Bourennane, Salah

Ghassemlooy, Zabih

Khalighi, Mohammad-Ali

Virieux, Thomas

Yang, Guowei

English

Northumbria Research Link

Citation:  Yang,  Guowei,  Khalighi,  M.  A.,  Virieux,  Thomas,  Bourennane  ,  Salah  and  Ghassemlooy,  Zabih  (2012)  Contrasting  space-time  schemes for  MIMO  FSO systems with  non-coherent  modulation.  In:  IWOW  2012:  Workshop  on  Optical  Wireless Communications, 22 October 2012, Pisa, Italy.Published by: UNSPECIFIEDURL: This  version  was  downloaded  from  Northumbria  Research  Link:  http://nrl.northumbria.ac.uk/10093/Northumbria  University  has  developed Northumbria  Research  Link  (NRL)  to  enable users to access the University’s research output.  Copyright  © and moral  rights  for  items on NRL  are retained by the individual  author(s) and/or other  copyright  owners.  Single  copies of full  items can be reproduced, displayed or performed, and given to third  parties  in  any  format  or  medium  for  personal  research or  study,  educational,  or  not-for-profit  purposes without  prior  permission  or  charge,  provided  the  authors,  tit le  and  full  bibliographic  details  are  given,  as  well  as  a  hyperlink  and/or  URL  to  the  original  metadata  page. The content  must  not  be changed in  any way.  Full  items must  not  be sold commercially  in  any format  or medium  without  formal  permission of the copyright  holder.  The full  policy is available online: http://nrl.northumbria.ac.uk/policies.htmlThis document  may differ  from the final,  published version of the research and has been made available online in  accordance with  publisher  policies. To read and/or cite from the  published  version  of the  research,  please visit  the  publisher’s  website  (a subscription  may be required.)Contrasting Space-Time Schemes for MIMOFSO Systems with Non-Coherent ModulationGuowei Yang, Mohammad-Ali Khalighi,Thomas Virieux, Salah BourennaneInstitut Fresnel, UMR CNRS 7249,E´cole Centrale Marseille, Marseille, FranceZabih GhassemlooyOptical Communications Research GroupNorthumbria University, Newcastle Upon Tyne, UKAbstract—For the case of multiple-input multiple-output(MIMO) free-space optical (FSO) communication systems,we consider the suitability of the spatial multiplexing schemewhen on-off keying modulation is employed. We show that,even with the optimal maximum likelihood detection atthe receiver, the performance is worse, compared to thecase of repetition coding (RC) under the condition of equaltransmission rate. This confirms the quasi-optimality of theRC scheme for MIMO FSO systems.I. INTRODUCTIONFree-space optical (FSO) communication is well knownfor its advantages of license-free spectrum, high data-rate,low energy consumption, and inherent security, comparedto radio frequency (RF) systems [1]. In near-groundFSO systems, one of the principal channel impairmentsis the atmospheric turbulence which induces intensityfluctuations at the receiver that can considerably degradethe system performance [2]. One solution for fading miti-gation is aperture averaging [3]. However, when workingat long link distances, the required collecting lens for effi-cient fading reduction becomes too large [4]. Under suchconditions, spatial diversity is a more suitable solution [5].In particular, significant fading reduction can be obtainedthrough the use of multiple apertures at the receiverand multiple beams at the transmitter [6], [7]. For thesemultiple-input multiple-output (MIMO) systems, one im-portant question is how to combine the information-bearing symbols at the transmitter in order to optimize thesystem performance, what is classically called space-time(ST) coding. This is an extensively-developed subject inRF systems. Here, we focus on the spatial multiplexing(SMux) scheme, where the information bearing signalsare just multiplexed at the transmitter. The interest ofSMux is that it has the maximum transmission rate. Ouraim is to investigate the practical interest of this schemeby taking into account the receiver performance and itscomputational complexity.In the remainder of the paper, we first present a state-of-the-art on ST coding in MIMO FSO systems and explainthe idea behind this work. General assumptions on thechannel model and signal transmission are then describedin Section III. Then, we present some numerical resultson the performance comparison of different ST schemesin Section IV. Finally, Section V concludes the paper.II. SPACE-TIME CODING FOR MIMO FSO SYSTEMSIn fact, most of the proposed ST schemes for RFapplications use phase rotation and amplitude weighting[8], [9], [10], requiring at least bipolar signaling whenapplied to the FSO context. In general, the ST schemesoptimized for RF systems provide full diversity in