Low complexity optimal joint detection for oversaturated multiple access communications

Optimal joint detection for interfering (nonorthogonal) users in a multiple access communication system has, in general, a computational complexity that is exponential in the number of users. For this reason, optimal joint detection has been thought to be impractical for large numbers of users. A number of suboptimal low-complexity joint detectors have been proposed for direct sequence spread spectrum user waveforms that have properties suitable for mobile cellular and other systems. There are, however, other systems, such as satellite systems, for which other waveforms may be considered. This paper shows that there are user signature set selections that enable optimal joint detection that is extremely low in complexity. When a hierarchical cross-correlation structure is imposed on the user waveforms, optimal detection can be achieved with a tree-structured receiver having complexity that is, in typical cases, a low-order-polynomial in the number of users. This is a huge savings over the exponential complexity needed for the optimal detection of general signals. Previous work has shown that a hierarchically structured signal set can achieve oversaturation (more users than dimensions) with no growth in the required signal-to-noise ratio. The proposed tree detector achieves low-complexity optimal joint detection even in this oversaturated case