Algorithm 1 Optimal phase shift using Wiener filter

Input: S: the number of samples N: the number of reflecting elements I: the number of receiver antennas $\mathbf{R}$: array of shape (S, I, I) representing the auto-correlation of the received signal ${\mathbf{H}}_{eff}$: array of shape (S, N, I) representing the channel gain matrix Output: $\mathbf{W}$: array of shape (S, N, I) containing the optimal phase shift vectors Algorithm: 1: Initialize an array $\mathbf{W}$ of shape (S, N, I) with complex zeros. 2: For i = 0 to S − 1: Compute the optimal phase shift vector for sample i: (i). Compute the inverse of the matrix $\mathbf{R}\left[i\right]$. (ii). Compute the complex conjugate transpose of the matrix ${\mathbf{H}}_{eff}\left[i\right]$. (iii). Multiply the inverse of $\mathbf{R}\left[i\right]$ with the complex conjugate transpose of ${\mathbf{H}}_{eff}\left[i\right]$. (iv). Assign the resulting matrix to $\mathbf{W}\left[i\right]$. 3: Return $\mathbf{W}$.