Bit error probability of the M‐QAM scheme under η‐μ fading and impulsive noise in a communication system using spatial diversity

This paper presents a new and exact expression for the bit error probability (BEP) of the square M‐ary quadrature amplitude modulation (M‐QAM) scheme, with the channel under double gated additive white Gaussian noise (G²AWGN) and η‐μ fading in a communication system using the spatial diversity technique. The expression for the BEP is written in terms of the Appell function. The BEP curves are presented under different values of the number of branches of the maximum ratio combining (MRC) receiver, order of the constellation M, and parameters that characterize mathematically the channel, corroborated by simulations performed with Monte Carlo method.     

Application of best relay selection approach to cooperative DF IDMA systems over Rayleigh/Weibull fading channels

This paper analyzes the performance of cooperative decode‐and‐forward (DF) interleave‐division multiple‐access (IDMA) networks with best relay selection over Rayleigh/Weibull fading environments. In the analysis, approximate outage probability (OP) and bit error probability (BEP) expressions are derived for the considered system. Further, a 2‐hop DF IDMA system is also designed to compare with cooperative one. We propose OP and BEP expression for 2‐hop DF IDMA systems. Numerical results are obtained by changing the number of relays and the value of fading parameter in the proposed expressions. Also, simulations are provided to corroborate the exactness of the derived approximate OP and BEP expressions.     

Growth of 1‐eV GaNAsSb‐based photovoltaic cell on silicon substrate at different As/Ga beam equivalent pressure ratios

We report the performance of 1‐eV GaNAsSb‐based photovoltaic samples grown on a Si substrate using molecular beam epitaxy at different As/Ga beam equivalent pressure (BEP) ratios. The light current–voltage curve and spectral response of the samples were measured. The sample grown at an As/Ga BEP ratio of 10 showed the highest energy conversion efficiency with an open circuit voltage (V_OC) of 0.529 V and a short circuit current density of 17.0 mA/cm². This measured V_OC is the highest ever reported value in GaNAsSb 1‐eV photovoltaic cell, resulting in the lowest ever reported E_g/q‐V_OC of 0.50 eV. The increase in the As/Ga BEP ratio also resulted in an increase in the bandgap‐voltage offset value (E_g/q‐V_OC) and a decrease in quantum efficiency up to As/Ga BEP ratio of 18. Copyright © 2015 John Wiley & Sons, Ltd.     

General switch‐and‐examine relaying for demodulate‐and‐forward cooperative diversity

Two new demodulate‐and‐forward schemes of multi‐relay cooperative diversity with switch‐and‐examine relaying (SER) are analyzed. To reduce relay usage and enhance bandwidth efficiency, the two new cooperative diversity schemes employ a switch‐based relay selection. The proposed schemes consume less communication resource than regular relaying schemes, such as the selection combining (SC) or maximal ratio combining (MRC) schemes that always use all relays, and also achieve better performance than distributed switch‐and‐stay schemes. In the first scheme, the decision statistic for relay usage and selection is based on the signal‐to‐noise ratio (SNR). In the second scheme, the log‐likelihood ratio (LLR) of received signals is used for the decision of relay usage and selection. With the two SER schemes, the bit error probability (BEP) of binary phase shift keying (BPSK) and the average number of used paths are derived and expressed in closed‐form for the independent and identically distributed (i.i.d.) Rayleigh fading channels. Numerical and simulation results are presented for performance illustrations. According to the numerical results, the LLR‐based SER not only achieves a lower BEP but also consumes less relay resource than the SNR‐based SER. Furthermore, the LLR‐based SER scheme even outperforms the corresponding SNR‐based SC scheme for a range of average SNR. Copyright © 2014 John Wiley & Sons, Ltd.     

Efficient bit error probability expression and very tight bound for maximal ratio combining diversity systems over Rayleigh fading channel

Bit Error Probability （BEP） provides a fundamental performance measure for wireless diversity systems. This paper presents two new exact BEP expressions for Maximal Ratio Combining （MRC） diversity systems. One BEP expression takes a closed form, while the other is derived by treating the squared-sum of Rayleigh random variables as an Erlang variable. Due to the fact that the extant bounds are loose and could not properly characterize the error performance of MRC diversity systems, this paper presents a very tight bound. The numerical analysis shows that the new derived BEP expressions coincide with the extant expressions, and that the new approximation tightly bounds the accurate BEP.     

Further results in the unified analysis of digital communicationsystems

Stein's (1964) method can be extended to the analysis of the bit error probability (BEP) of quadrature phase shift keying (QPSK), staggered QPSK, and minimum shift keying (MSK) communication systems. The resultant noisy reference BEP waterfall curves are presented. The numerical advantages of this technique and some practical results are discussed. In a parallel manner, the BEP for quadrature amplitude modulation (QAM) communication systems can be analyzed. This technique is numerically more intensive but is used to generate noisy reference BEP waterfall curves for 16-QAM and 64-QAM modulations. Unfortunately, few carrier synchronizers produce a complex Gaussian reference signal, but pragmatically many reference signals can be accurately approximated by a complex Gaussian at moderate to high SNR. Actual BEP performance and the approximate results are compared     

Approximate average bit error probability for DQPSK over fading channels

The bit error probability (BEP) of DQPSK with Gray coding over an AWGN channel can be computed simply, although it is hard to integrate and derive the average BEP for fading channels. Presented are novel approximations of the average BEP of DQPSK with Gray coding over fading channels. Numerical results show that the novel formulations are quite accurate.     

