Performance of linear reduced-rank multistage receivers for DS-CDMA in frequency-selective fading channels

Sau-Hsuan Wu*, Urbashi Mitra, C. C. Jay Kuo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The performance of a set of linear reduced-rank multistage filter banks is studied in the context of multiuser detection for direct-sequence (DS) code-division multiple-access (CDMA) systems. The set of filter banks under consideration is comprised of the minimum mean-square error (MMSE), the minimum output energy (MOE), the best linear unbiased estimator (BLUE), and the maximum-likelihood (ML) detector. Based on a common framework for the multistage implementations of the aforementioned filter banks, the signal-to-interference plus noise ratios (SINRs) and bit-error rates (BERs) of these reduced-rank filter banks are studied for multipath Rayleigh-fading channels. A generic BER formula is provided for coherent detection and noncoherent differential detection schemes constructed under this common framework. Analysis shows that all of these performance measures are characterized by a kernel matrix Kmmse, whose trace forms the output SINR of the MMSE filter bank. Through investigating the recursive structure of Kmmse, the output SINRs are proven to be monotonically increasing with the number of stages and upper-bounded by a number equal to the paths of the desired user's channel. The condition for asymptotically achieving this upper bound is also provided, which leads to the notion of effective user capacity of linear reduced-rank multiuser detection as well as serves as a test for the existence of a BER floor for coherent detection. In addition, the channel mismatch due to differential detection is also shown to yield a BER floor for noncoherent detection. Based on this analysis, a simple yet effective rule for choosing the number of stages is provided for both coherent and noncoherent linear multistage multiuser detection.

Original languageEnglish
Article number1512422
Pages (from-to)3493-3517
Number of pages25
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - 1 Oct 2005


  • Best linear unbiased estimator (BLUE)
  • Code-division multiple-access (CDMA)
  • Maximum likelihood (ML)
  • Minimum mean-square error (MMSE)
  • Minimum output energy (MOE)
  • Multipath fading channels
  • Multistage Wiener filtering (MSWF)
  • Multiuser detection
  • Reduced-rank filtering
  • Time-varying channels


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