BER computation of 4/M-QAM hierarchical constellations

Pavan K. Vitthaladevuni*, Mohamed Slim Alouini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

118 Scopus citations


Hierarchical constellations offer a different degree of protection to the transmitted messages according to their relative importance. As such they found interesting application in digital video broadcasting systems as well as wireless multimedia services. Although a great deal of attention has been devoted in the recent literature to the study of the bit error rate (BER) performance of uniform quadrature amplitude modulation (QAM) constellations, very few results were published on the BER performance of hierarchical QAM constellations. Indeed the only available expressions are "leading-term" approximate BER expressions for 4/16-QAM and 4/64-QAM. In this paper, we obtain exact and generic expressions in M for the BER of the 4/M-QAM (square and rectangular) constellations over additive white Gaussian noise (AWGN) and fading channels. For the AWGN case, these expressions are in the form of a weighted sum of complementary error functions and are solely dependent on the constellation size M, the carrier-to-noise ratio, and a constellation parameter which controls the relative message importance. Because of their generic nature, these new expressions readily allow numerical evaluation for various cases of practical interest. In particular numerical results show that the leading-term approximation gives significantly optimistic BER values at low carrier-to-noise ratio (CNR) in particular over Rayleigh fading channels but is quite accurate in the high CNR region.

Original languageEnglish (US)
Pages (from-to)228-239
Number of pages12
JournalIEEE Transactions on Broadcasting
Issue number3
StatePublished - Sep 2001
Externally publishedYes


  • BER computation
  • Digital broadcasting
  • Embedded modulation
  • Fading channels
  • Gray mapping
  • Hierarchical modulations
  • Multiresolution transmission
  • QAM constellations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Media Technology


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