Constant modulus and reduced PAPR block differential encoding for frequency-selective channels

Yngvar Larsen, Geert Leus, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Frequency-selective channels can be converted to a set of flat-fading subchannels by employing orthogonal frequency-division multiplexing (OFDM). Conventional differential encoding on each subchannel, however, suffers from loss of multipath diversity, and a very high peak-to-average power ratio (PAPR), which causes undesirable nonlinear effects. To mitigate these effects, we design a block differential encoding scheme over the subchannels that preserves multipath diversity, and in addition, results in constant modulus transmitted symbols. This property is shown to ensure that the PAPR of the continuous-time transmitted waveform is reduced by a large factor. The maximum-likelihood decoder for the proposed scheme, conditioned on the current and previous received block, is shown to have linear complexity in the number of subcarriers. The constant modulus scheme will yield good bit-error rate performance with full rate only if short blocks are used. However, one may mitigate this problem by relaxing the constant modulus requirement. We show that in a practical OFDM system, we can group the subcarriers into shorter subblocks in a certain manner, and apply the constant modulus technique to each subblock. Thus, we improve diversity at a very low decoder complexity, and at the same time, we introduce an upper bound on the discrete-time PAPR, which, in turn, may lead to appreciable reduction in continuous-time PAPR, depending on the system parameters. Finally, in situations where we can sacrifice rate, additional complex field coding may be used to exploit the multipath diversity provided by channels longer than those the simple scheme can handle.

Original languageEnglish (US)
Pages (from-to)622-631
Number of pages10
JournalIEEE Transactions on Communications
Issue number4
StatePublished - Apr 2004

Bibliographical note

Funding Information:
Paper approved by C. Tellambura, the Editor for Modulation and Signal Design of the IEEE Communications Society. Manuscript received August 16, 2002; revised May 5, 2003 and August 16, 2003. The work of Y. Larsen was supported by the Research Council of Norway under Contract 134676/432. Prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. This work was also supported by the National Science Foundation Wireless Initiative under Grant 99-79443. This paper was presented in part at the 36th Annual Conference on Information Sciences and Systems, Princeton, NJ, March 2002.


  • Block differential encoding
  • Frequency-selective channels
  • Orthogonal frequency-division multiplexing (OFDM)
  • Peak-to-average power ratio (PAPR)

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