空间分集自由空间光通信的误码率性能分析

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"这篇文章主要探讨了自由空间光学（Free-Space Optical, FSO）通信中采用空间分集技术来改善误码率（Bit Error Rate, BER）性能的问题。在FSO通信系统中，大气湍流会导致严重的信号衰落，从而降低链路性能。通过部署多个激光发射器/接收器实现空间分集，可以有效缓解这一问题，提高错误率性能。作者们分析了在对数正态大气湍流衰落信道中，FSO链接采用空间分集时的BER性能，考虑了发射器/接收器孔径之间独立和相关的通道情况。分析基于对相关对数正态随机变量求和的近似方法，得出的BER解析表达式对于理解和优化FSO通信系统的设计具有重要意义。" 在自由空间光学通信中，光信号在大气中传播时会受到各种因素的影响，特别是大气湍流。这种湍流会导致光束的折射指数随机变化，进而引起信号强度的快变衰落，严重影响通信质量。为了提高系统的稳定性和可靠性，空间分集技术被引入到FSO通信中。通过使用多个发射器和接收器，可以在不同的空间位置捕获信号，利用它们之间的相关性来抵消由于大气湍流引起的衰落。在该研究中，作者们分析了两种情况下的BER性能：一是发射器/接收器孔径之间的通道独立，即各接收端接收到的信号互不影响；二是通道相关，意味着不同接收端接收到的信号之间存在一定的关联性。通过对数正态模型来描述大气湍流的影响，他们推导出了一种近似计算相关对数正态随机变量之和的方法，以此来估算FSO链路的BER。这个近似方法有助于简化复杂的数学分析，使我们能够更好地理解在特定条件下，如何通过调整空间分集参数（如接收器的数量、间距等）来优化系统的BER性能。此外，这些结果对于设计和优化FSO通信系统，尤其是在恶劣的环境条件或长距离通信场景下，提供了重要的理论指导。 "BER Performance of Free-Space Optical Transmission with Spatial Diversity" 这篇文章深入探讨了FSO通信中的关键挑战——大气湍流导致的信号衰落，并提出了解决方案，即利用空间分集技术提高通信的可靠性。通过精确的数学模型和分析，文章为实际应用中的系统设计提供了宝贵的参考。

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 8, AUGUST 2007 2813

BER Performance of Free-Space Optical Transmission with

Spatial Diversity

S. Mohammad Navidpour, Member, IEEE, Murat Uysal, Member, IEEE, and Mohsen Kavehrad, Fellow, IEEE

Abstract— 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 transmit-

ters/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 approxima-

tion to the sum of corr elated log-normal random variables. The

derived BER expressions quantify the effect of spatial diversity

and possible spatial correlations in a log-normal channel.

Index Terms— Atmospheric turbulence, bit error rate, error

rate performance analysis, free space optical communication, log-

normal channel, MIMO.

I. INTRODUCTION

REE-SPACE optical (FSO) communications is a cost-

effective, license-free, and high b andwidth access tech-

nique, which has attracted signiﬁcant attention recently for a

variety of applications [1]-[4]. Despite the major advantages

of FSO communications, its widespread use is hampered

by several challenges in practical deployment. For example,

aerosol scattering caused by rain, snow, and fog results in

performance degradations, leaving the FSO link vulnerable to

adverse weather conditions [5]. Another possible impairment

over FSO links is building-sway as a result of wind loads,

thermal expansion, and weak earthquakes [6], [7]. A major

impairment is the effect of atmospheric turbulence [8], which

will be the focus of this paper. Atmospheric turbulence occurs

as a result of the variations in the refractive index due to

inhomogeneties in temperature and pressure changes. This

results in rapid ﬂuctuations at the received signal, i.e., signal

fading, impairing the link performance severely. Although

Manuscript received February 11, 2006; revised September 15, 2006

and January 26, 2007; accepted January 28, 2007. The associate editor

coordinating the review of this letter and approving it for publication was X.

Wang. This paper was presented in part at IEEE VTC’04-Fall, Los Angeles,

California, USA, September 2004. The work of S. M. Navidpour and M.

Kav e hrad is supported in part by a DARPA Grant sponsored by the U.S.

Air Force Research Laboratory/Wright-Patterson AFB Contract-FA8650-04-

C-7114 and The Pennsylvania State University CICTR. The work of M. Uysal

is supported in part by an NSERC Special Opportunity Grant (SROPJ305821-

05).

S. M. Navidpour and M. Kavehrad are with the Department of Electrical

Engineering, Pennsylvania State University, University Park, PA 16802 USA

(e-mail: navidpour@psu.edu, mkavehrad@psu.edu).

M. Uysal is with the Department of Electrical and Computer Engineer-

ing, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 (e-mail:

muysal@ece.uwaterloo.ca).

Digital Object Identiﬁer 10.1109/TWC.2007.06109.

FSO links are built taking into account a certain dynamic

margin, the practical limitations on link budgets do not allow

very high margins leaving the link vulnerable to deep fades.

Powerful fading-mitigation techniques need to be deployed

for FSO links particularly with transmission range of 1 km or

longer. Error control coding in conjunction with interleaving

can be employed in FSO communications to combat fading

[9], [10]. However, optical links with their transmission rates

of order of gigabits exhibit high temporal correlation. For

most scenarios, this requires large-size interleavers to achieve

the promised coding gains. Based on the statistical properties

of turbulence-induced fading, maximum likelihood sequence

detection (MLSD) is proposed in [11] as another solution

for fading mitigation. However, MLSD requires comp licated

multidimensional integr ations and suffers from excessive com -

putational complexity. Some sub-optimal temporal-domain

fading mitigation techniques are further explored in [11 ], [12].

Spatial diversity techniques

[13], i.e., the employment

of multiple transmit/receive apertures, provide an attractive

alternative approach for fading compensation with their inher-

ent redundancy. Besides its role as a fading-mitigation tool,

multiple-aperture designs signiﬁcantly reduce the potential for

temporary blockage of the laser beam by obstructions (e.g.,

birds). Further justiﬁcation for the employment of multiple

apertures comes from limitations in transmit power d ensity

(expressed in ter ms of m illiwatts per square centimeter). The

allowable safe laser power depends on the wavelength and ob-

viously a higher power at the receiver side allows the system to

support longer distances and through heavier attenuation while

achieving higher data rates. Information theoretic bounds for

MIMO FSO links have been ﬁrst studied in [14], where

ergodic capacity and outage capacity are derived for intensity-

modulation/direct-detection (IM/DD) FSO links operating in

log-normal modeled atmospheric turbulence. Under the as-

sumption of shot-noise-limited regime with Poisson statistics,

it is demonstrated that ergodic capacity scales as the number

of transmit apertures times the number of receive apertures

for high signal-to-background noise ratio. Outage probability

for MIMO FSO links are d erived in [15] assuming Gaussian

noise statistics that can be considered as a limiting case of

Poisson statistics. We should also note an earlier experimental

study in [16] where Kim et.al. measure the performance of

a MIMO FSO link and discuss practical design issues such

as transm itter spacing an d spacing patterns, e.g., circular vs.

rectangular.

This paper does not consider space-time coding or multiplexing tech-

niques. In the following, MIMO (multi-input multi-output) term is sometimes

used to refer to the deployment of multiple-transmit and multiple-recei ve

apertures.

1536-1276/07$25.00

 2007 IEEE

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