A One Bit Feedback Based Beamforming Scheme for FSO MISO System Over Gamma-Gamma Fading

In this paper, we study a beamforming scheme for multiple-input single-output (MISO) free space optical (FSO) system over Gamma-Gamma fading channels. The considered beamforming scheme requires feedback of only one information bit from the receiver about the channel state information. If the feedback bit is always received error free, then the beamforming technique reduces to best transmit aperture selection scheme. It is inferred by bit error rate (BER) analysis in a 2 × 1 FSO system over Gamma-Gamma fading links, that repetition coding is the best of all arbitrary beamforming schemes with non-zero transmit weights. Further, it is also analytically shown that the simple transmit aperture selection scheme (or one bit feedback based beamforming with error free feedback) has a coding gain advantage over repetition coding in 2 × 1 FSO system over Gamma-Gamma fading links. However, it is shown by analysis that the simple transmit aperture selection based beamforming scheme is very sensitive to errors in the feedback bit and loses diversity gain even for very small error in the feedback. Then we establish conditions under which a 2 × 1 FSO system, employing one bit based beamforming with erroneous feedback, achieves full diversity. A simplified asymptotic upperbound of BER of the proposed scheme is obtained by using the order statistics and an optimized beamforming vector is found by minimizing this upperbound. We also analyze the BER performance of a general FSO MISO system that employs equal partitioning of transmit apertures for beamforming, based on one bit feedback. It is shown by simulations that the proposed beamforming scheme

[1]  Siavash M. Alamouti,et al.  A simple transmit diversity technique for wireless communications , 1998, IEEE J. Sel. Areas Commun..

[2]  L. Andrews,et al.  Laser Beam Scintillation with Applications , 2001 .

[3]  Edward A. Lee,et al.  Digital communication (3. ed.) , 2003 .

[4]  Manav R. Bhatnagar,et al.  Differential Decoding of SIM DPSK over FSO MIMO Links , 2013, IEEE Communications Letters.

[5]  Victor Adamchik,et al.  The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system , 1990, ISSAC '90.

[6]  Yu. A. Brychkov,et al.  Integrals and series , 1992 .

[7]  Zabih Ghassemlooy,et al.  Fading correlation and analytical performance evaluation of the space-diversity free-space optical communications system , 2014 .

[8]  Julian Cheng,et al.  Subcarrier intensity modulated MIMO optical communications in atmospheric turbulence , 2013, IEEE/OSA Journal of Optical Communications and Networking.

[9]  Zabih Ghassemlooy,et al.  BPSK Subcarrier Intensity Modulated Free-Space Optical Communications in Atmospheric Turbulence , 2009, Journal of Lightwave Technology.

[10]  A. García-Zambrana,et al.  Asymptotic error-rate analysis of FSO links using transmit laser selection over gamma-gamma atmospheric turbulence channels with pointing errors. , 2012, Optics express.

[11]  Ali Mansour,et al.  Diversity techniques for a free-space optical communication system in correlated log-normal channels , 2014 .

[12]  Mohamed-Slim Alouini,et al.  Digital Communication over Fading Channels: Simon/Digital Communications 2e , 2004 .

[13]  A. Garcia-Zambrana,et al.  Selection Transmit Diversity for FSO Links Over Strong Atmospheric Turbulence Channels , 2009, IEEE Photonics Technology Letters.

[14]  Murat Uysal,et al.  Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels , 2006, IEEE Transactions on Wireless Communications.

[15]  Manav R. Bhatnagar,et al.  On the Performance of Alamouti Scheme in Gamma-Gamma Fading FSO Links With Pointing Errors , 2015, IEEE Wireless Communications Letters.

[16]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[17]  George K. Karagiannidis,et al.  Optical wireless links with spatial diversity over strong atmospheric turbulence channels , 2009, IEEE Transactions on Wireless Communications.

[18]  Hossein Samimi.  Performance analysis of free-space optical links with transmit laser selection diversity over strong turbulence channels , 2011, IET Commun..

[19]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[20]  Murat Uysal,et al.  Do We Really Need OSTBCs for Free-Space Optical Communication with Direct Detection? , 2008, IEEE Transactions on Wireless Communications.

[21]  Chadi Abou-Rjeily.  On the Optimality of the Selection Transmit Diversity for MIMO-FSO Links with Feedback , 2011, IEEE Communications Letters.

[22]  K. Peppas,et al.  Average Symbol Error Probability of General-Order Rectangular Quadrature Amplitude Modulation of Optical Wireless Communication Systems Over Atmospheric Turbulence Channels , 2010, IEEE/OSA Journal of Optical Communications and Networking.

[23]  Giwan Yoon,et al.  Average Bit-Error Rate of the Alamouti Scheme in Gamma-Gamma Fading Channels , 2011, IEEE Photonics Technology Letters.

[24]  Robert Schober,et al.  On space-time coding for free-space optical systems , 2010, IEEE Transactions on Communications.

[25]  Ranjan K. Mallik,et al.  Performance analysis of MIMO free-space optical systems in gamma-gamma fading , 2009, IEEE Transactions on Communications.

[26]  Albert Guillén i Fàbregas,et al.  Outage probability of the Gaussian MIMO free-space optical channel with PPM , 2009, IEEE Transactions on Communications.