Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels

Error control coding can be used over free-space optical (FSO) links to mitigate turbulence-induced fading. In this paper, we derive error performance bounds for coded FSO communication systems operating over atmospheric turbulence channels, considering the recently introduced gamma-gamma turbulence model. We derive a pairwise error probability (PEP) expression and then apply the transfer function technique in conjunction with the derived PEP to obtain upper bounds on the bit error rate. Simulation results are further demonstrated to confirm the analytical results.     

Pointing error effects on performance of free-space optical communication systems using SC-QAM signals over atmospheric turbulence channels

In this paper, we theoretically analyze pointing error effects on performance of free-space optical (FSO) communication systems using subcarrier intensity quadrature amplitude modulation (SC-QAM) signals over atmospheric turbulence channels. Unlike previous studies, we take into account both atmospheric turbulence channels and the pointing error effect. In order to model atmospheric turbulence channels, we employ a log-normal distribution for weak-to-moderate turbulent condition and a gamma–gamma distribution for strong turbulent condition. Moreover, we study the pointing error effect by taking into account the influence of beamwidth, aperture size and jitter variance. In addition, we use a combination of these models to analyze the combined effect of atmospheric turbulence and pointing error to FSO/SC-QAM systems. Finally, we derive analytical expressions to evaluate the average symbol error rate (ASER) performance of such systems. Numerical results present the impact of pointing error on the performance of FSO/SC-QAM systems and how we use proper values of aperture size and beamwidth to improve the performance of such systems. In addition, simulation results of FSO/SC-QAM performance over strong atmospheric turbulence and pointing errors show that the closed-form expression can provide a precision for evaluating ASER of such systems.     

New tight bounds on the pairwise error probability for unitary space-time modulations

We present two upper bounds and one lower bound on the pairwise error probability (PEP) of unitary space-time modulation (USTM) over the Rayleigh fading channel. The two new upper bounds are the tightest so far, and the new lower bound is the tightest at low signal-to-noise ratio. Some implications for USTM constellation design are also pointed out.     

Pairwise codeword error probability for coded atmospheric optical communication systems

In atmospheric optical channels ,turbulence affects theperformance of I M/DDatmospheric optical communica-tion systems seriously,especiallyinthe range of 1kmormore.Using error-control code (error-correcting code orchannel code) it can be i mproved remarka…     

Bounds on the pairwise error probability of coded DS/SSMAcommunication systems in Rayleigh fading channels

Arbitrarily tight upper and lower bounds on the pairwise error probability (PEP) of a trellis-coded or convolutional-coded direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system over a Rayleigh fading channel are derived. A new set of probability density functions (PDFs) and cumulative distribution functions (CDFs) of the multiple-access interference (MAI) statistic is derived, and a modified bounding technique is proposed to obtain the bounds. The upper bounds and lower bounds together specify the accuracy of the resulting estimation of the PEP, and give an indication of the system error performance. Several suboptimum decoding schemes are proposed and their performances are compared to that of the optimum decoding scheme by the average pairwise error probability (APEP) values. The approach can be used to accurately study the multiple-access capability of the coded DS/SSMA system without numerical integrations     

Impact of pointing errors and turbulence effects on POLSK and coherent OWC-based FSO system over generalized turbulence channel model

The emerging technology in wireless communication, free space optics (FSO) offers a myriad of merits over current radio frequency links due to its wide license-free bandwidth, ease of installation, high security features and viable cost for short-distance communication. Its unparallel high-speed data rate and immunity against electromagnetic interference makes FSO the emerging technology of today. Atmospheric conditions like absorption, scattering, turbulence and pointing error prevail during wireless transmission. Through this paper we aim at elucidating the effect of the error introduced by misalignment between the transmitter and receiver that are ideally required to be in the line of sight rendering pointing error. Pointing error and turbulence effects are the main limitation parameters for our analysis. For this purpose, we have taken into consideration three different modulation techniques polarization shift keying, coherent OWC and on–off keying FSO communication system. We derived the novel expressions for the average spectral efficiency (ASE) over the generalized turbulence model for these modulation techniques. The ASE is analyzed against average transmitted optical power with the maximum ASE of 50 bits/s/Hz at the transmitted power of 10 dBm for coherent OWC technique.     

BER Performance of FSO Links over Strong Atmospheric Turbulence Channels with Pointing Errors

In this letter, we investigate the error rate performance of free-space optical (FSO) links over strong turbulence fading channels together with misalignment (pointing error) effects. First, we present a novel closed-form expression for the distribution of a stochastic FSO channel model which takes into account both atmospheric turbulence-induced fading and misalignment-induced fading. Then, we evaluate the average bit-error rate in closed form of a FSO system operating in this channel environment, assuming intensity modulation/direct detection with on-off keying. Numerical examples are further provided to collaborate on the derived analytical expressions.     

