Symbol Error Rate Formula Research Articles

SER performance of millimeter-wave communications with multiple reconfigurable intelligent surfaces and transmit antenna selection

This paper proposes a combination of transmit antenna selection (TAS) scheme and multiple reconfigurable intelligent surfaces (RISs) for significantly reducing the symbol error rate (SER) of the millimeter-wave (MW) communications. In particular, TAS scheme is applied to dramatically decrease the computational complexity in the multi-RIS-aided MW communications. The SER formula of the multi-RIS-aided MW communications with TAS is derived over Nakagami-m channels. Then, it is validated through Monte-Carlo simulations. Numerical results confirm the joint and separate benefits of TAS scheme and multi-RIS in the MW communications. Specifically, the SER of the multi-RIS-aided MW communications with TAS is considerably lower than SER of multi-RIS-aided MW communications without TAS. Consequently, applying TAS can dramatically decrease the transmit power of the transmitter in comparison with the case without TAS when the SER target is a constant. Moreover, the SERs of multi-RIS-aided MW communications with and without TAS are much lower than those of MW communications without RISs in the cases with and without RISs, respectively. Besides these features, many methods such as an increase in the number of transmit antennas, a suitable choice of carrier frequencies in MW bands, and the appropriate locations of the RISs’ positions for performance enhancement of multi-RIS-aided MW communications with TAS are investigated.

Performance analysis of spatial multiplexing MIMO-MFSK based on energy detection for fast-fading environments

In fast-fading scattering environments such as high-speed rail and low-altitude communications, mobile communication systems need to quickly and robustly estimate and equalize fast-fading, time-varying channels. Under these circumstances, noncoherent multiple-input multiple-output (MIMO) has received attention in recent years, since it is less influenced by factors such as phase fluctuations and has fewer requirements for channel estimation and synchronization. Spatial multiplexing MIMO-MFSK based on energy detection is different from conventional noncoherent MIMO in that it can achieve higher spatial multiplexing gain in the independent distribution of channel fading statistics. At the receiver, partial real channel state information (CSI) is available, which can improve the capacity while ensuring the reliability of the link. With partial real CSI replacing instantaneous CSI, the system performance is inferior to conventional coherent MIMO under the influence of noise. As a result, it is necessary to analyze its theoretical detection performance. By energy detection, the noise of the MIMO-MFSK system conforms to the generalized gamma distribution. On the basis of this distribution, the optimal decision rule of the system and the symbol error rate (SER) formula are derived. Additionally, we investigate the signal-dependent noise problem of minimum Euclidean distance detection. Numerical results show that the SER formula fits well with the simulation results under the condition of a high signal-to-noise ratio.

Analysis of symbol error rate for intelligent reflecting surface aided communications

The recently proposed intelligent reflecting surface (IRS) is considered as a promising technology to combat the propagation distance problem in the future communications. However, due to the lack of quantitative analysis and IRS selection scheme from the perspective of symbol error rate (SER) performance, the performance analysis method of asymptotically tight approximation SER is proposed. Firstly, a communication system model aided by an IRS is established. Then, through the reasonable reconstruction between the reflection coefficient and the link coefficient of IRS, the SNR on the forwarding link of IRS satisfies the harmonic mean form. Finally, based on the calculation method of moment generating function (MGF), the asymptotically tight approximation SER formula of the system with simple structure is derived. The simulation results show that, the asymptotically tight approximation SER formula can accurately describe the system SER performance under the low SNR condition. Before the number of IRS reflection unit increases to a certain value, the system SER performance can be effectively improved. Compared with the AF multi-relay system, IRS aided system has the slightly better SER performance only in the case of low SNR. Our work will provide the important theoretical basis for the IRS selection in practical communications.

