Expressions For Symbol Error Rate Research Articles

Performance analysis of two way decode and forward relay network with maximum ratio transmission

In this paper, a two way decode and forward (DF) system employing maximum ratio transmission (MRT) technique is studied. In particular, two source terminals equipped with multiple antennas wishes to communicate each other with the help of a single antenna DF relay over Nakagami-m fading channels. To study the system performance, we obtain closed form expressions of sum symbol error rate (SSER) and outage probability (OP). Moreover, high SNR analysis is performed to gain insights about diversity and array gain. In order to increase the system performance, optimum relay location is analyzed. Our results which are validated with Monte Carlo simulations show that the system performance with MRT can be a preferable scheme for next generation wireless systems.

Error probability analysis of STBC-OFDM systems with CFO and imperfect CSI over generalized fading channels

In this paper, the closed form expressions of symbol error rate (SER) are derived for a space time block coded OFDM system subject to carrier frequency offset (CFO) under frequency-selective generalized fading scenarios. Apart from this, the effect of imperfect channel state information (CSI) is also taken into account for error rate analysis. The derived expressions are valid for any family of fading PDFs and the results of zero CFO with perfect CSI are found to be a special case. Numerical results are verified by extensive simulations.

Performance of spectral amplitude coded multiple pulse position modulation with non-uniform energy slots and fading.

Multiple-pulse position modulation (MPPM) is an advanced modulation method for optical wireless communication (OWC), which could provide better performance when channel information is not available. We consider the evaluation of a symbol error rate (SER) expression for MPPM applied within OWC. In the proposed model, MPPM is realized by spectral-amplitude coding (SAC) with non-uniform spectral slot energies. The derived fading channel SER expression is applicable for an arbitrary fading distribution, which may be due to either atmospheric turbulence or transceiver pointing error. A detailed theoretical analysis of the SER is provided and the resulting SER expression is verified by simulation.

Performance of scheduled space–time block coding scheme in cognitive multiple‐input–single‐output networks with imperfect channel state information

In this study, the authors study a cognitive multiple-input-single-output network, where the secondary base station (BS) communicates with a secondary destination scheduled from K candidate users. Assuming the scheduled space–time block coding scheme, they investigate the system performance and obtain the exact expressions for the outage probability (OP), symbol error rate (SER) and the achievable rates, taking into account the imperfect channel state information in the secondary BS to secondary receiver Rx link and secondary BS to primary Rx link. Furthermore, the asymptotic expressions for OP and SER in high sigal-to-noise ratio region are obtained, from which the coding and diversity gains are readily deduced. Finally, extensive performance evaluation results accompanied with equivalent ones obtained by simulations are provided to verify their analysis.

Performance evaluation for underlay cognitive satellite-terrestrial cooperative networks

With the continuously increasing demand for broadband applications and services, underlay cognitive satellite-terrestrial networks, enabling to accommodate better wireless services within the scarce spectrum, have attracted tremendous attentions recently. In this network, satellite communications are allowed to operate in the frequency bands allocated to terrestrial networks under the interference constraints imposed by terrestrial network, which may lead to a performance degradation of the satellite network. To guarantee the performance of the primary terrestrial network as well as the secondary satellite network, we introduce the cooperation into cognitive satellite-terrestrial networks and investigate the performance of the new framework, i.e., cognitive satellite-terrestrial cooperative network (CSTCN). Specifically, by restricting the transmit power of satellite communications with interference power constraints imposed by terrestrial communications, we firstly obtain the received signal-to-interference-plus-noise ratio (SINR) of the considered network. Moreover, by employing themoment generating function (MGF) approach, closed-form expressions for symbol error rate (SER) and outage probability (OP) of the considered cognitive network are derived. The analytical results obtained in this paper can provide theoretical support for optimizing the performance of satellite-terrestrial networks.

Symbol error rate of MIMO single and double-Weibull fading channels with OSTBC and MRC

PurposeThis paper aims to exploit an orthogonal space-time block code (OSTBC) and maximal ratio combining (MRC) techniques to evaluate error rate performance of multiple-input multiple-output system for different modulation schemes operating over single- and double-Weibull fading channels.Design/methodology/approachThe authors provided a novel analytical expression for cumulative distribution function (CDF) of double-Weibull distribution in the form of Meijer-G function. They also evaluated probability density function (PDF) and CDF for single- and double-Weibull random variables. CDF-based closed-form expressions of symbol error rate (SER) are computed for the proposed systems’ design.FindingsBased on simulation and analytical results, the authors have shown that double-Weibull fading which shows the cascaded nature of channel gives significantly poor SER performance compared to that of single-Weibull fading. Moreover, MRC offers an improved error rate performance compared to that of OSTBC. As the fading parameter increases for any modulation technique, the required signal-to-noise ratio (SNR) gap between single- and double-Weibull fading decreases. Finally, it is observed that the analytical results are a good approximation to simulation results.Practical implicationsFor practical implication, the authors use a number of antennas at the base station, but solely to maximize performance, one can use receive diversity, i.e. MRC.Originality/valueUsing higher-order modulation (i.e. 16-QAM), 4 and 1 dB less SNR is required at high and less fading, respectively, in single-Weibull fading as compared to double-Weibull fading. Hence, at higher-order modulation, double-Weibull channel model performs better as compared to lower-order modulation.