FSOsystems but are not optimized concerning the codinggain [11]. ST schemes can be classified into orthogonaland non-orthogonal schemes. Orthogonal schemes, whichusually provide full diversity, have received more atten-tion because of their low-complexity optimal detection[9]. Non-orthogonal schemes are generally designed tooptimize both diversity and coding gains and have mostlya better performance than their orthogonal counterparts[12]. They have also shown to be more robust againstchannel turbulence when using coherent modulations [13].However, their optimal detection is of high computationalcomplexity. Also, they can not be used in the FSO systemsusing intensity modulation with direct detection (IM/DD).In classical MIMO FSO systems, one does not do anyST coding at the transmitter and the same symbol is sentover the multiple beams. This is usually referred to asrepetition coding (RC) [14]. On the other hand, most ofthe orthogonal ST block codes (OSTBCs) can be modifiedto be adapted to IM/DD FSO systems. For instance, forthe case of two transmitter beams, a modified Alamoutischeme [15] is proposed in [16] which is adapted toIM/DD optical systems by introducing a bias to overcomeunipolar signaling used in these systems. This idea is thengeneralized in [17] to ON-OFF keying (OOK) modulationwith any pulse shape. In fact, Both RC and OSTBCsprovide full diversity but RC is shown to outperform thelatter, and the performance gap increases with increasednumber of transmitter beams [18].In fact, RC seems to be quasi-optimum, as explainedin [11]. However, it is of rate one and does not exploitthe MIMO channel to increase the transmission rate. Onthe contrary, SMux maximizes the transmission rate but atthe expense of reduced diversity gain. Recently, a new STscheme, called optical spatial modulation (OSM) has beenproposed by which only one ON symbol is transmittedfrom the M beams at a given channel use [19], [20]so as to avoid inter-channel interference. The ST codingrate of OSM is log2M symbols per channel-use. At thereceiver, optimal maximum likelihood detection (MLD)can be used to estimate the corresponding beam [21].Here, we are specially interested to investigate theusefulness of SMux in FSO systems. We know fromprevious works on RF MIMO systems that the simplelinear detection methods like the minimum mean-square-error (MMSE) detection do not provide a satisfyingperformance. An interesting linear and low-complexityreceiver is the vertical BLAST (V-BLAST) architecture[22]. This method uses successive interference cancelationand signal detection based on zero-forcing (ZF) or MMSEcriterion and has been shown to have a significantly betterperformance than the simple ZF or MMSE detectors.It is not clear whether or not for OOK modulationthis method preserves its interest, however. Also, it isknown that forM transmitters andN receivers, V-BLASTdetection can benefit from a diversity of N − M + 1[23], and consequently, it is practically interesting onlywhen N > M . This is not usually the case in most FSOsystems, however, as we have M = N in most systems.To partially circumvent this problem, it is proposed in[24] for M > 2 to consider pairwise Alamouti codedtransmitted symbols and to perform QR decompositionof the fading channel at the receiver.Our aim is to consider the SMux and OSM schemes atthe transmitter and to compare their performance with RCand OSTBC. In order to make a fair comparison, we fixthe total data transmission rate for all cases. For this, wereduce the symbol duration for RC, OSTBC, and OSMschemes accordingly. For the case of SMux, we considerdifferent detection methods including the optimal MLDto investigate the receiver performance, regardless of thecomputational complexity issues.III. CHANNEL MODEL AND ASSUMPTIONSWe consider the use of a Gaussian beam at the trans-mitter and a PIN photodiode at the receiver and assumethat the dominant receiver noise is the thermal noise. Thisis modeled as additive white Gaussian with the unilateralpower spectral density N0. We consider a single-beamsingle-aperture system of aperture diameter 200mm asreference and denote its receiver noise variance by σ2n.We denote this system by SISO (for single-input single-output). When using multiple apertures, the noise varianceis considered the same at each receiver whatever its aper-ture size is. For channel turbulence modeling, we considerthe Gamma-Gamma distribution by which the normalizedreceived intensity is considered as the product of twoindependent random variables, representing the large- andsmall-scale irradiance fluctuations, respectively [25]. For(M ×N) MIMO structure, we assume that the spacingsbetween the transmitter beams and the receiver aperturesare large enough so as to ensure independent fadingbetween