## 3 Proposed Methodology
### System Description  
All of the subcarriers have been modulated using different techniques. The results have been simulated using the QPSK modulation technique. The next step in aligning the bit stream over the subcarriers is the mapping of the subcarriers. In the OFDM design, the Wiener filter is employed because it reduces the mean square error between the actual transmitted signal and the received signal. Here, L = 7 is the Wiener filter order under consideration. Initially, the incoming signal information is transmitted through pilot sequences and modulation schemes such as the QPSK scheme [48,49]. The QPSK scheme consists of the advantages and noise factor. Another advantage of this scheme is a higher information transmission rate than another modulation scheme with minimal bandwidth. The signal shift consists of '4' signal states with the transmission of information through the QPSK scheme as 2 bits/symbol. Each signal in the system is modified by 1 bit thanks to the encoding strategy. The transmitted signal is represented by the sine and cosine of the following Equation (1):  
\[g_{n}(t)=\sqrt{\frac{2S_{e}}{D_{s}}}\cos\left(2\pi f_{c}t+(2n-1)\frac{\pi}{4} \right),n=1,2,3,4 \tag{1}\]  
Here, \(g_{n}(t)\) signifies the signal based on the time, \(S_{e}\) represents the symbol energy, symbol duration is denoted as \(D_{s}\), whereas \(f_{c}\) is defined as the baseband of the signal. In the modulator of the MIMO scheme, 4 phases of the signal are generated, which consists of 2D signal space with unit function \(\varphi_{1}(t)\) and \(\varphi_{2}(t)\) denoted as follows Equations (2) and (3)  
\[\varphi_{1}(t)=\sqrt{\frac{2}{D_{s}}}\cos 2\pi f_{c}t,\ 0\leq t\leq T \tag{2}\]  
\[\varphi_{2}(t)=\sqrt{\frac{2}{D_{s}}}\sin 2\pi f_{c}t,\ 0\leq t\leq T \tag{3}\]  
Figure 1: Block diagram of channel estimation in MIMO-OFDM system with Wiener filter model. From the above, Equations (2) and (3) \(\varphi_{1}(t)\) and \(\varphi_{2}(t)\) are used to measure the quadrature and in-phase components. According to Equation (4), an OFDM signal is conceptually composed of four signal constellations based on four points in the signal space. \[\left(\pm\sqrt{\frac{S_{e}}{2}},\pm\sqrt{\frac{S_{e}}{2}}\right) \tag{4}\]  
Here, the system's full power, distributed equally between the two carriers involved, is represented by the signal factor \(1/2\). At the receiving end, the symbols are demodulated by removing the carrier phase factor, and the continuously received robot in phase 2 is determined from the input data. Let \(p_{t}(t)\) indicates the transmit-side P.S.F. for each symbol and \(p_{r}(t)\) signifies the receive antenna side matched the filter. The composite channel is symbolized as \(H(t)\). The \((I_{R},I_{T})\) time-domain signal received at the \(i_{R}\) antenna is as follows:  
\[h_{iR,iT}(n)=\sum_{i_{T}=1}^{N_{T}}h_{iR,iT}(n)\otimes x_{iT}+N \tag{5}\]  
Here, Equation (5) represents/denotes noise placed in the uncorrelated spatial and temporal region and/or represents the presence of noise in transmitting the time-domain signal at their antenna. After the removal of I.S.I., with the utilization of IFFT, ISI is eliminated. Moreover, it uses the symbol mapping technique at each transmitter side. Fourier analysis is performed in frequency domain components for signal transmutes in time or spatial domain factors. IFFT is implemented at the receiver end to improve flexibility, execution speed, and precision. Different complexes and data points are transformed for the same number of time-domain points when the IFFT procedure is used. The IFFT involved in the execution of N-point receiver operation in Equation (6) IFFT is presented mathematically as follows:  
\[u(n)=\frac{1}{N}\sum_{n=1}^{N-1}U(k)e^{\frac{-jnkn}{N}},n=0,1,\ldots.,N-1 \tag{6}\]  
The represented data frame transforms where/the size or the number of signal points. \(k=0,1,\,\ldots,\,N-1\), and \(U(k)\) indicates the FFT frequency output at the \(k\)th end. Then, FFT analysis transforms the signal in the receiver block in the time domain.