Average Symbol Error Rate Research Articles

Performance analysis of spectrum sharing‐based multi‐hop decode‐and‐forward over Nakagami‐ m fading channels subject to additive white generalised Gaussian noise

In this work, the authors study the performance of decode-and-forward cognitive multi-hop networks in an underlay spectrum sharing strategy for Nakagami-m fading channels with additive white generalised Gaussian noise. To this end, new exact analytical expressions for the average bit error rate of M-ary quadrature amplitude modulation (M-QAM) and M-ary phase shift keying are derived and evaluated. In addition, an exact expression for the average symbol error rate of M-QAM is provided. Moreover, lower- and upper-bound expressions for the ergodic capacity are obtained. Different scenarios are presented to study the influence of various key system parameters, such as fading severity, noise shaping parameter, and interference temperature, on the system performance. The obtained analytical results are supported with Monte Carlo simulations to confirm the accuracy of the analytical derivations.

One-Bit Precoding and Constellation Range Design for Massive MIMO With QAM Signaling

The use of low-resolution digital-to-analog converters (DACs) for transmit precoding provides crucial energy efficiency advantage for massive multiple-input multiple-output (MIMO) implementation. This paper formulates a quadrature amplitude modulation (QAM) constellation range and one-bit symbol-level precoding design problem for minimizing the average symbol error rate (SER) in downlink massive MIMO transmission. A tight upper-bound for SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of one-bit precoding can be interpreted as a decrease in the effective minimum distance of the QAM constellation. Using the obtained SER expression, we propose a QAM constellation range design for the single-user case. It is shown that in the massive MIMO limit, a reasonable choice for constellation range with one-bit precoding is that of the infinite-resolution precoding with per-symbol power constraint, but reduced by a factor of $\sqrt{2/\pi}$ or about $0.8$. The corresponding minimum distance reduction translates to about 2dB gap between the performance of one-bit precoding and infinite-resolution precoding. This paper further proposes a low-complexity heuristic algorithm for one-bit precoder design. Finally, the proposed QAM constellation range and precoder design are generalized to the multi-user downlink. We propose to scale the constellation range for infinite-resolution zero-forcing (ZF) precoding with per-symbol power constraint by the same factor of $\sqrt{2/\pi}$ for one-bit precoding. The proposed one-bit precoding scheme is shown to be within 2dB of infinite-resolution ZF. In term of number of antennas, one-bit precoding requires about 50% more antennas to achieve the same performance as infinite-resolution precoding.

ASER Analysis of Hexagonal and Rectangular QAM Schemes in Multiple-Relay Networks

In this paper, analytical lower bound expressions of average symbol error rate (ASER) for general-order hexagonal quadrature amplitude modulation (QAM) and rectangular QAM (RQAM) schemes are derived for multiple amplify-and-forward relay networks over independent and nonidentically distributed Nakagami-m fading channels with an integer-valued fading parameter using a well-known cumulative distribution-function-based approach. Furthermore, ASER expressions for 32-cross QAM, differentially encoded quadriphase shift keying (QPSK), and π/4-QPSK modulation schemes are derived for the considered systems. The asymptotic ASER expression is also derived for the RQAM scheme, which is useful to examine system's diversity order. Numerically evaluated results are verified by Monte Carlo simulation.

Impact of Imperfect CSI on ASER of Hexagonal and Rectangular QAM for AF Relaying Network

In this letter, we derive the closed-form expression of outage probability for a dual-hop variable-gain amplify-and-forward relay network. The maximal ratio combining receiver over independent and non-identically distributed frequency flat Nakagami-m fading channels with integer-valued fading parameter and imperfect channel state information (CSI) is considered. Asymptotic analysis on outage probability is also performed. Average symbol error rate (ASER) expressions are derived for general-order hexagonal and rectangular QAM schemes using the cumulative distribution function-based approach. The impact of the fading parameter and imperfect CSI are highlighted on the system performance. Comparative analysis of ASER performance for different QAM constellations is also illustrated. Monte Carlo simulations are performed to validate the derived analytical results for both perfect and imperfect CSI.

