defined by $$\label{eq:System}
    \mathbf{Y} = \mathbf{G}_{n_T}\mathbf{H}^T+  \mathbf{N}\;,$$ where $\mathbf{G}_{n_T}$ is the ($T \times n_T $) transmit matrix, $\mathbf{Y}=[\mathbf{y}_1,\dots,\mathbf{y}_{n_R}]$ is the ($T \times n_R$) receive matrix, $\mathbf{H}=[\mathbf{h}_1,\dots,\mathbf{h}_{n_T}]$ is a ($n_R \times n_T $) matrix characterizing the coherent channel, and $\mathbf{N}=[\mathbf{n}_1,\dots,\mathbf{n}_{n_R}]$ is the complex ($T
\times n_R$) white Gaussian noise (AWGN) matrix, where an entry $\{n_{ti}\}$ of $\mathbf{N}$ ($1\leq i \leq n_R$) denotes the complex noise at the $i$th receiver for a given time $t\,(1\leq t \leq T)$. The real and imaginary parts of $n_{ti}$ are independent and $\mathcal{N}$(0,$n_T/(2\mathrm{SNR})$) distributed. An entry of the channel matrix is denoted by {$h_{ij}$}. This represents the complex gain of the channel between the $j$th transmit ($1\leq j \leq
n_T$) and the $i$th receive ($1\leq i \leq n_R$) antenna, where the real and imaginary parts of the channel gains are independent and normal distributed random variables with $\mathcal{N}$(0,1/2) per dimension. The channel matrix is assumed to be constant for a block of $T$ symbols and changes independently from block to block. The average power of the symbols transmitted from each antenna is normalized to be $\nicefrac{1}{n_T}$, so that the average power of the received signal at each receive antenna is one and the signal-to-noise ratio (SNR) 