Double Spatial Modulation with Transmit Antenna Group for Communication Signal Transmission

In this paper, to make use of the idle transmit antennas for the improvement of multiplexing gain and the spectral efficiency, a new design of double spatial modulation (DSM) with transmit antenna group (DSM-TG) is proposed. More specifically, all of transmit antennas are grouped into G groups, each group implements a DSM system independently. Then, by using the vector combiner, G groups of DSM symbol vectors are constructed into a transmitted spatial vector. Furthermore, the average bit error ratio is analyzed. Finally, to make a fair comparison, simulation results are presented for the transmission of same data rate, and show the proposed DSM-TG achieves the better bit error rate (BER) performance gain as compared with other spatial modulation schemes.


Introduction
Index modulation (IM) technologies, which enhances the spectral efficiency by exploiting the index domain such as transmit antenna selection, time slot, frequency, have been widely nominated to play a significant role in the next generation of wireless communications system. Compared with Spatial Multiplexing (SMX), IM relaxes the inter-channel interference and inter-antenna synchronization.
In order to enhance the higher spectral efficiency, generalized spatial modulation (GSM) [1][2][3] is developed for the number of antenna index vectors by allowing two or more transmit antennas (TAs) to be simultaneously activated. On the combination of antenna index domain with constellation domain, quadrature spatial modulation (QSM) [4] is proposed to utilize two selected antenna index vectors including one non-zero element to modulate the real and quadrature parts of a data symbol, respectively. Furthermore, by using a rotation angle, two independent SM [5] vector symbols are superimposed into a transmitted spatial vector (TSV). Thus, double spatial modulation (DSM) [6] provides two-fold spectral efficiency compared to classical SM.
To improve the spectral efficiency and bit error ratio (BER) performance of wireless communication, GSM with transmit antenna grouping [7] is proposed by grouping of transmit antennas and quadrature index modulation with three dimension constellation (QIM-TDC) reported in [8] is proposed by designing three-dimension (3D) constellation. Furthermore, using code index modulation (CIM) to carry extra index information bits, for instance, CIM aided SM (CIM-SM) [9]. In this paper, in order to further achieving the higher spectral efficiency and to further enhancing the BER performance by making use of the idle transmit antennas, a new scheme, referred as DSM with transmit antenna group (DSM-TG), is proposed. In the DSM-TG system, all of the TAs are divided into multiple groups, each group is used to transmit a DSM vector symbol independently. Furthermore, the average pairwise error probability (PEP) is provided. Finally, simulation results by Monte Carlo method demonstrate the DSM-TG system outperforms other schemes (e.g. GSM, QSM, QIM-TDC, CIM-SM) in terms of the average bit error ratio performance.

System
Model Consider a MIMO system which consist of t N TAs and r N receiver antennas, as shown in Fig.1. With the aid of the antenna index modulator and the symbol modulator, the bits stream of B are mapped into a spatial vector . Then, the spatial vector S is transmitted over the wireless communication complex channel matrix H and experiences the additive white Gaussian noise n . Therefore, the received vector signal y can be expressed as: is an independent and identically distributed (i.i.d) complex Gaussian random variable obeying is assumed to be the complex Gaussian noise vector with zero mean and variance 0 N .

The Proposed Scheme
In this paper, we consider the transmitter of the DSM-TG system, as illustrated in Fig.1.
TAs, which need to be restricted to be integer of power of 2.
Thus, the number of the spatial index bits conveyed by the each group is As shown in Fig.1 Finally, in the Vector Combiner, Concatenating these G groups of g S the creates a transmitted spatial vector tv V , which is expressed as tv 1 2 = , , , , , Before transmission, since the transmit power follows 1 P = , the transmitted spatial vector tv V need to be normalized as E tv tv av

ML Detector
Assuming at the receiver the channel knowledge is perfect, the constellation symbol index bits and the spatial index bits are jointly detected using the maximum likelihood (ML) detection algorithm recover the original bits, as follows: Where 1 2, , , g g g g x x κ ξ denote the detected two symbols and two spatial index numbers corresponding the -th g DSM system, respectively.

Average Bit Error Probability
In this section, the average pairwise error probability (APEP) is presented. According to the theory of [9], an upper bound on the APEP for the bits stream B can be computed as follows: ( ) Where ( ) For Rayleigh fading channels, based on the theoretical analysis of PEP [9], the expectation of PEP on condition of the channel response H can be given by (8)

Performance Results
In this section, to verify the advantage of the DSM-TG system, simulation results with Monte Carlo method are provided and discussions under the condition that the wireless channel belongs to the Rayleigh fading channel and perfect knowledge, ( ) ( ) t r , = 8,8 N N . Moreover, in the simulations, the TSV is randomly generated and transmitted over the Rayleigh fading channel, and detected with ML detector at the receiver.
In Fig.2, the BER curves of DSM-TG are evaluated for 12 bps/Hz, and compared with GSM with 4-8QAM and =3 n , where n is the number of active antennas; QSM with 64QAM; DSM with 8PSK; QIM-TDC with 32-3DCII; ESM with 64QAM; GSM-MIM with (2,1,2,16); CIM-SM with =3 L and 8QAM. From Fig. 2, obviously, we observe that DSM-TG has significantly better performance than other schemes (e.g. GSM, QSM, QIM-TDC, CIM-SM) in terms of BER performance. For instance, DSM-TG provides about 9.5 dB SNR gain over QSM at the value of 10 -4 . In Fig.3

Conclusions
In this paper, by making use of the idle TAs, we introduced a new design, referred as DSM-TG. In DSM-TG system, all of TAs are divided into multiple groups, each of which implements a DSM system independently, for enhancing the spectral efficiency and achieving the multiplexing gains. Then, the average bit error probability is presented and analyzed. Furthermore, through computer simulation results, it can be shown that DSM-TG offers significant improvement of BER performance compared with other schemes at the transmission of same data rate. Next, our future research will focus on the detection complexity of DSM-TG, which is not discussed in this paper.