Maximum likelihood (ML) amplitude and noise variance estimation without having to jointly estimate the frequency and the phase and based only on information from the noisy received signal magnitude, is studied for a single sinusoid in complex additive white Gaussian noise. This estimation problem is equivalent to the classic problem of parameter estimation for the Rician distribution. While solving the likelihood equation is impossible in general, we propose a new approach based on a large argument approximation. For the case with known noise variance, a closed-form ML amplitude estimator is obtained, which outperforms the conventional root-mean-square estimator. For the case with unknown noise variance, the closed-form joint amplitude and noise variance estimators obtained do not require prior knowledge of one another.

中文翻译：

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最大似然，基于幅度的幅度和噪声方差估计

对于复杂的加性高斯白噪声中的单个正弦波，研究了最大似然（ML）幅度和噪声方差估计，而不必共同估计频率和相位，并且仅基于来自嘈杂接收信号幅度的信息。此估计问题等效于Rician分布的参数估计的经典问题。虽然一般来说不可能求解似然方程，但我们提出了一种基于大自变量近似的新方法。对于已知噪声方差的情况，获得了一个封闭形式的ML幅度估计器，它优于传统的均方根估计器。对于噪声方差未知的情况，获得的闭合形式联合幅度和噪声方差估计器不需要先验知识。