## 4 Semi-Blind Receiver
\begin{bmatrix}1&1\\ 0&1\\ 1&1\\ 1&0\\ 1&1\end{bmatrix} \]

In scheme 2, we assume \(M_{S}=3\), \(R=3\), and \(P=7\). Three different antenna-to-slot allocation matrixes are given as follows:

\[\mathbf{Q}_{4}= \begin{bmatrix}1&0&0\\ 1&0&0\\ 1&0&1\\ 1&0&0\\ 0&1&0\\ 1&0&1\end{bmatrix} ,\ \ \ \ \ \ \ \mathbf{Q}_{5}= \begin{bmatrix}1&0&1\\ 1&1&0\\ 1&1&1\\ 1&1&0\\ 1&1&1\end{bmatrix} \]

The BER and NMSE performance of the proposed receiver for different schemes is shown in Figure 9. For scheme 1, the proposed receiver with \(\mathbf{Q}_{2}\) has a better BER and NMSE performance than that of the proposed receiver with \(\mathbf{Q}_{1}\). The reason is that the allocation matrix \(\mathbf{Q}_{2}\) provides a higher transmit spatial diversity gain than the allocation matrix \(\mathbf{Q}_{1}\). For the same reason, the allocation matrix \(\mathbf{Q}_{3}\) outperforms \(\mathbf{Q}_{2}\), and the allocation matrix \(\mathbf{Q}_{5}\) outperforms \(\mathbf{Q}_{4}\). We also observe in Figure 9 that scheme 2 has a better BER and NMSE performance than scheme 1. The reason is that scheme 2 can provide a higher coding diversity than scheme 1. It is worth noting that scheme 1 has higher spectral efficiency compared with scheme 2. The transmission rates for scheme 1 and scheme 2 are about 5/6 and 3/7 (data symbols per symbol period), respectively. In summary, a desired tradeoff between estimation performance and transmission rate can be obtained by designing a suitable scheme. Figure 9: Performances of the proposed receiver for different schemes. In final example, the multi-user massive MIMO system with a fully-connected hybrid precoding architecture was considered, where \(M_{S}=48\), \(M\times M_{D}=6\times 6\), and \(L_{m}=2\) for all \(m=1,\ldots,M\). The carrier frequency of this system is set as 28 GHz [37], and \(d=\lambda/2\). We assume that AoAs/ AoDs are uniformly distributed in \([0,\ 2\pi]\). For the considering multi-user massive MIMO system, we also evaluate the estimation performance of the proposed receiver in terms of BER and NMSE of channel estimation. It can be seen from Figures 10 and 11 that the BER and NMSE of the proposed semi-blind receiver decrease as \(P\) and \(N\) increase, and increase as \(R\) increases. The increase of \(P\) will reduce the transmission rate, but the increase or decrease of \(N\) has no effect on the transmission rate. That means that we can improve the estimation performance of the proposed semi-blind receiver by increasing \(N\) if the channel is constant over a long time interval before changing to another realization. We also observed from Figures 10 and 11



## 7 Conclusions

We have developed a robust semi-blind receiver combined with the Tucker-2 model in multiple-antenna systems. The proposed receiver could jointly estimate the information symbol and channel parameters. Compared with existing semi-blind receivers, the proposed one gave better estimation performance, and had a higher spectral efficiency Moreover, the proposed semi-blind receiver was also applicable to multi-user massive MIMO systems. Perspectives of this work include an extension to relay-assisted massive MIMO systems by applying the antenna allocation matrix at the relays. Since both the source-relay and the relay-destination channel matrices have low-rank property, new identifiability conditions and efficient fitting algorithms will be deduced and developed, respectively. Another perspective considers extending the proposed robust semi-blind receiver into mmwave MIMO systems for joint channel parameter estimation, which includes AOAs, fading coefficients and time delays [38; 39]. Conceptualization J.D. ; methodology, J.D. ; software, M.H. and H.L. ; validation, M.H. and Y.H. ; writing-original draft preparation, J.D. and M.H. ; writing-review and editing, Y.H., Y.C. and H.L. ; supervision, J.D. and Y.C. This research was supported by the grant from the National Natural Science Foundation of China (Nos. 61601414, 61701448, 61702466), the National Key Research and Development Program of China (No.