## 1 Introduction  
Index modulation (IM) is a relatively new technique in which information is conveyed to the receiver using the conventional signal symbols and/or the index(es) of additional system resources [1]. The index represents a physical antenna in spatial modulation (SM) and space shift keying (SSK) [2, 3], spreading codes [4], polarities [5], sub-carriers [6], combinations of angles [7], virtual channels [8], among others. SM attracted an increasing attention because it achieves a multiple-input multiple-output (MIMO) gain in terms of spectral efficiency while keeping the transmitter as simple as that of the single-input systems. The generalized SM (GSM) reduces the number of transmit antennas required to achieve a given spectral efficiency as compared to SM. GSM transmits a single signal symbol from a combination of antennas, instead of a single antenna as in SM [9]. The parallel SM (PSM) divides the available antenna set into groups, and the conventional SM is independently performed in each group using the same signal symbol. Therefore, the PSM reduces the number of transmit antennas at no cost in terms of the spectral efficiency [10, 11]. Recently, a new constellation that reduces the asymptotic error performance was designed in [12]. Quadrature SM (QSM) is an extension of SM, where the real and imaginary part of a single signal symbol are transmitted from an in-phase and quadrature spatial dimension, respectively, leading to an improvement in the spectral efficiency [13]. To further increase the spectral efficiency, an improved QSM (IQSM) is presented to transmits two signal symbols at each channel use, where the real parts and imaginary parts are transmitted from antenna combinations of length of 2 on the orthogonal cosine and sine carriers, respectively [14]. A high-performance parallel implementation of the improved QSM was recently proposed in [15]. A complex QSM (CQSM) was proposed in [16; 17], where two signal symbols are transmitted from two physical antennas whose indices also carry information. The two signal symbols are drawn from two distinct constellations, where the second is a rotated version of the first. The optimization and the convergence tendencies of the constellation are investigated in [17]. It was shown that the convergence of rotation angle is dominated by the probability of the event that the two symbols are transmitted from the same antenna. An improved CQSM is proposed in [18], where the transmitter is equipped with an additional antenna that is used only when the two signal symbols are supposed to be transmitted in the CQSM. The first signal symbol is transmitted from its designated antennas; the second signal symbol from the additional antenna. The design of the modulation set of the improved CQSM is addressed in [19]. In this category of algorithms, the optimization of the rotation angles plays a very crucial role in determining the error performance of the system. As such, the constellation should be carefully optimized, as mentioned in the above works. A generalized multiple active antennas SM (MA-SM) was proposed in [20], where each activated antenna transmits an independent signal symbol, leading to further improvement in the spectral efficiency. In addition to the idea of MA-SM, authors in [20] proposed two additional algorithms for the MA-SM: 1) A simple detection algorithm, and 2) 3-dimensional constellation. The proposed simple alternative to the optimal maximum-likelihood (ML) detector comes at a cost in terms of the bit-error rate (BER) and the diversity order. Building upon the pioneering work in [20], Several works have addressed the detection process of the MA-SM and proposed more efficient detectors with low computational complexity (c.f. [21; 22]). On the other hand and to the best of our knowledge, the merits of the 3-dimensional constellation was not verified in the original work nor by any other researchers. **Contributions**: We believe that the verification of the proposed technique in the literature should be as important as introducing new techniques.