Abstract
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.
Highlights
To date, there has been a significant increase in interest in digitally modulated signals, mainly due to the widespread use of multi-input and multi-output (MIMO) systems
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)
The simulation results show that for SER = 10−5 the energy gain of BFSK-MAPSK signals compared to BFSKMPSK signals are around 0.73 dB, 0.76 dB, and 0.48 dB for M = 8, M = 10 and M = 13, respectively, which once again indicates the advantage of BFSK-MAPSK over BFSK-M-ary phase-shift keying (MPSK) systems
Summary
There has been a significant increase in interest in digitally modulated signals, mainly due to the widespread use of multi-input and multi-output (MIMO) systems. Concerning SER characteristics good results are obtained for four-dimensional (4D) signals, which represent certain combinations of binary frequency shift keying (BFSK) and M-ary phase-shift keying (MPSK) modulations (BFSK-MPSK signals) Several such signals were presented in combination with channel coding schemes [4] [5], and later, as the components of Spatial Modulation (SM) systems [6]. For modulation indexes h ≤ 0.5 and alphabet sizes 5 ≤ M ≤ 16, we construct new BFSK-MAPSK signal constellations and present the parameters of the best of them in the form of a table We illustrate their advantages over systems from [4] [5] [7] concerning the SER performance using computer simulations for the additive white Gaussian noise channel.
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