Quadrature spatial modulation–performance analysis and impact of imperfect channel knowledge

This chapter discusses the average bit error ratio (ABER) performance analysis for the different space modulation techniques (SMTs). The ABER is computed for space shift keying (SSK), spatial modulation (SM), quadrature space shift keying (QSSK), and quadrature spatial modulation (QSM) over Rayleigh flat fading channels. The chapter proposes a general framework for the performance analysis of the different SMTs over arbitrary fading channels, in the presence of spatial correlation and imperfect channel estimation. The derivation of the average error probability for SMTs can be computed by deriving the pairwise error probability (PEP). The chapter presents Monte Carlo simulation results to study the ABER performance of SMTs, generalized space modulation techniques (GSMTs), quadrature space modulation techniques (QSMTs), and differential space modulation techniques (DSMTs) system with different configurations. The derivation of the instantaneous PEP in the presence of imperfect channel knowledge at the receiver is similar to the derivation of perfect channel knowledge.

SummaryThe modified generalized quadrature spatial modulation (mGQSM) scheme is introduced to improve the transmission rate of the spatial modulation (SM) and quadrature SM (QSM). In mGQSM, the information symbols are separated as real and imaginary coefficients, which are modulated on in‐phase and quadrature dimensions, respectively. In addition, this scheme presented a novel codebook design to enhance the rate of 1 bit per channel use over generalized QSM (GQSM). In this paper, we present mGQSM and reduced codebook mGQSM (RC‐mGQSM) system performances over Nakagami‐m, Rayleigh, and Rician fading channels. However, the Rayleigh fading is a special case of Nakagami‐m fading when m = 1. For the computer simulations, we use several values for the Nakagami parameter, m, and Rician factor, K. We present the mGQSM and RC‐mGQSM system performances and compare them to the GQSM, QSM, and SM system performances, using the maximum‐likelihood (ML) detection. For the RC‐mGQSM scheme, we present a low‐complexity detection method. We also present the performances of mGQSM and SM systems in the presence of imperfect channel conditions.

In this paper, a new multiple-input multiple-output (MIMO) transmission technique, which is called double spatial modulation (DSM), is proposed as a new high-rate generalized spatial modulation (SM) scheme. DSM scheme aims to improve the spectral efficiency of classical SM by increasing the number of active transmit antennas. In the DSM scheme, incoming data bits determine two modulated symbols as well as their corresponding activated transmit antenna indices. One of the modulated symbols is directly transmitted over its corresponding activated transmit antenna, while the other one is transmitted with a rotation angle, which is optimized for M-ary quadrature amplitude modulation (M-QAM) signal constellation, over the second activated transmit antenna. The error performance of the proposed DSM scheme is compared with the recently proposed emerging SM schemes such as quadrature SM (QSM) and enhanced SM (ESM). Our computer simulations show that the DSM scheme provides considerably better error performance than QSM and ESM schemes for different spectral efficiency values. In addition, the pairwise error probability (PEP) of DSM is derived and the average bit error probability (ABEP) over uncorrelated Rayleigh fading channels is obtained for different M-QAM constellations.

In this paper, the average bit error rate performance of quadrature spatial modulation (QSM) transmission technique over double complex Nakagami-m fading channels is investigated. In the proposed scheme, in which all terminals are in motion as mobiles or vehicles. The average bit error rate is derived by using pairwise error probability and upper bound union expressions, which are defined for the QSM transmission technique. In this context, the mean vector and variance matrix of double complex Nakagami-m fading channels has been presented using of properties of its statistics. Furthermore, at the receiver side, the impact of Gaussian imperfect channel state information on the performance is considered, and analytical expression is presented. Finally, it has been demonstrated that Monte Carlo simulation results prove the exactness of analytical results under different system settings and the severity of fading parameters.

Quadrature spatial modulation (QSM) has been recently proposed for MIMO communication systems. It comes to enhance the overall throughput over conventional spatial modulation (SM) techniques. This article investigates the using of this new SM technique in Multi-user MIMO networks, denoted here as MU-QSM. Unlike existing SM techniques, the QSM creates additional spatial constellation dimension, and hence higher overall throughput can be obtained. The performance of the system mentioned is numerically analyzed for a number of users and compared to point-to-point networks. In addition, the experienced interference and receiver-complexity are analyzed too.

