## 3 Optimized Joint Signal Processing Schemes
### Improved Communication Signal Detection  
In communication applications, the received signal is the superposition of the transmitted signal polluted by Gaussian noise. The conventional processing of posterior distribution is to search all possible transmitted signal blocks exhaustively, but its complexity is high in the case of large signal blocks. Sequential Monte Carlo (SMC) is an inference method for estimating nonlinear and non-Gaussian state space models, which has been widely used in wireless communication [47; 48]. The SMC method approximates the posterior distribution of a state variable by generating high-dimensional Monte Carlo samples dimension by dimension. Specifically, symbol samples are extracted from a defined set in a certain order, and new sequential particles are created by the extracted samples. Then, the importance weight associated with each particle is updated by the probability distribution characteristics. The research shows that the detector based on SMC can achieve a near-maximum likelihood performance while the cost of the receiver is lower. However, the basic SMC can not fully meet the application requirements, so it is necessary to study improved methods suitable for different scenarios. In this section, to reduce the complexity and obtain a better communication performance, we propose an improved SMC signal detection method. For the communication receiver, we first need to achieve high-precision communication synchronization according to the cross-correlation between all GI sequences and the received communication signal. Then, the interference cancellation method in [49] is adopted to effectively reduce the interference between signals. Meanwhile, the position information of the OFDM signal block carrying modulation symbols is extracted by using the relative position relationship between sequences. All GI sequences will be removed after synchronization is completed. In addition, \(N_{c}\)-point fast Fourier transform (FFT) is adopted at each receiving antenna, and the signal block in the frequency domain is obtained by the \(I\times N_{c\_sub}\) block deinterleaver. Specifically, for the subcarriers of each OFDM-IM subblock, the received signal vectors of the \(i\)th subblock can be stacked as follows:  
\[\mathbf{f}^{i}(m,k)=\alpha\Big{[}\mathbf{H}^{i}(m,k)\Big{]}^{\text{T}}\mathbf{d}^{i}(m,k)+ \mathbf{\omega}^{i}(m,k) \tag{38}\]  
where \(\mathbf{f}^{i}(m,k)=\Big{[} \begin{array}{cccc}f_{1}{}^{i}(m,k)&f_{2}{}^{i}(m,k)& \cdots&f_{N_{r}}{}^{i}(m,k)\end{array} \Big{]}^{\text{T}}\) is the received signal vector, \(\alpha\) is the balance factor, \(\mathbf{\omega}^{i}(m,k)\) is the Gaussian noise vector with zeros mean and unit variance, \(\mathbf{d}^{i}(m,k)=\Big{[} \begin{array}{cccc}d_{1}{}^{i}(m,k)&d_{2}{}^{i}(m,k)& \cdots&d_{N_{t}}{}^{i}(m,k)\end{array} \Big{]}^{\text{T}}\) is the modulated transmission signal vector, and \(\mathbf{H}^{i}(m,k)\) is the channel frequency responses matrix, which can be written as  
\[\mathbf{H}^{i}(m,k)=\left[ \begin{array}{cccc}h_{1,1}^{i}(m,k)&h_{1,2}^{i}(m,k)& \cdots&h_{1,N_{r}}^{i}(m,k)\\ h_{2,1}^{i}(m,k)&h_{2,2}^{i}(m,k)&\cdots&h_{2,N_{r}}^{i}(m,k)\\ \vdots&\vdots&\ddots&\vdots\\ h_{N_{t},1}^{i}(m,k)&h_{N_{t},N_{r}}^{i}(m,k)&\cdots&h_{N_{t},N_{r}}^{i}(m,k) \end{array} \right] \tag{39}\]  
To reduce the complexity, we propose an improved communication signal detection method based on SMC. Without changing the noise-whitening characteristics, we need to perform matched filtering and noise whitening on the received signal vector to maximize the signal-to-noise ratio (SNR).