Performance of Adaptive Link Selection With Buffer-Aided Relays in Underlay Cognitive Networks

In this paper, we investigate the performance of a three-node dual-hop cognitive radio network with a half-duplex decode-and-forward buffer-aided relay. We derive expressions for the average rate and symbol error rate (SER) performance of an adaptive link selection based channel-aware buffer-aided relay scheme that imposes peak-power and peak-interference constraints on the secondary nodes, and compare them with those of conventional non-buffer-aided relay and conventional buffer-aided relay schemes for a delay-tolerant system. For a finite-sized buffer, we analyze the performance of a modified threshold-based scheme for fixed-rate transmission. We analyze the tradeoffs between the delay, throughput, and SER. Computer simulation results are presented to demonstrate accuracy of the derived expressions.

Performance analysis of outage probability and error rate of square M-QAM in mobile wireless communication systems over generalized α-μ fading channels with non-Gaussian noise

This paper derives new and exact closed-form expressions for the average symbol error rate (SER) of square M-ary quadrature amplitude modulation (M-QAM) in wireless communication systems over the α-μ fading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.

Analytical Characterization of Dual-Band Multi-User MIMO-OFDM System with Nonlinear Transmitter Constraints

Recent studies have shown that carrier-aggregated multi-user (MU) multi-input-multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems can deliver unprecedented improvements in network throughput and capacity when compared with existing systems. However, most of these studies fail to take into account the nonlinear constraints that limit the performance of such systems. This paper proposes an analytical framework to evaluate the end-to-end performance of a carrier-aggregated dual-band (DB) MU-MIMO-OFDM system in the presence of transmitter nonlinearity. Specifically, we derive the closed-form expression for signal-to-interference-plus-noise ratio (SINR) and further utilize this expression to evaluate the average capacity and symbol error rate of a nonlinear DB MU-MIMO-OFDM system in a multi-path Rayleigh fading channel. We show that the transmit preprocessing technique conventionally used to mitigate inter-user interference in a linear DB MU-MIMO-OFDM system fails to eliminate inter-user interference in a nonlinear DB MU-MIMO-OFDM system. As a consequence, there is an irreducible error floor which is function of number of aggregated bands as well as number of users present in the system. The irreducible error floor has been shown to considerably deteriorate the performance of nonlinear DB MU-MIMO-OFDM system. Simulation results are also reported to validate the efficacy of the proposed analysis.

Performance Analysis of NOMA-Based Land Mobile Satellite Networks

Non-orthogonal multiple access (NOMA) scheme, which has the ability to superpose information in the power domain and serve multiple users on the same time/frequency resource, is regarded as an effective solution to increase transmit rate and fairness. In this paper, we introduce the NOMA scheme in a downlink land mobile satellite (LMS) network and present a comprehensive performance analysis for the considered system. Specifically, we first obtain the power allocation coefficients by maximizing the sum rate while meeting the predefined target rates of each NOMA user. Then, we derive the theoretical expressions for the ergodic capacity and the energy efficiency of the considered system. Moreover, the outage probability (OP) and average symbol error rate performances of NOMA users are derived analytically. To gain further insights, we derive the asymptotic OP at the high signal-to-noise ratio regime to characterize the diversity orders and coding gains of NOMA users. Finally, simulation results are provided to validate the theoretical analysis as well as the superiority of employing the NOMA scheme in the LMS system, and show the impact of key parameters, such as fading configurations and user selection strategy on the performance of NOMA users.

A Blind Detection for Massive MIMO Outdoor Optical Wireless Communication System

In this paper, we concentrate on a massive MIMO outdoor optical wireless communication system, in which power modulation is utilized through an atmospheric turbulence. Then, we proposed a maximum likelihood blind detection algorithm based on channel statistics. Following that, we provide the optimal decision thresholds. Furthermore, we analyze the average symbol error rate of the algorithm under a given average transmit power constraint to improve system performance.

