Expressions For Average Error Probability Research Articles

Comments on "tight bounds and invertible average error probability expressions over composite fading channels"

In the paper Tight Bounds and Invertible Average Error Probability Expressions over Composite Fading Channels of Wang et al. [1], they derived the algebraic formulas of upper- and lower-bounds for the average symbol error probability (ASEP) of M-ary phase shift keying (M-PSK) in a class of composite fading channels by using mixture gamma (MG) distribution, which is based on the assumption of the lack of closed-form expression for exact ASEP. However, the exact ASEP can be represented in closed-form by utilizing hypergeometric functions. Therefore, in this paper, we formulate the closed-form formulas of the exact and asymptotic ASEPs for general M-PSK in a class of the composite fading channels over MG distribution. We present some numerical results to validate our derived analytical results.

Performance analysis of angular diversity receiver based MIMO–VLC system for imperfect CSI

Visible light communication (VLC) has emerged as a promising technology for 5G and beyond communication networks in the last few years. In this paper, a multiple-input multiple-output (MIMO) VLC system using angular diversity receiver is proposed. In particular, the repetition coding is adopted at the transmitter and receiver diversity schemes, i.e. maximum-ratio combining (MRC), equal gain combining (EGC) and selection best combining (SBC), are adopted at the receiver for further performance enhancement. The closed-form expressions for average error probability of the proposed system are derived in the presence of imperfect channel state information (CSI). This research investigates that the increment in SNR is not sufficient to offset the effect of channel estimation error especially at high estimation error. The error performance analysis of the proposed MIMO–VLC system with and without estimation error is presented for different receiver locations and semi-half angles of the transmitting light emitting diodes (LEDs). Analytical results are verified with the simulation results.

Tight bounds and invertible average error probability expressions over composite fading channels

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K (K G ), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian O-fu notion, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

코히런트 무선 광통신 시스템에서 펄스 재밍으로 인한 비트오류율 분석

In this letter, we investigate the performance of coherent free-space optical(FSO) systems under pulsed noise jamming conditions. In particular, we derive the average bit error probability of the coherent FSO systems with the pulsed noise jamming in a closed-form. Also, we derive the optimal fraction of symbol time of the jammer. We confirm the derived average error probability expressions by the exactly matching Monte-Carlo simulation results.

Performance study of opportunistic scheduling in dual‐hop multi‐user underlay cognitive network

In this study, the authors investigate the performance of opportunistic scheduling for the dual-hop amplify-and-forward multi-user cognitive relaying network. Expressions are derived for the cumulative distribution function (CDF) and probability density function of the equivalent signal-to-noise ratio (SNR). From the derived CDF, the outage performance of the cognitive network is investigated. Then, an expression for average error probability is derived. Furthermore, simple and generic asymptotic expressions for the outage and error probabilities are obtained and discussed. In addition, a closed-form expression for the system's ergodic capacity is derived. Their asymptotic results show that opportunistic scheduling has no impact on diversity gain. It is confirmed that the array gain determines the SNR advantage of opportunistic scheduling over the single-user scenario. Moreover, they study adaptive power allocation under the total transmit power constraint in order to minimise the average error probability. As expected, the results show that optimum power allocation improves system performance compared with uniform power allocation. Finally, numerical results and Monte Carlo simulations are also provided to support the correctness of the analytical calculations.

Impact of Pointing Errors on the Performance of Coherent Free-Space Optical Systems

In this letter, we investigate the performance of a coherent free-space optical (FSO) communications system considering geometric spread and pointing errors as well as atmospheric turbulence fading and path loss. In particular, we derive the outage probability and average error probability of the coherent FSO system, considering the combined effects of path loss, geometric spread and pointing errors, and amplitude fluctuations and phase aberrations in series representations forms. Numerical and Monte Carlo simulation results confirm the validity of the derived outage probability and average error probability expressions.

Error rate performance analysis of multiantenna MC DS-CDMA system over η–μ frequency selective fading channels with arbitrary parameters

Wireless communication channels have harmful impact on the performance of the wireless communication systems due to the severe influences of multipath fading, path loss, shadowing, intentional and unintentional interference, and noise, respectively. In this paper, we investigate the performance of the orthogonal multicarrier direct sequence code division multiple access (MC DS-CDMA) system coupled with multiple input multiple output (MIMO) system operating over independent nonidentically distributed (i.ni.d) η–μ multipath fading channels in terms of average error probability. Based on moment generating function (MGF) and probability density function (PDF) approaches, closed form expressions for average error probability of binary phase shift keying (BPSK), multilevel phase shift keying (MPSK), and square M-ary quadrature amplitude modulation (MQAM) schemes are derived and expressed in terms of Appell's hypergeometric functions and Lauricella's multivariate hypergeometric functions. The numerical results show that the effects of arbitrary fading parameters, decaying power factor (d), and signal constellation size on the system performance can be reduced using spatial and temporal path diversities. We validate the correctness of the analytical approaches using Monte Carlo simulation techniques.

