## 5 Results and Discussion
### CAZAC-TD and CAZAC-FD SNR Estimators' Performance
The NMSE performance of the non-adaptive \(2\times 2\) STBC-assisted MIMO-OFDM system that invoked CAZAC-TD and CAZAC-FD was further enhanced when invoked in the \(4\times 4\) STBC-assisted MIMO-OFDM system for both the AWGN and SUI-5 channels. Figure 12: The estimated SNR performance for the SUI-5 channel with a zoomed-in view in the inset. Figure 13: The NMSE performance of the non-adaptive STBC-assisted MIMO-OFDM system for the AWGN channel. In the third set of results, the CAZAC-TD and CAZAC-FD SNR estimators are also evaluated in terms of BER for AWGN and SUI-5 channels, as shown in Figures 15 and 16, respectively. As seen from Figure 15, the \(2\times 2\) non-adaptive STBC-assisted MIMO-OFDM system that employed the CAZAC-TD SNR estimator achieved a significant BER performance improvement compared to that of the corresponding CAZAC-FD and Milan-FD SNR estimators. Specifically, at BER = \(10^{-4}\), the MIMO-OFDM system with the CAZAC-TD SNR estimator was capable of enhancing the achievable SNR performance by about 2 dB and 0.3 dB over the Milan-FD and CAZAC-FD SNR estimators, respectively, when communicating over the AWGN channel. The BER performance of the CAZAC-TD SNR estimator was further enhanced, exhibiting an improvement in SNR gain by about 0.2 dB when it was invoked in the \(4\times 4\) STBC-assisted MIMO-OFDM system. Figure 14: The NMSE performance of the non-adaptive STBC-assisted MIMO-OFDM system for the SUI-5 channel. Figure 15: The BER performance of the non-adaptive STBC-assisted MIMO-OFDM system for the AWGN channel. For transmission over the SUI-5 channel, at BER =\(10^{-4}\), the non-adaptive \(2\times 2\) and \(4\times 4\) STBC-assisted MIMO-OFDM system employing the CAZAC-TD SNR estimator exhibited SNR gain by about 0.75 dB and 0.18 dB, when comparing with Milan-FD and CAZAC-FD SNR estimators, respectively, as seen in Figure 16. For both the AWGN and SUI-5 channels, the CAZAC-TD SNR estimator outperformed the Milan-FD and CAZAC-FD SNR estimators, as seen in Figures 15 and 16, respectively. The floating point operations per second (FLOPs) complexity metric can be used to assess the complexity of the CAZAC-TD SNR estimation algorithm. Generally, FLOPs refer to the number of computations needed for a single SNR estimate. As stated in Section 4.1, CAZAC-TD SNR estimation is based on the autocorrelation of the STBC-decoded signal, which is performed in the time domain. The signal power and noise power are estimated using Equation (12) and Equation (13), respectively. Generally, the autocorrelation function of the STBC-decoded signal is the product of the STBC-decoded signal and its lagged version at each time step, and then these products are summed for all time steps within the overlapping range. Therefore, the computational complexity is only based on the multiplication of N bits and \((N-1)\) additions. Hence, the CAZAC-TD SNR estimator required \((N+N-1=2N-1)\) FLOPs for one SNR estimation, while the second-order moment criteria are applied to the OFDM-demodulated signal in both the Milan-FD and CAZAC-FD SNR estimators, which involves \((4N+2)\) FLOPs to compute one SNR estimate [18].