the underlying sub-channels. Also, we assumewe have perfect channel knowledge at the receiver.We consider a diverging Gaussian beam at λ =1550 nm of beam waist W0 = 1.59 cm and the curvatureradius of the phase front of F0 = −69.9m. Concerningthe channel turbulence, we set C2n = 6.5× 10−14m−2/3and the inner and outer scales of turbulence of l0 =6.1mm and L0 = 1.3m. These parameters correspond tothe experimental works reported in [3]. The link distanceis given as L = 5 km for which the Rytov varianceσ2R = 24.7. We use the uncoded OOK modulation andfix the total receiver aperture diameter to Dr = 200mm.To make a fair comparison between the performancesof different ST schemes, we fix the average transmitoptical power Pav . Considering OOK modulation, thiscorresponds to a peak optical intensity of Pt = 2Pavin On slots for the reference SISO system, for example.For the case of MIMO systems, the peak intensity ateach transmitter is set to Pt/M , except for OSM whereit is set to Pt/(log2M). Also, we set the diameter ofeach aperture to Dr/√N so as to fix the total receivedintensity. Furthermore, we fix the transmission rate for thedifferent systems and denote it by Rb. Accordingly, forthe MIMO case, we set the pulse duration to 1/Rb for thecases of RC and OSTBC, and toM/Rb and (log2M)/Rbfor the SMux and OSM cases, respectively.IV. NUMERICAL RESULTSHere we present some simulation results to comparethe performances of the different ST schemes. The per-formance is considered as the bit-error-rate (BER) versusthe electrical signal-to-noise ratio (SNR) in the formof Eb/N0, with Eb being the average total receivedenergy per information bit. We have Eb = P2t /2Rb,N0 = 2σ2n/Rb. For signal detection at the receiver, weconsider MLD for all schemes, as well as simple MMSEand MMSE V-BLAST for SMux. We also present theBER performance for the reference SISO system for thesake of completeness. We consider two case studies ofM = N = 2 and M = N = 4 in the following.A. Case of (2 × 2) FSO systemThe performance of RC, OSTBC, OSM, and SMuxschemes are compared in Fig. 1. As OSTBC, we considerthe modified Alamouti scheme, proposed in [16]. Wenotice that the RC scheme remains the best. For instance,at BER= 10−4, MMSE V-BLAST detection provides 7 dBgain in SNR, compared to simple MMSE. However,the MMSE V-BLAST performs 30 dB worse than theoptimal MLD detection. We notice that the performancesof OSM and SMux with MLD are very close. On theother hand, the rate-one schemes, i.e., RC and OSTBC,perform much better than OSM and SMux with MLDdetection. Remember that for these schemes, we use halfthe symbol duration of the SMux case so as to have thesame total transmission rate. In fact, although dividing thesymbol duration results in an increase of factor 2 in thereceiver thermal noise variance, compared to the SMuxcase, the overall performance is still better than this lattercase. Another interesting point is that RC and OSTBCoutperform the reference SISO system only at low BER.This is due to the trade-off between aperture averagingand spatial diversity and also the increased total receivernoise in MIMO systems.B. Case of (4 × 4) FSO systemFigure 2 contrasts the performances of RC, OSTBC,OSM, and SMux schemes. As OSTBC, we consider theJafarkhani’s scheme [26] that we modify in the same wayas it is done in [16] to adapt it to OOK modulation.Note that this scheme is orthogonal for this case. Wenotice again that RC is preferred to OSTBC and OSM,−20 0 20 40 60 80 10010−610−510−410−310−210−1100Eb/N0 (dB)BER(1×1)(2×2), RC & MLD(2×2), OSTBC & MLD(2×2), OSM & MLD(2×2), SMux & MMSE(2×2), SMux & V−BLAST(2×2), SMux & MLDFig. 1. Contrasting BER performance of different ST schemes for a(2×2) MIMO FSO system. Z = 5Km, D = 200mm. Uncoded OOK,thermal noise limited receiver.−20 0 20 40 60 80 10010−610−510−410−310−210−1100Eb/N0 (dB)BER(1×1)(4×4), RC & MLD(4×4), OSTBC & MLD(4×4), OSM & MLD(4×4), SMux & MMSE(4×4), SMux & V−BLAST(4×4), SMux & MLDFig. 2. Contrasting BER performance of different ST schemes for a(4×4) MIMO FSO system. Z = 5Km, D = 200mm. Uncoded OOK,thermal noise limited receiver.and also to SMux even with MLD. Note that OSM hereoutperforms SMux-MLD.V. CONCLUSIONWe investigated the interest of SMux in MIMO FSOsystems and compared its performance to those of RC,OSTBC, and OSM. Our study confirmed the quasi-optimality of the full-diversity RC scheme due to its lowercomplexity and better performance, compared to the otherST schemes. We conclude from our study that when ahigher data rate is required, it is preferable to directlyreduce the symbol duration instead of resorting to a higherrate ST scheme like SMux.REFERENCES[1] V. W. S. Chan, “Free-space optical communications,” Journal ofLightwave Technology, vol. 24, no. 12, pp. 4750–4762, Dec. 2006.