Efficient Implementation of a Quasi-Maximum-Likelihood Detector Based on Semi-Definite Relaxation

Existing approaches to the maximum-likelihood (ML) detection problem in digital communications either suffer from exponential complexity (e.g. sphere decoder and its variants) or exhibit significant bit-error-rate (BER) degradation (e.g. LMMSE detector). In this paper we present an efficient implementation of a semi-definite relaxation-based detector (SDR Detector) which can achieve near-optimal BER performance with worst-case polynomial complexity. This implementation (available online) can be 100 times faster than an off-the-shelf SeDuMi-based implementation, outperforms sphere decoder in low signal-to-noise ratio (SNR) or high dimension regimes, and matches the speed of sphere decoder in the high SNR regime. The core of the detector is an optimized dual-scaling interior-point method (implemented in C) for the relaxed semi-definite program. SNR-sensitive improvements are achieved by a dimension reduction strategy and a warm start technique based on a truncated version of the sphere decoding algorithm. Extensive numerical simulations show that the BER performance and the running time of SDR detector compare favorably to that of other near-optimal detection strategies.