Realizable ideal D/C and C/D conversions for band-limited periodic signals and characterization of single-carrier block transmission

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Abstract

For a real band-limited periodic signal, there are reconstruction formulas that realize the ideal discrete-to-continuous (D/C) conversion within one period of the signal. However, the previous results may not be suitable for general complex band-limited periodic signals. For complex band-limited periodic signals, in this paper we first propose the reconstruction formulas, which lead to realizable forms of ideal D/C conversion. We then derive the correlation function of the interpolation pulse, and this helps us construct a matched filter that can implement the exact sampling (C/D conversion) of a complex band-limited periodic signal. When there exists noise in the sampling process, comparing with the ideal impulse sampling, the proposed C/D conversion can maintain finite output noise variance. The correlation function of the output noise is also given, and the oversampling effect of noise is analyzed. For a complex interpolation pulse, in general we cannot decouple the ideal D/C (or C/D) conversion into two independent D/C (or C/D) conversions for the real and imaginary parts of the signal. We also give the extended forms and decomposition forms of the proposed D/C and C/D conversions. Our results are applied to derive the ideal D/C and C/D conversions in the precoded orthogonal frequency-division multiplexing (POFDM) system. The resulted interpolation pulses are used to characterize the single-carrier (SC) block transmission under the POFDM architecture. We give characteristics that distinguish the SC block transmission from traditional SC transmission.

Original languageEnglish
Article number5658167
Pages (from-to)1670-1682
Number of pages13
JournalIEEE Transactions on Signal Processing
Volume59
Issue number4
DOIs
Publication statusPublished - 2011 Apr 1

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Interpolation
Sampling
Orthogonal frequency division multiplexing
Carrier communication
Matched filters
Decomposition

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

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abstract = "For a real band-limited periodic signal, there are reconstruction formulas that realize the ideal discrete-to-continuous (D/C) conversion within one period of the signal. However, the previous results may not be suitable for general complex band-limited periodic signals. For complex band-limited periodic signals, in this paper we first propose the reconstruction formulas, which lead to realizable forms of ideal D/C conversion. We then derive the correlation function of the interpolation pulse, and this helps us construct a matched filter that can implement the exact sampling (C/D conversion) of a complex band-limited periodic signal. When there exists noise in the sampling process, comparing with the ideal impulse sampling, the proposed C/D conversion can maintain finite output noise variance. The correlation function of the output noise is also given, and the oversampling effect of noise is analyzed. For a complex interpolation pulse, in general we cannot decouple the ideal D/C (or C/D) conversion into two independent D/C (or C/D) conversions for the real and imaginary parts of the signal. We also give the extended forms and decomposition forms of the proposed D/C and C/D conversions. Our results are applied to derive the ideal D/C and C/D conversions in the precoded orthogonal frequency-division multiplexing (POFDM) system. The resulted interpolation pulses are used to characterize the single-carrier (SC) block transmission under the POFDM architecture. We give characteristics that distinguish the SC block transmission from traditional SC transmission.",
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