A closed-form expression for the exact BER of generalized PAM and QAM constellations

Pavan Kumar Vitthaladevuni*, M. S. Alouini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


We derive an explicit closed-form expression for the exact bit-error rate (BER) computation of generalized hierarchical M-ary pulse amplitude modulations over additive white Gaussian noise (AWGN) and fading channels. This expression can also be used to obtain the exact BER of generalized hierarchical quadrature amplitude modulations (square and rectangular). 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.

Original languageEnglish (US)
Pages (from-to)698-700
Number of pages3
JournalIEEE Transactions on Communications
Issue number5
StatePublished - May 2004
Externally publishedYes


  • Bit-error rate (BER) computation
  • Digital broadcasting
  • Embedded modulation
  • Gray mapping
  • Hierarchical modulations
  • Pulse amplitude modulation (PAM) constellations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


Dive into the research topics of 'A closed-form expression for the exact BER of generalized PAM and QAM constellations'. Together they form a unique fingerprint.

Cite this