Sparse code multiple access (SCMA) is one of the competitive non-orthogonal multiple access (NOMA) techniques for the next generation communication systems. In this paper, we put forward a simple and efficient design method named divided extended mother codebook (DEMC) to construct SCMA codebooks based on golden angle modulation (GAM) constellation points. First, we generate a vector defined by the GAM. Second, we design the extended mother codebook (EMC) by introducing the power and phase dependent constraints of symbols in multi-dimension codewords. The power constraints can ensure the power of each codeword is the same which leads to the optimal peak to average power ratio (PAPR) especially for the uplink channel. Third, we divide the EMC into several mother codebooks (MCs) to generate the constant bit rate (CBR) or variable bit rate (VBR) SCMA codebooks. The structure of the VBR SCMA codebooks is compatible with that of CBR. The VBR codebooks and CBR codebooks use the same factor graph, therefore, the users employed the VBR codebooks can also utilize the efficient message passing algorithm (MPA) for multi-user detection. Simulations reveal that the bit error rate (BER) performance of the proposed CBR DEMC-SCMA codebooks is outstanding with low complexity. The VBR DEMC-SCMA codebooks can flexibly satisfy the different service requirements, and the BER performance of the VBR DEMC-SCMA codebooks is close to each other though their modulation orders are various. This feature shows that the users can apply for a high order codebook to get a faster information transfer rate without increasing transmission power and bandwidth.

In this study, we propose a method named decomposition of the superposed constellation (DCSC) to design sparse code multiple access (SCMA) codebooks for the additive white Gaussian noise (AWGN) channel. We prove that the power of the user symbols (USs) is accurately determined by the power of the superposed constellation (SC). Thus, we select quadrature amplitude modulation (QAM) constellations as the SC and decompose the SC into several groups of USs with power diversity. The minimum Euclidean distance (MED) between superposed symbols (SS-MED) in the receiver is determined by the selected QAM and MED between the multi-dimensional codewords (CW-MED) is optimized by matching the symbols on different dimensions. We propose a simplified DCSC (S-DCSC) by modifying the factor graph and avoiding the transmission of USs with low power, which greatly reduces the complexity of the message passing algorithm (MPA). The simulations show that the SS-MEDs of DCSC and S-DCSC are larger than those in previous papers and the BER performance of the proposed codebooks is better than others.

This letter designs an orthogonal time-frequency space (OTFS) enabled network-coded multiple access (NCMA) system for enhancing the throughput in high-mobility scenarios. For the designed system, the impact of power distribution and relative phase offset is theoretically analyzed and the upper-bound symbol error probability is derived into a closed-form expression. To further minimize the upper-bound symbol error probability, a joint amplitude-phase optimization scheme is proposed with using genetic algorithm. Finally, the simulation results reveal that the proposed scheme achieves significant throughput enhancement in high mobility scenarios.

In the Non-Terrestrial Networks (NTNs) formed by the integration of fifth-generation mobile communication systems and Low Earth Orbit (LEO) satellites, Doppler frequency offsets can severely degrade the performance of OFDM signal detection. Particularly for the Physical Uplink Control Channel (PUCCH), conventional detection algorithms suffer significant performance degradation due to the difficulty of accurately estimating and compensating for Doppler frequency offsets at the receiver. Consequently, achieving robust signal detection under conditions with high Doppler frequency offsets becomes particularly critical. To address this challenge, we propose a maximum-likelihood detection algorithm robust to both Doppler frequency and time offsets. In the first step, we derive the frequency-offset matrix, which directly affects the detection peaks. Subsequently, we develop a novel two-dimensional search algorithm that jointly considers UCI and frequency offset. Finally, based on the sparse characteristics of the dominant elements in the frequency offset matrix, we simplify the implementation of the frequency offset matrix, reducing computational complexity to 9% of the original algorithm while achieving negligible performance loss. This approach satisfies the requirements for onboard implementation.