  Sphere decoding (SD) is a low complexity maximum likelihood (ML) detection algorithm, which has been adapted for different linear channels in digital communications. The complexity of the SD has been shown to be exponential in some cases, and polynomial in others and under certain assumptions. The sphere radius and the number of nodes visited throughout the tree traversal search are the decisive factors for the complexity of the algorithm. The radius problem has been addressed and treated widely in the literature. In this paper, we propose a new structure for SD, which drastically reduces the overall complexity. The complexity is measured in terms of the floating point operations per second (FLOPS) and the number of nodes visited throughout the algorithm tree search. This reduction in the complexity is due to the ability of decoding the real and imaginary parts of each jointly detected symbol independently of each other, making use of the new lattice representation. We further show by simulations that the new approach achieves 80% reduction in the overall complexity compared to the conventional SD for a 2x2 system, and almost 50% reduction for the 4x4 and 6x6 cases, thus relaxing the requirements for hardware implementation. 
Reduced Complexity Sphere Decoding for Square QAM via a New Lattice   Representation