Effect of channel estimation error on M-QAM BER performance in rayleigh fading

Xiaoyi Tang, Mohamed Slim Alouini, Andrea J. Goldsmith

Research output: Contribution to journalArticlepeer-review

229 Scopus citations


We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates. Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider.

Original languageEnglish (US)
Pages (from-to)1856-1864
Number of pages9
JournalIEEE Transactions on Communications
Issue number12
StatePublished - 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


  • Channel estimation error
  • M-QAM
  • PSAM
  • Rayleigh fading


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