The system model consists of:
A uniform linear array (ULA) with \(N\) equally \(d\)-spaced antenna elements and,
A set of \(S\) sources emitting or echoing narrow-band independent signals $\textbf{x}_1,\ldots,\textbf{x}_S$.
The direction of arrival (in azimuth) of these signals at the ULA are $\theta_1,\ldots,\theta_S$.
The signal $\textbf{a}(t)=[a_1(t),\ldots,a_N(t)]$ received by the ULA at time \(t\) can be expressed in matrix form as $\textbf{a}=\textbf{D}\times\textbf{x}+\textbf{w}$ where $\mathbf{D}=[d_{\theta_1},\ldots,d_{\theta_S}]^T$ and $\textbf{d}_{\theta_k}$ is the \(k\)-th steering vector for the ULA. The vector $\textbf{w}$ is uncorrelated white Gaussian noise. The data vectors $\textbf{a}(t)$ may be collected into a $128 \times 8$ snapshot matrix $\textbf{A}$ to collect one sample from each of \(8\) elements of the array obtained over \(128\) consecutive time instants. The following diagram shows the ULA receiving scenario.