Circularly Symmetric Companding Quantization-Inspired Hybrid Constellation Shaping for APSK Modulation to Increase Power Efficiency in Gaussian-Noise-Limited Channel

In this paper we address hybrid probabilistic-geometric constellation shaping (HCS) of amplitude phase shift keying (APSK) constellation based on the reversed model of optimal companding quantization for circularly symmetric sources with the goal to increase the constellation power efficiency in Gaussian-noise-limited channel. To empirically optimize the proposed APSK constellation such that a symbol-error rate (SER) reaches its minimum under given constraints with respect to signal-to-noise ratio (SNR) and the prior probabilities of constellation points, for various settings of constellation parameters, we investigate SER dependence on SNR and determine the constellation parameters achieving minimum SER. The SER dependence on SNR we estimate theoretically by deriving approximate formula for SER of uncoded APSK constellation in Gaussian-noise-limited channel and practically by performing simulation. The obtained results are well-matched verifying the accuracy of approximate SER formula. The results also show that our APSK constellation outperforms some previous APSK and M-ary QAM constellations in terms of power efficiency. Thus, for SER equal to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> the gain in power efficiency amounts up to 2.35 dB, 2.23dB and 1.64 dB compared with the maximum mutual information-optimized 4+12-APSK, 4+12+16-APSK and 4+12+20+28-APSK constellations, respectively. This means that by employing APSK constellation we propose instead the traditional APSK constellations the transmitted signal power can be reduced by a third enabling lower power consumption. The improved power efficiency of our APSK constellation makes it suitable for application in power-limited communications such as fiber-optic communications, satellite communications, power-line communications, and multiple-input multiple-output wireless transmissions.

Enhanced Biased ASK Modulation Performance for SWIPT With AWGN Channel and Dual-Purpose Hardware

A lot of small sensors are deployed in Internet of Things applications. Simultaneous wireless information and power transfer (SWIPT) is a solution to avoid a large amount of batteries, while exchanging information with the sensors. Combining both energy harvesting and information receiving in dual-purpose hardware lowers power consumption while also decreasing sensor size. Biased amplitude shift keying (ASK) is introduced as a solution for the SWIPT modulation technique. In particular, the design of enhanced biased ASK modulation in case of an additive white Gaussian noise channel is analyzed in this paper. Novel formulas for symbol error rate are derived, while improvements of the modulation scheme are proposed based on measurements, taking rectifier nonlinearity into account and resulting in reducing the transmitted power by 14 dB for fixed error rate.

Rician-Nakagami 페이딩 채널에서 M-PSK와 M-DPSK 시스템에 대한 효과적인 점근적 심볼 에러 확률 성능 분석

Using the existing exact but quite complicated symbol error rate (SER) expressions for M-ary phase shift keying (M-PSK) and M-ary differential phase shift keying (M-DPSK), we derive effective and concise closed-form asymptotic SER formulas especially in Rician-Nakagami fading channels. The derived formulas can be utilized to efficiently verify the achievable error rate performances of M-PSK and M-DPSK systems for the Rician-Nakagami fading environments. In addition, by exploiting the modulation gains directly obtained from the asymptotic SER formulas, we also theoretically demonstrate that M-DPSK suffers an asymptotic SER performance loss of 3.01dB with respect to M-PSK for a given M in Rician-Nakagami fading channels at high signal-to-noise ratio (SNR).

Concise SER Analysis of Differential Quaternary Phase Shift Keying with Gray Coding Over Composite Multipath Shadowing Channels

To effectively assess the symbol error rate (SER) performance achieved by π/4 differential quaternary phase shift keying (π/4-DQPSK) with Gray coding over Rician-Nakagami fading channels, a simple closed-form asymptotic SER formula is derived, which is much simpler than the existing exact SER expression. From the proposed simple closed-form formula, we can obtain some useful insights into the achievable error rate performance for the DQPSK modulation with Gray coding for various channel conditions in the high signal-to-noise ratio (SNR) regions.