Quantized Feedback-Based Diagonal Precoding for $N \times 1$ MISO System With Generalized Orthogonal Space-Time Block Codes

In this paper, we propose an imperfect quantized feedback-based diagonal precoding scheme for generalized orthogonal space-time block codes in an $N \times 1$ multiple-input single-output (MISO) wireless communication system employing $M$ -QAM constellation. It is well known that a feedback-based precoding scheme aids channel adaptive signaling in wireless communication system and capitulates large improvements in almost all performance metrics. However, a practical feedback link is susceptible to error due to wireless channel fading and leads to wrong precoder selection. Therefore, a signal-to-noise ratio (SNR) adaptive error-tolerant weighting scheme is introduced which provides significant gain in comparison with another proposed arbitrarily fixed SNR error-tolerant weighting scheme. At first, a tight approximate closed-form expression of average symbol-error-rate (SER) and an exact analytical expression of outage probability are derived under imperfect feedback information with the help of order statistics. By minimizing the derived average SER, optimized transmit weights for the diagonal precoding matrix (based on feedback bits) are obtained. Later, a closed-form expression of the ergodic capacity with erroneous feedback bits for arbitrary MISO system is also provided by using the moment generating function approach. Further, numerical results show that the considered error-tolerant schemes outperform the uniform power allocation scheme in term of all the investigated performance metrics.

Performance Evaluation of QAM Schemes for Multiple AF Relay Network Under Rayleigh Fading Channels

In this work, we propose theoretical expressions of the moments for instantaneous signal to noise ratio (SNR), the amount of fading, and the average symbol error rate (ASER) for rectangular quadrature amplitude modulation (RQAM), 32-cross QAM, differentially encoded quadri-phase shift keying and $$\pi /4$$ź/4-QPSK modulation schemes in multiple amplify-and-forward relay network for maximal ratio combining receiver. To measure the number of independent fading paths over the channel, we provide asymptotic analysis of ASER expression for RQAM at high SNR. The impact of system parameters is also highlighted on the performance metrics. To investigate the correctness of theoretical expressions, we compare numerical results with Monte' Carlo simulations.

Performance Analysis of Amplify-and-Forward Relaying FSO/SC-QAM Systems over Weak Turbulence Channels and Pointing Error Impairments

AbstractIn this paper, the end-to-end performance of free-space optical (FSO) communication system combining with Amplify-and-Forward (AF)-assisted or fixed-gain relaying technology using subcarrier quadrature amplitude modulation (SC-QAM) over weak atmospheric turbulence channels modeled by log-normal distribution with pointing error impairments is studied. More specifically, unlike previous studies on AF relaying FSO communication systems without pointing error effects; the pointing error effect is studied by taking into account the influence of beamwidth, aperture size and jitter variance. In addition, a combination of these models to analyze the combined effect of atmospheric turbulence and pointing error to AF relaying FSO/SC-QAM systems is used. Finally, an analytical expression is derived to evaluate the average symbol error rate (ASER) performance of such systems. The numerical results show that the impact of pointing error on the performance of AF relaying FSO/SC-QAM systems and how we use proper values of aperture size and beamwidth to improve the performance of such systems. Some analytical results are confirmed by Monte-Carlo simulations.

Performance Analysis of Distributed Single Carrier Systems With Distributed Cyclic Delay Diversity

This paper investigates a distributed cyclic delay diversity (CDD) transmission scheme for cyclic-prefixed single carrier systems in non-identically and identically distributed frequency selective fading channels. The distinguishable feature of the proposed scheme lies in providing a transmit diversity gain while reducing the burden of estimating the channel state information, which is a challenging task in distributed and cooperative systems. To effectively use the distributed CDD scheme at the transmitters, two sufficient conditions are derived to eliminate the intersymbol interference at the receiver and leveraged to convert the multi-input single-output channel into a single-input single-output channel. These conditions allow the system to achieve the maximum diversity for frequency selective fading channels at a full rate. To achieve this maximum diversity, a fixed number of CDD transmitters are selected based on the channel conditions, symbol block size, and maximum time dispersion of the channel, and a new two-stage transmission mode is proposed. Based on the distributed CDD and the proposed selection schemes, a new expression for the signal-to-noise ratio at the receiver is obtained with the aid of order statistics, and then closed-form expressions for the outage probability and average symbol error rate (ASER) are derived. As far as the identically distributed frequency selective fading channel model is concerned, the achievable maximum diversity gain is proved, with the aid of asymptotic analysis, to be equal to the product of the total number of transmitters in the system and the number of multipath components. Link-level simulations are also conducted to validate the analytical expressions for outage probability, ASER, and maximum achievable diversity gain.

