## 4 Results and Discussion
Note that in the latter two cases, a subset of antennas is selected that maximizes the received SNR over all multipath components; hence,  
\[S_{n}\leftarrow\underset{j\in TR}{\operatorname{argmax}}\|\prod_{l=1}^{L}\mathbf{ H}_{n,j,l}\| \tag{16}\]  
where \(S_{n}\) is the set of transmit antennas for the \(n\)th node, \(\mathbf{H}_{n,j,l}\) is the equivalent channel matrix considering transmission from the antennas in the subset \(j\), and the set \(TR\) includes all possible combinations of transmit antennas. For example, considering a use case scenario with two selected transmit antennas, \(TR\) = {(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}. As can be observed from Figure 6, as expected, transmission from all antennas is the best solution in terms of radiated transmitted power. For 21 nodes, when selecting three transmit antennas, the mean transmission power is almost 0.97 W, while the corresponding value for two transmit antennas is 0.89 W. Hence, compared to the case where no AS takes place, in the case of three transmit antennas, we have a power increment of almost 9%, which increases to 19% for the case of two transmit antennas. Note that AS burden is transferred to the BMS central BS, which gathers and processes all channel coefficients and then informs via feedback signals all nodes for the appropriate selection of transmit antennas. In the final set of simulations, the spatial multiplexing transmission mode was considered. For a fair comparison with the previous cases of diversity combining, it is assumed that the input powers of the spatial multiplexing simulator are the ones that have been calculated at the diversity combining transmission mode, properly weighted. In this context, in the first case, a 2 \(\times\) 2 MIMO orientation has been considered, while \(PG\) equals 64 in the diversity combining case and 128 in spatial multiplexing transmission mode. Note that, in both cases, the equivalent transmission rate is 60 Kbps, as in spatial multiplexing two different input streams are sent from the transmit antennas. In the second case, simulations are repeated for a 4 \(\times\) 4 MIMO orientation, where now \(PG\) equals 32 in the diversity combining case and 128 in spatial multiplexing transmission mode. Figure 6: Mean power of nodes for various MIMO orientations with antenna selection—diversity combining transmission mode. Results are presented in Figure 7, where mean bit error rate (BER) is plotted on a logarithmic scale for the aforementioned cases (DC stands for diversity combining and SM for spatial multiplexing. Details on theoretical BER calculations for spatial multiplexing transmission are provided in the Appendix A). Note that, in this particular set of simulations, an SNR of 10 dB has been considered and a building orientation with one floor. Mobile nodes may vary from 1 to 21, as in the previous set of simulations, with a step of 2. Finally, the power per node in the spatial multiplexing cases (2 \(\times\) 2 and 4 \(\times\) 4) has been set to be double the value of the corresponding power in diversity combining mode for a 1 \(\times\) 2/2 \(\times\) 4 MIMO system, respectively, as now the diversity order of the system is reduced to half. As can be observed in Figure 7, in all cases of mobile nodes, spatial multiplexing transmission worsens the mean BER. This result is rather expected, as spatial multiplexing can be severely affected both by MAI and multiple reflections in indoor environments [22]. Note that BER in SM is affected to a greater extent in the 4 \(\times\) 4 MIMO case, as MAI is the main capacity limiting factor due to the multiple antennas. This particular simulation scenario with four different input streams corresponds to four independent diversity combining cases (i.e., 1 \(\times\) 4). Therefore, each receive antenna now undergoes a greater amount of interference, as it receives \(M_{t}\times L\) independent signals. Hence, diversity combining is the most appropriate solution for this type of communication, especially if we are interested in low-rate communications.