Hexagonal Quadrature Amplitude Modulation Research Articles

Performance analysis of energy harvesting‐enabled relay networks in κ‐μ fading channels

AbstractIn this paper, we investigate the performance of an energy harvesting (EH)‐enabled multiple relay network operating over generalized ‐ fading channels. Our approach involves utilizing a partial relay selection strategy and employing an amplify and forward relay protocol for efficient EH from RF signals. Additionally, we integrate a selection combining scheme at the receiver to combine both direct and relaying path signals. In our research, we first obtain the exact closed‐form expression of the cumulative distribution function (CDF) for the system under investigation. Subsequently, we derive expressions for the outage probability (OP) and the moment generating function (MGF) using the derived CDF expression. Furthermore, with the assistance of a CDF‐based approach, we derive closed‐form expressions for the average symbol error rate (ASER) for coherent quadrature amplitude modulation (QAM) schemes, including rectangular QAM (RQAM) and hexagonal QAM (HQAM). We also analyze the ASER expression for non‐coherent frequency shift keying (NCFSK), leveraging the derived MGF expression. To gain valuable insights into the performance of EH‐enabled multiple relay networks, we assess the asymptotic expression of the OP. The outcomes indicate how the behavior of the system is affected by various factors such as time switching ratio, channel fading components, number of relays, and the distance between nodes. To corroborate the accuracy of the analytical findings, Monte Carlo simulations are executed.

On the performance of energy harvesting‐assisted Nth best relay cooperative networks in Nakagami‐m fading

SummaryWe study the energy harvesting (EH)‐assisted system model based on the performance of a dual‐hop cooperative communication system that is subjected to Nakagami‐ fading. Through the partial relay selection method, the selection of th best relay (BR) is performed among amplify and forward (AF) relays, which can harvest energy from radio frequency signals. At the receiver, the selection combining scheme is considered to select between the signals of th best relaying path and the direct path. For this considered system, we compute the closed‐form expressions of outage probability (OP) and the average symbol error rate (ASER) for higher order quadrature amplitude modulation (QAM) techniques, especially for rectangular QAM, cross QAM, and hexagonal QAM. Further, a new moment‐generating function expression is obtained which is used to derive the ASER expression related to the generalized non‐coherent modulation technique. We also give the asymptotic expression of OP to find out the diversity order. Furthermore, we study the effect of fading parameters, th BR, and other factors on system behavior. Finally, we verify the derived expressions with Monte Carlo simulations.

Mirror activation pattern selection for energy efficient hexagonal QAM aided media‐based modulation

AbstractIn this article, three mirror activation pattern (MAP) selection techniques are used to improve the performance of energy‐efficient hexagonal quadrature amplitude modulation (HQAM) aided media‐based modulation (MBM) system called HMBM. These three MAP selection (MS) aided HQAM techniques: (i) capacity‐optimized MS‐based HMBM (CMS‐HMBM) scheme, (ii) MAP correlation (MC) aided MS‐based HMBM (MMS‐HMBM) scheme, (iii) Euclidean distance (ED) based MS aided HMBM (EMS‐HMBM) scheme. MBM technique, one of the newest and most competitive candidates of the index modulation family, increases spectral efficiency linearly and significantly improves error performance. When MS techniques are integrated into telecommunication techniques, they significantly increase the performance of the system. Extensive computer simulations with Monte Carlo for the considered systems are performed on Rayleigh fading channels. The suggested system offers superior error performance than the conventional MBM scheme since it incorporates CMS, MMS, and EMS techniques. Additionally, the suggested new method offers greater energy efficiency than ‐QAM constellation schemes since HQAM constellation schemes are by their very nature high energy efficiency. It is shown that the proposed CMS‐HMBM, MMS‐HMBM, and EMS‐HMBM systems provide better error performance than capacity‐optimized antenna selection (COAS) aided hexagonal spatial modulation (COAS‐HSM), antenna correlation‐based AS aided HSM (ACAS‐HSM), Euclidean distance optimized AS aided HSM (EDAS‐HSM), SM, and MBM systems for the same spectral efficiency. The suggested systems are envisaged for usage in sixth‐generation and later wireless networks because of their high performance provided by the CMS, MMS, and EMS methods in the proposed system and the high spectral efficiency provided by the HMBM approach.