DF MISO system with arbitrary beamforming in atmospheric turbulence and misalignment errors

A dual-hop decode-and-forward relay-assisted \(2\times 1\) multiple-input single-output free-space optical (FSO) communication system is considered. Error performance of the considered FSO system is analyzed with an arbitrary beamforming scheme in Gamma–Gamma distributed atmospheric turbulence and misalignment errors. The misalignment errors in the receive apertures of relay and destination are assumed to be zero-boresight, where the radial displacement in the receiver plane is modeled by Rayleigh distribution. The probability density function and moment generating function of received signal-to-noise ratio (SNR) for both the hops are derived first. By utilizing the derived statistics, the expressions of average symbol error rate for subcarrier intensity modulated-based M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM) constellations are obtained in the destination. Monte-Carlo simulations are presented to support the analysis.

Bayesian Optimal Data Detector for mmWave OFDM System With Low-Resolution ADC

Orthogonal frequency division multiplexing (OFDM) has been widely used in communication systems operating in the millimeter wave (mmWave) band to combat frequency-selective fading and achieve multi-Gbps transmissions, such as IEEE 802.15.3c and IEEE 802.11ad. For mmWave systems with ultra high sampling rate requirements, the use of low-resolution analog-to-digital converters (ADCs) (i.e., 1-3 bits) ensures an acceptable level of power consumption and system costs. However, orthogonality among sub-channels in the OFDM system cannot be maintained because of the severe non-linearity caused by low-resolution ADC, which renders the design of data detector challenging. In this study, we develop an efficient algorithm for optimal data detection in the mmWave OFDM system with low-resolution ADCs. The analytical performance of the proposed detector is derived and verified to achieve the fundamental limit of the Bayesian optimal design. On the basis of the derived analytical expression, we further propose a power allocation (PA) scheme that seeks to minimize the average symbol error rate. In addition to the optimal data detector, we also develop a feasible channel estimation method, which can provide high-quality channel state information without significant pilot overhead. Simulation results confirm the accuracy of our analysis and illustrate that the performance of the proposed detector in conjunction with the proposed PA scheme is close to the optimal performance of the OFDM system with infinite-resolution ADC.

Statistical performance of dual‐hop variable gain AF relaying over Nakagami‐m fading

This paper evaluates the general statistical performance of dual‐hop variable gain amplify‐and‐forward relay over independently but not necessarily identically distributed Nakagami‐m fading channels, where m = m′/2 and m′ is a positive integer. This model is flexible enough to encompass a great variety of fading environments, such as one‐sided Gaussian distribution (m′ = 1) and Rayleigh fading (m′ = 2). Based on the configuration, we first present closed‐form formulas for the cumulative distribution function and probability density function of the equivalent signal‐to‐noise ratio (SNR) at a destination. Armed with these statistical results, we derive outage probability, moments of the SNR, and higher‐order statistics of the capacity, which can be effectively used to elucidate system performance. To provide a further insight into relay systems, we characterize a general expression for average symbol error rate in the context of an additive white generalized Gaussian noise. Simulation results are fully consistent with our theoretical analysis. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Performance analysis of AF OFDM system using multiple relay in presence of nonlinear‐PA over inid Nakagami‐m fading

SummaryIn this paper, performance of an orthogonal frequency division multiplexing–based variable‐gain amplify and forward cooperative system using multiple relay with relay selection is analyzed over independent but not necessarily identically distributed frequency selective Nakagami‐m fading channels. For the analysis, nonlinear power amplifier is considered at the relay, and selection combining is adopted at destination node. Closed‐form expressions of the outage probability for various threshold signal‐to‐noise ratio (SNR) values and average symbol error rate for M‐ary quadrature amplitude modulation techniques are derived for the considered system. Further, the outage probability analysis is performed in high SNR regime to obtain the diversity order. Furthermore, impact of different fading parameters, multiple relay, and nonlinear power amplifier is highlighted on the outage probability and asymptotic outage probability for various threshold SNRs and on the average symbol error rate for various quadrature amplitude modulation constellations. The derived analytical expressions are generalized for various fading environments while considering the integer‐valued fading parameters. Finally, all the analytical results are verified through the Monte Carlo simulations for various SNR levels and system configurations.

