Reduced complexity sphere decoding using probabilistic threshold based Schnorr–Euchner enumeration

The use of multiple antennas at both the transmitter and the receiver is the key technology for future wireless communications since it achieves higher spectral efficiency. Symbol decoding at the receiver for such a system is still a challenge. We propose a new enumeration technique, termed as probabilistic threshold-based Schnorr–Euchner (PSE) enumeration, to reduce the complexity of sphere decoding (SD). The conventional SE-SD algorithm visits all nodes satisfying the sphere constraint in ascending order of their branch metric values. However, this algorithm is computationally expensive in real-time scenarios. Therefore, we use a threshold limit for the branch metric values in the Schnorr–Euchner (SE) enumeration which is based on the noise statistics, to reduce the overall complexity. In each layer of the decoding process, the proposed PSE-SD technique performs a threshold test before visiting the next candidate in an SE ordered list. As a result, unlikely nodes, which do not satisfy the threshold test, are pruned earlier than in the conventional SE-SD algorithm. From the simulation results, we examine the influence of the proposed probabilistic threshold for various MIMO configurations and witness that the PSE-SD technique achieves a significant complexity reduction over existing methods with only a negligible performance loss.