Trellis coded quadrature spatial modulation

Abstract

In this paper, a novel multiple-input multiple-output (MIMO) transmission scheme called trellis coded quadrature spatial modulation (TC-QSM), is proposed. In the proposed scheme, trellis coded modulation (TCM) principle is applied to the emerging quadrature spatial modulation (QSM) scheme, and a trellis encoder and a QSM mapper are jointly designed to benefit from both coding and multiplexing gains. At the receiver side, a soft-decision Viterbi decoder is used along with a QSM decoder to obtain the optimum error performance. Considering our design criterion, TC-QSM schemes are designed for different number of trellis states, transmit antennas and spectral efficiencies. The pairwise error probability (PEP) of the TC-QSM scheme is derived over quasi-static Nakagami-$m$, Rician and Rayleigh fading channels and an upper bound on the average bit error probability (BEP) is obtained. Through comprehensive Monte Carlo simulations, the effect of signal and spatial bits on uncoded and trellis coded SM and QSM schemes over Nakagami-$m$ and Rician fading channels are investigated for different fading parameters. Moreover, the error performance of the TC-QSM and SM with trellis coding (SM-TC) schemes are compared for different spectral efficiency values, where it is revealed that the proposed TC-QSM scheme provides an interesting trade-off between performance and implementation cost, and achieves an improved error performance over reference schemes including SM, QSM and SM-TC.

Introduction

Spatial modulation (SM) technique has created a new dimension for multiple-input multiple-output (MIMO) communication technology. In the SM transmission technique, unlike traditional MIMO systems [1], only one of the available transmit antennas is activated and a data symbol selected from $M$-ary phase shift keying or quadrature amplitude modulation ($M$-PSK/QAM) constellations is transmitted through this active antenna while the remaining transmit antennas are kept inactive [2]. Since only one transmit antenna is active at any particular time instant in SM, interchannel interference (ICI) is entirely avoided at the receiver side. Its attractive advantages, such as low complexity and high energy efficiency, make SM an alternative to the traditional MIMO systems [3], and this has led researchers to design various SM-based MIMO transmission methods in the past few years. Among many SM-based schemes, two popular forms of SM are space-shift keying (SSK) [4] and generalized SM (GSM) [5]. In the SSK modulation technique, the information is transmitted only through antenna indices. In the GSM scheme, the SM transmission technique is generalized for multiple active antennas in order to improve the spectral efficiency of the classical SM scheme and facilitate the use of arbitrary number of transmit antennas.

SM-based transmission systems enable low-cost and energy-efficient hardware implementation. In [6], for the first time, the bit error rate (BER) performance of the classical SM scheme is experimentally validated. The practical implementation of SSK and GSM schemes are respectively studied in [7] and [8]. The hardware considerations and transmitter designs of different SM-based transmission schemes are proposed in [9].

Quadrature spatial modulation (QSM) is the one of the recently introduced promising MIMO transmission schemes [10]. While, the data symbol is directly transmitted through its related active antenna in SM, a complex $M$-QAM symbol is separated into its real and imaginary parts in QSM, and these parts are transmitted through their corresponding active antennas, whose indices are independently determined by incoming data bits. Since the real and imaginary parts of a complex $M$-QAM symbol are conveyed by two orthogonal carriers, ICI is also avoided in the QSM scheme. The QSM technique preserves the inherent advantages of the SM scheme while providing a considerable improvement in the spectral efficiency. Although QSM is a recent MIMO technique, it has attracted substantial attentions in the past two years. Performance of the QSM scheme is analyzed for Nakagami-$m$ [11], Rician [12] and Weibull [13] fading channels. The error performance of QSM is investigated in the presence of imperfect channel knowledge for Rayleigh [14] and $\alpha$-$\mu$, $\kappa$-$\mu$ and $\eta$-$\mu$ fading channels [15]. In order to reduce the receiver complexity of the QSM based transmission schemes, compressive sensing (CS) [[16], [17]], sphere decoding [18], minimum mean square error (MMSE) [19], equivalent maximum likelihood (ML) [20] and zero forcing (ZF) precoding [21] based low-complexity detectors are designed. In [[22], [23]], the QSM scheme is adopted in traditional cooperative relaying systems and in [[24], [25], [26]], QSM-based cognitive radio (CR) systems are designed to use the spectrum in a more efficient way. In [27], classical QSM scheme is combined with space–time codes to achieve transmit diversity and spatial multiplexing gains at the same time. Furthermore, in [28] and [29], millimeter-wave (mmWave) communications technique, which is a promising transmission technology for next-generation communication systems, is combined with the classical QSM scheme and capacity analysis of the QSM-based mmWave scheme is presented.

Error performance of SM-based systems has been enhanced by a variety of techniques. In [30], the well-known space–time block coding (STBC) principle, the Alamouti’s STBC, is combined with the classical SM transmission scheme to simultaneously achieve transmit diversity and spatial multiplexing gains. In [31], polar codes, recently invented by Arikan [32], are integrated to classical SM scheme, and the capacity and the performance results of the system are given. In [[33], [34]], trellis coded modulation (TCM) techniques that are commonly used to improve the error performance without any increase in bandwidth [35], are developed for the SM-MIMO transmission schemes by combining TCM with classical SM in order to simultaneously achieve both coding and multiplexing gains. In [36], the trellis coded SM (TCSM) scheme given in [33] is transformed into a turbo-coded modulation form to further improve the performance of the TCSM scheme. In the SM with trellis coding (SM-TC) scheme [34], after the incoming bits are encoded by a trellis encoder, the coded bits are mapped in accordance with a classical SM mapper, i.e. each branch of the trellis carries a modulated symbol and the index of its corresponding active antenna. At the receiver side of SM-TC, a soft-decision Viterbi decoder is used to process the soft information provided by a SM decoder. The optimum SM-TC schemes are designed for different number of trellis states and spectral efficiency values. In [37], super orthogonal trellis codes (SOTCs) are designed for the classical SM scheme, and finally, the TCM approach is applied to the SSK transmission scheme in [38]. However, the design of trellis coded QSM schemes remains an open and challenging research problem.

In this paper, a novel MIMO transmission technique, which is called trellis coded quadrature spatial modulation (TC-QSM), is proposed by combining the aforementioned QSM and TCM schemes. For each transmission interval of the TC-QSM scheme, incoming data bits are encoded by a trellis encoder. The encoded output bits enter a QSM mapper to generate the QSM transmission signals. At the receiver side, a soft-decision Viterbi decoder is utilized to process the soft information provided by an optimum QSM decoder. For different spectral efficiency values, optimum TC-QSM schemes are designed and their corresponding octal generator matrices are given. In addition, theoretical performance analysis of the TC-QSM scheme is performed for Nakagami-$m$, Rician and Rayleigh fading channels and an upper bound on the average bit error probability (ABEP) is obtained. The considerable bit error rate (BER) improvement of TC-QSM over SM, QSM and SM-TC schemes is demonstrated by computer simulations.

The rest of this paper is organized as follows. The TC-QSM scheme is introduced in Section 2. In Section 3, performance analysis and design criterion of TC-QSM are given. Computer simulation results and our conclusions are presented in Sections 4 Simulation results, 5 Conclusion, respectively.