Efficient Approximated Q-Function Form for Error Probability over Rayleigh Fading Channels

Error rate probability is considered as important metric to evaluate the behavior of communication system. Gaussian Q-function is gaining more intention from researchers due to its direct relation in computing the error probability in terms of symbol error rate (SER) or bit error rate. In literature, several approximated functions have been proposed to evaluate and analyze the error rate in fading channel. In this paper, a novel, simple and accurate closed form for Gaussian Q-function is derived. In contrast to previous related approximated functions; it is noticeable that the designed formula improves the accuracy for large range of positive argument. Furthermore, an efficient SER formula is derived for additive white Gaussian noise and for Rayleigh fading channel. Numerical analysis and simulation were conducted to verify and validate the designed approximated functions. The results show that the proposed form can achieve high accuracy compared to that of previous work; and also simplify the evaluation analysis of SER in fading channels.

Effect of feedback delay on dual‐hop fixed gain relay networks over mixed fading channels

ABSTRACTIn this paper, we investigate the effect of feedback delay on a dual‐hop fixed gain amplify‐and‐forward relay network over Rayleigh–Rician mixed fading channels, where the source and destination are all equipped with multiple antennas, while the relay has a single antenna. By using the model of beamforming with feedback delay, the equivalent output signal‐to‐noise ratio (SNR) of the amplify‐and‐forward relay network is first obtained. Then, based on the infinite series representation, the analytical expressions for the outage probability and the probability density function of the output SNR are derived. Furthermore, the analytical formulas of the ergodic capacity and the average symbol error rate formulas with various modulation formats are developed. To reveal the diversity order and array gain of the multi‐antenna relay network, the asymptotic average symbol error rates at high SNR are also presented. Finally, computer simulations are provided to validate the theoretical analysis and to indicate the effect of antenna number, feedback delay and channel parameters on the system performance. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Analysis and Compensation of DC Offset in OFDM Systems Over Frequency-Selective Rayleigh Fading Channels

Direct-conversion receivers have become popular in radio-frequency (RF) circuit design for their advantages of low cost, low power consumption, and fewer chip components over other architectures such as heterodyne receivers. However, the direct-conversion receiver architecture often suffers from direct current (dc) offset, which is a consequence of the imperfect direct-conversion process. In this paper, we study the effects of dc offset on the symbol error rate (SER) performance of orthogonal frequency-division multiplexing (OFDM) systems in multipath Rayleigh fading channels. Since OFDM system performance is sensitive to carrier frequency offset (CFO), the CFO must be estimated and compensated at the receiver. Due to CFO compensation, the dc offset caused by direct-conversion receivers and/or mixed-signal circuits no longer only affects the dc subcarrier and is spread over all subcarriers. By deriving the analytical SER formulas for OFDM systems with various modulation formats, the dependency of SER on dc offset and CFO is clearly quantified. These SER formulas can help system designers determine suitable specifications of RF components and understand whether digital DC offset compensation is necessary or not. Finally, we propose and analyze a simple DC offset estimation and cancellation scheme under the assumption that DC offset holds constant in one OFDM symbol duration. Numerical results demonstrate the effectiveness of the proposed DC offset-cancellation scheme.

Precoded Differential Orthogonal Space-Time Modulation Over Correlated Ricean MIMO Channels

In this paper, we study a differential system employing orthogonal space-time block codes (OSTBC) with -PSK, -PAM, and -QAM constellations, over arbitrarily correlated Ricean fading channels. The symbol error rate (SER) performance analysis of such a differential system is performed using a memoryless precoding matrix at the transmitter. Monte Carlo simulations are carried out to verify the validity of the SER expressions. The SER formulas can predict the behavior of differential system closely for moderate to high values of signal to noise ratio (SNR). The proposed precoded differential codes differ from the previous works by: 1) the precoded differential code is proposed for the arbitrarily correlated Ricean channels, whereas, existing work is applicable for Rayleigh fading channels using Kronecker model with transmit correlation only. 2) the previous work is applicable to the OSTBC with -PSK signal constellations only, whereas, the proposed precoded differential coding works with -PSK, -QAM, and -PAM constellations. 3) the precoder design is proposed to minimize the approximate SER, whereas the previous precoder is based on minimizing an upper bound of the approximate SER. In addition, the proposed precoded orthogonal differential code performs better than the previously proposed eigen-beamforming based precoded differential OSTBC.