Multicell Multiway Massive MIMO Relay Networks

A generic performance analysis framework is developed for multicell amplify-and-forward (AF) multiway massive multiple-input multiple-output (MIMO) relay networks. The detrimental effects of imperfect channel state information (CSI), including channel estimation errors and outdated/delayed CSI for multicell massive MIMO AF multiway relay networks, are investigated. Thereby, for the first time in the open literature in the context of massive MIMO relay networks, the cumulative detrimental effects of pilot contamination and channel aging caused by the reuse of nonorthogonal pilot sequences and relative movements of user nodes, respectively, are quantified. The asymptotic signal-to-interference-plus-noise ratio and the achievable spectral efficiency expressions corresponding to three transmit power scaling laws at the user nodes and relay are derived whenever the number of antennas at the relay is substantially higher than the number of user nodes. The asymptotic performance analysis is generic in the sense that the individual effects of the practical transmission impairments, such as cochannel interference, pilot contamination, and channel aging, can be decomposed. The average symbol error rate (SER) and asymptotic SER are derived in closed form. The optimal pilot sequence length, which maximizes the achievable spectral efficiency, is derived in closed form. Our asymptotic analysis for the perfect CSI case reveals that the detrimental effects of cochannel interference can be asymptotically mitigated. Nevertheless, the performance degradation caused due to the cumulative effects of pilot contamination and channel aging cannot be mitigated, even in the limit of infinitely many relay antennas.

Effects of CEE and Feedback Error on Performance for AF-ORS with PSA-CE Schemes Over Quasi-Static Rayleigh Fading Channels

In this paper, we propose the analytical approach for amplify-and-forward (AF) opportunistic relaying schemes (ORS). When operation of AF-ORS consists of relay selection and data transmission phases based on pilot symbol assisted-channel estimation (PSA-CE) methods over quasi-static Rayleigh fading channels, we show that the relay selection phase can be implemented by pilots symbols transmission for source-relay and relay-destination. Moreover, the feedback method for the selected relay index is proposed to have a simple fashion. Then, we investigate the effects of both a channel estimation error and an estimated noise variance, which are obtained by PSA-CE methods, on the received signal-to-noise ratio (SNR). The average SNR loss is also derived in terms with the number of pilots in PSA-CE methods. Moreover, the average symbol error rate, the outage probability, and the normalized channel capacity of the ORS are derived in approximated closed-form expressions for an arbitrary link SNR when the channel state information in the source-relay-destination link is estimated based on transmitted pilots symbols. As the number of pilot symbols, the derived analytical approach is verified, and by comparing it with simulation results, the accuracy is demonstrated. In addition, it is verified that the effect of the feedback error can be neglected for PAS-CE methods over quasi-static fading channels.

Performance evaluation of cognitive underlay multi-hop networks with interference constraint in Rayleigh fading channels perturbed by non-Gaussian noise

In this paper, the performance of regenerative decode-and-forward (DaF) cognitive multi-hop underlay networks over independent but non-identically distributed (i.n.i.d.) Rayleigh fading channels with additive white generalized Gaussian noise (AWGGN) is analyzed. Precisely, we derive exact analytical expressions for the average bit error rate (BER) of M-ary quadrature amplitude modulation (M-QAM) and M-ary phase shift keying (M-PSK). Besides, an exact expression for the average symbol error rate (SER) of M-QAM is obtained. In addition, lower- and upper-bound expressions for the end-to-end ergodic capacity is provided. Some representative numerical examples are presented to study the impact of the noise shaping parameter and average power of the interfering and secondary links on the system performance. Our obtained analytical results are supported with Monte-Carlo simulations to validate the accuracy of the analytical derivations.