## 3 Proposed Joint Iterative Semi-Blind Scheme Version  
In this section, we propose a joint iterative semi-blind channel estimation and decoding scheme version, named JISB_DSICED3 for Joint Iterative Semi-Blind Digital Self-Interference Cancellation, Equalisation, Demodulation, De-interleaving, and Decoding scheme. The process of the semi-blind algorithm is shown in Figure 3, in which the proposed scheme was developed on the principle that the processes of SI cancellation and the intended channel estimation can benefit from each other via the feedback loop after each joint iteration \(i\), where \(i\in[1,i_{max}]\). We emphasise that, different from the iteration \(j\) performing the iteration decoding in the conventional algorithm in Section 2.1, the iteration \(i\) in the proposed algorithm is for the joint SI cancellation and the intended propagation channel estimation via feedback. Based on the knowledge of pilot symbols transmitted by Node B, the system does not need to perform the temporary decoding and encoding for feedback. Indeed, it only performs the feedback loop by these pilot symbols \(\mathbf{x}_{pilot}\). Denote \(\beta E\), where \(\beta\) is the pilot symbol coefficient and \((0<\beta\leq 1)\), as the number of pilot symbols that is added to the \(E\) modulated symbols of the information signal sequence after the encoding, interleaver, and modulation process to form \(E^{\prime}=(1+\beta)E\) symbols for a transmission frame. It should be noted that for \(i=1\) (first iteration), a first SI cancellation and intended channel estimation is performed for all \(E^{\prime}\) symbols, which is used to avoid a significant number of errors and obtain a good level of convergence when starting the process of the iterative algorithm. For the remaining iterations, i.e., \(i\in[2,i_{max}]\), the system only performs the feedback loop by the known pilot symbols \(\mathbf{x}_{pilot}\) with the length of \(\beta E\). After the system completely performs the joint iterative process, i.e., \(i=i_{max}\), the estimations of the SI channel and intended channel are used to fully cancel the SI component and achieve the equalised signal, respectively. Then, these pilot symbols are removed from the equalised signal \(\tilde{y}^{\prime}[n]\), and the system continues to perform the decoder process by the de-modulation, de-interleaver, and decoding processes, in order to achieve the intended message sequence \(\mathbf{x}_{Sol}\). It should be noted that performing many \(j\) iterations in the decoding process will increase the latency and complexity because of the high computational complexity in the SPA decoding process [53]. Therefore, when we achieve the best channel estimation (\(i=i_{max}\)), the proposed scheme will only consider one iteration of decoding (\(j_{max}=1\)) in the SPA decoding algorithm to obtain a good result, because if we include more decoding iterations \(j\), this does not improve the performance significantly. The graphical presentation of the proposed joint iterative semi-blind SI cancellation and equalisation processes algorithm is shown in Figure 4, and the proposed iterative algorithm with the three main steps is summarised in Algorithm 1. Figure 2: Encoder and decoder processes. Figure 4: Graphical presentation for the joint iterative semi-blind scheme version. Figure 3: SISO FD transmission with the proposed JISB_DSICED3 process.