Rectangular Quadrature Amplitude Modulation Research Articles

Spectrally efficient M‐ary QAM based multi‐antenna cooperative system over TWDP fading channel

AbstractTo cater the ever‐increasing demand of wireless high‐speed data access and mobile users, one of the potential enablers toward the sustainable improved network capacity is the network densification at different layers of the radio access system. In this article, a possible solution to achieve a spectrally efficient, ultradense network (UDN) for cellular communication is analyzed. In particular, the performance of the generalized M‐ary quadrature amplitude modulation (M‐QAM) scheme for multiantenna cooperative decode‐and‐forward (DF) system over two‐wave with diffuse power (TWDP) fading is presented. The TWDP fading is evaluated using the moment generating function (MGF) based approach on spectral efficient QAM transmission. In this article, novel closed‐form expressions for the exact average symbol error rate (ASER) for the generalized rectangular‐QAM (R‐QAM) and square‐QAM (S‐QAM) schemes are presented. The obtained expressions are in the form of Appell's and Laureicella's confluent hypergeometric function which can be evaluated mathematically either in the series or the integral‐form. Further, the asymptotic analysis is also presented for the considered system to get better insights into the system. The analytical results derived are corroborated by simulations to validate the accuracy of the analysis.

On the ASER Performance of UAV-Based Communication Systems for QAM Schemes

In this letter, we derive an average symbol error rate (ASER) expression of rectangular quadrature amplitude modulation (RQAM) scheme for unmanned aerial vehicle-enabled communication systems operating over double-shadowing and double-scattering composite fading channel. A moment generating function for the receiver output signal-to-noise ratio is obtained to analyze the ASER expression of non-coherent modulation schemes. An asymptotic expression of ASER for RQAM scheme is also derived to examine diversity order of the considered system. Further, the impact of composite fading parameters and path loss on ASER performance is highlighted. Finally, we validate all the theoretical results through Monte Carlo simulations.

Investigation on the PAPR performance of odd-bit QAM constellations for DFT spread OFDM systems

<p>Adaptive quadrature amplitude modulation (QAM) is a crucial scheme that enables the modern communication systems to overcome the adverse effects of channel fluctuations and maintain an acceptable spectral efficiency. In order to enhance adaptive modulation even further, adoption of odd-bit QAM constellations alongside even constellations had been suggested to improve the transmission efficiency of adaptive QAM modulation. Hence, odd-bit QAM had been extensively studied, analyzed, and tested by many researchers for various patterns, sizes, and communication systems in terms of bit error rate (BER) and peak to average power ratio (PAPR). However, the PAPR performance of odd-bit QAM constellation with single carrier transmission systems adopted in the uplink of the 4G long term evolution (LTE) standards caught almost no research interest. In this paper, the PAPR performance of both cross and rectangular odd-bit QAM constellations are investigated for DFT-S-OFDM systems. Complementary cumulative distribution functions (CCDFs) and probability density functions (PDFs) curves for PAPR are also obtained. Finally, an equation for PAPR PDF is empirically derived for odd-bit cross QAM based DFT-S-OFDM. The results show that cross odd-bit QAM outperforms the rectangular odd-bit QAM in terms of PAPR by 1.02 dB for 8-QAM and 1.3 dB for 32-QAM. This proves that cross odd-bit QAM is a better choice in terms of PAPR for DFT-S-OFDM systems. </p>

ASER of SISO system with rectangular QAM scheme over α-μ fading channels

ABSTRACT In this study, analytical expressions are developed for average symbol error rate (ASER) of rectangular quadrature amplitude modulation (RQAM) scheme over fading channels. Initially, the ASER expression for RQAM under fading channels is acquired by applying Chernoff approximation of Gaussian -function. Further, another ASER expression of RQAM scheme covering fading conditions is derived by adopting Chiani approximation of Gaussian -function.

A Survey on Higher-Order QAM Constellations: Technical Challenges, Recent Advances, and Future Trends

Communication system's performance is sensitive to bandwidth, power, cost etc. There have been various solutions to improve the performance, out of them, one of the fundamental solutions over the years is design of optimum modulation schemes. As the research on beyond 5G heats up, we survey and explore power and bandwidth efficient modulation schemes for the next generation communication systems in details. In the existing literature, initially square quadrature amplitude modulation (SQAM) was considered. However, only square constellations are not sufficient for varying channel conditions and rate requirements, thus, efficient odd power of 2 constellations were introduced. For odd power of 2 constellations, rectangular QAM (RQAM) is most commonly used. However, RQAM is not a good choice and modified cross QAM (XQAM) constellation is preferred which provides improved power efficiency over RQAM due to its energy efficient two dimensional (2D) structure. The increasing demand for high data-rates has further encouraged research towards more compact 2D constellations which leads to hexagonal lattice structure based hexagonal QAM (HQAM) constellations. In this work, various QAM constellations are discussed and detailed study of star QAM, XQAM, and HQAM is presented. Generation, peak and average energies, peak-to-average-power ratio, symbol-error-rate, decision boundaries, bit mapping, Gray code penalty, and bit-error-rate of star QAM, XQAM, and HQAM constellations for different constellation orders are presented. Finally, a comparative study of various QAM constellations is presented which justifies the supremacy of HQAM over other QAM constellations for various wireless communication systems and a potential modulation scheme for future standards.