[2] Z. Ghassemlooy and W. O. Popoola, Mobile and WirelessCommunications Network Layer and Circuit Level Design, chapterTerrestrial Free-Space Optical Communications, InTech, Jan.2010.[3] F. S. Vetelino, C. Young, L. C. Andrews, and J. Recolons,“Aperture averaging effects on the probability density of irradiancefluctuations in moderate-to-strong turbulence,” Applied Optics, vol.46, no. 11, pp. 2099–2108, Apr. 2007.[4] M. A. Khalighi, N. Schwartz, N. Aitamer, and S. Bourennane,“Fading reduction by aperture averaging and spatial diversity inoptical wireless systems,” IEEE/OSA Journal of Optical Commu-nications and Networking, vol. 1, no. 6, pp. 580–593, Nov. 2009.[5] G. Yang, M. A. Khalighi, and S. Bourennane, “Performance ofreceive diversity FSO systems under realistic beam propagationconditions,” CSNDSP Symposium, 2012, Poznan, Poland, acceptedfor publication.[6] S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke,“Optical repetition MIMO transmission with multipulse PPM,”IEEE on Selected Areas in Communications, vol. 23, no. 9, pp.1901– 1910, Sept. 2005.[7] N. Cvijetic, S. G. Wilson, and M. Brandt-Pearce, “Performancebounds for free-space optical MIMO systems with APD receiversin atmospheric turbulence,” IEEE Journal on Selected Areas inCommunications, vol. 26, no. 3, pp. 3–12, Apr. 2008.[8] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codesfor high data rate wireless communication: Performance analysisand code construction,” IEEE Transactions on Information Theory,vol. 44, no. 2, pp. 744–765, Mar. 1998.[9] V. Tarokh, H. J. Jafarkhani, and A. R. Calderbank, “Space-timeblock codes from orthogonal designs,” IEEE Transactions onInformation Theory, vol. 45, no. 5, pp. 1456–1467, July 1999.[10] B. Vucetic and J. Yuan, Space-Time Coding, John Wiley & SonsLtd, Chichester, England, 2003.[11] E. Bayaki and R. Schober, “On space-time coding for free-spaceoptical systems,” IEEE Transactions on Communications, vol. 58,no. 1, pp. 58–62, Jan. 2010.[12] S. M. Aghajanzadeh and M. Uysal, “Diversity-multiplexing trade-off in coherent free-space optical systems with multiple receivers,”IEEE/OSA Journal of Optical Communications and Networking,vol. 2, no. 12, pp. 1087–1094, Dec. 2010.[13] S. M. Haas, J. H. Shapiro, and V. Tarokh, “Space-time codes forwireless optical communications,” EURASIP Journal on AppliedSignal Processing, vol. 3, pp. 211220, Mar. 2002.[14] S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque,“Free-space optical MIMO transmission with Q-ary PPM,” IEEETransactions on Communications, vol. 53, no. 8, pp. 1402–1412,Aug. 2005.[15] S.M. Alamouti, “A simple transmit diversity technique for wirelesscommunications,” IEEE Journal on Selected Areas in Communi-cations, vol. 16, no. 8, pp. 14511458, Oct 1998.[16] M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time cod-ing for free-space optical communication with direct detection,”IEEE Transactions on Wireless Communications, vol. 4, no. 1, pp.35–39, Jan. 2005.[17] A. Garcia-Zambrana, “Error rate performance for STBC infree-space optical communications through strong atmosphericturbulence,” IEEE Communications Letters, vol. 11, no. 5, pp.390–392, May 2007.[18] M. Safari and M. Uysal, “Do we really need OSTBCs forfree-space optical communication with direct detection?,” IEEETransactions on Wireless Communications, vol. 7, no. 11, pp.4445–4448, Nov. 2008.[19] R. Mesleh, H. Elgala, and H. Haas, “Optical spatial modulation,”IEEE/OSA Journal of Optical Communications and Networking,vol. 3, no. 3, pp. 234–244, Mar. 2011.[20] M. D. Renzo, H. Haas, and P. M. Grant, “Spatial modulation formultiple-antenna wireless systems: A survey,” IEEE Communica-tions Magazine, vol. 49, no. 12, pp. 182–191, Dec. 2011.[21] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Spatial mod-ulation: optimal detection and performance analysis,” IEEECommunications Letters, vol. 12, no. 8, pp. 545–547, 2008.[22] G. D. Golden, G. J. Foschini, R. A. Valenzuela, and P. W. Wol-niansky, “Detection algorithm and initial laboratory results usingthe V-BLAST space-time communication architecture,” ElectronicLetters, vol. 35, no. 1, pp. 1415, 1999.[23] A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bolcskei, “Anoverview of MIMO communications: a key to gigabit wireless,”Proceedings of the IEEE, vol. 92, no. 2, pp. 198218, Feb. 2004.[24] M. Arar and A. Yongacoglu, “Efficient detection algorithm for2n×2n MIMO systems using alamouti code and QR decomposi-tion,” IEEE Communications Letters, vol. 10, no. 12, pp. 819–821,Dec. 2006.[25] L. C. Andrews and R. L. Phillips, Laser Beam PropagationThrough Random Media, SPIE Press, second edition, 2005.[26] H. Jafarkhani, “A quasi-orthogonal space-time block code,” IEEETrans. on Communications, vol. 49, no. 1, pp. 1–4, Jan. 2001.

