Optimal selection of spatial dimensions of signal subspace for relay constellation decoding

The dimension of the right null space is only one for traditional signal space alignment with the minimum configuration of antennas. Then, the direction of a pair of alignment signal space is fixed and cannot be flexibly adjusted. Although the different alignment directions are mutually independent to facilitate relay decoding, the minimum Euclidean distance between modulated signals code words is small, which affects the decoding accuracy. In this paper, we design a novel alignment signal transmission scheme using degrees of freedom of null space generated by redundant antennas. The scheme selects the mutually orthogonal space dimension in the redundant null space as the signal alignment direction. It optimizes the minimum Euclidean distance in the system by maximizing the minimum constellation point distance. Simulation results show that the distances between the constellation points of different code symbols become significantly larger. The larger constellation distance of different coded symbols can improve the decoding accuracy. By optimizing the distance between the minimum constellation points, the transmission performance of each link is balanced and the whole system performance is improved.