Energy efficiency in the low-SNR regime under queueing constraints and channel uncertainty

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21 Scopus citations


Energy efficiency of fixed-rate transmissions is studied in the presence of queueing constraints and channel uncertainty. It is assumed that neither the transmitter nor the receiver has channel side information prior to transmission. The channel coefficients are estimated at the receiver via minimum mean-square-error (MMSE) estimation with the aid of training symbols. It is further assumed that the system operates under statistical queueing constraints in the form of limitations on buffer violation probabilities. The optimal fraction of power allocated to training is identified. Spectral efficiencybit energy tradeoff is analyzed in the low-power and wideband regimes by employing the effective capacity formulation. In particular, it is shown that the bit energy increases without bound in the low-power regime as the average power vanishes. A similar conclusion is reached in the wideband regime if the number of noninteracting subchannels grow without bound with increasing bandwidth. On the other hand, it is proven that if the number of resolvable independent paths and hence the number of noninteracting subchannels remain bounded as the available bandwidth increases, the bit energy diminishes to its minimum value in the wideband regime. For this case, expressions for the minimum bit energy and wideband slope are derived. Overall, energy costs of channel uncertainty and queueing constraints are identified, and the impact of multipath richness and sparsity is determined.

Original languageEnglish (US)
Article number5772060
Pages (from-to)2006-2017
Number of pages12
JournalIEEE Transactions on Communications
Issue number7
StatePublished - Jul 2011
Externally publishedYes


  • Bit energy
  • QoS constraints
  • channel estimation
  • effective capacity
  • energy efficiency
  • fading channels
  • fixed-rate transmission
  • imperfect channel knowledge
  • low-power regime
  • minimum bit energy
  • spectral efficiency
  • wideband regime
  • wideband slope

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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