## 4 Semi-Blind Receiver
The per-iteration complexity of the O-LM algorithm is higher than that of the T-ALS algorithm. However, because of the robustness of the O-LM algorithm, the O-LM algorithm needs fewer iterations compared with the T-ALS algorithm. Therefore, the proposed algorithm has lower complexity compared with the existing T-ALS algorithm. The mean processing times required in the T-ALS and O-LM algorithms are shown in \[\left(\mathbf{J}^{(i)}{}^{H}\mathbf{J}^{(i)}+\lambda^{(i)}\mathbf{I}_{Q} \right)\Delta\mathbf{u}^{(i)}=-\mathbf{g}^{(i)} \tag{34}\]0 We observe that the mean processing time required in the O-LM algorithm is shorter than that of the T-ALS algorithm, especially when the channel becomes strongly correlated. From Figure 6 we can also observe that the advantage of the O-LM algorithm is obvious as \(L\) decreases from 8 to 7 compared with the T-ALS algorithm. \[\left(\mathbf{J}^{(i)}{}^{H}\mathbf{J}^{(i)}+\lambda^{(i)}\mathbf{I}_{Q} \right)\Delta\mathbf{u}^{(i)}=-\mathbf{g}^{(i)} \tag{34}\]1 Normalized mean square error (NMSE) performance of different receivers versus SNR. \[\left(\mathbf{J}^{(i)}{}^{H}\mathbf{J}^{(i)}+\lambda^{(i)}\mathbf{I}_{Q} \right)\Delta\mathbf{u}^{(i)}=-\mathbf{g}^{(i)} \tag{34}\]2 BER and NMSE performance of traditional alternating least squares (T-ALS) and O-LM algorithms for different \(L\) and \(\rho\). In the fourth example, the influence of design parameters \((P,\ R)\) for the proposed receiver is studied. In the left subfigure of Figure 7, it can be seen that the BER decreases when \(P\) increases, which expounds the performance gain brought by the time diversity. It can also be seen from this subfigure that the BER increases as the number of data streams \(R\) increases. The impact of design parameters \((P,\ R)\) on the NMSE performance is shown in the right subfigure of \[\left(\mathbf{J}^{(i)}{}^{H}\mathbf{J}^{(i)}+\lambda^{(i)}\mathbf{I}_{Q} \right)\Delta\mathbf{u}^{(i)}=-\mathbf{g}^{(i)} \tag{34}\]3 As expected, we can observe that the NMSE decreases linearly as a function of \(P\), and increases as \(R\) increases. Hence, appropriate values for the design parameters \(P\) and \(R\) can be selected according to requirements of the system performance and transmission rate. In the fifth example, we assume \(M_{S}=3\), \(R=4\), and \(N=P=8\) for our semi-blind receiver. The influence of the receive antenna was analyzed. We also compared the performance of our chosen coding tensor (OCCT) \(\underline{\mathbf{B}}\) with the random coding tensor (RCT) whose entries are circularly-symmetric Gaussian random variables. In Figure 8, it can be seen that both the BER and NMSE decrease when \(M_{D}\) increases, which expounds the performance gain brought by the receive diversity. We also observed from Figure 8 that OCCT has a better performance than RCT. Although OCCT is suboptimal, this choice has good symbol and channel identifiability properties, which is advantageous from a receiver design viewpoint. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline
**SNR** & **0** & **2** & **4** & **6** & **8** & **10** & **12** & **14** & **16** & **18** & **2



In the sixth example, we studied the estimation performance of two different transmission schemes for our semi-blind receiver. The default values of the system parameters were set to \(M_{D}=5\) and \(N=6\). In scheme 1, we assume \(M_{S}=2\), \(R=5\), and \(P=6\). Three different antenna-to-slot allocation matrices are given as follows:

\[\left(\mathbf{J}^{(i)}{}^{H}\mathbf{J}^{(i)}+\lambda^{(i)}\mathbf{I}_{Q} \right)\Delta\mathbf{u}^{(i)}=-\mathbf{g}^{(i)} \tag{34}\]4 Influence of the receive antenna and the coding tensor. \[\left(\mathbf{J}^{(i)}{}^{H}\mathbf{J}^{(i)}+\lambda^{(i)}\mathbf{I}_{Q} \right)\Delta\mathbf{u}^{(i)}=-\mathbf{g}^{(i)} \tag{34}\]5 BER and NMSE performance of the proposed receiver for different \(P\) and \(R\). \[\mathbf{Q}_{1}= \begin{bmatrix}1&0\\ 0&1\\ 1&0\\ 1&0\\ 0&1\\ 1&0\end{bmatrix} ,\ \ \mathbf{Q}_{2}= \begin{bmatrix}0&1\\ 1&1\\ 1&0\\ 0&1\\ 1&1\\ 1&0\end{bmatrix} ,\ \ \mathbf{Q}_{3}=