## 4 Results  
### PCA with Theoretical Antenna Radiation Patterns  
In order to evaluate the performance of the proposed approach, Monte Carlo (MC) simulations were performed in various MIMO topologies. In the first set of results (i.e., Figures 2-4), the goal was to calculate mean BER and compare output values with the ones derived from the theoretical model as described in Section 2.2. For this reason, three different MIMO orientations (i.e., 4 \(\times\) 2, 4 \(\times\) 3 and 8 \(\times\) 4) were considered, with two and six resolvable multipath components. The equivalent SNR was set to 10 dB, while a uniform power delay profile regarding the individual powers of the multipath components was taken into account. In figure legend, notation (\(M_{t}\),\(M_{r}\),\(L\),\(PG\),\(SNR\),\(Sim\) or \(Th\)) has been carried out. Assuming independent data streams per different transmit antenna, then user throughput is set to \(R\times\min(M_{t}\),\(M_{r})\) Kbps, where \(R\) is the basic transmission rate of 30 Kbps that corresponds to the ratio of the system's bandwidth (3.84 MHz for the WCDMA, [1]) to the processinggain. Moreover, it is assumed that each mobile terminal is equipped with a number of RAKE fingers that equals the number of multipath components. Finally, the number of active users may vary from 1 to 40 with a step of 5. As it is evident from Figures 2-4, there is a good agreement among the Gaussian approximation for the error probability and consequently the mean BER and BER results derived from MC simulations. In addition, the selection of all multipath components (i.e., 6) leads to improved BER compared to the case of two multipath components. As expected, this gain reduces for high values of overall throughput, since to the increased number of active users, MAI can be significantly increased. In Table 1, the mean number of repeats of the proposed MSNR-PCA algorithm that are required for convergence is presented, versus the number of power terms that are taken into account i.e., parameters \(C\) in Equation (24)). Moreover, in Figures 5 and 6 the mean BER is presented for a \(4\times 2\) MIMO orientation, five active users and SNR equal to 5 dB and 10 dB, respectively, versus the number of power terms. Two simulation cases have been considered: In the first one, correlation matrix per user is formulated considering only the primary eigenvector and eigenvalue from PCA. In the second case, all eigenvalues and eigenvectors are taken into account. In both cases, \(PG\) can be either 32 (high data rate services) or 128 (low data rate services). As derived from Figure 5, for high number of power terms there are practically no BER deviations per group of curves. However, even for reduced number of power terms, BER deviations are kept to a minimum. In particular, for 36 power terms, the mean BER is 7.9 \(\times\) 10\({}^{-3}\). For one eigenvector in PCA and 18 power terms, the mean BER is 8.1 \(\times\) 10\({}^{-3}\). Hence, in this case there is an error of almost 2.6%. However, it follows from Table 1 that there is also a complexity reduction gain of almost 10%, as the mean number of repeats is 108 for 36 power terms and reduces to 98 repeats for 18 power terms. Note that in the corresponding cases for \(PG\) equal to 32, there are practically no deviations among the two calculated BER values (1 and 6 eigenvalues and eigenvectors, respectively). Finally, in Figure 6, where SNR is set to 10 dB, convergence is achieved for higher number of power terms compared to the previous case of 5 dB SNR. In particular, for \(PG\) equal to 32, there are practically no BER deviations among 24 and 36 power terms. However, for \(PG\) equal to 128, convergence is achieved for 30 power terms. Figure 2: Simulation and theoretical Bit Error Rate (BER) values for a Multiple Input Multiple Output –Wideband Code Division Multiple Access (MIMO–WCDMA) network (\(M_{t}=4\), \(M_{r}=2\), \(PG=128\), \(SNR=10\) dB). Figure 4: Simulation and theoretical BER values for a MIMO–WCDMA network (\(M_{t}=8\), \(M_{r}=4\), \(PG=128\), \(SNR=10\) dB).