Linear Diversity Analysis for M‐ary Square Quadrature Amplitude Modulation over Nakagami Fading Channels

We derive and analyze the exact closed‐form expression for the average bit error probability (BEP) of M‐ary square quadrature amplitude modulation (QAM) for diversity reception in frequency‐nonselective Nakagami fading. A maximal ratio combining (MRC) diversity technique with independent or correlated fading cases are considered. Numerical results demonstrate error performance improvement with the use of MRC diversity reception. The presented new expressions offer a convenient way to evaluate the performance of M‐ary square QAM with an MRC diversity combiner for various cases of practical interest.     

Thermo‐Phototronic Effect Enhanced InP/ZnO Nanorod Heterojunction Solar Cells for Self‐Powered Wearable Electronics

Enhancing interfacial charge transfer by the inner electric field is crucial for improving photovoltaic performance of heterojunction solar cells. Recent studies are focusing on how to utilize piezo‐phototronic effect (strain‐induced inner electric field) to modulate the interfacial charge transfer, whereas the preservation of solar cells from structure damage and performance decline under long‐term strain becomes increasingly challenging. Here, without use of strain, a thermo‐phototronic effect is presented to enhance the interfacial charge transfer in InP/ZnO nanorod heterojunction solar cells. Under a temperature gradient of 3.5 °C across the device, the output current and voltage of the solar cell under weak light illumination are enhanced by 27.3 and 76%, respectively. Moreover, the performance enhancement can be further regulated by applying different temperature gradients. This study serves as proof‐of‐principle for the thermo‐phototronic effect and pushes forward the maximum utilization of solar energy by a one‐circuit‐based photovoltaic‐thermoelectric system.     

A simple bit error probability analysis for square QAM in rayleigh fading with channel estimation

A new approach is presented for analyzing the bit error probability (BEP) of square, multilevel, quadrature amplitude modulation over a nonselective Rayleigh fading channel, with imperfect channel estimation employing pilot-symbolassisted- modulation. It is much simpler and more powerful than those in the literature, and the average BEP is obtained by calculating the BEP for each individual bit. The results are given in simple, exact, closed-form expressions that do not require any numerical integration. These expressions show explicitly the behavior of the BEP as a function of various system parameters. Three channel estimation schemes are investigated. It is shown that existing channel estimation schemes using sinc interpolation and Gaussian interpolation can be improved.     

A symbol-by-symbol channel estimation receiver for space-time block coded systems and its performance analysis on the nonselective rayleigh fading channel

We present a symbol-by-symbol channel estimation receiver for an orthogonal space-time block coded system, and derive its analytical performance on a slow, nonselective, Rayleigh fading channel. Exact, closed-form expressions for its bit error probability (BEP) performance for M-ary phase shift-keying modulations are obtained, which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error. Our BEP expressions show explicitly the dependence of BEP on the mean square error of the channel estimates, which in turn depend on the channel fading model and the channel estimator used. Tight upper bounds are presented that show more clearly the dependence of the BEP on various system parameters. Simulation results using various fading models are obtained to demonstrate the validity of the analysis.     

Approximate results for the bit error probability of binary phaseshift keying with noisy phase reference

Approximate results for the bit error probability (BEP) of binary phase shift keying (BPSK) in the presence of a noisy carrier phase reference are presented. The results show correctly the behavior or the BEP as a function of SNR. The accuracy of the approximations is verified by simulations and numerical integration of the BEP formulas. The results are compared with existing bounds     

A comprehensive performance analysis of relay-aided CDMA communications over dissimilar fading channels

In this paper, bit error probability (BEP), outage probability (OP) and channel capacity (CC) of direct-sequence code-division multiple access systems with amplify-and-forward relaying are presented for different fading scenarios. In the first scenario, the source-destination link is assumed to experience Rayleigh fading while it is subject to Nakagami-m fading in the second scenario. The source-relay and relay-destination channels are considered to have Nakagami-m fading conditions in two scenarios. First, analytical expressions for the end-to-end probability density function (PDF) are derived by using the convolution integral. Then, BEP, OP and CC are obtained based on these PDFs in terms of infinite series. Truncation error analyses are presented for different parameter values in order to show that truncation error arising from the infinite series is negligible. Simple and easy-to-compute asymptotic expressions are also introduced for BEP and OP in order to simplify the performance analysis in high signal-to-noise ratio region. Simulation results are provided to show the accuracy of the proposed approximate and asymptotic expressions.     