A quasi-orthogonal space-time block code,”

A simple transmit diversity technique for wireless communications,”

Alamouti-type space-time coding for free-space optical communication with direct detection,”

An overview of MIMO communications: a key to gigabit wireless,”

Aperture averaging effects on the probability density of irradiance ﬂuctuations in moderate-to-strong turbulence,”

Detection algorithm and initial laboratory results using the V-BLAST space-time communication architecture,”

Diversity-multiplexing tradeoff in coherent free-space optical systems with multiple receivers,”

Do we really need OSTBCs for free-space optical communication with direct detection?,”

Efﬁcient detection algorithm for 2n×2n MIMO systems using alamouti code and QR decomposition,”

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

Fading reduction by aperture averaging and spatial diversity in optical wireless systems,”

Free-space optical communications,”

Free-space optical MIMO transmission with Q-ary PPM,”

Laser Beam Propagation Through Random Media,

On space-time coding for free-space optical systems,”

Optical repetition MIMO transmission with multipulse PPM,”

Optical spatial modulation,”

Performance bounds for free-space optical MIMO systems with APD receivers in atmospheric turbulence,”

Performance of receive diversity FSO systems under realistic beam propagation conditions,” CSNDSP Symposium,

Space-time block codes from orthogonal designs,”

Space-time codes for high data rate wireless communication: Performance analysis and code construction,”

Space-time codes for wireless optical communications,”

Space-Time Coding,

Spatial modulation for multiple-antenna wireless systems: A survey,”

Spatial modulation: optimal detection and performance analysis,”

Contrasting space-time schemes for MIMO FSO systems with non-coherent modulation

HAL AMU

Contrasting Space-Time Schemes for MIMO FSO Systems with Non-Coherent Modulation

Northumbria Research Link
Citation:  Yang,  Guowei,  Khalighi,  Mohammad-Ali,  Virieux,  Thomas,  Bourennane,  Salah  and 
Ghassemlooy,  Zabih  (2012)  Contrasting  space-time  schemes  for  MIMO  FSO systems  with  non-
coherent modulation. In: IWOW 2012: Workshop on Optical Wireless Communications, 22 October 
2012, Pisa, Italy. 
URL: 
This version was downloaded from Northumbria Research Link: http://nrl.northumbria.ac.uk/10093/
Northumbria University has developed Northumbria Research Link (NRL) to enable users to access 
the University’s research output. Copyright © and moral rights for items on NRL are retained by the 
individual author(s) and/or other copyright owners.  Single copies of full items can be reproduced, 
displayed or performed, and given to third parties in any format or medium for personal research or 
study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, 
title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata 
page. The content must not be changed in any way. Full items must not be sold commercially in any  
format or medium without formal permission of the copyright holder.  The full policy is available online: 
http://nrl.northumbria.ac.uk/pol  i cies.html  
This  document  may differ  from the  final,  published version of  the research  and has been made 
available online in accordance with publisher policies. To read and/or cite from the published version 
of the research, please visit the publisher’s website (a subscription may be required.)
                        
