Multi-Antenna Selection for Double Spatial Modulation

In this paper, to exploit the spatial domain of transmit antennas (TAs) for the transmit diversity gain in the double spatial modulation (DSM) system, a new scheme of multi-antenna selection for DSM (MAS-DSM) is designed. In the MAS-DSM system, the number of TAs are grouped into n groups, each of which corresponds to an sub-system of DSM. More specifically, a transmitted spatial vector is constructed by two spatial vectors (SVs). For the achievability of transmit diversity gain, one of the two SVs is obtained by using n antenna index (AI) vectors to modulate a data symbol, another of them is obtained by multiplying with a rotation angle after another n AI vectors to modulate another data symbol. Finally, the spectral efficiency and the average bit error ratio (BER) are analyzed. Simulation results by using Monte Carlo demonstrate that the proposed MAS-DSM system has better BER performance compared with the conventional spatial modulation schemes in wireless communication network.


Introduction
Generalized spatial modulation (GSM) reported in [1][2][3] is developed for achieving the transmit diversity of system, the activated transmit antenna (TA) in which simultaneously transmits the same version of one conventional modulated symbol (e.g. QAM/PSK) with more than one active TAs at one time slot. GSM not only achieves the transmit diversity gain but also relax the relation of both the antenna index information bits and the number of TAs. However, the spectral efficiency is only , where t N , a n , N denotes the number of TAs and the active TAs, the modulation order, respectively. By making fully use of the property of the spatial dimension in the constellation symbol, quadrature spatial modulation (QSM) reported in [4], extends the spatial dimension to the in-phase and quadrature dimension. The real and quadrature part of a data symbol are modulated by an antenna activated by an in-phase vector and another antenna activated by a quadrature vector, respectively. Compared with SM [5], QSM can transmit more 2t log N bits per a transmitted vector symbol. For further achieving the spectral efficiency, double spatial modulation (DSM) is proposed in [6] and provides two-fold spectral efficiency compared to classical SM. In fact, with the aid of a rotation angle, two independent SM transmission vectors are superimposed. To improve the system performance against the high channel correlation in massive MIMO systems, grouping GSM (gGSM) is proposed in [7]. Recently, based on the design concept of both SM and QSM, quadrature index modulation with three dimension constellation [8] (QIM-TDC) is proposed to enhance the spectral efficiency and to enhance the reliability of wireless communication system by the design of three-dimension (3D) constellation. However, based on the above researches, the transmit diversity is not better considered for the better performance and too many TAs are inactivated.
In this paper, for further achieving the transmit diversity, a new design, which is called as multiantenna selection for DSM (MAS-DSM), is proposed to further lower bit error ratio (BER) performance. In the proposed MAS-DSM system, the TAs are divided into multiple groups, which are used to transmit the two conventional modulated symbols with the aid of a rotation angle. Furthermore, the spectral efficiency and the average bit error ratio (BER) are provided. Finally, simulation results and comparisons show that the proposed MAS-DSM outperforms those existing transmission schemes in terms of the average BER performance.

MAS-DSM transmitter
The transmitter of the MAS-DSM system has t N TAs, as shown in Fig.1.
Hence, the expression of the spatial vector 1 S and 2 S may be as follows: According to the basic principle of DSM, before resulting in the transmitted spatial vector

MAS-DSM Receiver
The resulting spatial vector

Average Bit Error Probability
Assumed V is the erroneous detection of V . According to [9], the conditional pairwise error probability (CPEP) can be calculated as where ( ) Q  denotes the Gaussian Q function, ( ) ( ) The expectation of the CPEP on the channel response H can be given by Combing with the Q function, the expression of expectation of (8) can be calculated as

Performance Results
To validate the superiority of the proposed MAS-DSM system, simulation results using Monte Carlo for the proposed MAS-DSM system with tr = =8 NN are provided and discussions. Throughout all the simulations, the channel information state is assumed to be perfect.
At  Fig.3 also shows that the BER performance versus SNR curves of MAS-DSM with 4QAM; SM with 512QAM; GSM with 256QAM; QSM with 64QAM; DSM with 8QAM; ESM with 64QAM; QIM-TDC with 32-3DCII at the spectral efficiency of 12 bps/Hz. The simulation results demonstrate that the MAS-DSM system with =2 n has significantly better performance than all other schemes, and outperforms approximately 13 dB SNR gains over SM, 10 dB SNR gains over GSM, approximately 8 dB SNR gains over QSM, 7 dB SNR gains over DSM, 2.5 dB SNR gains over ESM, 1 dB SNR gains over QIM-TDC at BER value of 10 -4 .

Conclusion
In this paper, the MAS-DSM system is proposed for achieving the transmit diversity gains by activating the multiple TAs. By activating different number of TAs, we obtain that the larger the number of activated TAs, the better BER performance may not be. Then, compared with other schemes, simulation results using Monte Carlo demonstrates that the MAS-DSM system improves the BER performance at the same configuration. Furthermore, although the BER performance is improved,