Performance of IRS-Aided FD Two-Way Communication Network With Imperfect SIC

Intelligent reflecting surface (IRS) is a promising technology to deploy reconfigurable and cost-effective next-generation wireless communication systems. In this work, we investigate the performance of an IRS-aided two-way communication network over Rayleigh fading channels, where downlink and uplink transmission between the base station and the user equipment is established in full-duplex mode. We take into account the impact of residual self-interference (RSI), which results from imperfect self-interference cancellation. We derive the analytical expressions of outage probability (OP), asymptotic OP, and obtain diversity order of the system. We also derive ergodic capacity in terms of the Meijer-G function. Further, we derive the analytical expressions of average symbol error rate (ASER) for general order rectangular quadrature amplitude modulation (QAM), cross QAM, and hexagonal QAM. We highlight the impact of reflecting elements, RSI, and other system parameters on the performance of the considered network and also compare the ASER of various QAM constellations. Finally, Monte-Carlo simulations validate the derived analytical expressions.

Improved Chernoff Bound of Gaussian Q-function with ABC algorithm and its QAM applications to DB SC and MRC systems over Beaulieu–Xie channels

In this study, we propose an improved upper bound for the Gaussian Q function by using artificial bee colony algorithm. Then, we investigate the performance of the dual-branch (DB) selection combining (SC) and maximal ratio combining (MRC) systems over the Beaulieu–Xie fading channels. The probability density functions of the instantaneous signal to noise ratio for the considered systems are obtained. Employing the proposed upper bound, we derive closed-form expressions of the error probability for the quadrature amplitude modulation (QAM) techniques such as rectangular QAM (RQAM), cross QAM (XQAM), and hexagonal QAM (HQAM). Furthermore, the asymptotic error probability expressions for the DB SC system are also obtained to simplify the analyses. The effects of some key parameters in the systems are shown in the results. Comparisons of the different modulation types and the different upper bound approaches for the Gaussian Q function are presented. Finally, it has been shown that the upper bound approximation presented in this study can be widely used for many communication applications.

ASER analysis of generalized hexagonal QAM schemes for NOMA systems over Nakagami‐m fading channels

SummaryTo achieve high data rates expected from beyond 5G communications, higher‐order modulation techniques have been explored. The energy‐efficient modulation technique with a high data rate has encouraged researches towards an optimum two‐dimensional hexagonal‐shaped constellation, namely, hexagonal quadrature amplitude modulation (HQAM). Thus, in this work, we analyze the average symbol error rate (ASER) of HQAM schemes by considering a two‐user nonorthogonal multiple access (NOMA) pair. Closed‐form expressions for ASER of HQAM schemes for users are derived over generalized Nakagami‐ fading channels. Further, for the HQAM constellation feasibility in two‐user downlink NOMA systems, the power allocation criterion for the users is presented. Furthermore, the impact of modulation order of the users over the systems ASER analysis is investigated and valuable insights are drawn.

Error performance analysis of generalized quadrature spatial modulation using H-8QAM

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.

On the ASER performance of RF energy harvesting multiple relay networks

We present the average symbol error rate (ASER) of quadrature amplitude modulation (QAM) for radio frequency energy harvesting assisted dual-hop multiple amplify-and-forward (AF) relay network. In this relaying network, partial relay selection scheme is employed to select best relay among multiple relays, while selection combining is considered at destination to combine the signals coming from the direct path and the relaying path. In particular, we derive the exact ASER expressions of rectangular QAM (RQAM), hexagonal QAM and cross QAM schemes for the considered systems over independent and non-identically distributed Nakagami-m fading channels using cumulative distribution function method. Moreover, the asymptotic ASER expression of RQAM is determined to examine the system’s diversity order. Further, to verify the correctness of derived expressions, numerically evaluated results are compared with Monte Carlo simulations. Furthermore, the effects of fading parameter, number of relay, time switching ratio, and large scale fading are studied on the ASER performance.

On the Error Analysis of Hexagonal-QAM Constellations

Future communication systems are envisioned to support applications that require very high data rates in an energy efficient manner. To this direction, the use of hexagonal quadrature amplitude modulation (HQAM) provides high data rates and power efficiency, due to its compact allocation of symbols on the 2D plane. However, because of its hexagonal lattice, it is difficult, if not impossible, to evaluate exactly the error probability. In this letter, we propose a tight upper bound as well as a closed-form approximation for the symbol error probability of HQAM, which are validated from numerical and simulation results. Finally, exploiting the analytical results a novel low complexity detection scheme is presented.

