payload data transmission
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In the , the vector of received signals at the output of the $L_A$ chains (including the phase shifters) of the $m$th is given by $$\begin{split}
   {{\boldsymbol}{r}_u}_m=&\sqrt{P_u}\sum_{k'=1}^K {\boldsymbol}{g}_{mk'} \sqrt{\omega_{k'}} {s_u}_{k'} + {{\boldsymbol}{n}_u}_m \\
               =&\sqrt{P_u}{\boldsymbol}{G}_m {\boldsymbol}{\Omega}^{1/2} {\boldsymbol}{s}_u + {{\boldsymbol}{n}_u}_m,
\end{split}$$ where $P_u$ is the maximum average transmit power available at any of the active , ${\boldsymbol}{s}_u=[{s_u}_1\,\ldots\,{s_u}_K]^T$ denotes the vector of symbols transmitted by the $K$ active , ${\boldsymbol}{\Omega}=\operatorname{diag}([\omega_1\,\ldots\,\omega_K])$, with $0 \leq \omega_k \leq 1$, is a matrix containing the power control coefficients used at the , and ${{\boldsymbol}{n}_u}_m \sim \mathcal{CN}({\boldsymbol}{0},\sigma_u^2(N) {\boldsymbol}{I}_{L_A})$ is the vector of additive thermal noise samples at the output of the $L_A$ chains of the $m$th . The received vector of signals at each of the in the network is quantized and forwarded to the via the fronthaul links, where they are unquantized and jointly processed using a set of baseband combining vectors. Using a similar approach to that employed to model the transmission, the received vector of (unquantized) samples from the $m$th can be expressed as $${{\boldsymbol}{z}_u}_m=\hat{\mathcal{Q}}_{um}\left({{\boldsymbol}{r}_u}_m\right)={{\boldsymbol}{r}_u}_m + {{\boldsymbol}{q}_u}_m,$$ where ${{\boldsymbol}{q}_u}_m$ is the quantization noise vector, which is assumed to be statistically distributed as ${{\boldsymbol}{q}_u}_m \sim \mathcal{CN}\left({\boldsymbol}{0},\sigma_{q_{u m}}^2 {\boldsymbol}{I}_{L_A}\right)$. Now, assuming the use 