Quadrature spatial modulation (QSM) is recently developed modulation technique for massive multiple input multiple output (MIMO), where one can transmit the real and imaginary part of modulated symbols from different antennas to increase the bit error rate (BER) and spectral efficiency performance of spatial modulation (SM). The usage of maximum likelihood (ML) based detection in QSM results in increased complexity. In this paper, we use low complex detection techniques for QSM which is a combination of signal vector-based detection (SVD) and ordered block minimum mean square error methods (OB-MMSE). By using these two methods we estimate the transmitted antennas combination and transmitted symbol. The projected hybrid scheme simplifies the receiver complexity and offers performance similar to ML.

Motivated to enhance the error performance (EP) of generalised complex quadrature spatial modulation (GCQSM) systems, this study proposes a scheme that builds on GCQSM and uses hexagonal quadrature amplitude modulation (H-QAM) constellations which have the advantages of a maximised Euclidean distance with relatively low peak-to-average power ratio, compared to conventional QAM (C-QAM) systems. This in turn, leads to an enhancement of the EP of GCQSM schemes. The proposed scheme utilises a rotated hexagonal 8QAM (H-8QAM) set. Thus, the proposed scheme is herein named; Generalised QSM using H-8QAM (GQSM-H-8QAM). In this study, the EP of the proposed GQSM-H-8QAM scheme is investigated over Rayleigh frequency flat-fading channels with additive white Gaussian noise. Additionally, a theoretical average bit error probability (ABEP) expression of the GQSM-H-8QAM scheme is formulated and validated using Monte Carlo simulations. Compared to simulation results, the ABEP proves to be increasingly tight at high signal-to-noise ratio values. Obtained simulation results also show an improvement in the EP of the GQSM-H-8QAM scheme over various SM schemes like GCQSM, C-QSM and conventional-generalized spatial modulation (C-GSM), at the same spectral efficiency (SE). An improvement in the EP of 0.61 dB with SE of 8 bits/s/Hz is seen in 4times 4 GQSM-H-8QAM over 4times 4 GCQSM using C-8QAM, 2.58 dB over 4times 4 C-QSM-C-64QAM and a gain of 4.85 dB over 4times 4 C-GSM-C-64QAM.

Spatial modulation (SM) presents a pragmatic approach for transmitting information, where the modulator uses well known amplitude/phase modulation (APM) techniques such as phase shift keying (PSK) and quadrature amplitude modulation (QAM), but also employs the antenna index to convey additional information. Nevertheless, the spectral efficiency of SM can be further improved. On this note, to further enhance the spectral efficiency of SM, quadrature SM (QSM) modulation was proposed. In coded channels, therefore, typically soft-output detection coupled with soft-input channel decoding yields significant signal-to-noise ratio (SNR) gain. Hence, in this paper, soft-output maximum-likelihood detector (SOMLD) for QSM modulated system is proposed. Monte Carlo simulation results demonstrate that there is a close agreement between the error performances of the proposed SOMLD scheme and those of its hard-decision maximum-likelihood detector counterpart in uncoded channels, while significant signal-to-noise ratio (SNR) gains are yielded in coded channels. Keywords: Multiple-input multiple-output, quadrature spatial modulation, soft-output detection, space shift keying, spatial modulation

The idea of media-based modulation (MBM), introduced in [1] [2], is to embed information in the variations of the transmission media (channel states). This is in contrast to legacy wireless systems which embeds data in a radio frequency (RF) source prior to the transmit antenna. MBM offers several advantages over legacy systems, including “additivity of information over multiple receive antennas” and “inherent diversity over a static fading channel”. MBM is particularly suitable for transmitting high data rates using a single transmit unit and multiple receive antennas (single input multiple output MBM, or SIMO-MBM). Furthermore, layered multiple input multiple output MBM (LMIMO-MBM) [3] addresses hardware and decoding complexity along with training overhead when transmitting high data rates using a single MBM transmit unit. The current article compares the performance of MBM and LMIMO-MBM vs. legacy multiple input multiple output (MIMO) and emerging modulation techniques, spatial modu-lation (SM), and its variants, such as generalized SM (GSM) and quadrature SM (QSM). These comparisons demonstrate considerable performance gains for MBM and LMIMO-MBM vs. these notable schemes.

