New four‐dimensional signal constellations construction

Four-Dimensional Signal Constellations Based on Binary Frequency-Shift Keying and <i>M</i>-ary Amplitude-Phase-Shift Keying

“…k = E H /E L . Therefore, the optimal BFSK-MAPSK system construction method presented in this paper is a general one, which can be used to obtain the optimal signal system of both types-BFSK-MAPSK or BFSK-MPSK [7]. We note that the method used in [7] allows us to build only BFSK-MPSK.…”

“…In [7] based on the Gram-Schmidt orthonormalization procedure for BFSK-MPSK signals we constructed the basic vectors of 4D space. Similarly, for BFSK-MAPSK signal coordinates we get:…”

“…Numerous new 4D BFSK-MPSK signal characteristics are listed in [7], where their advantage (according to SER) is shown compared to the best M-ary amplitude-phase shift keying (MAPSK) signals discussed in [1] [8]. The constellations with usual size ( 2 i M = , where i is a natural number), as well as atypical size ( 2 i M ≠ ) are presented in [6], whose use has been particularly convenient and fruitful in MIMO SM systems.…”

“…To further improve the signal distance and, accordingly, SER characteristics, in this article we will discuss 4D constructions of hybrid type constellations of size M, which will be built based on a combination of BFSK and MAPSK modulations (the so-called BFSK-MAPSK signals). The main novelty of this paper is the presentation of a general regular method of constructing such 4D constellations that uses an analysis line different from [7] and for particular cases leads to the optimal construction of [7]. In the new scheme, MAPSK modulation uses two-level circular signal constellations with energy levels-high (E H ) and low (E L ).…”

“…Using the proposed method, 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. Furthermore, we illustrate their advantages over systems from [4] [5] [7] concerning the SER performance using computer simulations for the additive white Gaussian noise channel. MIMO SM techniques appear as competitive candidates for next-generation (5G and beyond) wireless networks due to the attractive advantages they offer in terms of spectral and energy efficiency as well as hardware simplicity.…”