Performance Analysis of Wireless Powered DF Relay System Under Nakagami-$m$ Fading

In this paper, we analyze the average symbol error rate (SER) for a wireless powered three-node decode-and-forward (DF) relaying system in Nakagami- $m$ fading environment. $M$ -ary phase-shift keying modulated data at source is communicated to destination through energy-constrained relay node in three time slots. In the first slot, the signal transmitted by the source is used for energy harvesting at the relay node. Next two slots are employed for selective DF relaying, where relay transmits using the energy harvested from the source node. The source node is assumed to have a dedicated power supply. We analyze the end-to-end average SER expressions using the moment generating function based approach for two relaying scenarios: i) the direct link between the source and the destination exists and ii) the direct link is deeply faded and therefore can be ignored. The asymptotic approximations of the average SER are also obtained to determine the optimal energy allocated for each transmission. Since energy is related to the power transmitted at a node and the slot duration, the optimal energy expression can be judiciously used to optimize power and time for the corresponding slot. The effects of modulation order, relay placement, and channel conditions on the performance of the system with and without optimal resource allocation are investigated. The achievable diversity order and the throughput are also analyzed.

Performance analysis of OFDM based 3-hop AF relaying network over mixed Rician/Rayleigh fading channels

In this paper, performance of an orthogonal frequency division multiplexing (OFDM) based 3-hop variable-gain amplify and forward (AF) relaying network is analyzed over independent and non-identically distributed (i.n.i.d.) mixed Rician/Rayleigh fading environment. Analytical expression of outage probability is derived and diversity order of the considered system is found. Further, average symbol error rate (ASER) expressions of general order hexagonal quadrature amplitude modulation (HQAM), general order rectangular QAM (RQAM) and 32-XQAM are derived. A comparative analysis of ASER for different QAM schemes with different constellations is also presented. Ergodic capacity with optimum rate adaptation is also derived for the considered system model. Further, the impact of Rician K-factor on the performance of the considered system is highlighted. Finally, the derived analytical results are verified through Monte-Carlo simulations for different signal-to-noise ratio (SNR) levels.

Adaptive Spatial Modulation Based Visible Light Communications: SER Analysis and Optimization

Recently, the spatial modulation technique has been proposed for visible light communication (VLC). This paper investigates the average symbol error rate (SER) for the VLC using an adaptive spatial modulation (ASM). In the system, the analysis of the average SER is divided into two aspects: the error probability of the spatial domain and the error probability of the signal domain when the spatial domain is correctly estimated. Based on the two aspects, the theoretical expression of the average SER is derived. To further improve the performance of the system, an optimization problem is proposed to optimize the modulation orders on the LEDs. The ASM-based and the candidate-reduction-ASM-based optimization algorithms are proposed to solve the problem, respectively. Numerical results show that the derived theoretical values of the average SER are quite accurate to evaluate the system performance. Moreover, compared with the existing schemes, the proposed two algorithms are better choices for the VLC.

Analysis and Optimization Study of Antenna Selection in Dual Hop Relay Networks over Weibull Fading Channels

Field experiments show that Weibull distribution can be considered as the most suitable distribution to model weak to high signal power levels in indoor and outdoor environments. Recently, Exponentiated Weibull which is a special case of Weibull fading, have been widely adopted in free-space optical communication systems to model weak and high levels of turbulence effects. Motivated from the increasing use of Weibull distribution, this paper studies the popular dual-hop amplify-and-forward relay network with joint transmit and receive antenna selection where closed form ergodic capacity, symbol error rate and outage probability expressions are derived for Weibull fading channels. With the help of high SNR analysis, diversity gain, array gain and optimum relay location are obtained. Finally, theoretical findings are validated by simulation results.

Performance of multihop detect‐and‐forward relaying system over fluctuating two‐ray fading channels

AbstractThe performance of multihop detect‐and‐forward relaying system is analyzed over fluctuating two‐ray fading channels for 28 GHz millimeter wave communications. Exact closed‐form expressions for outage probability and average symbol error rate of various modulation schemes over nonidentically distributed fluctuating two‐ray fading channels have been obtained. The derived expressions are given in terms of the Lauricella hypergeometric functions and . Moreover, the derived expressions also accommodate several others reported results in the literature for two‐wave diffuse power, Rician, Rician shadowed, Nakagami‐m, and Hoyt fading channels. Asymptotic outage probability and average symbol error rate expressions are also derived, which provide useful insights on the factors governing the performance of the considered system. The numerical results have been verified with Monte‐Carlo simulation results.