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.

Error performance of QAM schemes for SIMO and MIMO networks

In this paper, we analyze the average symbol error rate (ASER) of single-input multiple-output (SIMO) networks for rectangular quadrature amplitude modulation (RQAM) and cross-QAM (XQAM) subject to Rayleigh fading. Then, we investigate the performance of RQAM for a SIMO system under κ-μ fading conditions. And also, we consider a multiple-input multiple-output with single transmit antenna selection and maximal ratio combining over Rayleigh fading environments. To analyze the key parameters on the network performances, we propose the analytical expressions of ASER for the considered networks. Assuming flat fading, the obtained exact and approximate expressions for ASER based on the probability density function approach. Furthermore, we present asymptotic expressions of RQAM and XQAM schemes for a SIMO system over Rayleigh fading at the high signal to noise ratio to evaluate the network performance in terms of diversity gain. Finally, simulations are ensured to confirm the correctness of our frameworks in this study.

Bit Error Probability of MQAM in the Presence of Phase Noise

In Gray coded rectangular and square quadrature amplitude modulation (QAM), for each bit, the bit decision boundaries are distributed only along one dimension. Consequently, the exact calculation of bit error probability (BEP) of rectangular and square QAM in the additive white Gaussian noise (AWGN) channel results in simple one-dimensional (1-D) error/Q-functions. This is while the symbol decision boundaries involve two dimensions. This paper presents exact and general expressions for the BEP of Gray coded M -ary rectangular and square QAM in the presence of phase noise in the AWGN as well as flat-fading channels. In doing so, we first derive exact expressions for the BEP of MQAM in the presence of a fixed phase error. The expression will be a weighted sum of 1-D complementary error functions for the AWGN channel. For the flat-fading channels, these formulas consist of only single integrals or simple functions. We then integrate the formulas across noise distribution, to derive the average BEP expression of Gray coded MQAM in the presence of random phase error. Moreover, we provide an exact expression for the bit error floor (BEF) of MQAM in the presence of phase noise in the AWGN and fading channels. The exact expressions include numerous terms for higher order MQAM. Considering the most dominant terms of the exact expressions, we also propose simpler expressions. Simulation results validate the accuracy of the proposed exact expressions for arbitrary levels of input SNR. Moreover, the results show very good performance for the approximate expressions.

On the BEP analysis of M-QAM and R-QAM under cascaded double η-μ, κ-μ or α-μ fading channels

This article presents new expressions for the bit error probability (BEP) of the M-ary quadrature amplitude modulation (M-QAM) and rectangular QAM (R-QAM) scheme in a frequency non-selective channel model with cascaded double fading, characterized in the links by the distributions η-μ, κ-μ or α-μ. In this paper, the probability density function (PDF) of the signal-to-noise ratio (SNR) of the double link is written in terms of an integral of the product of the PDF of the envelope of the first link by the PDF of the SNR of the second link. With this procedure, expressions for the BEP of the M-QAM and R-QAM scheme, with and without a maximum ratio combiner (MRC) associated, are obtained by means of the general expressions of Cho and Yoon, calculated with the help of the Gauss-Laguerre quadrature. The new expressions are written in terms of the integral of the moment generating function (MGF) of the instantaneous SNR from the second link, which are simpler than using expressions involving infinite series in terms of special functions like hypergeometric functions and the Meijer G-function. In addition, insights regarding the expressions obtained and comments about their complexity are provided. Several curves for the BEP are presented, for different parameters that characterize the channel and different numbers of branches of the MRC. All analytical expressions obtained in this paper are corroborated by computer simulations performed with the Monte Carlo method.