自由空间光通信中LT码的编码技术研究

为了克服大气湍流对自由空间光通信(FSO)链路的影响,将LT码应用到FSO系统中,并结合基于部分信息LT码的修正转移鲁棒孤子分布(ISRSD),模拟了不同大气湍流强度信道,采用不同的编码方案进行模拟比较,结果表明:与RS码相比,误码率为10-4时,LT码获得大约2 dB的编码增益;相比于RSD,ISRSD能使译码开销降低1％～2％,且LT码采用ISRSD后,误码率为10-7时,系统获得0.2～0.5 dB的编码增益.     

An Exact Close-form PEP and a new PEP for Space-Time Codes in Rayleigh Fading Channels

A close-form expression for the exact Pair-wise Error Probability (PEP) of Space-Time (S-T) codes in Rayleigh fading channel is derived using the general and close-form solution for the probability-density function (PDF) of a sum of independent exponential distributed random variables. The expression requires evaluating the coefficients for partial fraction expansion, so an easy analytical way is proposed for doing this. The exact PEP is subsequently used to develop a simple PEP using the upper bound. Both PEPs are used in the Union bound for error rate evaluation. Numerical calculations and Monte Carlo computer simulation are used to study the accuracies of these Union bounds for error rate evaluation of a rotation-based diagonal S-T code (D code) in Rayleigh fading channels. Four other PEPs based on different bounds, i.e., the Chernoff bound, the asymptotic bound, the tight asymptotic bound, and the Eigen-Geometric-Mean (EGM) bound, are also studied for comparison. Results show that our derived close-form PEP is an exact PEP and our proposed PEP is a very tight bound to the exact PEP.     

新型度分布的LT码在自由空间光通信中应用

由于自由空间光通信(FSO)受到大气湍流效应的影响,运用信道编码技术来保证FSO系统的稳定性。研究LT码原理,并将其引入FSO系统。分析LT码度分布需要满足的条件,引用泊松鲁棒孤子度分布来减小LT码译码开销、降低编译码复杂度,并应用于FSO系统来提高FSO系统性能。采用MATLAB进行仿真,比较泊松鲁棒孤子度分布与鲁棒孤子度分布的性能,并模拟在不同湍流信道中的FSO系统误码率。结果表明,泊松鲁棒孤子度分布具有较小的平均度值,能够减小LT的译码开销、降低编译码复杂度;且应用泊松鲁棒孤子度分布的LT码能够降低FSO系统中的误码率,保证FSO系统稳定。     

Error performance of MPSK trellis-coded modulation overnonindependent Rician fading channels

This paper presents new upper bounds on the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over nonindependent Rician fading channels. Cases considered are coherent and pilot-tone-aided detection and differential detection of trellis-coded multilevel phase-shift keying (TC-MPSK) systems. The average bit-error probability P_b can be approximated by truncating the union bound. This method does not necessarily lead to an upper bound on P_b, and, hence, the approximation must be used with simulation results. In addition, for Rayleigh fading channels with an exponential autocovariance function, bounds resembling those for memoryless channels have been derived. The bounds are substantially more accurate than Chernoff bounds and hence allow for accurate estimation of system performance when the assumption of ideal interleaving is relaxed     

Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence

In this letter, error rate performance for space-time block coding (STBC) in free-space optical (FSO) communication systems with direct detection operating over strong atmospheric turbulence channels is analyzed. Based on the modification of the Alamouti code presented by Simon and Vilnrotter, a generalized approach is adopted to consider space-time coded on-off keying (OOK) formats with any pulse shape and reduced duty cycle, allowing the increase of the peak-to-average optical power ratio (PAOPR) and, hence, a relevant improvement in error rate performance. Simulation results are further demonstrated to confirm the analytical results     

Performance analyses of subcarrier BPSK modulation over M turbulence channels with pointing errors

An aggregated channel model is achieved by fitting the Weibull distribution, which includes the effects of atmospheric attenuation, M distributed atmospheric turbulence and nonzero boresight pointing errors. With this approximate channel model, the bit error rate (BER) and the ergodic capacity of free-space optical (FSO) communication systems utilizing subcarrier binary phase-shift keying (BPSK) modulation are analyzed, respectively. A closed-form expression of BER is derived by using the generalized Gauss-Lagueree quadrature rule, and the bounds of ergodic capacity are discussed. Monte Carlo simulation is provided to confirm the validity of the BER expressions and the bounds of ergodic capacity.     

