## 2 MIMO-WCDMA Orientation
Moreover, \(\mathbf{r}_{n,l}\) is the multiplying maximal ratio combining (MRC) vector matrix, given by [18; 19]  
\[\mathbf{r}_{n,l}=\left(\mathbf{H}_{n,l}\mathbf{w}_{n}\right)^{\text{H}} \tag{4}\]  
While \(\rho\) and \(\bar{\rho}\) are the partial cross-correlations of the spreading sequences:  
\[\rho_{n,n^{\prime},l}=\int\limits_{0}^{l\text{T}_{c}}\overline{c_{n}(t-l \text{T}_{c})}c_{n^{\prime}}(t)dt \tag{5}\]  
\[\bar{\rho}_{n,n^{\prime},l}=\int\limits_{l\text{T}_{c}}^{T}\overline{c_{n}(t-l \text{T}_{c})}c_{n^{\prime}}(t)dt \tag{6}\]  
where \(\bar{\text{x}}\) is the conjugate of x. The desired signal power will be given by  
\[P_{s,n}=\frac{p_{n}}{TL_{n}}\mathbf{w}_{n}^{\text{H}}\Bigg{(}\left(\sum\limits _{l=1}^{L}\mathbf{r}_{n,l}\mathbf{H}_{n,l}\right)^{\text{H}}\Bigg{(}\sum\limits _{l=1}^{L}\mathbf{r}_{n,l}\mathbf{H}_{n,l}\Bigg{)}\Bigg{)}\,\mathbf{w}_{n} \tag{7}\]  
while multiple access interference (MAI) from the \(n^{\prime}\)th node (\(n^{\prime}\
eq n\)), intersymbol interference (ISI), and noise power will be given by Equations (8)-(10), respectively:\[P_{ISI,n}=\left|\sum\limits_{l=1}^{L}\sum\limits_{ \begin{array}{c}l^{\prime}=1 \\ l^{\prime}\
eq l\end{array} }^{L}\left(\mathbf{r}_{n,l}\mathbf{H}_{n,l^{\prime}} \mathbf{w}_{n}\right)\sqrt{\frac{p_{n}}{TL_{n}}}\Big{(}\rho_{n,n,|l-l^{\prime} |}+\bar{\rho}_{n,n,|l-l^{\prime}|}\Big{)}\right|^{2}+ \tag{8}\] \[\sum\limits_{l=1}^{L}\left(\mathbf{r}_{n,l}\mathbf{H}_{n,l} \mathbf{w}_{n}\sqrt{\frac{p_{n}}{TL_{n}}}\right)\sum\limits_{ \begin{array}{c} l=1\\ l^{\prime}\
eq l\end{array} }^{L}\left(\mathbf{r}_{n,l}\mathbf{H}_{n,l^{\prime}} \mathbf{w}_{n}\sqrt{\frac{p_{n}}{TL_{n}}}\right)\Big{(}\rho_{n,n,|l-l^{\prime }|}+\bar{\rho}_{n,n,|l-l^{\prime}|}\Big{)}+\] \[\sum\limits_{l=1}^{L}\left(\mathbf{r}_{n,l}\mathbf{H}_{n,l} \mathbf{w}_{n}\sqrt{\frac{p_{n}}{TL_{n}}}\right)\left(\sum\limits_{ \begin{array} []{c}l=1\\ l^{\prime}=1\end{array} }^{L}\left(\mathbf{r}_{n,l}\mathbf{H}_{n,l^{\prime}} \mathbf{w}_{n}\sqrt{\frac{p_{n}}{TL_{n}}}\right)\Big{(}\rho_{n,n,|l-l^{\prime }|}+\bar{\rho}_{n,n,|l-l^{\prime}|}\Big{)}\right)^{\mathrm{H}}\] \[P_{MAI,n^{\prime}}=\left(\left|\sum\limits_{l=1}^{L}\sum\limits_{ l^{\prime}=1}^{L}\left(\mathbf{r}_{n,l}\mathbf{H}_{n,l^{\prime}}\mathbf{w}_{n} \right)\Big{(}\rho_{n,n^{\prime},|l-l^{\prime}|}+\bar{\rho}_{n,n^{\prime},l^{ \prime}|-l^{\prime}|}\Big{)}\right|^{2}\right)\frac{p_{n^{\prime}}}{TL_{n^{ \prime}}}\] (9) \[P_{noise,n}=N_{o}\sum\limits_{l=1}^{L}\left\|\mathbf{r}_{n,l} \right\|_{F}^{2} \tag{10}\]  
where \(N_{o}\) is the thermal noise level. Therefore, overall signal-to-interference-plus-noise ratio (SINR) for the \(n\)th node is formulated as follows:  
\[SINR_{n}=\frac{P_{s,n}}{P_{ISI,n}+\sum\limits_{n^{\prime}=1,n^{\prime}\
eq n} ^{N}P_{MAI,n^{\prime}}+P_{noise,n}} \tag{11}\]  
Depending on channel conditions and network load, capacity is upper limited either by the soft or hard mechanism. Soft capacity is defined as the number of nodes for which the SINR criterion (i.e., SINR \(>\)_SINR_th, where _SINR_th is a given threshold for a specific type of service) is satisfied without power outage. On the other hand, hard capacity equals to the available number of spreading sequences in a given service area. Pathloss propagation among different floors is modeled according to ITU-R specifications, where \(v\) is the distance power loss coefficient, \(f\) is the frequency in MHz, \(d\) is the separation distance in meters between the central BS and a mobile node, \(L_{f}(n)\) is the floor penetration loss factor in dB, and \(n\) is the number of floors between central BS and mobile node. Considering propagation at 2 GHz, for the considered office environment, \(v=3\) and \(L_{f}(\text{dB})=15+4\) (\(n-1\)). Hence, net pathlosses and shadowing effect are calculated as follows [20]:  
\[ \begin{split}\text{L}_{\text{total}}&=20 log_{10}(f) +vlog_{10}(d)+L_{f}(n)\\ TL&=\text{L}_{\text{total}}+X_{\sigma}\end{split}  \tag{12}\]  
where \(X_{\sigma}\) is a log-normally distributed random variable corresponding to shadowing effects.