A novel multiple-input and multiple-output (MIMO) transmission scheme termed as generalized quadrature spatial modulation (G-QSM) is proposed. It amalgamates the concept of quadrature spatial modulation (QSM) and spatial multiplexing for the sake of achieving a high throughput, despite relying on a low number of radio frequency (RF) chains. In the proposed G-QSM scheme, the conventional constellation points of the spatial multiplexing structure are replaced by the QSM symbols, hence the information bits are conveyed both by the antenna indices as well as by the classic amplitude/phase modulated (APM) constellation points. The upper bounds of the average bit error probability (ABEP) of the proposed G-QSM system in high throughput massive MIMO configurations are derived. Furthermore, an efficient multipath orthogonal matching pursuit (EM-OMP)-based compressive sensing (CS) detector is developed for our proposed G-QSM system. Both our analytical and simulation results demonstrated that the proposed scheme is capable of providing considerable performance gains over the existing schemes in massive MIMO configurations.

The optimum detection of binary antipodal signals in additive white Gaussian noise (AWGN) channels with Gaussian channel estimation error has been studied in prior work. In this paper, we present the optimum detector based on the maximum- likelihood criterion for binary orthogonal signals in the presence of Gaussian distributed channel estimation error and AWGN. It is shown that the optimum detector is a linear combination of the optimum coherent and optimum noncoherent detectors. We derive the exact closed-form expression of the average bit error probability of the proposed optimum detector in Rayleigh fading channels with AWGN. It is found that if the variance of channel estimation error for a given average SNR is greater than a threshold, then orthogonal signalling outperforms antipodal modulation, and the analytical expression of this threshold is derived.

The performance of a multicarrier direct sequence code division multiple access (MC-DS-CDMA) system in fading environment has been extensively analysed in the literatures. The analysis that is available in the literatures did not take into account the impact of jamming and channel estimation errors on the performance of the system. In this study, closed-form expressions of the average bit error probability (BEP) of the MC-DS-CDMA system with channel estimation errors in the presence of partial band, broadband and multitone jamming are derived in a Rayleigh fading channel. The analysis shows that the magnitude of the normalised correlation between the actual and the estimated complex fading channel gain, A, greatly affects the performance of the MC-DS-CDMA system. For large signal-to-noise ratio, the average BEP with A=1 and without multiple access interference (MAI) tends to zero. When A≠1, the BEP of the system exhibits an error floor even without MAI. This error floor increases as the number of users increases. It is also shown that increasing the number of the system subcarriers enhances the system performance against jamming.

In this paper, we propose a robust transceiver design for MIMO interfering broadcast channels taking imperfect channel knowledge at each base station into consideration. By considering the worst-case transceiver design which maximizes the minimum signal-to-interference-plus-noise ratio (SINR), the proposed design can provide better sum rate and worst user rate performance compared to the conventional schemes. From simulation results, we show the resilience of the proposed design against imperfect channel knowledge.

In this paper, we propose a new multiple-input multiple-output (MIMO) transmission scheme, called parallel complex quadrature spatial modulation (PCQSM). The proposed technique is based on the complex quadrature spatial modulation (CQSM) to further increase the spectral efficiency of the communication system. CQSM transmits two different complex symbols at each channel use. In contrast with CQSM, the new transmission scheme splits the transmit antennas into groups, and modulates the two signal symbols using the conventional CQSM before transmission. Based on the selected modulation order and the number of possible groups that can be realized, the incoming bits modulate the two signal symbols and the indices of the transmit antennas in each group. We demonstrated that while the complexity and performance of the proposed scheme is the same as that of CQSM, the number of required transmit antennas is significantly reduced. The proposed PCQSM achieves such a benefit without requiring any additional radio frequency (RF) chains. The results obtained from Monte Carlo simulation showed that at a Bit Error Rate (BER) of 10−4, the performance of the PCQSM with two antenna groups closely matches that of CQSM, and outperformed quadrature spatial modulation (QSM) and parallel quadrature spatial modulation (PQSM) by over 0.7 dB. As the number of antenna groups increased to 4, the BER performance of PCQSM with reduced number of transmit antenna and modulation order matches that of QSM. The BER of the proposed scheme using maximum likelihood (ML) receiver is also analyzed theoretically and compared with the BER obtained via simulations.

In this chapter, the fundamental concepts of spatial modulation are introduced. We start in Chapter 2.1 with the channel models, i.e. the AWGN channel and the MIMO Rayleigh fading channel. The AWGN channel is employed in Chapter 3 to compare different signal constellations, whereas the Rayleigh fading channel is used for all MIMO transmission schemes. In Section 2.2, we discuss various spatial modulation transmission schemes from the literature, including spatial modulation, generalized spatial modulation, generalized multistream spatial modulation and the most recently-introduced spatial permutation modulation.