Different QAM schemes analyses for ARS fading channels

AbstractQuadrature amplitude modulation (QAM) techniques are employed for various communication systems due to its advantages such as efficient bandwidth and high rate. In this paper, the average symbol error rate (ASER) performances of single‐input single‐output networks are investigated to address the different QAM schemes combined use. The link in the network experiences the alternate Rician shadowed (ARS) fading which has the benefit of contributing left or right‐sided bimodality. Four different QAM schemes such as rectangular QAM, cross‐QAM, hexagonal QAM, and square QAM are used for the considered network. Under these assumptions, new closed‐form expressions for the ASER in terms of elementary functions and Meijer's G functions are derived. The derived ASER expressions are obtained by employing the Prony approximation with two terms which has fractional coefficients to provide precise results. Based on the second‐order exponential function approximation for Gaussian Q‐function, the ASER expressions of the considered system are also proposed. Additionally, we provide other important engineering insights based on the high signal‐to‐noise‐ratio analysis of the ASER performance over ARS fading channels. Finally, all our theoretical results are confirmed with simulations.

Average BER performance of rectangular QAM-UWOC over strong oceanic turbulence channels with pointing error

We theoretically analyze the average bit error rate (ABER) performance of underwater wireless optical communication (UWOC) systems using rectangular quadrature-amplitude modulation (QAM) over strong oceanic turbulence channels with pointing error. The strong oceanic turbulence channel is assumed to be a gamma-gamma model. The close-form expression for the ABER is derived by using the Meijer’s G-function. Based on this expression, various effects of system parameters, including QAM scheme, link distance, diameter aperture, ratio of source beam width to aperture radius, and four oceanic turbulence parameters on ABER performance are taken into account. Simulation results show that applying a smaller rectangular QAM dimension and link distance, or a larger aperture diameter and the ratio of beam width to aperture radius can improve the UWOC quality significantly. The contributions of four oceanic turbulence parameters also need to be considered in practical UWOC applications. The results reported in this paper will be benefit to design UWOC systems.

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.

Performance of Smart Grid Dynamic HAN With RQAM and GMSK Modulation

In smart grid communications, home area network (HAN) plays an important role in managing data transmission among communicating devices through a smart meter. Performance of the network depends on the efficiency of modulation schemes used in the communicating devices such as rectangular quadrature amplitude modulation (RQAM) and Gaussian minimum shift keying (GMSK). Saleh-Valenzuela (S-V) and Weibull fading channels are appropriate models for indoor communication channels. Average symbol error rate (ASER) and average channel capacity (ACC) performance of indoor dynamic HANs with communicating devices using RQAM and GMSK are analyzed for these channel models. Numerical results are presented to demonstrate the effect of traffic intensity, number of active devices in HAN, and the modulation types with parameters of practical interest.

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.

Performance analysis of NLOS ultraviolet communications with correlated branches over turbulent channels

Ultraviolet communication (UVC) is becoming increasingly popular due to its ability to effectively communicate in non-line-of-sight (NLOS) mode, which offers alternative communication system advantages over visible light communication and infrared links. However, the performance of UVC is affected by atmospheric turbulence, which is generally ignored under the assumption of short-distance links. In this paper, we consider a NLOS UVC system experiencing turbulence due to variation in the refractive index of the atmosphere. The atmospheric turbulence results in fading due to fluctuations in the received signal strength, thus deteriorating the quality of communication. Spatial diversity is proven to mitigate the effect of fading by introducing multiple parallel communication paths between the transmitter and receiver. We present a spatial diversity reception in the form of ${N_r}$-branches selection combining at the receiver. The channel coefficients are assumed to be exponentially correlated, and turbulence is modeled using log-normal distribution under weak turbulence conditions. Closed-form expressions for the outage probability and average symbol error rate for general order rectangular quadrature amplitude modulation (RQAM), cross-QAM, and hexagonal QAM schemes are derived. Furthermore, the ergodic capacity of the system is computed as a function of the channel correlation coefficient. The numerical values are compared with computer simulations to validate the accuracy of the theoretical analysis.

Error performance of digital modulations over Fisher-Snedecor F fading channels

In this paper, symbol error probability (SEP) and the average symbol error rate (ASER) of digital modulation schemes are derived in the presence of Fisher-Snedecor F fading. First, an analytical SEP expression is proposed based on complementary cumulative distribution function (CDF) for M-ary phase shift keying (M-PSK) and M-ary pulse amplitude modulation (M-PAM). Then, an asymptotic solution is also presented for the SEP of M-PSK and M-PAM modulations in order to get more insights on the performance at high signal-to-noise ratio (SNR) regime. Finally, an exact ASER expression for rectangular quadrature amplitude modulation (RQAM) is derived and then, the ASER performance is analyzed based on two different upper bound approximations of Gaussian Q-function in Fisher-Snedecor F fading channels. The proposed expressions are not only valid for integer values of fading and shadowing parameters but also valid for non-integer values. The performance results which are in good agreement with the exact simulations are illustrated for different modulation schemes and various configurations of fading and shadowing parameters.