Quasi-maximum-likelihood multiuser detection using semi-definite relaxation with application to synchronous CDMA

Wing Kin Ma, Timothy N. Davidson, Kon Max Wong, Zhi Quan Luo, Pak Chung Ching

Research output: Contribution to journalArticlepeer-review

294 Scopus citations


The maximum-likelihood (ML) multiuser detector is well known to exhibit better bit-error-rate (BER) performance than many other multiuser detectors. Unfortunately, ML detection (MLD) is a nondeterministic polynomial-time hard (NP-hard) problem, for which there is no known algorithm that can find the optimal solution with polynomial-time complexity (in the number of users). In this paper, a polynomial-time approximation method called semi-definite (SD) relaxation is applied to the MLD problem with antipodal data transmission. SD relaxation is an accurate approximation method for certain NP-hard problems. The SD relaxation ML (SDR-ML) detector is efficient in that its complexity is of the order of K 3.5, where K is the number of users. We illustrate the potential of the SDR-ML detector by showing that some existing detectors, such as the decorrelator and the linear-minimum-mean-square-error detector, can be interpreted as degenerate forms of the SDR-ML detector. Simulation results indicate that the BER performance of the SDR-ML detector is better than that of these existing detectors and is close to that of the true ML detector, even when the cross-correlations between users are strong or the near-far effect is significant.

Original languageEnglish (US)
Pages (from-to)912-922
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number4
StatePublished - Apr 2002

Bibliographical note

Funding Information:
Manuscript received December 7, 2000; revised December 6, 2001. This work was supported in part by the Hong Kong Research Grant Council and the Natural Sciences and Engineering Research Council of Canada. The fourth author was also supported by the Canada Research Chair program. The associate editor coordinating the review of this paper and approving it for publication was Dr. Inbar Fijalkow.


  • Maximum likelihood detection
  • Multiuser detection
  • Relaxation methods
  • Semi-definite programming


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