Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Peak and Average Power Reduction of OFDM Signals Based on Trellis Shaping with Controllable Region Expansion

  • 164 Accesses


Trellis shaping (TS) is an efficient and flexible signal controlling technique based on the trellis structure at the transmitter. It can be used for reducing both average power and peak-to-average power ratio (PAPR) of orthogonal frequency-division multiplexing (OFDM) signals. Most studies in the framework of TS have focused on the simple sign-bit shaping, which controls the signal transition with only a single controlling bit per quadrature amplitude modulation (QAM) symbol (or subcarrier). In this paper, we attempt to increase the number of the controlling bits so as to improve the PAPR reduction capability of OFDM signals. The resulting approach, which we refer to as a controllable region expansion, is a novel extension of the conventional TS where the number of the controlling bits per QAM is increased without imposing additional complexity. Through the investigation based on extensive computer simulations using a nonlinear power amplifier (PA) model, it is shown that the proposed extended TS can achieve a better trade-off compared to the conventional sign-bit TS in terms of PAPR reduction capability, PA efficiency, and resulting bit error rate (BER) performance.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. 1.

    Wunder, G., Fischer, R. F. H., Boche, H., Litsyn, S., & No, J.-S. (2013). The PAPR problem in OFDM transmission: New directions for a long-lasting problem. IEEE Signal Processing Magazine, 30(6), 130–144.

  2. 2.

    Rahmatallah, Y., & Mohan, S. (2013). Peak-to-average power ratio reduction in OFDM systems: A survey and taxonomy. IEEE Communications Surveys & Tutorials, 15(4), 1567–1592.

  3. 3.

    Li, X., & Cimini, L. J., Jr. (1998). Effects of clipping and filtering on the performance of OFDM. IEEE Communications Letters, 2(5), 131–133.

  4. 4.

    Bäuml, R. W., Fischer, R. F. H., & Huber, J. B. (2007). Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping. IEE Electronics Letters, 32(22), 2056–2057.

  5. 5.

    Ochiai, H., & Imai, H. (2002). Performance analysis of deliberately clipped OFDM signals. IEEE Transactions on Communications, 50, 89–101.

  6. 6.

    Forney, G. D., Jr. (1992). Trellis shaping. IEEE Transactions on Information Theory, 38, 281–300.

  7. 7.

    Henkel, W., & Wagner, B. (2000). Another application for trellis shaping: PAR reduction for DMT (OFDM). IEEE Transactions on Communications, 48(11), 1471–1476.

  8. 8.

    Ochiai, H. (2004). A novel trellis-shaping design with both peak and average power reduction for OFDM system. IEEE Transactions on Communications, 52(11), 1916–1926.

  9. 9.

    Yoshizawa, R., & Ochiai, H. (2013). Performance comparison of uncoded OFDM systems with trellis shaping over nonlinear channels. Wireless Personal Communications, 72(3), 1603–1617.

  10. 10.

    Nguyen, T. T., & Lampe, L. (2007). On trellis shaping for PAR reduction in OFDM systems. IEEE Transactions on Communications, 55(9), 1678–1682.

  11. 11.

    Rapp, C. (1991). Effects of HPA-nonlinearity on a 4-DPSK/OFDM-signal for a digital sound broadcasting system. In Proceedings of the 2nd European conference on satellite communications (ECSC) (pp. 179–184).

  12. 12.

    Cann, A. J. (2012). Improved nonlinearity model with variable knee sharpness. IEEE Transactions on Aerospace and Electronic Systems, 48(4), 3637–3646.

  13. 13.

    Ochiai, H. (2013). An analysis of band-limited communication systems from amplifier efficiency and distortion perspective. IEEE Transactions on Communications, 61(4), 1460–1472.

  14. 14.

    Ochiai, H., & Imai, H. (2000). Performance of the deliberate clipping with adaptive symbol selection for strictly band-limited OFDM systems. IEEE Journal on Selected Areas in Communications, 18(11), 2270–2277.

Download references


This work was supported in part by MEXT KAKENHI 23686058 and JSPS KAKENHI \(25\cdot 195\).

Author information

Correspondence to Masaki Mastuoka.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mastuoka, M., Yoshizawa, R. & Ochiai, H. Peak and Average Power Reduction of OFDM Signals Based on Trellis Shaping with Controllable Region Expansion. Wireless Pers Commun 93, 737–754 (2017). https://doi.org/10.1007/s11277-014-2225-x

Download citation


  • Orthogonal frequency-division multiplexing (OFDM)
  • Trellis shaping (TS)
  • Peak-to-average power ratio (PAPR) reduction
  • Power amplifier (PA) nonlinearity