Combined Index Modulation with Increased Spectral Efficiency for Noncoherent Reception

Introduction. Modern communication systems are supposed to use the allocated frequency band as efficiently as possible. This can be achieved by improving the spectral efficiency of such systems. One simple approach consists in introducing index modulation, which involves transmitting additional information by selecting one of possible combinations of the mutual arrangement of active and inactive resources. However, the presence of inactive resources hinder the achievement of maximal spectral efficiency, which makes it important to develop more sophisticated modulation schemes.

Aim. To develop a combined index modulation scheme with increased spectral efficiency and a receiver with acceptable computational complexity, as well as to obtain analytical expressions to estimate the noise immunity of this modulation scheme.

Materials and methods. Computer simulation in the MATLAB environment.

Results. A scheme of combined index modulation is proposed, in which all physical resources are active but have different power. In this case, high-level and low-level resources are used to transmit two separate signals. To further enhance the spectral efficiency, differential phase shift keying is introduced between the mentioned parts of the final signal. A receiver that processes each signal component separately, enabling significant expansion of the signal constellation and consequent improvement in spectral efficiency without substantial computational overhead is developed. Formulas for the error probability are obtained, the results of which are in good agreement with the simulation outcomes.

Conclusion. The developed method allows large-volume signal ensembles to be formed based on existing codebooks with insufficient spectral efficiency. The advantage of this approach to increasing spectral efficiency consists in the possibility of implementing a simplified reception method, in which the total number of arithmetic operations is determined by the sum, rather than by the product, of computational costs for processing individual signal components. Future research should extend the proposed approach by considering a combination of signals with index modulation patterns that have more than two levels.

1. Ericsson. 6G Spectrum – Enabling the Future Mobile Life Beyond 2030. Available at: https://www.ericsson.com/en/reports-and-papers/whitepapers/6g-spectrum-enabling-the-future-mobile-lifebeyond-2030/ (accessed 27.05.2025).

2. Basar E., Wen M., Mesleh R., Di Renzo M., Xiao Y., Haas H. Index Modulation Techniques for Next-Generation Wireless Networks. IEEE Access. 2017, vol. 5, pp. 16693–16746. doi: 10.1109/ACCESS.2017.2737528

3. Başar E., Aygölü Ü., Panayırcı E., Poor H. V. Orthogonal Frequency Division Multiplexing With Index Modulation. IEEE Transactions on Signal Processing. 2013, vol. 61, no. 22, pp. 5536–5549. doi: 10.1109/TSP.2013.2279771

4. Ni J., Zheng J. Index Modulation-Based NonCoherent Transmission in Grant-Free Massive Access. IEEE Transactions on Vehicular Technology. 2021, vol. 70, no. 1, pp. 1025–1029. doi: 10.1109/TVT.2020.3045448

5. Fazeli A., Nguyen H. H. Code Design for NonCoherent Index Modulation. IEEE Communications Let. 2020, vol. 24, no. 3, pp. 477–481. doi: 10.1109/LCOMM.2019.2961312

6. Fazeli A., Nguyen H. H., Hanif M. Generalized OFDM-IM with Noncoherent Detection. IEEE Transactions on Wireless Communications. 2020, vol. 19, no. 7, pp. 4464–4479. doi: 10.1109/TWC.2020.2983700

7. Hanif M., Nguyen H. H. Non-Coherent Index Modulation in Rayleigh Fading Channels. IEEE Communications Let. 2019, vol. 23, no. 7, pp. 1153–1156. doi: 10.1109/LCOMM.2019.2917085

8. Bian Y., Cheng X., Wen M., Yang L., Poor H. V., Jiao B. Differential Spatial Modulation. IEEE Transactions on Vehicular Technology. 2015, vol. 64, no. 7, pp. 3262–3268. doi: 10.1109/TVT.2014.2348791

9. Althunibat S., Mesleh R., Basar E. Differential Subcarrier Index Modulation. IEEE Transactions on Vehicular Technology. 2018, vol. 67, no. 8, pp. 7429–7436. doi: 10.1109/TVT.2018.2837691

10. Ishikawa N., Sugiura S. Rectangular Differential Spatial Modulation for Open-Loop Noncoherent MassiveMIMO Downlink. IEEE Transactions on Wireless Communications. 2017, vol. 16, no. 3, pp. 1908–1920. doi: 10.1109/TWC.2017.2657497

11. Xiao L., Xiao P., Xiao Y., Wu C., Mi D., Hemadeh I. A. Rectangular Differential OFDM with Index Modulation. IEEE 89th Vehicular Technology Conf. (VTC2019-Spring), Kuala Lumpur, Malaysia, 28 Apr.–01 May 2019. IEEE, 2019, pp. 1–6. doi: 10.1109/VTCSpring.2019.8746521

12. Dogukan A. T., Basar E. Orthogonal Frequency Division Multiplexing with Power Distribution Index Modulation. Electronics Let. 2020, vol. 56, no. 21, pp. 1156–1159. doi: 10.1049/el.2020.1692

13. Mao T., Wang Z., Wang Q., Chen S., Hanzo L. Dual-Mode Index Modulation Aided OFDM. IEEE Access. 2017, vol. 5, pp. 50–60. doi: 10.1109/ACCESS.2016.2601648

14. Mao T., Wang Q., Wang Z. Generalized DualMode Index Modulation Aided OFDM. IEEE Communications Let. 2017, vol. 21, no. 4, pp. 761–764. doi: 10.1109/LCOMM.2016.2635634

15. Sergienko A. B., Apalina P. V. Design of Constrained Codebooks Using Autoencoder Networks. Seminar on Networks, Circuits and Systems (NCS), St Petersburg, 29–30 Nov. 2023. IEEE, 2023, pp. 11–15. doi: 10.1109/NCS60404.2023.10397473

16. Proakis J. G. Digital Communications. 3 th ed. McGraw-Hill, 1995, 928 p.

17. Levin B. R. Teoreticheskie osnovy statisticheskoj radiotehniki [Theoretical Foundations of Statistical Radio Engineering]. Moscow, Radio i svyaz', 1989, 656 p. (In Russ.)