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.

In this paper, the distributed cooperative communication of unmanned aerial vehicles (UAVs) is studied, where the condition number (CN) and the inner product (InP) are used to measure the quality of communication links. By optimizing the relative position of UAVs, large channel capacity and stable communication links can be obtained. Using the spherical wave model under the line of sight (LOS) channel, CN expression of the channel matrix is derived when there are N_t transmitters and two receivers in the system. In order to maximize channel capacity, we derive the UAVs position constraint equation (UAVs-PCE), and the constraint between BS elements distance and carrier wavelength is analyzed. The result shows there is an area where no matter how the UAVs' positions are adjusted, the CN is still very large. Then a special scenario is considered where UAVs form a rectangular lattice array, and the optimal constraint between communication distance and UAVs distance is derived. After that, we derive the InP of channel matrix and the gradient expression of InP with respect to UAVs' position. The particle swarm optimization (PSO) algorithm is used to minimize the CN and the gradient descent (GD) algorithm is used to minimize the InP by optimizing UAVs' position iteratively. Both of the two algorithms present great potentials for optimizing the CN and InP respectively. Furthermore, a hybrid algorithm named PSO-GD combining the advantage of the two algorithms is proposed to maximize the communication capacity with lower complexity. Simulations show that PSO-GD is more efficient than PSO and GD. PSO helps GD to break away from local extremum and provides better positions for GD, and GD can converge to an optimal solution quickly by using the gradient information based on the better positions. Simulations also reveal that a better channel can be obtained when those parameters satisfy the UAVs position constraint equation (UAVs-PCE), meanwhile, theory analysis also explains the abnormal phenomena in simulations.