## 2 System Model
The multipath fading SIMO channel is modeled as a tapped delay line (TDL) with \(L\) taps (paths), and the channel matrix can be written as follows:  
\[\mathbf{H}(t)=\sum_{l=1}^{L}\mathbf{H}_{l}(t)\delta(t-\tau_{l}) \tag{1}\]  
where \(\mathbf{H}_{l}(t)\) is the SIMO channel matrix of the \(l\)-th path, \(\tau_{l}\) is the delay of the \(l\)-th path and \(\delta()\) is the delta function defined as \(\delta(t)=1\)_if_\(t=0,\delta(t)=0\), otherwise. Assuming that all paths are Rice distributed with mean power \(\gamma_{l}\), the matrix \(\mathbf{H}_{l}(t)\) can be separated into a fixed matrix \(\mathbf{H}_{l}^{\mathrm{F}}(t)\) representing the LOS (non variable) part, and a Rayleigh-distributed matrix \(\mathbf{H}_{l}^{\mathrm{V}}(t)\) which represents the NLOS (variable) part. The matrix \(\mathbf{H}_{l}(t)\) can be thus written as follows:  
\[ \begin{split}&\mathbf{H}_{l}(t)=\sqrt{\gamma_{l}}\Bigg{(}\sqrt{ \frac{\xi}{\zeta+1}}\mathbf{H}_{l}^{\mathrm{F}}(t)+\sqrt{\frac{1}{\zeta+1}} \mathbf{H}_{l}^{\mathrm{V}}(t)\Bigg{)}=\\ &\sqrt{\gamma_{l}}\Bigg{(}\sqrt{\frac{\zeta}{\zeta+1}}\begin{bmatrix} e^{\phi_{l}(t)}\\ e^{\phi_{l}(t)}\end{bmatrix}+\sqrt{\frac{1}{\zeta+1}}\begin{bmatrix}X_{1}(t)\\ X_{2}(t)\\ \vdots\\ X_{Q}(t)\end{bmatrix}\Bigg{)}\end{split}  \tag{2}\]  
where  
* \(X_{i}(t)\) is the coefficient of the \(i\)-th receiving antenna in the NLOS condition. The \(X_{i}\) coefficients are correlated complex Gaussian random variables with zero mean and unitary variance;
* \(\phi_{i}(t)\) is the phase difference between the transmitting and the \(i\)-th receiving antenna;
* \(\zeta\) is the Ricean factor;
* \(\gamma_{l}\) is the mean power of the \(l\)-th path at the receiver. Each tap \(\mathbf{H}_{l}(t)\) is composed by a cluster of individual propagation rays so that the complex Gaussian assumption is valid. The path loss model is a free space loss breakpoint model with two fixed slope values: a standard \(L_{FS}\) (slope of 2) up to the breakpoint distance and slope of 3.5 afterwards  
\[ \begin{cases}L(d)=L_{FS}(d),\ \ \ \text{for}\ \ \ d<=d_{BP}\\ L(d)=L_{FS}(d_{BP})+35\log_{10}(d/d_{BP}),\ \ \ \text{for}\ \ \ d>d_{BP}\end{cases}  \tag{3}\]  
where \(d\) is the distance [m] with \(5<d<100\) and \(d_{BP}\) is the breakpoint distance [m]. In our proposed system, we are interested in several channel attributes, not only those related to the signal amplitude. Hence, we have integrated the TGa model with the WINNER II [36] model for what concerns the delays and the angle of arrival (AoA) information. In particular, since paths delays are fixed in the TGa model in every channel realization, we used the distribution proposed by WINNER II to model the paths delays. In the WINNER II model, each user has a delay profile randomly selected: the average delay of each path, \(\tau_{l}^{\mathrm{avg}}\), is generated using an exponential distribution with parameter \(\lambda\)[36]. Moreover, to take into account the scatterers' movement in the surrounding environment as well as delays estimation errors, we introduced a certain variability of the delay values around their mean value, \(\tau_{l}^{\mathrm{avg}}\). The delay of each path, \(\tau_{l}\), is derived from an uniform distribution with mean \(\tau_{l}^{\text{avg}}\) and variance \(\sigma_{\tau}^{2}=1/\lambda\). For the same reasons and following a similar procedure also, AoA values are randomly distributed around their mean value. In particular, following the model in [36], AoA is normal distributed \(\mathcal{N}(\mu,\sigma_{AoA}^{2})\), where the mean value \(\mu\) is chosen as the geometrical direction of the sink-node link and the variance is \(\sigma_{AoA}^{2}\).