Contrasting Space-Time Schemes for MIMO
FSO Systems with Non-Coherent Modulation
Guowei Yang, Mohammad-Ali Khalighi,
Thomas Virieux, Salah Bourennane
Institut Fresnel, UMR CNRS 7249,
École Centrale Marseille, Marseille, France
Zabih Ghassemlooy
Optical Communications Research Group
Northumbria University, Newcastle Upon Tyne, UK
Abstract—For the case of multiple-input multiple-output
(MIMO) free-space optical (FSO) communication systems,
we consider the suitability of the spatial multiplexing scheme
when on-off keying modulation is employed. We show that,
even with the optimal maximum likelihood detection at
the receiver, the performance is worse, compared to the
case of repetition coding (RC) under the condition of equal
transmission rate. This confirms the quasi-optimality of the
RC scheme for MIMO FSO systems.
I. INTRODUCTION
Free-space optical (FSO) communication is well known
for its advantages of license-free spectrum, high data-rate,
low energy consumption, and inherent security, compared
to radio frequency (RF) systems [1]. In near-ground
FSO systems, one of the principal channel impairments
is the atmospheric turbulence which induces intensity
fluctuations at the receiver that can considerably degrade
the system performance [2]. One solution for fading miti-
gation is aperture averaging [3]. However, when working
at long link distances, the required collecting lens for effi-
cient fading reduction becomes too large [4]. Under such
conditions, spatial diversity is a more suitable solution [5].
In particular, significant fading reduction can be obtained
through the use of multiple apertures at the receiver
and multiple beams at the transmitter [6], [7]. For these
multiple-input multiple-output (MIMO) systems, one im-
portant question is how to combine the information-
bearing symbols at the transmitter in order to optimize the
system performance, what is classically called space-time
(ST) coding. This is an extensively-developed subject in
RF systems. Here, we focus on the spatial multiplexing
(SMux) scheme, where the information bearing signals
are just multiplexed at the transmitter. The interest of
SMux is that it has the maximum transmission rate. Our
aim is to investigate the practical interest of this scheme
by taking into account the receiver performance and its
computational complexity.
In the remainder of the paper, we first present a state-of-
the-art on ST coding in MIMO FSO systems and explain
the idea behind this work. General assumptions on the
channel model and signal transmission are then described
in Section III. Then, we present some numerical results
on the performance comparison of different ST schemes
in Section IV. Finally, Section V concludes the paper.
II. SPACE-TIME CODING FOR MIMO FSO SYSTEMS
In fact, most of the proposed ST schemes for RF
applications use phase rotation and amplitude weighting
[8], [9], [10], requiring at least bipolar signaling when
applied to the FSO context. In general, the ST schemes
optimized for RF systems provide full diversity in FSO
systems but are not optimized concerning the coding
gain [11]. ST schemes can be classified into orthogonal
and non-orthogonal schemes. Orthogonal schemes, which
usually provide full diversity, have received more atten-
tion because of their low-complexity optimal detection
[9]. Non-orthogonal schemes are generally designed to
optimize both diversity and coding gains and have mostly
a better performance than their orthogonal counterparts
[12]. They have also shown to be more robust against
channel turbulence when using coherent modulations [13].
However, their optimal detection is of high computational
complexity. Also, they can not be used in the FSO systems
using intensity modulation with direct detection (IM/DD).
In classical MIMO FSO systems, one does not do any
ST coding at the transmitter and the same symbol is sent
over the multiple beams. This is usually referred to as
repetition coding (RC) [14]. On the other hand, most of
the orthogonal ST block codes (OSTBCs) can be modified
to be adapted to IM/DD FSO systems. For instance, for
the case of two transmitter beams, a modified Alamouti
scheme [15] is proposed in [16] which is adapted to
IM/DD optical systems by introducing a bias to overcome
unipolar signaling used in these systems. This idea is then
generalized in [17] to ON-OFF keying (OOK) modulation
with any pulse shape. In fact, Both RC and OSTBCs
provide full diversity but RC is shown to outperform the
latter, and the performance gap increases with increased
number of transmitter beams [18].
In fact, RC seems to be quasi-optimum, as explained
in [11]. However, it is of rate one and does not exploit
the MIMO channel to increase the transmission rate. On
the contrary, SMux maximizes the transmission rate but at
the expense of reduced diversity gain. Recently, a new ST
scheme, called optical spatial modulation (OSM) has been
proposed by which only one ON symbol is transmitted
from the M beams at a given channel use [19], [20]
so as to avoid inter-channel interference. The ST coding
rate of OSM is log2 M symbols per channel-use. At the
receiver, optimal maximum likelihood detection (MLD)
can be used to estimate the corresponding beam [21].
Here, we are specially interested to investigate the
usefulness of SMux in FSO systems. We know from
previous works on RF MIMO systems that the simple
linear detection methods like the minimum mean-square-
error (MMSE) detection do not provide a satisfying
performance. An interesting linear and low-complexity
receiver is the vertical BLAST (V-BLAST) architecture
[22]. This method uses successive interference cancelation
and signal detection based on zero-forcing (ZF) or MMSE
criterion and has been shown to have a significantly better
performance than the simple ZF or MMSE detectors.
It is not clear whether or not for OOK modulation
this method preserves its interest, however. Also, it is
known that forM transmitters andN receivers, V-BLAST