Partial Dual-Relay Selection Protocols in Two-Way Relayed FSO Networks

In this paper, we present relay selection protocols for parallel relayed free-space optical (FSO) communication network, which consists of two non-line-of-sight terminal nodes and multiple two-way relays (TWR). The TWRs use the two time-phase decode-and-forward relaying protocol to establish a bidirectional link between the terminals. For the considered system, we propose a partial dual-relay selection (P-DRS) scheme, in which two TWRs are selected to participate in the communication process. By using two TWRs, the advantages of cooperative diversity are achieved. For the proposed relay selection scheme and assuming Gamma–Gamma fading channels with pointing errors and path loss, we derive an exact closed form expression for the system outage. Further, we derive an asymptotic expression for average error probability. The diversity order of the system is also presented. It is shown by numerical analysis that by using the proposed P-DRS scheme, the system performance can be significantly improved.

Error probability performance analysis for multicarrier direct sequence code division multiple access multiple‐input–multiple‐output systems over correlated η–µ fading channels

The authors investigate the performance of multiple-input–multiple-output multicarrier direct sequence code division multiple access system operating over arbitrarily and equally correlated η–µ fading channels in terms of average bit error probability and average symbol error probability. Closed form expressions for average error probability using moment generating function-based approach are derived and expressed in terms of Lauricella's multivariate hypergeometric functions. Furthermore, based on numerical results, they observe that the performance of the system improves when the number of multipath clusters increases as well as the number of subcarriers (frequency diversity). Similarly, substantial enhancement in system performance is observed due to the effect of spatial diversity. Finally, they verify the results via Monte Carlo simulation-based method to support the accuracy of the analytical approach and also compare with already published ones.

Optimal fusion rule for cooperative spectrum sensing in cognitive radio networks

In this paper, we analyze performance of cooperative spectrum sensing under counting rules when exponential model is utilized to characterize the burst nature of primary user (PU) link. Our objective is to minimize the average error probability (AEP) so that the link utilization in the considered link achieves its maximum. We derive a closed-form expression of AEP as well as the probability of interference (PoI) by classifying cognitive transmission into six events. Then, we consider the minimization of AEP over counting rules under the constraint of interference. As the solution, we develop an efficient algorithm to evaluate the optimal fusion rule. Finally, we verify our analysis in numerical results.

MIMO Zero-Forcing Detection Analysis for Correlated and Estimated Rician Fading

Experimental modeling of wireless fading channels performed by the WINNER II project has been shown to fit a Rician rather than Rayleigh distribution, the latter being assumed in many analytical studies of multiple-input-multiple-output (MIMO) communication systems. Unfortunately, a Rician MIMO channel matrix has a nonzero mean (i.e., specular component) that yields, for the matrix product that determines the MIMO performance, a noncentral Wishart distribution that is difficult to analyze. Previously, the noncentral Wishart distribution has been approximated, based on a first-order-moment fit, by a central Wishart distribution and used to derive average error probability (AEP) expressions for zero-forcing (ZF) detection. We first reveal that this approximation and the MIMO performance evaluation tools derived from it may be reliable only for rank-one specular matrices. We then exploit this approximation to derive an AEP expression for a lesser known, yet optimal, MIMO ZF approach that, unlike the conventional approach, accounts for channel estimation accuracy through the channel statistics. After validating this AEP expression for the rank-one case, it is shown that the ZF performance averaged over realistic (i.e., WINNER II) distributions of the Rician <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -factor and azimuth spread (AS) can be much worse than that for the average <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> and AS. Finally, through simulations, it is shown that the optimal detection approach can substantially outperform the conventional approach for ZF for full-rank specular matrices, as well as for minimum mean square error detection for both rank-one and full-rank specular matrices.

Maximal-ratio eigen-combining: a performance analysis

Maximal-ratio eigen-combining (MREC) for wireless communications channels, also known as eigen-beamforming for receivers equipped with antenna arrays, integrates conventional maximum average signal-to-noise-ratio beamforming (Max-ASNR BF) and maximal-ratio combining (MRC) to provide both high average SNR in high fading correlation as well as diversity in low fading correlation. Previous studies of MREC were based on simulation or limited analysis and suggested that MREC can outperform Max-ASNR BF and MRC in terms of average error probability (AEP). A comprehensive analysis of MREC is provided for BPSK signals and Rayleigh fading, including computable AEP and outage probability (OP) expressions for perfectly known, correlated channel gains. Particular cases of these expressions apply to Max-ASNR BF and MRC. For imperfectly known channels the analysis yields a new and general AEP expression for MREC, which is specialized to estimation based on pilot-symbol-aidedmodulation (PSAM) and interpolation. In particular, this AEP expression applies to Max-ASNR BF and, for PSAM and data-independent interpolation filters, to MRC. Numerical results for antenna arrays receiving signals with angle-of-arrival dispersion and imperfectly known channel gains confirm the potential advantage of MREC over Max-ASNR BF and MRC.