content(symbol): 噪声方差全文统一记为 \sigma(去 n 与 ^2)
B:10 早已声明"\sigma 表示方差",sec1/D 遵守,多星侧却用 \sigma_{n,\ell}^2
偏离。统一回归该约定:\sigma_{n,\ell}^2->\sigma_\ell、\sigma_n^2->\sigma
(去 n 与 ^2);推导中的方差平方 \sigma_{n,\ell}^4->\sigma_\ell^2;白化
标准差 1/\sigma_{n,\ell}->1/\sqrt{\sigma_\ell}(E:765);E 共同方差情形裸
\sigma^2->\sigma。D 里 \sigma=方差的幂次 \sigma^2/\sigma^4 本就正确、保留。
清理替换产生的循环定义(sec1/D)。如此推导上标即方差的真实幂次,不与
"方差自带 ^2"冲突。
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@@ -181,7 +181,7 @@ e^{-j 2\pi \frac{d}{\lambda_{\mathrm{c}}}(M-1)\sin\theta_k}
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where $d$ denotes the inter-element spacing and $\lambda_{\mathrm{c}}$ is the carrier wavelength.
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Assuming that the source signals are mutually uncorrelated and that the noise is spatially white with variance $\sigma_n^2$, the array covariance matrix is
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Assuming that the source signals are mutually uncorrelated and that the noise is spatially white with variance $\sigma$, the array covariance matrix is
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\begin{equation}
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\mathbf{R}_y
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@@ -190,7 +190,7 @@ Assuming that the source signals are mutually uncorrelated and that the noise is
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=
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\mathbf{A}(\boldsymbol{\theta}) \mathbf{R}_s \mathbf{A}^{\Herm}(\boldsymbol{\theta})
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+
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\sigma_n^2 \mathbf{I}_M,
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\sigma \mathbf{I}_M,
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\label{eq:music_covariance}
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\end{equation}
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@@ -543,7 +543,7 @@ where $\mathbf{n}_{\ell} \triangleq \vect(\mathbf{N}_{\ell})$ and
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is the spatio-temporal steering vector, with $\otimes$ denoting the Kronecker product. Hence, the joint angle-Doppler estimation problem can be recast as a standard subspace estimation problem in the augmented spatio-temporal domain.
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Assuming that the source signals are mutually uncorrelated and the noise is spatially and temporally white with variance $\sigma_n^2$, the covariance matrix of $\mathbf{y}_{\ell}$ is given by
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Assuming that the source signals are mutually uncorrelated and the noise is spatially and temporally white with variance $\sigma$, the covariance matrix of $\mathbf{y}_{\ell}$ is given by
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%
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\begin{equation}
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\mathbf{R}_y
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@@ -552,7 +552,7 @@ Assuming that the source signals are mutually uncorrelated and the noise is spat
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=
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\mathbf{B}_{\mathrm{st}}\mathbf{R}_{\zeta}\mathbf{B}_{\mathrm{st}}^\Herm
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+
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\sigma_n^2 \mathbf{I}_{MT},
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\sigma \mathbf{I}_{MT},
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\label{eq:covariance_st}
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\end{equation}
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