Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels

Baldur Steingrimsson, Zhi Quan Luo, Kon Max Wong

Research output: Contribution to journalArticlepeer-review

109 Scopus citations


The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless communication channels. We propose a soft quasi-ML detector that maximizes the log-likelihood function by deploying a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML SDR detector closely approximates the performance of the optimal ML detector in both coded and uncoded multiple-input, multiple-output (MIMO) channels with quadrature phase-shift keying (QPSK) modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, thus offering some favorable performance/complexity characteristics. In contrast to the existing sphere decoder, the new quasi-ML detector enjoys guaranteed polynomial worst-case complexity. The two detectors exhibit quite comparable performance in a variety of ergodic QPSK MIMO channels, but the complexity of the quasi-ML detector scales better with increasing number of transmit and receive antennas, especially in the region of low signal-to-noise ratio (SNR).

Original languageEnglish (US)
Pages (from-to)2710-2719
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number11
StatePublished - Nov 1 2003


  • Quasi-ML detection
  • Semi-definite relaxation
  • Soft channel decoding
  • Sphere decoding
  • Suboptimal ML detection

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