# Estimating the Performance of MIMO SC-FDE Systems Using SISO Measurements
## 5 Performance Results  
The Signal-to-Noise Ratio (SNR) is the ratio between signal and noise power. Therefore, if we assume that the noise power remains constant, we can derive the signal power as a function of the SNR. The SNR ratio can be expressed in decibels (dB), as denoted in Equation (33):  
\[SNR_{[dB]}=P_{S[dBm]}-P_{N[dB]}, \tag{33}\]  
where \(P_{S}\), and \(P_{N}\) denote signal and noise power, respectively. The \(E_{b}/N_{0}\) expression, in linear terms, can be written as:  
\[\left(\frac{E_{b}}{N_{0}}\right)=\frac{P_{S}\times B}{P_{N}\times R_{b}}\iff \left(\frac{E_{b}}{N_{0}}\right)=SNR_{linear}\times\frac{B}{R_{b}}, \tag{34}\]  
where \(B\), and \(R_{b}\) denote signal bandwidth and bit rate, respectively. In our analyses, \(B/R_{b}\) is negligible since it is the same for both SISO and MIMO. Thus, the Equation (33) can be rewriten as:  
\[E_{b}/N_{0[dB]}=P_{S[dBm]}-P_{N[dB]}. \tag{35}\]  
After some mathematical manipulation, it is possible to arrive at the relationship between the signal power in a SISO and in a MIMO system, indicated by Equation (36):  
\[Ps_{MIMO[dBm]}=Ps_{SISO[dBm]}-G\Delta_{[dB]} \tag{36}\]  
If we now assume that both the noise and the BER performance value remain constant, it is possible to estimate the coverage area of a MIMO system based on the coverage of a SISO system, considering a downlink scenario. In order to test this possibility of extending the coverage area of a SISO system to a MIMO system, a 4G antenna from a northern European country manufacturer was considered, working on a downlink frequency of 796 MHZ and a transmission power of 46 dBm. This scenario, illustrated in Figure 7, was taken from the Metric platform [5], which is a network monitoring and management web platform developed by the Multivision company [6]. This platform is currently used by several mobile operators worldwide, aggregating Configuration Management (CM) and Key Performance Indicators (KPI) data, as well as DTs from their networks. Figure 7: Considered scenario to validate our model. If the radiation pattern of the transmitting antenna was considered, with the gain in the receiving antenna of 0 dB, and the DT campaign measures taken, it is possible to apply the ACSPM model and to estimate the coverage area for this scenario as in [27], depicted in Figure 8.  
As mentioned above, \(E_{b}/N_{0}\) values improve by 2.4 dB (\(G\Delta=2.4\) dB) when changing from a SISO system to a MIMO system with an \(R/P=5\) and a BER of \(10^{-2}\). For example, if the power received at a given point in the SISO system that was estimated as \(-100\) dBm, the value corresponding to the MIMO system in this same scenario will now be estimated as \(-102.4\) dBm for the scenario presented. Accordingly, the coverage scenario presented in Figure 8 would then be changed to that depicted in Figure 9.  
Figure 8: Coverage area of the considered scenario. Figure 9: Coverage area extrapolated for a MIMO system with a BER of \(10^{-2}\) and for the first iteration of IB-DFE. If we consider a minimum sensitivity of \(-120\) dBm required for the correct establishment of communications between the base station and a mobile receiving terminal, and by comparing the coverage results depicted in Figures 8 and 9, it can be concluded that the useful area for communications has been reduced about 6%. If we now consider the third iteration of IB-DFE on the mobile receivers, the value of \(E_{b}/N_{0}\) reduces by approximately 1.3 dB (\(G\Delta=1.3\) dB), when extrapolating coverage from a SISO system to a MIMO system with 20 transmitting antennas and 2 receiving antennas; that is, an \(R/P\) ratio of 10, and a BER of \(10^{-4}\). The resulting coverage area for this system is depicted in Figure 10. In this case, we conclude that if we have MIMO coverage instead of SISO, the coverage area is reduced by about 3.5%. As we can verify from these results, the overall coverage area of a MIMO system is reduced, once the directivity of multiple antennas concentrates radiation in some more specific and desired areas.