ASER Analysis of Hybrid Receiver Based SWIPT Two-Way Relay Network

In this paper, we investigate the performance of a hybrid receiver-based simultaneous wireless information and power transfer (SWIPT) two-way relay network over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> faded channels. A hybrid receiver is adopted at the relay node that utilizes both the time switching (TS) and power splitting (PS) protocols for energy harvesting and information transmission. Amplify-and-forward relaying protocol is utilized at the relay node to process the information in half-duplex mode. In the considered network, impact of a practical non-linear power amplifier (NLPA) at the relay node is considered. Selection combining is performed at the destination node to utilize the direct-link and relay assisted signals. For the considered system, the analytical expressions of outage probability (OP) and asymptotic OP are derived over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> faded channels for both the integer and non-integer value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> . The analytical expression of the system throughput and energy efficiency of the considered network are also derived. Further, the analytical expression of ergodic capacity is derived in terms of the Meijer-G function. By utilizing a cumulative distribution function based approach, analytical expressions of average symbol error rate (ASER) for general order hexagonal quadrature amplitude modulation (QAM), general order rectangular QAM, and 32-cross QAM schemes are derived. For different QAM constellations, a comparative ASER analysis is also illustrated. Furthermore, the impact of TS factor, PS ratio, energy conversion efficiency, NLPA, and threshold data-rates on the considered network is also highlighted. Finally, Monte-Carlo simulations are performed for validation of the derived analytical expressions.

A new hexagonal quadrature amplitude modulation aided media‐based modulation

SummaryIn this paper, a new high‐data rated and energy‐efficient hexagonal quadrature amplitude modulation aided media‐based modulation scheme, called HQAM‐MBM, is proposed for the next‐generation communication systems. In MBM, mirror activation patterns (MAPs) of a reconfigurable antenna have been used to convey extra information in addition to conventional modulated symbols. Therefore, the MBM is seen as a promising index modulation (IM) scheme for the next generation of high‐data rated communication systems. On the other hand, the HQAM constellation scheme is more energy‐efficient than traditional QAM but also has a similar performance at high signal‐to‐noise ratio (SNR) values. Hence, the HQAM technique can appear as a promising energy‐efficient scheme for 5G and beyond networking systems. From this point forth, it has been found appropriate to propose the rational HQAM‐MBM technique, which uses an energy‐efficient HQAM constellation instead of a traditional QAM constellation, and also carries additional information with the indices of the MAPs of a reconfigurable antenna. Besides, it has been shown via computer simulations that the HQAM‐MBM system has lower transmission energy than QAM‐MBM systems. Performance analysis of the HQAM‐MBM scheme is evaluated on Rayleigh fading channels.

Performance analysis of Hexagonal QAM constellations on quadrature spatial modulation with perfect and imperfect channel estimation

In this study, the quadrature spatial modulation (QSM) technique, which is a rational multiple-input multiple-output (MIMO) transmission technique and frequently encountered in recent studies in the literature, and the hexagonal quadrature amplitude modulation (HQAM) constellation technique, which combines symbols in an “optimum” way are combined. This new MIMO scheme has been named by the authors as HQAM-QSM. Also, the impact of imperfect channel knowledge on the performance of the proposed scheme is examined. The HQAM constellation technique is a technique that provides better results under the same power assumption than the conventional QAM constellation in terms of symbol separation and is more often encountered when it comes to energy-efficiency. Due to the nature of HQAM symbols, error-floor occurs when the QSM system is applied. Hence, the optimum angle is obtained by rotating the HQAM symbols. With this optimum angle, it has been seen that the error-floor disappeared and the performance of the system is improved. Besides, the HQAM technique performs similar bit error rates (BER) to QAM at high signal-to-noise ratio (SNR) values. From this point forth, in our study, the rational HQAM-QSM technique, which uses energy-efficient HQAM symbols instead of traditional modulated QAM symbols and also carries information effectively on two active antennas, is proposed. Performance analysis of the HQAM-QSM technique is performed on Rayleigh fading channels.

