# Complex-Valued Phase Transmittance RBF Neural Networks for Massive MIMO-OFDM Receivers
## 4 Simulation Results
Higher-order QOSTBC architectures using Equation (8) are not simulated because of the extensive time required to perform maximum likelihood detection. Figure 8: Simulated and theoretical results for 4 th, 8 th, 16 th, and 64 th diversity orders. Figure 9: Simulated, reference, and theoretical results for equal diversity order and bitrate [11]. In order to represent more practical scenarios, we set the simulation system with a 3 GPP TS 38.211 specification [62] for 5G Physical channels and modulation. The Subcarrier Spacing (\(\Delta f\)) scales from 15 kHz to 240 kHz. The number of active carriers is 256, and the pilot sample rate (when applicable) is \(M_{T}\times 8\times f_{Doppler}\) with the conventional block-based pilot scheme [63]. We perform simulations in the extremes to demonstrate the robustness of the proposed approach. The radio channel realizations are created using the 3 GPP TR 38.901 report on 5G: Study on channel model for frequencies from 0.5 GHz to 100 GHz [64]. The 3 GPP channel models [64] are applicable for frequency bands in the range of 0.5 GHz to 100 GHz. From Tapped Delay Line (TDL) models in [64], TDL-B is selected from Table 7.7.2-2 (depicted in Table 1) for the channel model simulated in this work. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Tap \#** & **Normalized Delay** & **Power (dB)** & **Tap \#** & **Normalized Delay** & **Power (dB)** \\ \hline
1 & 0.0000 & 0.00 & 13 & 1.1021 & \(-\)4.80 \\ \hline
2 & 0.1072 & \(-\)2.20 & 14 & 1.2756 & \(-\)5.70 \\ \hline
3 & 0.2155 & \(-\)4.00 & 15 & 1.5474 & \(-\)7.50 \\ \hline
4 & 0.2095 & \(-\)3.20 & 16 & 1.7842 & \(-\)1.90 \\ \hline
5 & 0.2870 & \(-\)9.80 & 17 & 2.0169 & \(-\)7.60 \\ \hline
6 & 0.2986 & \(-\)1.20 & 18 & 2.8294 & \(-\)12.2 \\ \hline
7 & 0.3752 & \(-\)3.40 & 19 & 3.0219 & \(-\)9.80 \\ \hline
8 & 0.5055 & \(-\)5.20 & 20 & 3.6187 & \(-\)11.4 \\ \hline
9 & 0.3681 & \(-\)7.60 & 21 & 4.1067 & \(-\)14.9 \\ \hline
10 & 0.3697 & \(-\)3.00 & 22 & 4.2790 & \(-\)9.20 \\ \hline
11 & 0.5700 & \(-\)8.90 & 23 & 4.7834 & \(-\)11.3 \\ \hline
12 & 0.5283 & \(-\)9.00 & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Table 7.7.2-2. TDL-B. Figure 10: Simulation for the proposed coding scheme against theoretical results for equal bitrate and \(M_{T}=4\) and \(8\) with \(M_{R}=1\)[11]. In Table 1, as the channel model delays are normalized, they need to be scaled according to a desired delay spread in nanoseconds (ns):  
\[\tau_{scaled}=\tau_{model}DS_{ns} \tag{27}\]  
in which \(\tau_{model}\) is the normalized delay value of the TDL model, \(\tau_{scaled}\) is the new delay value (in [ns]), and \(DS_{ns}\) is the desired delay spread (in [ns]). From Table 7.7.3-1 [64], examples of scaling delay spreads are very short (\(DS_{ns}=10\) ns), short (\(DS_{ns}=30\) ns), nominal (\(DS_{ns}=100\) ns), long (\(DS_{ns}=300\) ns), and very long (\(DS_{ns}=1000\) ns). In this work, we use a delay spread of \(DS_{ns}=50\) ns. From the channel model of Table 1, a Rayleigh distribution is used to compute each sub-channel of \(\mathbf{H}\in\mathbb{C}^{M_{T}\times M_{R}}\) (MIMO channel matrix). The \(M\)-QAM BER figure for the AWGN channel is also used to define a lower bound on BER vs. \(E_{b}/N_{0}\) performance. Additionally, it is assumed that all received signals are uncorrelated [11]. A realistic scenario to assess the performance of a MIMO-OFDM system must also include the nonlinear effects of the transmitter power amplifiers [11]. This is necessary because the OFDM signal can have relatively high peak values (i.e., high PAPR) in the time domain since many subcarrier components are added via an IFFT operation. A high PAPR is one of the most detrimental aspects of the OFDM system, as it decreases the SQNR (signal-to-quantization noise ratio) of ADCs (analog-to-digital converters) and DACs (digital-to-analog converters), while also imposing a back-off that degrades the efficiency of the power amplifier in the transmitter.