In this article, we give the construction of new four-dimensional signal constellations in the Euclidean space, which represent a certain combination of binary frequency-shift keying (BFSK) and M-ary amplitude-phase-shift keying (MAPSK). Description of such signals and the formulas for calculating the minimum squared Euclidean distance are presented. We have developed an analytic building method for even and odd values of M. Hence, no computer search and no heuristic methods are required. The new optimized BFSK-MAPSK (M？= 5,6,···,16) signal constructions are built for the values of modulation indexes h =0.1,0.15,···,0.5 and their parameters are given. The results of computer simulations are also provided. Based on the obtained results we can conclude, that BFSK-MAPSK systems outperform similar four-dimensional systems both in terms of minimum squared Euclidean distance and simulated symbol error rate.
References
[1]
Proakis, J.G. and Salehi, M. (2008) Digital Communications. 5th Edition, McGraw Inc., New York.
[2]
Forney, G.D. and Wei, L.F. (1989) Multidimensional Constellations-Part I. Introduction, Figures of Merit, and Generalized Cross Constellations. IEEE Journal on Selected Areas in Communications, 7, 877-892. https://doi.org/10.1109/49.29611
[3]
Freudenberger, J. and Shavgulidze, S. (2015) New Four-Dimensional Signal Constellations From Lipschitz Integers for Transmission Over the Gaussian Channel. IEEE Transactions on Communications, 63, 2420-2427. https://doi.org/10.1109/TCOMM.2015.2441691
[4]
Padovani, R. and Wolf, J. (1986) Coded Phase/Frequency Modulation. IEEE Transactions on Communications, 34, 446-453. https://doi.org/10.1109/TCOM.1986.1096564
[5]
Periyalwar, S.S. and Fleisher, S.M. (1992) Multiple Trellis Coded Frequency and Phase Modulation. IEEE Transactions on Communications, 40, 1038-1046. https://doi.org/10.1109/26.142794
[6]
Ugrelidze, N., Shavgulidze S. and Sordia, M. (2019) New Generalized Multistream Spatial Modulation for Wireless Communications. 2019 Wireless Days (WD), Manchester, 24-26 April 2019, 1-7. https://doi.org/10.1109/WD.2019.8734195
[7]
Ugrelidze, N., Shavgulidze, S. and Sordia, M. (2020) New Four-Dimensional Signal Constellations Construction. IET Communications, 14, 1554-1559. https://doi.org/10.1049/iet-com.2019.0528
[8]
Thomas, C., Weidner, M. and Durrani, S. (1974) Digital Amplitude-Phase Keying with M-Ary Alphabets. IEEE Transactions on Communications, 22, 168-180. https://doi.org/10.1109/TCOM.1974.1092165
[9]
Freudenberger, J. and Shavgulidze, S. (2017) Signal Constellations Based on Eisenstein Integers for Generalized Spatial Modulation. IEEE Communications Letters, 21, 556-559. https://doi.org/10.1109/LCOMM.2016.2630701
[10]
Freudenberger, J., Rohweder, D. and Shavgulidze, S. (2018) Generalized Multistream Spatial Modulation With Signal Constellations Based on Hurwitz Integers and Low Complexity Detection. IEEE Wireless Communications Letters, 7, 412-415. https://doi.org/10.1109/LWC.2017.2780092