Transmit Antenna Selection for Spatial Modulation Based on Hexagonal Quadrature Amplitude Modulation

There is a tremendous demand from various industries for next-generation 5G networks, which has dramatically increased the need for high data rates and energy efficiency. It is an indisputable fact that next-generation networks should be not only energy-efficient but also resource-efficient. Given the fact that 10% of the current energy consumption in the world is caused by Information and Communication Technology, it is evident that energy-efficiency has become the most crucial performance criteria in the next-generation communication techniques. Based on these needs, we previously suggested the hexagonal quadrature amplitude modulation (HQAM) aided spatial modulation (SM) technique (HQAM-SM) to the literature. In this study, we found it appropriate to do this research to further increase the performance of the HQAM-SM scheme through the antenna selection technique and to investigate the effects of antenna selection technique on HQAM-SM. Moving from this point, in this article, rational capacity-optimized antenna selection (COAS), SM, and energy-efficient HQAM techniques are combined, and a new system called COAS-HSM is presented. Hexagonal constellations are to optimize the constellation points to form a hexagonal constellation to minimize the Hamming distance between the constellation points. This layout not only offers better energy efficiency than traditional QAM constellations but also performs almost the same BER performance as QAM at high signal-to-noise ratio (SNR) values. On the other hand, antenna selection algorithms are one of the transmission schemes that have been frequently encountered in the literature in recent years, and that considerably increases the performance of various multiple-input multiple-output (MIMO) communication structures. In particular, the COAS transmission scheme is an intelligent method of selecting transmission antennas over the highest channel amplitudes. Performance analysis of the proposed COAS-HSM technique is carried out in Rayleigh fading channels.

Performance of Multiple Relay DF NLOS UVC System With CSI Imperfections

Ultraviolet communication (UVC) is emerging as an attractive alternative to the existing optical wireless communication (OWC) technologies. UVC experiences negligible noise on the earth's surface, and also has the ability to operate in non-line-of-sight (NLOS) mode, thereby making it a perfect choice for outdoor communication. However, due to strong interaction of ultraviolet waves with atmospheric particles, it suffers from a very high path loss and turbulence-induced fading, which limits UVC system's performance. We consider a decode-and-forward based cooperative relaying technique to improve the performance of NLOS UVC system, and to extend its communication range. We consider the practical case of imperfect channel state information at the receiver and derive outage probability of the system. We also consider impact of elevation angles, receiver field-of-view (FOV), and turbulence strength on the system performance. We compute the relative diversity order of the system and demonstrate its convergence through asymptotic analysis. Next, we obtain the novel expression of probability density function of the end-to-end instantaneous signal-to-noise-ratio. We use single subcarrier intensity modulation employing quadrature amplitude modulation (QAM) and derive the novel generalized analytical expressions for rectangular QAM, cross QAM, and futuristic hexagonal QAM schemes. We carry out a detailed performance study considering different system configurations and several interesting insights are highlighted, which reinforces UVC as a futuristic OWC technology. Correctness of the derived analytical expressions is confirmed using Monte-Carlo simulations.

Dual-branch SC wireless systems with HQAM for beyond 5G over η-μ fading channels

In this study, the performance of hexagonal quadrature amplitude modulation (HQAM) for a dual-branch selection combining (SC) receiver for beyond fifth-generation (B5G) is analyzed in detail. For general applicability, the links are modeled with η-μ fading channels. In this context, analytical expressions of error probability (EP) are derived in terms of the Chernoff, Chiani, Prony (2 and 3 terms), and Trapezoidal approximations for Gaussian Q-function. For the high signal to noise ratio (SNR) analysis, asymptotic EP expression is also derived by using the Chernoff approximation. Further, for the comparison, the analytical EP expressions with rectangular QAM and quadrature phase-shift keying modulation schemes are obtained by using the Chiani approximation. Moreover, a comprehensive work of various modulation schemes is presented and the effects of fading parameters, type of Gaussian Q-function approximations, and average SNR values of first and second links are highlighted on the EP performance. Finally, to show the accuracy of the proposed analytical derivations, some results for the exact simulations and numerical results are demonstrated.

