## 5 Result and Discussion  
Figure 1 illustrates the relationship between BER and SNR for different values of \(\eta\), including 0.98, 0.99, and 1, for a \(4\times 1\) system with a transmit antenna correlation \(\rho=0.9\). The error floor for ML is established between 10 and 12 SNR for \(\eta=0.99\) and 0.98, as shown in Table 2. In contrast, techniques I, II, and III do not have an error floor because they employ QR decomposition. No further modifications are made to the BER for SNR of 9 dB. Technique III outperforms Technique II, and the simulation results shows improved performance across all three partial CSIRs (\(\eta=0.98\), 0.99, and 1) due to the utilization of QR decomposition. The QR decomposition procedure reduces the complexity of data detection systems by simplifying the received signal. As a result, symbol or bit detection is made easier, particularly in situations involving partial CSI where the channel information is limited. QR decomposition also helps mitigate interference caused by channel effects through the decomposition of the channel matrix, enhancing the accuracy of symbol detection even when the receiver has access to only a portion of the CSI. This section compares the MIMO BER simulation outcomes of three detection methodologies (technique I, technique II, and technique III) by utilizing different parameter values for channel state information at the receiver (1, 0.99, and 0.98) and a transmit antenna correlation parameter of 0.9. The simulation is conducted using \(N_{t}=4,N_{r}=1,p=2\), and \(m=8\) with 4-QAM modulation. The outcomes are illustrated in Figure 1.  
From Table 3, it has been observed that ML (\(\eta\) = 0.98, SNR = 18 dB) gives 0.0037 BER and Technique III (\(\eta\) = 0.98, SNR = 18 dB) gives 0.000246 BER, whereas ML (\(\eta\) = 1, SNR = 18 dB) gives 0.0001875 BER and Technique III (\(\eta\) = 1, SNR = 18 dB) gives 0.0002525 BER. It has been proved that the performance of ML degraded with partial CSIR (\(\eta\) = 0.98) from full CSIR (\(\eta\) = 1), which has been improved with techniques I, II, and III using QR decomposition. Figure 2 shows how the BER performance of the proposed GQSM-QOSTBC system changes with average SNR under different Nakagami-\(m\) fading conditions (\(m=0.5\), \(m=1\), and \(m=1.5\)), which represent one-sided Gaussian, Rayleigh, and Rician fading channels, respectively. The analysis of three detection schemes--DQR, LCML, and QRIC--uses a fixed transmit antenna correlation of \(\rho=0.9\) and full channel state information at the receiver (\(\eta=1\)). As anticipated, BER increases as \(m\) increases, demonstrating the system's increased resilience under less severe fading situations. DQR has the largest BER across all channel conditions, whereas MLD performs the best among the detection methods, closely followed by QRIC and LCML. The BER quickly drops, and QRIC's performance gets close to MLD's, especially in Rician fading (\(m=1.5\)), demonstrating its effectiveness with less complexity. Interestingly, up to 30 dB SNR, no BER floor is seen, suggesting consistent \begin{table}
\begin{tabular}{c c} \hline \hline
**TAS Scheme** & **SNR Required** \\ \hline No TAS & Not achievable \\ Conventional TAS & 1.85 dB \\ Best II Random II TAS & 2.9 dB \\ Near conventional TAS & 1.85 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Lowest Estimated SNR for \((4,6;2)\) MIMO with various Transmit Antenna Selection (TAS) schemes under imperfect channel state information available at receiver (\(\rho=0.96\))—for video (\(10^{-3}\) SER) application. Figure 1: Bit Error Rate (BER) vs. Average Signal to Noise Ratio (SNR) of QQSM—QQSTBC using three distinct low detection techniques, each with a transmit antenna correlation of \(\rho=0.9\) and partial channel state information available to the receiver (\(\eta\) = 0.98, 0.99, and 1). detection accuracy across all channels and schemes.