDF. This optimal CME cannot be calculated analytically because the true channel PDF is generally unknown. We present mild conditions which allow us to prove the convergence of the GMM-based CME to the optimal CME as the number of GMM components is increased. Additionally, we investigate the estimator's computational complexity and present simplifications based on common model-based insights. Further, we study the estimator's behavior in numerical experiments including multiple-input multiple-output (MIMO) and wideband systems.