## 3 Optimized Joint Signal Processing Schemes
### Improved Communication Signal Detection
The traditional deterministic SMC algorithm can be used to obtain the noise-whitening matrix [47], which can be written as  
\[\mathbf{U}^{i}(m,k)=\left\{\left[\mathbf{H}^{i}(m,k)\right]^{*}\left[\mathbf{H}^{i}(m,k) \right]^{\mathsf{T}}\right\}^{\frac{1}{2}} \tag{40}\]  
According to the theoretical basis of the continuous interference cancellation method, we perform QR decomposition on the noise whitening matrix obtained in (40), which can be specifically represented as  
\[\mathbf{U}^{i}(m,k)=\mathbf{Q}^{i}(m,k)\mathbf{R}^{i}(m,k) \tag{41}\]  
where \(\mathbf{Q}^{i}(m,k)\) denotes a unitary matrix and \(\mathbf{R}^{i}(m,k)\) denotes an upper triangular matrix. After matched filtering, noise whitening, and triangulation of the received signal vector, (38) can be transformed into the following formula:  
\[\hat{\mathbf{f}}^{i}(m,k)= \left[\mathbf{Q}^{i}(m,k)\right]^{\mathrm{H}}\left[\mathbf{U}^{i}(m,k) \right]^{-1}\left[\mathbf{H}^{i}(m,k)\right]^{*}\hat{\mathbf{f}}^{i}(m,k) \tag{42}\] \[= \left[\mathbf{Q}^{i}(m,k)\right]^{\mathrm{H}}\left[\left\{\left[\mathbf{ H}^{i}(m,k)\right]^{*}\left[\mathbf{H}^{i}(m,k)\right]^{\mathsf{T}}\right\}^{ \frac{1}{2}}\right]^{-1}\left[\mathbf{H}^{i}(m,k)\right]^{*}\] \[\times\left\{\alpha\left[\mathbf{H}^{i}(m,k)\right]^{\mathsf{T}}\bm {d}^{i}(m,k)+\mathbf{\omega}^{i}(m,k)\right\}\] \[= \alpha\left[\mathbf{Q}^{i}(m,k)\right]^{\mathsf{H}}\left\{\left[\mathbf{ H}^{i}(m,k)\right]^{*}\left[\mathbf{H}^{i}(m,k)\right]^{\mathsf{T}}\right\}^{ \frac{1}{2}}\mathbf{d}^{i}(m,k)+\hat{\mathbf{\omega}}^{i}(m,k)\] \[= \alpha\mathbf{R}^{i}(m,k)\mathbf{d}^{i}(m,k)+\hat{\mathbf{\omega}}^{i}(m,k)\]  
Due to the high complexity of directly calculating the posterior probability of each subblock, we adopt a sequential iterative method to numerically approach the true posterior probability infinitely. According to the structure in (42), the symbolic information detection is performed in the order of the antenna index. Since the states of the subcarriers corresponding to each transmitting antenna are independent, the SMC method can iteratively enumerate the symbolic information in the order of the antenna index. The traversal process of symbol information starts from the first subcarrier, so the number of subcarrier state combinations \(l_{sub}\) and the number of samples \(\varepsilon\) will increase continuously. We set the lower limit value of the number of state combinations as \(L_{sub}\) and the upper limit of the number of samples as \(\varepsilon^{\prime}\). The sample extraction process is realized by the important weight of each piece of symbol information. Combining the results of (42) with the characteristics of maximum likelihood detection, we can obtain the sequence of probability distributions \(\mathbf{d}^{i}(m,k)\) conditioned on \(\hat{\mathbf{f}}^{i}(m,k)\) as  
\[p\left[\hat{\mathbf{f}}^{i}(m,k)|\mathbf{d}^{i}(m,k)\right]=\frac{1}{\pi}e^{-\left| \hat{\mathbf{f}}^{i}(m,k)-\alpha\mathbf{R}^{i}(m,k)\mathbf{d}^{i}(m,k)\right|^{2}} \tag{43}\]  
Suppose that subcarriers in the same subblock are uniformly activated; the prior probability of symbols in any subblock can be expressed as  
\[p\left[\mathbf{d}_{g}{}^{i}(m,k)\right]=\left\{ \begin{array}{cc}\frac{K}{MN_{c,sub}}&\mathbf{d}_{g}{}^{i}(m,k)\in d_{M}(m,k)\\ \frac{N_{c,sub}-K}{N_{c,sub}}&\text{otherwise}\end{array} \right.