equipped with a one-dimensional uniform linear array (ULA),[^6] with antennas separated by one-half wavelength. Then the BS array response vector corresponding to the incidence angle $\theta$ with respect to the perpendicular to the array is given by [@Clerckx13MIMO] $$\begin{aligned}
\label{eq:ula steer vec}
  {{\mathbf{v}}_{M,\theta}}&=\bigg[1\quad{\exp\left(-{\bar{\jmath}}\pi{\sin\left(\theta\right)}\right)}\quad\ldots{\notag\\}&\qquad\ldots\quad{\exp\left(-{\bar{\jmath}}\pi(M-1){\sin\left(\theta\right)}\right)}\bigg]^{T}\in{\mathbb{C}}^{M\times 1}.\end{aligned}$$ We assume that the signals seen at the BS are constrained to lie in the angle interval ${\mathcal{A}}=[-\pi/2,\pi/2]$, which can be achieved through the use of directional antennas at the BS, and thus no signal is received at the BS for incidence angles $\theta\notin{\mathcal{A}}$ [@You15Pilot].

We consider OFDM modulation with ${N_{\mathrm{c}}}$ subcarriers, performed via the ${N_{\mathrm{c}}}$-point inverse DFT operation, appended with a guard interval (a.k.a. cyclic prefix) of length ${N_{\mathrm{g}}}\left(\leq{N_{\mathrm{c}}}\right)$ samples. We employ ${T_{\mathrm{sym}}}=\left({N_{\mathrm{c}}}+{N_{\mathrm{g}}}\right){T_{\mathrm{s}}}$ and ${T_{\mathrm{c}}}={N_{\mathrm{c}}}{T_{\mathrm{s}}}$ to denote the OFDM symbol duration with and without the guard interval, respectively, where ${T_{\mathrm{s}}}$ is the system sampling duration [@Dahlman11LTE]. We assume that the guard interval length ${T_{\mathrm{g}}}={N_{\mathrm{g}}}{T_{\mathrm{s}}}$ is longer than the maximum channel delay of all the UTs [@Edfors98OFDM; @Li98Robust].

We assume that the channels remain constant during one OFDM symbol, and evolve from symbol to symbol. We denote the uplink (UL) channel gain between the antenna of the [$k$th]{} UT and the [$m$th]{} antenna of the BS 