## 2 System Model  
Consider a MISO system where gNodeB of \(N_{t}\) multiple transmitting antennas and the UE with a single antenna are deployed. The communication between the gNodeB and the UE is through intelligently controlled reflecting surfaces. These IRS units are coordinated by a smart software controller, which sets the phase shift for each element. The controller ensures the effective coordination of the reflecting modes of the IRS units. The system model is shown in Figure 1. Table 1 illustrates the parameters that are used throughout the core of this paper.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Description** \\ \hline \(\alpha\) & The amplitude coefficient with values from 0 to 1 \\ \hline \(\theta_{1}\) & IRS phase angle (value from 0\({}^{\circ}\) to 90\({}^{\circ}\)) \\ \hline \(\varphi\) & Diagonal matrix of the adjustable phase \\ \hline \(E_{s}\) & Energy per symbol \\ \hline \(H\) & The cascaded fading channel coefficient \\ \hline \(\mathbf{H_{bI}}\) & The channel between the gNodeB and the IRS (\(N\times N_{t}\)) \\ \hline \(\mathbf{H_{bI}}\) & The channel between the UE and the gNodeB (\(N_{t}\times 1\)) \\ \hline \(\mathbf{H_{II}}\) & The channel between the UE and the IRS (\(N\times 1\)) \\ \hline \(h_{l}\) & The cascaded channel between transmitting antenna \(i\) and IRS \\ \hline \(\hat{l}_{l_{i}}\) & The recovered cascaded channel of the transmitting antenna \(i\) \\ \hline \(K\) & The number of modulated symbols during each \(T_{s}\) \\ \hline \(M\) & Modulation order \\ \hline \(m\) & Number of information bits \\ \hline \(N\) & Number of IRS reflecting elements \\ \hline \(N_{t}\) & Number of transmitting antennas \\ \hline \(\mathbf{W}\) & Additive White Gaussian Noise Vector (AWGN) (\(1\times N_{t}\)) \\ \hline \(R\) & Space time block code rate \\ \hline \(\mathbf{S}\) & Set of all possible symbols in the constellation \\ \hline \(s_{i}\) & Symbol i in the set of all possible symbols in the constellation \(\mathbf{S}\) \\ \hline \(T_{s}\) & The number of transmission time slots \\ \hline \(\mathbf{X}\) & The transmission orthogonal symbol matrix \\ \hline \(\mathbf{X^{H}}\) & The conjugate transpose of the matrix \(\mathbf{X}\) (\(\mathbf{X}\) Hermitian) \\ \hline \(x\) & Modulated Symbol \\ \hline \(\hat{x}\) & The likelihood received symbol \\ \hline \(\overset{\sim}{x}\) & Decision statistics of the symbol \\ \hline \(\mathbf{Y}\) & The row vector for the received signals (\(1\times N_{t}\)) \\ \hline \(y_{i}\) & The received signal at time slot \(i\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of parameters with description.  
The received signal is the summation of all reflected Electromagnetic (EM) waves from the smart reflecting surfaces with different phase shifts and the EM waves from the gNodeB to the UE.  
Figure 2 shows the detailed fully utilized MISO system that employs the concept of OSTBC and IRS. Fully utilized means that all transmitting antennas and IRS reflecting elements are utilized. As shown in Figure 2, in the STBC encoder, the initial step involves modulating each set of m information bits, where \(m=log_{2}M\) and M is the modulation scheme order. Subsequently, the encoder proceeds with an encoding operation, taking a group of modulated symbols, \(x_{1}\), \(x_{2}\), \(\ldots x_{k}\), and mapping them onto the transmit antennas based on a code matrix. Suppose that an M-ary modulation scheme is deployed. \(\mathbf{H}_{bl}\) is the channel between the gNodeB and the IRS. \(\mathbf{H}_{lU}\) is the channel between the UE and IRS. \(\mathbf{H}_{bU}\) is the channel between the UE and the gNodeB. \(\hat{h}_{l}\) is the recovered cascaded channel of the transmitting antenna \(i\), assuming that the UE has a perfect channel state information. The following section illustrates the OSTBC encoder and decoder in detail.