# Joint Iterative Decoding Design of Cooperative Downlink SCMA Systems
## 1 Introduction
The authors in [44] propose a two-stage relay selection strategy for cooperative NOMA by allowing users to require different qualities of service. The closed form expressions of the outage probabilities and diversity order for this cooperative NOMA are also determined. The closed form ergodic sum rate and outage probability of the downlink cooperative NOMA system have been studied over Nakagami-m fading channels under both decode-and-forward and amplify-and-forward protocols [45], where only statistical channel state information is available. The spatial modulation-aided cooperative NOMA [46] has been proposed for multiple-input and multiple-output systems, where the bit-error rate and ergodic sum-rate metrics have been investigated. A cooperative NOMA scheme is proposed to enhance the quality of user experience of the extended reality devices by striking a trade-off between the system throughput and fairness [47]. Bit-error rates, achievable rates and outage probabilities [48] are investigated for the two-stage massive multiple-input multiple-output cooperative relay NOMA network. The discrete-time Markov chain is utilized to demonstrate the processes of charging and discharging of the relay station under amplified-and-forward and decoded-and-forward cooperative transmission modes [49]. Then, the closed-form outage probabilities are also considered through mathematical analysis. Apart from many solutions for cooperative PD-NOMA systems, this paradigm has just emerged for the cooperative SCMA system in [50], where exact expressions of average outage probabilities are analyzed. However, the efficient decoding strategy has not been considered. To this end, we propose the cooperative downlink SCMA system to enhance system performance, where the relay works in the decode-and-forward manner. Moreover, to utilize the received signal in two phases, the joint iterative decoding strategy is designed for this downlink cooperative SCMA system by stacking the signal from the direct link and the relay together. Closed-form BER performance is also derived. The main contributions of this paper are summarized as follows:* The cooperative downlink SCMA system is introduced to enhance its performance robustness where two-phase transmission is involved, i.e., the direct link and the relay transmission. * By stacking the signal from both the direct link and the relay transmission together, we propose a joint iterative decoding design of the cooperative downlink SCMA system with the aid of the augmented codebook and the joint virtual factor graph. * To investigate the BER performance of cooperative downlink SCMA system, a closed-form solution is also provided. * Simulation results confirm the validity of our proposed joint iterative decoding design of the cooperative downlink SCMA system, which can significantly improve the BER performance as compared to the non-cooperative one. The rest of this paper is organized as follows. Section 2 introduces the system model for the downlink cooperative SCMA systems. In Section 3, we propose a joint iterative decoding scheme for the cooperative SCMA system detection. Section 4 provides the BER analysis for the cooperative SCMA system. Numerical results are provided in Section 5, followed by conclusions in Section 6.