detection can benefit from a diversity of N − M + 1
[23], and consequently, it is practically interesting only
when N > M . This is not usually the case in most FSO
systems, however, as we have M = N in most systems.
To partially circumvent this problem, it is proposed in
[24] for M > 2 to consider pairwise Alamouti coded
transmitted symbols and to perform QR decomposition
of the fading channel at the receiver.
Our aim is to consider the SMux and OSM schemes at
the transmitter and to compare their performance with RC
and OSTBC. In order to make a fair comparison, we fix
the total data transmission rate for all cases. For this, we
reduce the symbol duration for RC, OSTBC, and OSM
schemes accordingly. For the case of SMux, we consider
different detection methods including the optimal MLD
to investigate the receiver performance, regardless of the
computational complexity issues.
III. CHANNEL MODEL AND ASSUMPTIONS
We consider the use of a Gaussian beam at the trans-
mitter and a PIN photodiode at the receiver and assume
that the dominant receiver noise is the thermal noise. This
is modeled as additive white Gaussian with the unilateral
power spectral density N0. We consider a single-beam
single-aperture system of aperture diameter 200mm as
reference and denote its receiver noise variance by σ2n.
We denote this system by SISO (for single-input single-
output). When using multiple apertures, the noise variance
is considered the same at each receiver whatever its aper-
ture size is. For channel turbulence modeling, we consider
the Gamma-Gamma distribution by which the normalized
received intensity is considered as the product of two
independent random variables, representing the large- and
small-scale irradiance fluctuations, respectively [25]. For
(M ×N) MIMO structure, we assume that the spacings
between the transmitter beams and the receiver apertures
are large enough so as to ensure independent fading
between the underlying sub-channels. Also, we assume
we have perfect channel knowledge at the receiver.
We consider a diverging Gaussian beam at λ =
1550 nm of beam waist W0 = 1.59 cm and the curvature
radius of the phase front of F0 = −69.9m. Concerning
the channel turbulence, we set C2n = 6.5× 10
−14m−2/3
and the inner and outer scales of turbulence of l0 =
6.1mm and L0 = 1.3m. These parameters correspond to
the experimental works reported in [3]. The link distance
is given as L = 5 km for which the Rytov variance
σ2R = 24.7. We use the uncoded OOK modulation and
fix the total receiver aperture diameter to Dr = 200mm.
To make a fair comparison between the performances
of different ST schemes, we fix the average transmit
optical power Pav . Considering OOK modulation, this
corresponds to a peak optical intensity of Pt = 2Pav
in On slots for the reference SISO system, for example.
For the case of MIMO systems, the peak intensity at
each transmitter is set to Pt/M , except for OSM where
it is set to Pt/(log2 M). Also, we set the diameter of
each aperture to Dr/
√
N so as to fix the total received
intensity. Furthermore, we fix the transmission rate for the
different systems and denote it by Rb. Accordingly, for
the MIMO case, we set the pulse duration to 1/Rb for the
cases of RC and OSTBC, and toM/Rb and (log2 M)/Rb
for the SMux and OSM cases, respectively.
IV. NUMERICAL RESULTS
Here we present some simulation results to compare
the performances of the different ST schemes. The per-
formance is considered as the bit-error-rate (BER) versus
the electrical signal-to-noise ratio (SNR) in the form
of Eb/N0, with Eb being the average total received
energy per information bit. We have Eb = P
2
t /2Rb,
N0 = 2σ
2
n/Rb. For signal detection at the receiver, we
consider MLD for all schemes, as well as simple MMSE
and MMSE V-BLAST for SMux. We also present the
BER performance for the reference SISO system for the
sake of completeness. We consider two case studies of
M = N = 2 and M = N = 4 in the following.
A. Case of (2 × 2) FSO system
The performance of RC, OSTBC, OSM, and SMux
schemes are compared in Fig. 1. As OSTBC, we consider
the modified Alamouti scheme, proposed in [16]. We
notice that the RC scheme remains the best. For instance,
at BER= 10−4, MMSE V-BLAST detection provides 7 dB
gain in SNR, compared to simple MMSE. However,
the MMSE V-BLAST performs 30 dB worse than the
optimal MLD detection. We notice that the performances
of OSM and SMux with MLD are very close. On the
other hand, the rate-one schemes, i.e., RC and OSTBC,
perform much better than OSM and SMux with MLD
detection. Remember that for these schemes, we use half
the symbol duration of the SMux case so as to have the
same total transmission rate. In fact, although dividing the
symbol duration results in an increase of factor 2 in the
receiver thermal noise variance, compared to the SMux
case, the overall performance is still better than this latter
case. Another interesting point is that RC and OSTBC
outperform the reference SISO system only at low BER.
This is due to the trade-off between aperture averaging
and spatial diversity and also the increased total receiver
noise in MIMO systems.
B. Case of (4 × 4) FSO system
Figure 2 contrasts the performances of RC, OSTBC,
OSM, and SMux schemes. As OSTBC, we consider the
Jafarkhani’s scheme [26] that we modify in the same way
as it is done in [16] to adapt it to OOK modulation.
Note that this scheme is orthogonal for this case. We
notice again that RC is preferred to OSTBC and OSM,
−20 0 20 40 60 80 100
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
E
b
/N
0
 (dB)
B
E
R
(1×1)
(2×2), RC & MLD
(2×2), OSTBC & MLD
(2×2), OSM & MLD
(2×2), SMux & MMSE
(2×2), SMux & V−BLAST
(2×2), SMux & MLD
Fig. 1. Contrasting BER performance of different ST schemes for a
(2×2) MIMO FSO system. Z = 5Km, D = 200mm. Uncoded OOK,
thermal noise limited receiver.
−20 0 20 40 60 80 100
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
E
b
/N
0
 (dB)
B
E
R
(1×1)
(4×4), RC & MLD
(4×4), OSTBC & MLD
