Capacity analysis for non-orthogonal overloading transmissions under constellation constraints

In this work, constellation constrained (CC) capacities of a series of non-orthogonal overloading transmission schemes are derived in AWGN channels. All these schemes follow a similar transmission structure, in which modulated symbols are spread on to a group of resource elements (REs) in a sparse manner, i.e., only a part of the REs have nonzero components while the others are filled with zeros. The multiple access schemes follow this structure is called sparse code multiple access (SCMA) in general. In particular, a complete SCMA scheme would combine multi-dimensional modulation and the low density spreading (LDS) together such that the symbols from the same data layer on different REs are different but dependent. If the spread symbols are the same, it is a simplified implementation of SCMA and is called LDS. Furthermore, depending on whether the numbers of non-zero components for each data layer are equal or not, there are regular LDS (LDS in short) and irregular LDS (IrLDS), respectively. The paper would show from theoretical derivation and simulation results that the complete SCMA schemes outperform the simplified version LDS/IrLDS. Moreover, we also show that the application of phase rotation in the modulator can significantly boost the link performance of such non-orthogonal multiple access schemes.