to be transmitted by the $m$th . Due to the distortion introduced by the quantization/unquantization processes, we have that [@Zamir96; @Femenias18] $$\hat{\mathcal{Q}}_{dm}({\boldsymbol}{x})\triangleq {\mathcal{Q}_d}_m^{-1}({\mathcal{Q}_d}_m({\boldsymbol}{x}))={\boldsymbol}{x}+{{\boldsymbol}{q}_d}_m,$$ where ${{\boldsymbol}{q}_d}_m$ is the quantization noise vector, which is assumed to be statistically distributed as ${{\boldsymbol}{q}_d}_m \sim \mathcal{CN}\left({\boldsymbol}{0},\sigma_{q_{dm}}^2 {\boldsymbol}{I}\right)$. As shown by Zamir *et al.* in [@Zamir96], this assumption is supported by the fact that large-block lattice quantization codes are able to approximate a Gaussian quantization noise distribution. Thus, the mathematical operations describing the - functional split considered in this paper can be summarized as $$\begin{split}
   {\boldsymbol}{x}_m=\mathcal{P}_m({\boldsymbol}{s}_d)&={\boldsymbol}{W}_m^{RF} \hat{\mathcal{Q}}_{dm}\left({\boldsymbol}{W}_{d\,m}^{BB} {\boldsymbol}{\Upsilon}^{1/2} {\boldsymbol}{s}_d\right) \\
                                   &={\boldsymbol}{W}_m^{RF} \left({\boldsymbol}{W}_{d\,m}^{BB} {\boldsymbol}{\Upsilon}^{1/2} {\boldsymbol}{s}_d + {{\boldsymbol}{q}_d}_m\right),
\end{split}
\label{eq:bsxm}$$ where ${\boldsymbol}{W}_d^{BB} = \left[{{\boldsymbol}{W}_{d\,1}^{BB}}^T\ \ldots\ {{\boldsymbol}{W}_{d\,M}^{BB}}^T\right]^T\ \in\ \mathbb{C}^{M L_A \times K}$, with ${\boldsymbol}{W}_{d\,m}^{BB}=\left[{\boldsymbol}{w}_{dm1}^{BB}\ \ldots\ {\boldsymbol}{w}_{dmK}^{BB}\right]\ \in\ \mathbb{C}^{L_A \times K}$ denoting the baseband precoding matrix affecting the signal transmitted by the $m$th , and ${\boldsymbol}{\Upsilon}=\operatorname{diag}\left([\upsilon_1\,\ldots\,\upsilon_K]\right)$ is a $K \times K$ diagonal matrix containing the power control coefficients in its main diagonal, which are chosen to satisfy the following necessary power constraint at the $m$th $$\begin{split}
   \mathbb{E}\left\{\left\|{\boldsymbol}{x}_m\right\|_F^2\right\} &= \sum_{k=1}^K \upsilon_k \theta_{mk}^{BB/RF}+{\sigma_q^2}_{dm} \left\|{\boldsymbol}{W}_m^{RF}\right\|_F^2 \\
                                                        &= \sum_{k=1}^K \upsilon_k \theta_{mk}^{BB/RF} + {\sigma_q^2}_{dm} L_A N \leq \overline{P}_m,
\end{split}
\label{eq:Power_constraint}$$ where we have used the definition $$\theta_{mk}^{BB/RF}=\mathbb{E}\left\{\left\|{\boldsymbol}{W}_m^{RF} {\boldsymbol}{w}_{dmk}^{BB}\right\|_F^2\right\}.$$

Using the proposed hybrid approach, the signal 