(4×4), OSM & MLD
(4×4), SMux & MMSE
(4×4), SMux & V−BLAST
(4×4), SMux & MLD
Fig. 2. Contrasting BER performance of different ST schemes for a
(4×4) MIMO FSO system. Z = 5Km, D = 200mm. Uncoded OOK,
thermal noise limited receiver.
and also to SMux even with MLD. Note that OSM here
outperforms SMux-MLD.
V. CONCLUSION
We investigated the interest of SMux in MIMO FSO
systems and compared its performance to those of RC,
OSTBC, and OSM. Our study confirmed the quasi-
optimality of the full-diversity RC scheme due to its lower
complexity and better performance, compared to the other
ST schemes. We conclude from our study that when a
higher data rate is required, it is preferable to directly
reduce the symbol duration instead of resorting to a higher
rate ST scheme like SMux.
REFERENCES
[1] V. W. S. Chan, “Free-space optical communications,” Journal of
Lightwave Technology, vol. 24, no. 12, pp. 4750–4762, Dec. 2006.
[2] Z. Ghassemlooy and W. O. Popoola, Mobile and Wireless
Communications Network Layer and Circuit Level Design, chapter
Terrestrial Free-Space Optical Communications, InTech, Jan.
2010.
[3] F. S. Vetelino, C. Young, L. C. Andrews, and J. Recolons,
“Aperture averaging effects on the probability density of irradiance
fluctuations in moderate-to-strong turbulence,” Applied Optics, vol.
46, no. 11, pp. 2099–2108, Apr. 2007.
[4] M. A. Khalighi, N. Schwartz, N. Aitamer, and S. Bourennane,
“Fading reduction by aperture averaging and spatial diversity in
optical wireless systems,” IEEE/OSA Journal of Optical Commu-
nications and Networking, vol. 1, no. 6, pp. 580–593, Nov. 2009.
[5] G. Yang, M. A. Khalighi, and S. Bourennane, “Performance of
receive diversity FSO systems under realistic beam propagation
conditions,” CSNDSP Symposium, 2012, Poznan, Poland, accepted
for publication.
[6] S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke,
“Optical repetition MIMO transmission with multipulse PPM,”
IEEE on Selected Areas in Communications, vol. 23, no. 9, pp.
1901– 1910, Sept. 2005.
[7] N. Cvijetic, S. G. Wilson, and M. Brandt-Pearce, “Performance
bounds for free-space optical MIMO systems with APD receivers
in atmospheric turbulence,” IEEE Journal on Selected Areas in
Communications, vol. 26, no. 3, pp. 3–12, Apr. 2008.
[8] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes
for high data rate wireless communication: Performance analysis
and code construction,” IEEE Transactions on Information Theory,
vol. 44, no. 2, pp. 744–765, Mar. 1998.
[9] V. Tarokh, H. J. Jafarkhani, and A. R. Calderbank, “Space-time
block codes from orthogonal designs,” IEEE Transactions on
Information Theory, vol. 45, no. 5, pp. 1456–1467, July 1999.
[10] B. Vucetic and J. Yuan, Space-Time Coding, John Wiley & Sons
Ltd, Chichester, England, 2003.
[11] E. Bayaki and R. Schober, “On space-time coding for free-space
optical systems,” IEEE Transactions on Communications, vol. 58,
no. 1, pp. 58–62, Jan. 2010.
[12] S. M. Aghajanzadeh and M. Uysal, “Diversity-multiplexing trade-
off in coherent free-space optical systems with multiple receivers,”
IEEE/OSA Journal of Optical Communications and Networking,
vol. 2, no. 12, pp. 1087–1094, Dec. 2010.
[13] S. M. Haas, J. H. Shapiro, and V. Tarokh, “Space-time codes for
wireless optical communications,” EURASIP Journal on Applied
Signal Processing, vol. 3, pp. 211220, Mar. 2002.
[14] S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque,
“Free-space optical MIMO transmission with Q-ary PPM,” IEEE
Transactions on Communications, vol. 53, no. 8, pp. 1402–1412,
Aug. 2005.
[15] S.M. Alamouti, “A simple transmit diversity technique for wireless
communications,” IEEE Journal on Selected Areas in Communi-
cations, vol. 16, no. 8, pp. 14511458, Oct 1998.
[16] M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time cod-
ing for free-space optical communication with direct detection,”
IEEE Transactions on Wireless Communications, vol. 4, no. 1, pp.
35–39, Jan. 2005.
[17] A. Garcia-Zambrana, “Error rate performance for STBC in
free-space optical communications through strong atmospheric
turbulence,” IEEE Communications Letters, vol. 11, no. 5, pp.
390–392, May 2007.
[18] M. Safari and M. Uysal, “Do we really need OSTBCs for
free-space optical communication with direct detection?,” IEEE
Transactions on Wireless Communications, vol. 7, no. 11, pp.
4445–4448, Nov. 2008.
[19] R. Mesleh, H. Elgala, and H. Haas, “Optical spatial modulation,”
IEEE/OSA Journal of Optical Communications and Networking,
vol. 3, no. 3, pp. 234–244, Mar. 2011.
[20] M. D. Renzo, H. Haas, and P. M. Grant, “Spatial modulation for
multiple-antenna wireless systems: A survey,” IEEE Communica-
tions Magazine, vol. 49, no. 12, pp. 182–191, Dec. 2011.
[21] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Spatial mod-
ulation: optimal detection and performance analysis,” IEEE
Communications Letters, vol. 12, no. 8, pp. 545–547, 2008.
[22] G. D. Golden, G. J. Foschini, R. A. Valenzuela, and P. W. Wol-
niansky, “Detection algorithm and initial laboratory results using
the V-BLAST space-time communication architecture,” Electronic
Letters, vol. 35, no. 1, pp. 1415, 1999.
[23] A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bolcskei, “An
overview of MIMO communications: a key to gigabit wireless,”
Proceedings of the IEEE, vol. 92, no. 2, pp. 198218, Feb. 2004.
[24] M. Arar and A. Yongacoglu, “Efficient detection algorithm for
2n×2n MIMO systems using alamouti code and QR decomposi-
tion,” IEEE Communications Letters, vol. 10, no. 12, pp. 819–821,
Dec. 2006.
[25] L. C. Andrews and R. L. Phillips, Laser Beam Propagation
Through Random Media, SPIE Press, second edition, 2005.
[26] H. Jafarkhani, “A quasi-orthogonal space-time block code,” IEEE
Trans. on Communications, vol. 49, no. 1, pp. 1–4, Jan. 2001.


Contrasting space-time schemes for MIMO FSO systems with non-coherent modulation

Abstract

Similar works

Full text

Available Versions

Northumbria Research Link

HAL AMU

Northumbria Research Link

Crossref