Performance analysis of orthogonal space‐time block codes over Nakagami‐qMIMO RFID backscattering channels

The authors employ the conditional moment generating function approach to analyse the performance of orthogonal space-time block codes over Nakagami- q (Hoyt) multiple-input multiple-output radio frequency identification backscattering channels. New exact and asymptotic symbol error rate expressions are derived for the case of two and four receiving antennas N = 2 , 4 . The exact expressions are in the form of a sum of infinite series while the asymptotic ones are in the closed form. The diversity order that the system can achieve is found to be L , where L is the number of tag antennas, and the performance of this system is found to be more sensitive to the channel condition (the q parameter) of the forward link than that of the backscattering link. The theoretical results (exact and asymptotic) are verified through comparison with simulation results.

Impact of pointing errors on the SER performance of free space optical communication system with two decision thresholds over exponentiated Weibull fading channels

The impact of pointing errors on the symbol error rate (SER) performance of multiple pulse-position modulation (MPPM) free space optical (FSO) system with optimized decision threshold (ODT) and dynamic decision threshold (DDT) is investigated over exponentiated Weibull atmospheric turbulence channels. The probability density function (PDF) of the aggregated channel model is derived on the basis of Meijer’s G-function and the closed-form SER expression is then obtained by Gauss–Laguerre quadrature function. The variations of SER performance with different jitter variances, beam width, aperture sizes, and turbulence strengths for these two decision threshold schemes are analyzed in detail. The study shows that the impact of jitter variances is more apparent for ODT than that for DDT scheme and the performance difference between ODT and DDT schemes decreases with the increase of beam width. Monte Carlo simulation is also provided to verify the correctness of the proposed SER models. This work is beneficial to the design of FSO system.

Lyapunov Optimized Cooperative Communications With Stochastic Energy Harvesting Relay

Energy harvesting (EH) wireless communications have become more and more popular due to its capability of effectively reducing the battery replacement time. In this paper, we focus on decode-and-forward-based cooperative wireless communications with an EH relay. The stochastic characteristics of the harvestable energy and the wireless channel make it difficult to optimally manage the energy harvested at the relay for better communication performance. We formulate such a problem as an optimization by minimizing the long-term average symbol error rate (SER) subject to a battery constraint. Based on the Lyapunov optimization theory, we utilize the virtual queue technique and transform the optimization problem into a drift-plus-penalty minimization. Then, we conduct theoretic analysis of the optimal energy strategy derived by the proposed scheme. Specifically, we show the convexity of the drift-plus-penalty minimization problem, and prove that the virtual queue is bounded and the battery constraint is always satisfied. We also show that the proposed optimal energy management strategy is limited by an upper bound that is independent of the operation time index, derive the closed-form expression for the asymptotical average SER, and analyze the corresponding diversity order and EH gain. Finally, simulation results using the real solar irradiance data show that the proposed algorithm can achieve much better performance in terms of both average SER and diversity order, compared with the Markov decision process-based method.

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.

Performance analysis of scheduled STBC using statistical CSI under multiple interferers with different power in CR-MIMO systems

This paper studies the impact of the multiple interferers with different power on performance of a scheduled space–time block coding (STBC) using the statistical channel state information (CSI) in cognitive radio-multiple input multiple output (CR-MIMO) systems. This paper derives the exact closed-form cumulative density function (CDF) expression of the instantaneous post-processing signal to noise plus interference ratio (SINR) random variable at the user terminal of the proposed system. Using the derived CDF, the exact closed-form symbol error rate (SER) expression of the proposed system is derived for M-ary quadrature amplitude modulations (QAM). Further, this paper derives the exact closed-form expressions of outage probability and capacity for the proposed system. From the results, we know that the performance of the proposed system is saturated at different peak power constraint depending on the peak interference constraint. Also, the performance floor gets better by multi-user diversity and receive spatial diversity below the peak interference constraint in the presence of multiple interferers.

A Space-Time Transmission Scheme for Large MIMO Systems

In this letter, we propose a space-time transmission scheme (STTS) for large multiple-input multiple-output (MIMO) communication systems. These systems are primarily used to transmit a huge amount of data. The existing space-time block codes (STBCs) are not suitable for these systems due to the fact that these STBCs require very large channel coherence time (more than the number of transmit antennas), render poor data rate (less than one), and aim at full spatial diversity. In a practical large MIMO system with one thousand transmit and one thousand receive antennas, the diversity order of ${10}^{{6}}$ can be achieved; however, such a high value of diversity order is not required in practical systems. Therefore, an STTS with good data rate, parsimoniously utilized temporal dimensions, and symbol-wise decoding is essentially required for practical large MIMO systems. In this letter, we emphasize design of a new STTS by relaxing the constraint of achieving full spatial diversity. In the proposed STTS, the data rate of the large MIMO system is increased at the expense of the reduction in spatial diversity order. An approximate expression of symbol error rate of the proposed system is obtained-based on the moment generating function of the instantaneous received signal-to-noise ratio. Further, it is shown that the diversity order of the proposed STTS-based system is one less than the number of receive antennas.

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.