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

Baldur Steingrimsson, Zhi Quan Luo, Kon Max Wong

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113 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 2003

Bibliographical note

Funding Information:
Manuscript received November 7, 2002; revised June 3, 2003. This work was supported by the Natural Sciences and Engineering Research Council of Canada and the Canada Research Chair program. Part of this work was presented at the IEEE 2003 International Conference on Communications, Anchorage, AK, May 11–15, 2003. The associate editor coordinating the review of this paper and approving it for publication was Dr. Michael P. Fitz.


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


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