The information-theoretic optimality of QPSK

Sergio Verdú

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


Quadrature Phase Shift Keying (QPSK) finds ubiquitous use in coherent communication systems. In this paper we show that in the low-power wideband regime, QPSK is a capacity-maximizing strategy for additive-noise Gaussian complex-valued channels subject to fading where the receiver has full information about the channel realization. The traditional asymptotic optimality criterion used since Shannon (1948) is that the derivative at zero SNR be optimal. However, this optimality criterion is not strong enough to withstand the test of spectrally efficient finite-bandwidth communication. In contrast, in this paper we propose a new asymptotic optimality criterion where both the first and second derivatives at zero SNR are required to be optimal. The setting of this paper is general enough to encompass multiantenna channels, frequency selectivity, and multiaccess channels. We also illustrate the robustness of QPSK in the absence of full receiver knowledge of the channel.

Original languageAmerican English
Pages (from-to)167-173
Number of pages7
Issue number170
StatePublished - 2002
Event4th International ITG Conference on Source and Channel Coding - Berlin, Germany
Duration: Jan 28 2002Jan 30 2002

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture

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