Bit error probability for MDPSK and NCFSK over arbitrary Ricianfading channels

In this paper, we analyze the bit error probability (BEP) of binary and quaternary differential phase shift keying (2/4 DPSK) and noncoherent frequency shift keying (NCFSK) with postdetection diversity combining in arbitrary Rician fading channels. The model is quite general in that it accommodates fading correlation and noise correlation between different diversity branches as well as between adjacent symbol intervals. We show that the relevant decision statistic can be expressed in a noncentral Gaussian quadratic form, and its moment generating function (MGF) is derived. Using the MGF and the saddle point technique, we give an efficient numerical quadrature scheme to compute the BEP. The most significant contribution of the paper, however, lies in the derivation of a closed-form cumulative distribution function (cdf) for the decision statistic. As a result, a closed-form BEP expression in the form of an infinite series of elementary functions is developed, which is general and unifies previous published BEP results for 2/4 DPSK and NCFSK for multichannel reception in Rician fading. Specialization to some important cases are discussed and, as a byproduct, a new and general finite-series expression for the BEP in arbitrarily correlated Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and NCFSK performance for independent and correlated Rician fading channels; and some interesting findings are presented     

Differential phase shift keying in two-path Rayleigh channel withadjacent channel interference

A formula is derived for the error probability of M-ary differential phase-shift keying with differential phase detection in a two-path Rayleigh fading channel taking into account adjacent channel interference (ACI), cochannel interference (CCI), intersymbol interference (ISI), and Doppler frequency shift. Square-root Nyquist filters are used with roll-off, β, the transmitter and receiver as in the proposed US digital mobile radio system. The presence of the second path has a profound effect on increasing the bit error probability (BEP) because it causes ISI. In the absence of ISI, ACI has a smaller effect on BEP than CCI. In the presence of ISI their effect is essentially the same. For a given bit energy-to-noise ratio, the binary system has the lowest BEP; however, the bit rate is also the lowest for a given bandwidth. When the main interference is ACI or CCI, a quaternary system has a lower BEP than the octal system. When the main interference is ISI, this is reversed     

Optimum Cooperation of the Cooperative Coding Scheme for Frequency Division Half-Duplex Relay Channels

This paper analyzes the effects of the level of cooperation (LOC) on the performance of a practical cooperative coding scheme for frequency division half-duplex relay links in general wireless ad-hoc networks. The end-to-end bit error probability (BEP) and the corresponding optimum LOG minimizing the end-to-end BEP are investigated for specific realizations using a family of rate compatible punctured convolutional (RCPC) codes. This paper shows that the BEP of the cooperative coding scheme depends on the LOC and there exists an optimum LOC for every specific realization. Further, it is shown that more than a certain level of cooperation is required to achieve possible cooperative gains in practical signal-to-noise ratio (SNR) regions, and increasing LOC does not effect much on the BEP performance for sufficiently large LOCs     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

Gray Coding for Multilevel Constellations in Gaussian Noise

The problem of finding the optimal labeling (bit-to-symbol mapping) of multilevel coherent phase shift keying (PSK), pulse amplitude modulation (PAM), and quadrature amplitude modulation (QAM) constellations with respect to minimizing the bit-error probability (BEP) over a Gaussian channel is addressed. We show that using the binary reflected Gray code (BRGC) to label the signal constellation results in the lowest possible BEP for high enough signal energy-to-noise ratios and analyze what is "high enough" in this sense. It turns out that the BRGC is optimal for PSK and PAM systems whenever the target BEP is at most a few percent, which covers most systems of practical interest. New and simple closed-form expressions are presented for the BEP of PSK, PAM, and QAM using the BRGC     

Performance analysis of threshold digital relaying M2M cooperative networks

Exact average bit error probability (BEP) expressions for mobile-to-mobile cooperative networks employing threshold digital relaying over N-Nakagami fading channels are derived. The power allocation problem is formulated for performance optimization. The average BEP performance is evaluated via numerical simulation to verify the accuracy of the analysis with binary phase shift keying (BPSK) modulation. The simulation results showed that the fading coefficient, number of cascaded components, relative geometrical gain, and power-allocation parameter have a significant influence on the performance.     

Analytical Methods for CDMA Systems with Parallel Interference Cancellation: The Large Deviation Approach

For a simple CDMA system, we compute the bit-error probability (BEP)with soft-decisionparallel-interference-cancellation (SD-PIC). Instead of approximatingthe signal-to-noise ratio, we use a different measure to calculateperformance. This measure is the exponential rate of the BEP, i.e., thelimit of n^–1 log(BEP) = –I, for the processinggain n , where I depends only on the number of users. Weshow, using the rate as a measure, that SD-PIC improves the performance.The values of I follow as the solution of an optimization problem whichcan be calculated numerically. We use these results to derive theasymptotic behaviour of the rate for large k. We also derive results forthe second order asymptotics of the BEP. Inclusion of second orderasymptotics leads to excellent approximations.