Exact Max-Log MAP Soft-Output Sphere Decoding via Approximate Schnorr–Euchner Enumeration

The complexity gains of sphere decoders (SDs) with Schnorr-Euchner enumeration and nonconstant amplitude constellations are limited by the required node ordering. Aiming at improving the implementation efficiency of SD without compromising optimality, this paper proposes a novel tree traversal for soft-output SDs providing the exact max-log MAP decoder performance. It consists of a predefined visiting order that approximates the exact Schnorr-Euchner enumeration (SEE) and a modified pruning metric that preserves the exact max-log MAP despite the approximate ordering. The proposed approach significantly improves both the computational complexity and the implementation cost of exact soft-output SDs compared with previous techniques. In particular, simulations show gains of 30%-56% in the required calculations for a 4 × 4 multiple-input multiple-output system with 16-quadrature amplitude modulation (QAM), and field-programmable gate array (FPGA) implementations show an average power reduction of 34%-50%.