On the Performance Analysis of Higher Order QAM Schemes Over Mixed RF/FSO Systems

In this work, the performance of a dual-hop variable gain amplify-and-forward (AF) mixed radio frequency (RF)/free space optics (FSO) system is analyzed in details. As variable gain AF relay network is considered, processing delay results in outdated channel state information (CSI) during amplification at the relay. For general applicability, the RF link is modeled with the generalized Nakagami-m fading. The FSO link is modeled with the Gamma-Gamma distribution which is affected with the atmospheric turbulence and pointing error impairments, and both the intensity modulation with direct detection (IM/DD) and heterodyne detection are employed at the FSO receiver. In this context, analytical expressions of outage probability and ergodic capacity are derived in terms of Meijer-G function and extended generalized bivariate Meijer-G function. For diversity order, asymptotic outage probability expression is also derived. Further, cumulative distribution function based generalized average symbol error rate expressions for various quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived in terms of Meijer-G function. Furthermore, a detailed comparative study of various modulation schemes is presented and the impact of pointing error, atmospheric turbulence, outdated CSI, and Nakagami-m parameter are highlighted on the system performance. Finally, all the analytical results are verified through Monte-Carlo simulations.

On ASER performance of higher order QAM schemes in two‐way multiple‐relay networks under imperfect CSI

In this study, the authors present an analytical approach to evaluate the performance of a two-way multi-relay system with direct link using a three-phase analogue network coding and opportunistic relay selection scheme. Herein, the imperfect channel state information is considered over independent and non-identically distributed Nakagami-m fading channels with integer-valued fading parameter. For analysis, initially, the closed-form expressions of cumulative distribution function and moment generating function (MGF) for the considered system are derived. Further, by using the MGF-based approach, generalised expressions of average symbol error rate (ASER) for higher-order quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived. They then analyse the asymptotic behaviour of ASER expression to evaluate the system's diversity order. Furthermore, a comparative analysis of the ASER performance for various QAM constellations is illustrated and impact of the number of relays, fading parameter, relay location, and channel estimation error are highlighted on the system's performance. Finally, all the analytical results are validated through Monte-Carlo simulations.

On impact of imperfect channel state information on dual-hop nonline-of-sight ultraviolet communication over turbulent channel

Nonline-of-sight (NLOS) ultraviolet (UV) communication is expected to play a prominent role in wireless communications with enhanced connectivity due to the aerosol and strong molecular scattering and availability of large unlicensed bandwidth. We investigate the performance of NLOS UV co-operative communication over a log-normal fading channel by considering the channel estimation error, as experienced in practical UV communication systems. An analytical framework for a dual-hop amplify-and-forward UV NLOS cooperative relay is developed. We derive the closed-form expressions of lower-bound outage probability and the average symbol error rate for the energy efficient modulation schemes, such as hexagonal quadrature amplitude modulation (QAM) and rectangular QAM schemes. The derived analytical results are validated through the Monte Carlo simulations.

On ASER Analysis of Energy Efficient Modulation Schemes for a Device-to-Device MIMO Relay Network

In this paper, we investigate the performance of a device-to-device (D2D) multiple-input and multiple-output (MIMO) communications using an amplify-and-forward relaying for various energy-efficient modulation schemes. For analysis, transmit antenna selection strategy is employed at the transmitter to select the best transmit antenna which maximizes the received signal power. In the analysis, we optimized the relay location to obtain the lowest outage probability possible and derived the generalized upper-bound average symbol error rate expressions of energy-efficient futuristic modulation schemes such as square quadrature amplitude modulation (QAM), rectangular QAM, cross QAM, and hexagonal QAM for D2D network. Further, we have derived the ergodic capacity expression to calculate the achievable rates. Comparative analysis of different QAM schemes for various constellation orders is also presented. Furthermore, the impact of the relative position of relay, path loss, and the number of antennas are also highlighted. Finally, the derived analytical results are verified through Monte-Carlo simulations.

On Impact of Imperfect CSI Over Hexagonal QAM for TAS/MRC-MIMO Cooperative Relay Network

In this letter, we investigate the effect of imperfect channel state information (CSI) on quadrature amplitude modulation (QAM) schemes for a multi-input and multi-output (MIMO) variable gain non-regenerative cooperative network over the generalized Nakagami-m fading channel. Energy-efficient and standardized transmit antenna selection strategy is employed, to evaluate the system performance by considering the antenna link, which maximizes the received signal power. Framework for the upper-bound outage probability (OP), asymptotic OP and the average symbol error rate for hexagonal QAM, rectangular QAM, and 32-cross QAM are provided. Useful insights are drawn from comparative ASER analysis of various QAM schemes by considering the impact of both the fading parameter and the imperfect CSI for MIMO channels. Finally, the derived analytical results are validated through Monte-Carlo simulations.