## 3 Diversity-Controlled MUST Technique
### Receiver Design at an MUST-Based UE  
Figure 3 shows the overall structure of the proposed receiver at the MUST-based UE. Recall that the signal of the \(i\)-th MUST-based UE is assumed to be sent via the \(i\)-th OFDM sub-carrier. Then, the received signal of the \(i\)-th MUST-based UE with \(N_{r}\) antennas is given by  
\[\mathbf{y}_{B,i}=\mathbf{h}_{B,i}(i)\sqrt{\mathcal{E}}s_{i}+\mathbf{w}_{B,i}, \tag{3}\]  
where \(\mathcal{E}\) indicates the transmit power of \(s_{i}\) and \(\mathbf{h}_{B,i}(i)\in\mathbb{C}^{N_{r}\times 1}\) denotes the wireless channel vector from the BS to the \(i\)-th MUST-based UE. We assume that \(\mathcal{E}\) is a fixed value over frequencies but it can be adaptively controlled to satisfy a certain performance requirement. We assume that each element of \(\mathbf{h}_{B,i}(i)\) follows identically and independently distributed (i.i.d.) complex-valued normal Gaussian distribution, i.e., \(\mathbf{h}_{B,i}(i)\sim\mathcal{CN}(\mathbf{0},\mathbf{I}_{N_{r}\times N_{r}})\), where \(\mathbf{I}_{N_{r}\times N_{r}}\) indicates the identity matrix of dimension \(N_{r}\). Furthermore, \(\mathbf{w}_{B,i}\in\mathbb{C}^{N_{r}\times 1}\) denotes the additive white Gaussian noise (AWGN) vector at the \(i\)-th MUST-based UE, i.e., \(\mathbf{w}_{B,i}\sim\mathcal{CN}(\mathbf{0},N_{0}\mathbf{I}_{N_{r}\times N_{r}})\), where \(N_{0}\) indicates the power spectral density of the Gaussian noise.  
Figure 2: Transmitter design of the diversity-controlled MUST technique.  
With maximum ratio combining, the received signal vector at the MUST-based UE can be represented as  
\[\bar{y}_{B.i} =\mathbf{h}_{B.i}(i)^{H}\mathbf{y}_{i}\] \[=\left\|\mathbf{h}_{B.i}(i)\right\|^{2}\sqrt{\mathcal{E}}s_{i}+ \mathbf{h}_{B.i}(i)^{H}\mathbf{w}_{B.i}\] \[=\left\|\mathbf{h}_{B.i}(i)\right\|^{2}\sqrt{\mathcal{E}}\left( \sqrt{\alpha-1}x_{B.i}+\sqrt{\alpha}x_{E.i}\right)+\mathbf{h}_{B.i}(i)^{H} \mathbf{w}_{B.i},\]  
where \(\mathbf{A}^{H}\) denotes the conjugate transpose matrix of \(\mathbf{A}\). Let \(W_{B.i}\triangleq\mathbf{h}_{B.i}(i)^{H}\mathbf{w}_{B.i}\). Then, due to properties of the circular symmetric Gaussian random vector [11], \(W_{B.i}\) can be represented by  
\[W_{B.i}\sim\mathcal{CN}\left(0,N_{0}\right). \tag{4}\]  
Assuming that \(\alpha<0.5\), \(x_{B.i}\) determines the signs of \(s_{i}\) as shown in Figure 1. In other words, \(Sgn\left(\Re\left(x_{B.i}\right)\right)\) and \(Sgn\left(\Im\left(x_{B.i}\right)\right)\) equal to \(Sgn\left(\Re\left(s_{i}\right)\right)\) and \(Sgn\left(\Im\left(s_{i}\right)\right)\), respectively, where \(Sgn(\cdot)\) denotes the sign function. If \(b_{B.1}^{i}=1\), then  
\[\Re(s_{i})\in\left\{\sqrt{\frac{1}{2}}\left(\sqrt{1-\alpha}-\sqrt{\alpha} \right),\sqrt{\frac{1}{2}}\left(\sqrt{1-\alpha}+\sqrt{\alpha}\right)\right\} :=\left\{d_{1},d_{2}\right\} \tag{5}\]  
according to the transmitter design. Thus, the decoding function for \(b_{B.i}^{i}\) from \(\bar{y}_{B.i}\) is given as:  
\[\left(\hat{b}_{B.1}^{i},\hat{b}_{B.2}^{i}\right)=\mathcal{M}^{-1}\left(Sgn( \Re(\bar{y}_{B.i})),Sgn(\Im(\bar{y}_{B.i}))\right), \tag{6}\]  
where \(\hat{b}_{B.1}^{i}\) and \(\hat{b}_{B.2}^{i}\) denote the estimated bits for \(b_{B.1}^{i}\) and \(b_{B.2}^{i}\), respectively. \(\mathcal{M}^{-1}(\cdot)\) represents the QPSK demodulation function.  
Table 2 summarizes the computation complexity of the proposed receiver at the MUST-based UE in terms of the complex number of operations.