Performance Analysis of Combined Transmit Selection Diversity and Receive Generalized Selection Combining in Rayleigh Fading Channels

We analyze the average symbol error rate (SER) of M-PSK and M-QAM modulations with transmit antenna selection diversity (SD) and receive generalized selection combining (GSC) in Rayleigh fading channels. SER formulas are derived in closed form, and numerical results show that transmit SD and receive GSC are flexible to tradeoff performance for complexity.

Exact Symbol Error Probability of a Cooperative Network in a Rayleigh-Fading Environment

In a distributed spatial diversity wireless system, not all antennas are located at one station as in classical transmit diversity systems, but are dispersed at different, possibly mobile, stations in the network. Transmit diversity is created when the selected stations assist a sender by relaying its information signal to the destination. In this letter, we present an exact average symbol error rate analysis for the distributed spatial diversity wireless system with K amplifying relays in a Rayleigh-fading environment. The average symbol error rate formula allows us to clearly illustrate the advantage that the distributed diversity system has in overcoming the severe penalty in signal-to-noise ratio caused by Rayleigh fading. Using simple bounds on the probability of error, we show that the cooperative network presented in this letter achieves full diversity order.

A General SER Formula for an OFDM System With MDPSK in Frequency Domain Over Rayleigh Fading Channels

A closed-form formula for symbol-error rate (SER) of an orthogonal frequency-division multiplexing (OFDM) system with M-ary differential phase-shift keying (MDPSK) in frequency domain over Rayleigh fading channels is obtained. It is found that, by MDPSK in frequency domain, identical SERs can be achieved on all subcarriers. However, both time and frequency dispersion in the channel will introduce error floors. A comparison between OFDM-MDPSK in frequency domain and that in time domain reveals that the former system offers superior SER performance in a fast fading environment, while the latter performs better if the channel is mainly frequency selective. Moreover, the former system has lower implementation complexity.

Error Probability Minimizing Pilots for OFDM With M-PSK Modulation Over Rayleigh-Fading Channels

Orthogonal frequency division multiplexing (OFDM) with pilot symbol assisted channel estimation is a promising technique for high rate transmissions over wireless frequency-selective fading channels. In this paper, we analyze the symbol error rate (SER) performance of OFDM with M-ary phase-shift keying (M-PSK) modulation over Rayleigh-fading channels, in the presence of channel estimation errors. Both least-squares error (LSE) and minimum mean-square error (MMSE) channel estimators are considered. For prescribed power, our analysis not only yields exact SER formulas, but also quantifies the performance loss due to channel estimation errors. We also optimize the number of pilot symbols, the placement of pilot symbols, and the power allocation between pilot and information symbols, to minimize this loss, and thereby minimize SER. Simulations corroborate our SER performance analysis, and numerical results are presented to illustrate our optimal claims.

Switched Dual Diversity Reception of M-ary DPSK Signals on Nakagami Fading Channels

The paper deals with dual diversity reception of M-ary differential phase-shift keying modulated signals in the presence of additive white Gaussian noise and Nakagami-distributed slow and nonselective fading. The performance of a switched diversity system is analysed and compared to that of the predetection selection diversity combining scheme. The general case of correlated diversity branches is considered, without restrictions on the fading severity parameter. Average symbol error rate formulas are analytically derived in terms of integral expressions that can be easily computed via numerical integration routines. Moreover, the numerical evaluation of the optimum switching threshold is carried out and the influence of the fading severity parameter, the branch correlation, and the cardinality of the symbol alphabet is analysed. Finally, three fixed switching threshold strategies that allow to obtain a satisfactory diversity gain are considered.