BER Performance of Free-Space Optical Transmission with Spatial Diversity

Free space optical (FSO) communications is a cost-effective and high bandwidth access technique, which has been receiving growing attention with recent commercialization successes. A major impairment in FSO links is the turbulence- induced fading which severely degrades the link performance. To mitigate turbulence-induced fading and, therefore, to improve the error rate performance, spatial diversity can be used over FSO links which involves the deployment of multiple laser transmitters/receivers. In this paper, we investigate the bit error rate (BER) performance of FSO links with spatial diversity over log- normal atmospheric turbulence fading channels, assuming both independent and correlated channels among transmitter/receiver apertures. Our analytical derivations build upon an approximation to the sum of correlated log-normal random variables. The derived BER expressions quantify the effect of spatial diversity and possible spatial correlations in a log-normal channel.     

Coding and signal space diversity for a class of fading and impulsive noise channels

The transmission over the Gaussian mixture noise channel with perfect channel state information at the receiver side is considered. Lower and upper bounds on the achievable pairwise error probability (PEP) are derived for finite and infinite codeword lengths. It is shown that diversity codes, i.e., unitary transforms, can be applied to achieve a diversity gain. A large class of diversity codes is determined for which-if the codeword length is increased-the PEP between any two codewords approaches either zero or the lower bound on the PEP.     

Enhancing spectral efficiency of FSO system using adaptive SIM/M‐PSK and SIMO in the presence of atmospheric turbulence and pointing errors

This paper proposes an adaptive transmission modulation (ATM) technique for free‐space optical (FSO) links over gamma‐gamma turbulence channels.The ATM technique provides efficient utilization of the FSO channel capacity for improving spectral efficiency, by adapting the order of the phase‐shift keying modulation scheme, according to the channel conditions and the required bit error rate (BER). To overcome the channel degradation resulting from the turbulence effects as well as the pointing errors (PEs), single‐input multiple‐output (SIMO) system with maximal ratio combining (MRC) is proposed. Exact closed‐form expressions of BER and upper bound of the capacity are derived and verified by Monte Carlo simulations. The numerical results show that the proposed adaptive technique improves the spectral efficiency (SE) five times higher than the nonadaptive technique at the same BER threshold (10^?3).This improvement is achieved at signal‐to‐noise ratio (SNR) equals 27 and 42  dB in the case of atmospheric turbulence without and with PE, respectively. Furthermore, this SE could be obtained while the SNR = 30  dB by using ( 1 × 4 ) SIMO scheme with MRC and PE and having the same transmitting optical power.     

Macrocell multiple-input multiple-output system analysis

We develop a semi-deterministic semi-stochastic channel model for the multiple-input multiple-output (MIMO) system under the macrocell environment with local-to-mobile and local-to-base scatterers. We show that employing closely-spaced antennas (e.g., phased array) at the base station is capable of achieving diversity via the local-to-base scatterers, which avoids impractical large aperture requirement for the spatial diversity at the base station. We evaluate the system performance in terms of ergodic capacity, average pairwise error probability (PEP), and signal-to-noise ratio (SNR); derive closed-form expressions for lower and upper bounds on the capacity and PEP; and show that the capacity, multiplexing and diversity gains are limited by the number of multipaths around the base station. The base-station array affects the lower bound on the capacity and the upper bound on the error probability through the same metric; thus, optimal design of the base station array based on this metric will optimize the two different information theoretic measures simultaneously. The fading correlation matrix also appears in the two bounds in the same form. To improve the performance of the macrocell MIMO system, we propose using artificial scatterers and discuss optimal design issues. Numerical examples demonstrate the accuracy of our analytical results and tightness of performance bounds.     

A cross-layer analysis of TCP/link adaptation technologies over free-space optical links with Markov error model

This paper presents a comprehensive cross-layer framework on the performance of transmission control protocol (TCP) over a free-space optical (FSO) link, which employs automatic repeat request (ARQ) and adaptive modulation and coding (AMC) schemes. Not similar to conventional works in the literature of FSO, we conduct a Markov error model to accurately capture effects of burst errors caused by atmospheric turbulence on cross-layer operations. From the framework, we quantify the impacts of different parameters/settings of ARQ, AMC, and the FSO link on TCP throughput performance. We also discuss several optimization aspects for TCP performance.     

On improved bounds on the decoding error probability of block codesover interleaved fading channels, with applications to turbo-like codes

We derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved Rician fading channels, coherently detected and maximum-likelihood (ML) decoded. We assume that the fading coefficients during each symbol are statistically independent (due to a perfect channel interleaver), and that perfect estimates of these fading coefficients are provided to the receiver. The improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity, and are found by generalizing some previously introduced upper bounds for the binary-input additive white Gaussian nose (AWGN) channel. The advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low-density parity-check (LDPC) codes, and it is especially pronounced in a portion of the rate region exceeding the cutoff rate. Our generalization of the Duman and Salehi bound (Duman and Salehi 1998, Duman 1998) which is based on certain variations of Gallager's (1965) bounding technique, is demonstrated to be the tightest reported upper bound. We therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo-like codes, referring to the optimal ML decoding. For certain ensembles of uniformly interleaved turbo codes, the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms