Iterative Near Maximum-Likelihood Sequence Detection for MIMO Optical Wireless Systems

Transcription

1 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. X, NO. XX, XXXXX Iterative Near Maximum-Likelihood Sequence Detection for MIMO Optical Wirele Sytem Netor D. Chatzidiamanti, Student Member, IEEE, Murat Uyal, Senior Member, IEEE, Theodoro A. Tifti, Member, IEEE and George K. Karagiannidi, Senior Member, IEEE Abtract A major performance-limiting factor in terretrial optical wirele OW) ytem i turbulence-induced fading. Exploiting the additional degree of freedom in the patial dimenion, multiple laer tranmitter combined with multiple receive aperture provide an effective olution for fading mitigation. Although MIMO Multiple-Input Multiple-Output) OW ytem have been extenively tudied in recent year, mot of thee work are mainly limited to ymbol-by-ymbol decoding. Maximum Likelihood Sequence Detection MLSD) exploit the temporal correlation of turbulence-induced fading and promie further performance gain. In thi paper, we invetigate MLSD for IM/DD intenity-modulation/direct-detection) MIMO OW ytem over log-normal atmopheric turbulence channel. Even with a low-order modulation cheme uch a On-Off keying which i typically ued in OW ytem, the complexity of MLSD might be prohibitive. We therefore preent an iterative equence detector baed on the expectation-maximization EM) algorithm. The complexity of the propoed algorithm i coniderably le than a direct evaluation of the log-likelihood function and it i independent of the channel fading tatitic. The Monte- Carlo imulation reult demontrate that the EM-baed algorithm outperform the ymbol-by-ymbol decoder and achieve a performance which lie within 0.3 db of that of the optimal MLSD. Index Term Atmopheric turbulence, Expectation Maximization EM) algorithm, Free-pace optical communication, Maximum Likelihood Sequence Detection MLSD), Maximum Likelihood ymbol-by-ymbol detection, patial diverity I. INTRODUCTION Wirele technology i traditionally aociated with radiofrequency RF) tranmiion although tranmiion via carrier in the other part of electromagnetic pectrum might be more advantageou for variou application [1]. Operating at unlicened optical wavelength, terretrial optical wirele OW) ytem offer the potential of broadband communication capacity that no other wirele tranmiion. A a cot-effective Thi paper wa partially preented at the IEEE International Conference on Communication, Dreden, Germany, 009. N. D. Chatzidiamanti and G. K. Karagiannidi are with the Wirele Communication Sytem Group WCSG), Department of Electrical and Computer Engineering, Aritotle Univerity of Thealoniki, GR-5414 Thealoniki, Greece {netora, geokarag}@auth.gr). Murat Uyal i with the School of Engineering, Özyeğin Univerity, 3466, Altunizade, Ukudar, Itanbul, Turkey murat.uyal@ozyegin.edu.tr). T. A. Tifti i with the Department of Electrical Engineering, Technological Educational Intitute TEI) of Lamia, Lamia, Greece tifti@teilam.gr). Copyright c) 009 IEEE. Peronal ue of thi material i permitted. However, permiion to ue thi material for any other purpoe mut be obtained from the IEEE by ending a requet to pub-permiion@ieee.org. alternative and/or complement to RF counterpart, OW ytem preent an attractive remedy for the lat mile problem, i.e., to provide broadband wirele extenion to Internet backbone bridging the gap between the end uer and the infratructure already in place []. With their broadband capacity, they can be further deployed for other high data rate application uch a metropolitan area network extenion, enterprie/local area network connectivity, fiber backup, and back-haul for wirele cellular network. Due to their feature uch a flexibility, rapid deployment time, high ecurity, and immunity to RF interference, OW ytem are alo appealing a a redundant link for relief effort, diater recovery, and military application. Depite their ignificant advantage, OW ytem unfortunately have ome hortcoming which need to be addreed to make poible their widepread deployment. The major limitation in the performance of OW ytem i their high vulnerability to advere atmopheric condition. Even in a clear ky, due to inhomogeneitie in temperature and preure change, the refractive index of the atmophere varie and reult in atmopheric turbulence. Thi caue rapid fluctuation at the received ignal, known a turbulence-induced fading. Such fluctuation lead to an increae in the error rate performance, thereby everely affecting the reliability of OW link. Over the lat year, everal fading mitigation technique have been propoed for deployment in OW link to combat the degrading effect of atmopheric turbulence. One of uch technique i error control coding ECC) which ha been invetigated in [3] and [4]. ECC in conjunction with interleaving i known in the RF literature to provide an effective time-diverity olution for rapidly-varying fading channel. In the OW ytem, data rate can typically be of the order of gigabit per econd. With a correlation time of the order of 10 3 to 10 econd, OW channel exhibit low fading; therefore the practical ue of ECC in OW link i rather limited due to the required large-ize interleaver to achieve the promiing coding gain theoretically available. An effective olution for fading mitigation i patial diverity technique which involve the deployment of multiple tranmit/receive aperture. Introducing additional degree of freedom in the patial dimenion, MIMO multiple-input multiple-output) OW ytem promie ignificant performance gain. The performance of MIMO OW ytem ha been extenively tudied by variou author auming different type of fading channel, noie tatitic and modulation type [5]- [8]. Thee work however are mainly limited to the aumption of ymbol-by-ymbol decoding. It i known that

2 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. X, NO. XX, XXXXX 009 Maximum Likelihood Sequence Detection MLSD) exploit the temporal characteritic of the fading channel and outperform the conventional ymbol-by-ymbol maximum likelihood ML) decoder. It prove to be particularly effective for lowly-varying fading or quai-tatic fading channel a the turbulence-induced fading turn out to be. MLSD in the context of OW communication ha been firt invetigated by Zhu and Kahn in [9], [10] and [11], for a SISO ingleinput ingle-output) cenario. However, MLSD involve the computation of complicated multidimenional integral and therefore uffer from high complexity. Furthermore it require knowledge of the channel fading tatitic. To addre the complexity iue, ub-optimal, yet of low-complexity, MLSD metric have been propoed in [1] and [13] for different detection model; till, thee metric require knowledge of the channel tatitic. Other detection method uch a pilotymbol aited modulation PSAM) or blind detection, which both don t require knowledge of the channel fading tatitic have been alo applied to SISO OW ytem in [11] and [14] repectively. In thi work, we aim to invetigate MLSD olution for MIMO OW ytem a a powerful combination for fading mitigation in atmopheric turbulence channel. Since MLSD in a MIMO cenario uffer from exceive complexity and i infeaible for mot practical purpoe, we propoe an iterative ML equence detector baed on the expectation-maximization EM) algorithm. The EM algorithm ha been originally propoed by Dempter, Laird, and Rubin [15] in the tatitic literature a a general procedure for iterative ML etimation. Since then, it ha been widely applied to a variety of communication problem [16]- [18]. Thi algorithm i particularly ueful when the etimation problem i made difficult by the abence of certain information, e.g. abence of full channel tate information in a data detection problem. In thi paper, we propoe EM algorithm a a low-complexity olution for MLSD in the MIMO OW ytem under conideration. A benchmark, we alo invetigate the performance of ymbol-by-ymbol ML detector, blind detector of [14], PSAM and MLSD in a MIMO cenario. The propoed detector outperform ymbolby-ymbol ML detector, blind detector and PSAM method. Moreover, it performance lie within 0.3 db of the MLSD at a much lower complexity and converge to MLSD a the trength of turbulence increae. The remainder of the paper i organized a follow. In ection II, we decribe the MIMO OW ytem and the turbulenceinduced fading model. In ection III, we preent ymbolby-ymbol and equence-baed ML detector, which will be ued a benchmark for ytem performance and complexity, and introduce the EM algorithm for the MIMO OW ytem under conideration. In ection IV, we preent Monte-Carlo imulation reult to demontrate the error rate performance of the propoed detection technique and compare it with benchmarking cheme. Finally, in ection V, we provide our concluding remark. Notation: x T denote the tranpoe of the matrix x ; E [ ] denote tatitical expectation; x denote the norm of the vector x; N µ, σ ) denote Gauian ditribution with mean µ and variance σ. II. SYSTEM AND CHANNEL MODEL We conider a MIMO OW link with N tranmit and M receive aperture. At the tranmitter, data block of length L are modulated uing On-Off keying OOK) and tranmitted through the N aperture uing repetition coding; an efficient tranmiion cheme for MIMO OW link [19]. We aume operation in the high ignal-to-noie ratio SNR) regime where the hot noie caued by ambient light i dominant and therefore Gauian noie model i ued a a good approximation of the Poion photon counting detection model [9]. Furthermore, a large field of view i conidered for each receiver indicating that multiple tranmitter are imultaneouly oberved by each receiver. Thi actually lead to the collection of larger amount of background radiation which further jutifie the ue of Gauian noie model. Let = 1) )... L) ) T be the L 1 column vector containing the L modulated ymbol within a data frame. The received ignal at the mth receive aperture i given a r l) m = l) η N n=1 I l) nm + υ m, m = 1,...M, l = 1,...L 1) where l) {0, 1} i the tranmitted information bit, η i the optical-to-electrical converion coefficient, and υ m i additive white Gauian noie AWGN) with zero mean and variance συ = N o /. The fading coefficient, which model the atmopheric turbulence in the optical channel between the nth tranmit aperture and the mth receive aperture during the l-th ymbol interval, i given by ) l) = I o exp x l) nm ) where I o i the ignal light intenity without turbulence and x l) nm are identically ditributed normal random ) variable with mean µ x and variance σx, i.e. f x x l) = N µ x, σx). Therefore, l) follow a lognormal ditribution with probability denity function pdf) given by f ) l) = 1 I l) nm 1 exp πσ x nm ln ) I l) nm I o 8σ x ) µ x 3) To enure that the fading doe not attenuate or amplify the average power, we normalize the fading coefficient uch that [ ] I E l) nm I o = 1. Doing o require the choice of µ x = σx [8]. The variance of log-amplitude fluctuation of plane and pherical wave can be found in [0]. Atmopheric turbulence reult in a very lowly-varying fading in OW ytem. For the ignalling rate of interet, ranging from hundred to thouand of Mbp [1], the fading coefficient can be conidered a contant over hundred of thouand or million of conecutive ymbol, ince the coherence time of the channel i about 1-100m [5]. Hence, it i aumed that l) remain contant over the ymbol of a frame and therefore we drop the time index l, i.e. I l) nm =, l = 1,..L. 4)

3 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. X, NO. XX, XXXXX and 1) can be written in a vector form a N r m = η + υ m, m = 1,...M 5) n=1 ) T where r m = r m 1) r m )... r m L) and υm i a L 1 column vector containing noie ample. Moreover, it i aumed that the ditance between the tranmitter and receiver aperture are large compared to the correlation length of intenity fluctuation. Thi aumption i realitic for many OW ytem a it i decribed in [5]. Hence, the underlying channel can be conidered a independent in pace. At the receiver, we aume equal gain combining EGC), whoe performance i very cloe to maximal ratio combining MRC) [8] e.g., within 0.5 db for N =, 3 aperture and σ x = 0.3). Thu, after combining the received ignal of the M aperture, the output of the receiver can be written in matrix form a r = 1 M r m = η M m=1 N + n 6) where n i a L 1 column vector which contain noie 1 ample. Note that a caling factor appear in 6). The factor 1 N i included in order to enure that the total tranmit power i the ame with that of a ytem with no tranmit 1 diverity. The factor M, on the other hand, enure that the um of the M receive aperture area i the ame with the aperture area of a ytem with no receive diverity. III. ML DETECTION TECHNIQUES FOR MIMO OW SYSTEMS In thi ection, we preent detection technique which are baed on the maximum likelihood ML) criterion and can be employed when intantaneou channel tate information CSI) i not available at the receiver. A. ML Symbol-by-Symbol Detection The ML ymbol-by-ymbol detector chooe the ymbol ŝ baed on the rule [] ŝ = arg max p r ) 7) where p r ) i the conditional probability of the received ignal r when i tranmitted. The likelihood function for SISO OW ytem i given by [9, Eq. 30]. For the MIMO OW ytem under conideration, the ML deciion rule take the form of ŝ = arg max x f x x) exp r η M N o ) N e xnm r dx where x = {x nm } and, ince it i aumed that the intenity fluctuation are independent in pace, 8) f x x) = M N f x x nm ). An efficient computation of 8) can be performed uing the um of log-normal approximation and Gau-Hermite quadrature formula a dicued in [8]. B. ML Sequence Detection MLSD) Thi detection cheme exploit the temporal correlation of turbulence-induced fading over conecutive tranmitted ymbol. MLSD i baed on the aumption that the receiver ha knowledge of the marginal joint ditribution of the intenity fluctuation, but not of their intantaneou tate. It wa firt invetigated in [9] for OW communication, auming a SISO cenario. For the MIMO OW ytem with OOK, the MLSD compute the likelihood ratio of each of the L poible equence and chooe according to the deciion rule a given by 9) in the top of the next page, where r = [r 1, r,..., r L ] repreent the received data. A major drawback of MLSD i it computational complexity, ince it require the computation of the M N-dimenional integral of 9) for each of the L poible equence. A uboptimal low-complexity implementation ha been propoed in [10], adopting Markov model; it till require the numerical integration to be performed in each branch metric in the trelli earch. In [1] and [13], another efficient low complexity implementation i propoed, which ue analytically tractable deciion metric and earche over a ubet of all poible equence; however, in that cae, there i a difficulty in calculating the parameter of the low complexity deciion metric and knowledge of the channel tatitic i required. C. EM-Baed Sequence Detection In thi ub-ection, we propoe an EM-baed equence detector a a low complexity alternative to the original MLSD. Thi cheme i a two-tep iterative procedure which etimate both the tranmitted equence and the channel tate baed on it previou etimate. A general decription of the EM algorithm can be found in [15]. For it application in fading channel and MIMO RF communication ytem, the reader i urged to read [16]- [18]. With the available data only, i.e., the incomplete data et according to the EM terminology, finding the ML etimate might be computationally intenive a in our cae. Including a proper election of another data et reulting in o-called complete data et, it might be made eaier to compute the ML etimate. Since not all the element of the complete data et are known, the EM algorithm make ue of the log-likelihood function for the complete data in a two-tep iterative procedure, iterating between expectation tep E-tep) and maximization tep M-tep). In our work, the received equence r i the incomplete data et. Let the complete data be y = r,{ }). After uing the likelihood function for MIMO OW ytem, a in 9), the loglikelihood function for the complete data in vector form, i obtained by l r, { }) = 1 N o r η M N 10)

4 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. X, NO. XX, XXXXX ŝ = arg max p r ) = arg max x L r l) l) f x x) exp l=1 ) M N η e x nm N o dx 9) After dropping ome unneceary term, 10) reduce to l r, { }) = r T η M N 1 η M N or equivalently l r, { }) = 11) L r l) l) η M N l=1 ) 1 L l) η M N 1) l=1 At the E-tep of the k-th iteration of the algorithm, the log-likelihood function for the complete data i calculated, conditioned on the received equence r and the k-th etimate of the tranmitted equence k. Hence, baed on 11) or 1) we obtain Q k ) = r T I k 1 I k 13) where [ I k η M = E ] N k, r = 1 L k r T k 14) on and L k on i the number of the bit of the k-th etimate of the tranmitted equence k that correpond to the On-tate. A better etimate of the tranmitted equence, k+1, i obtained at the econd tep of the k-th iteration of the algorithm, the M-tep. M-tep perform the maximization of 13) which yield k+1 = arg max r T I k 1 I k ) 15) Since the tranmitted data bit are randomly choen, i.e. no coding cheme i employed, maximizing 15) over the L- bit equence i equivalent to making ymbol-by-ymbol deciion on each bit. In other word, if k+1 i the equence that maximize 15), it component are eaily obtained through k+1 ) l) = arg max l) r l) l) I k 1 l) I k ), l = 1,..., L 16) Unlike MLSD, thi detection cheme doe not require knowledge of the marginal joint ditribution of the intenity fluctuation at the receiver. Moreover, it avoid the numerical calculation of 9), which can be very complex for high SNR. However, it need an initial etimate of the channel tate, I 0, in order to initialize the algorithm. The inertion of pilot channel etimation bit at each data frame at the tranmitter i one poible way to obtain an initial channel etimate. Aume that pilot ymbol are inerted into the modulated data block at every J ymbol. In making deciion, the receiver make obervation on data vector of F ub-block, each with a length of J i.e., L = F J ymbol), for ome integer F. Of the J ymbol in the ub-block, the firt i a pilot ymbol, which i in the On-tate. The initial etimate of the channel tate i obtained by taking the average of the pilot ymbol, i.e. I 0 = 1 F F 1 i=0 r 1+iJ) 17) The implementation of the blind detection method of [14] i another poible way to initialize EM algorithm. Thi method avoid the ue of pilot ymbol and obtain an initial etimate of the tranmitted equence, 0, by performing ymbol-byymbol detection, according to deciion rule ) 0 l) = 1 r l) ) τ blind, l = 1,...L 18a) 0 l) = 0 where τ blind = 1 L L l=1 r l) 18b) Hence, by uing 14), the channel etimate that i needed in order to initialize the EM algorithm, can be obtained. It hould be noted that the quality of the initial channel etimate and/or the length of the data frame determine the convergence of the performance of the EM-baed receiver to that of the perfect CSI receiver [16]. IV. SIMULATIONS RESULTS AND DISCUSSION In thi ection, we preent imulation reult for the bit error rate ) performance of the MIMO OW communication ytem with EM-baed receiver for variou number of tranmit/receive aperture. We further compare it performance with other competing detection technique. In Fig. 1, we conider a MISO multiple-tranmit ingleoutput) OW ytem with N = 3 tranmit aperture and a MIMO ytem with N = 3 tranmit and M = 3 receive aperture over the lognormal turbulence channel with σ x = 0.3. The performance of the propoed EM algorithm that ue pilot ymbol for initialiation, along with ML ymbol-by-ymbol decoder and MLSD i illutrated. We aume two iteration in the implementation of EM algorithm ince further iteration reult in a negligible performance improvement. Among the three competing cheme, ymbol-by-ymbol detection cheme perform wort. Thi i expected, ince thi detector doe not take advantage of the fading correlation between ucceive ymbol that exit in turbulence channel. Hence,

5 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. X, NO. XX, XXXXX ML Symbol-by-Symbol EM, F=1 J=5 MLSD, L=4 EM, F= J=5 MLSD, L=8 Genie bound MIMO N=3 M=3 MISO N=3 M= Average Electrical SNR, db ML Symbol-by-Symbol EM, F=1 J=5 MLSD, L=4 EM, F= J=5 MLSD, L=8 Genie Bound MIMO N=3 M=3 MISO N=3 M= Average Electrical SNR, db Fig. 1. Comparion of ymbol detection technique for MIMO and MISO OW ytem when σ x = 0.3. Fig.. Comparion of ymbol detection technique for MIMO and MISO OW ytem when σ x = 0.4. the ue of equence detection technique, uch a MLSD or EM i fully jutified. A an ultimate benchmark, we alo include the performance of genie receiver which aume perfect CSI and act a a lower bound on the performance of other detection type. MLSD perform very cloe to the genie bound and lightly outperform the EM detector. Specifically, there i an SNR improvement of approximately 0.3 db at = 10 4 between MLSD of L = 4 and EM of F = 1, J = 5) or between MLSD of L = 8 and EM of F =, J = 5) in both MIMO OW ytem. However, it hould be noted that the complexity of the MLSD implementation i much higher than that of EM algorithm, i.e. MLSD require the calculation of an -dimenional intergral for each of the L + 1) poible equence 1, which i very difficult epecially for the SNR regime under conideration. That i alo the ame reaon why we retricted ourelve to mall value of frame length. Otherwie, imulation of MLSD would not be poible for comparion purpoe. Fig. depict the performance of the MIMO OW ytem under conideration for the ame number of tranmit and receive aperture, but for tronger turbulence condition with σ x = 0.4. It i oberved that the propoed EM-baed detection technique till perform very cloe to the optimal MLSD, depite the increae of the turbulence trength. Specifically, the SNR improvement in thi cae i approximately 0.1 db for the ame combination of L, F, and J in both MIMO OW ytem. Thi convergence of the EM-baed detection to the MLSD i expected, ince the propoed algorithm depend motly on the frame length, in contrat with MLSD which ha a trong dependency from the channel tatitic. In Fig. 3, we invetigate the performance of EM algorithm for a large frame length, which would be prohibitive for MLSD implementation. Furthermore, large frame length make the lo due to pilot inertion negligible. Specifically, we conider 1 In imulation, the low complexity earch algorithm, preented in [1] and [13], wa employed which evaluate the MLSD metric for L + 1) out of the L poible equence. the SISO and the MISO OW ytem with L = 100 over the lognormal turbulence-induced fading model with σ x = 0.3, auming ub-block length of J = 100 and pilot ymbol number F = 1. The performance of propoed EM algorithm i illutrated auming one and two iteration. It i oberved that the performance of EM detector lie within 0.1 db of the genie bound for F = 1 and J = 100. A another benchmark, we alo include the performance of PSAM with variable threhold [11], i.e. the deciion rule for the detection of each ymbol in the frame, i defined entirely by the channel etimate of the pilot ymbol. The EM algorithm outperform PSAM by approximately 1 db. Fig. 4 depict the performance of the EM-baed receiver, when σ x = 0.3, for different frame length, auming variou combination of F and J value. Specifically, we aume the combination of F = 1 and J = 5, F = 1 and J = 10, F = and J = 5, F = and J = 10, F = 4 and J = 5 and, finally, F = 1 and J = 100. It i oberved that the increae of the length and/or the number of pilot ymbol help EM-baed receiver to perform cloer to the genie bound. It hould be noted that the complexity of the algorithm doe not increae ignificantly a the length of data block increae, becaue EM implementation doe not involve the computation of dimenional integral and, unlike MLSD, the increae of frame length increae only the number of the ymbol-by-ymbol deciion performed at the M-tep of the algorithm. Finally, in Fig. 5, we invetigate the performance of EMalgorithm that ue the blind detection method of [14] for algorithm initialization, when σ x = 0.3 and N = 3 tranmit and M = 1 receive aperture are aumed. It i obviou from the figure that the application of the EM algorithm ignificantly increae the ytem performance compared to the blind detection cheme of [14]. Specifically, there i an improvement of db at =10 4 ) when L = 3, while the error floor are reduced when maller equence length are conidered L = 4 and L = 8). Furthermore, when compared with the pilot-ymbol aited EM-baed receiver, it

6 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. X, NO. XX, XXXXX SISO 10 - PSAM 1-iteration -iteration Genie bound N=3 M= Average Electrical SNR Fig. 3. Performance of EM-baed receiver for F = 1 and L = 100 and comparion with PSAM. Blind Det., L=4 EM-baed Blind Det., L=4 EM with pilot ymbol, F=1, J=5 Blind Det., L=8 EM-baed Blind Det., L=8 EM with pilot ymbol, F=, J=5 Blind Det., L=3 EM-baed Blind Det., L=3 Genie Bound Average Electrical SNR, db Fig. 5. Performance of EM-baed blind detection cheme along with the blind detection without EM and the pilot ymbol aited EM PSAM 1-iteration -iteration Genie bound SISO N=3 M= Average Electrical SNR to it high complexity. In our work, we have propoed a lowcomplexity equence detector baed on the EM algorithm. EM algorithm provide an iterative ML olution, which avoid the calculation of the difficult multi-dimenional integral involved in the MLSD. Moreover, ince it doe not take into conideration the channel fading tatitic, it can be applied in different turbulence condition, regardle their trength. Our imulation reult demontrate that the propoed EM olution perform very cloe to that of MLSD. Specifically, it ha been oberved that the performance of EM lie within 0.3 db when σ x = 0.3 or within 0.1 db when σ x = 0.4 at =10 4 ) of that of MLSD for the MIMO OW ytem under conideration. Fig. 4. Performance of EM-baed receiver for variou number of pilot ymbol F and data-block length L L = F J). i oberved that the latter ha better performance for the ame frame length no error floor are oberved). However a the frame length increae, the performance of the EM-baed blind detection i improved, ince the quality of the initial etimate i improved, and converge to the genie bound. Hence, both EM implementation can be employed with the ame ucce for large frame length, i.e. large number of conecutive ymbol where the fading coefficient remain contant, which i eaily jutified for the lowly varying atmopheric turbulence channel. V. CONCLUSIONS We have invetigated equence detection technique for MIMO OW ytem in the preence of turbulence-induced fading. Sequence detection exploit the temporal correlation of OW channel and promie ignificant performance gain over the ymbol-by-ymbol decoding. However, optimal ML equence detector i infeaible for mot practical purpoe due REFERENCES [1] L. Andrew, R. L. Philip, and C. Y. Hopen, Laer Beam Scintillation with Application. SPIE Pre, 001. [] D. Kedar and S. Arnon, Urban optical wirele communication network: The main challenge and poible olution, IEEE Communication Magazine, vol. 4, no. 5, pp. 7, Feb [3] X. Zhu and J. M. Kahn, Performance bound for coded free-pace optical communication through atmopheric turbulence channel, IEEE Tran. on Commun., vol. 51, no. 8, pp , Aug [4] M. Uyal, S. M. Navidpour, and J. Li, Error rate performance of coded Free-Space optical link over trong turbulence channel, IEEE Communication Letter, vol. 8, no. 10, pp , Oct [5] E. Lee and V. Chan, Part 1: Optical communication over the clear turbulent atmopheric channel uing diverity, IEEE Journal on Selected Area in Commun., vol., no. 9, pp , Nov [6] S. G. Wilon, M. Brandt-Pearce, C. Qianling, and M. Baedke, Optical repetition MIMO tranmiion with multipule PPM, IEEE Journ. on Sel. Area in Commun., vol. 3,, no. 9, pp , 005. [7] T. A. Tifti, H. G. Sandalidi, G. K. Karagiannidi, and M. Uyal, Optical wirele link with patial diverity over trong atmopheric turbulence channel, IEEE in Tranaction on Wirele Communication, vol. 8, no., pp , Feb [8] S. M. Navidpour and M. Uyal, performance of free-pace optical tranmiion with patial diverity, IEEE Tran. Wirele Commun., vol. 6, no. 8, pp , Aug [9] X. Zhu and J. M. Kahn, Free-pace optical communication through atmopheric turbulence channel, IEEE Tran. Commun., vol. 50, no. 8, pp , Aug. 00.

7 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. X, NO. XX, XXXXX [10], Markov chain model in maximum-likelihood equence detection for free-pace optical communication through atmopheric turbulence channel, IEEE Tran. on Commun., vol. 51, no. 3, pp , Mar [11], Pilot-ymbol aited modulation for correlated turbulent freepace optical channel, in Proc. of SPIE Intl. Symp. on Optical Science and Technol., San Diego, CA, 001. [1] M. L. B. Riediger, R. Schober, and L. Lampe, Fat Multiple-Symbol Detection for Free-Space Optical communication, IEEE Tran. on Commun., vol. 57,, no. 4, pp , Apr [13], Fat Multiple-Symbol Detection for Photon-Counting MIMO Free-Space Optical communication, IEEE Tran. on wirele Commun., vol. 7,, no. 1, pp , Dec [14], Blind detection of On-Off keying for Free-Space Optical communication, in CCECE/CCGEI, Niagara Fall, Canada, 008, pp [15] A. Dempter, N. M. Laird, and D. B. Rubin, Maximum-likelihood from incomplete data via the EM algorithm, J. Roy. Statit. Soc, vol. 39, pp. 1 17, [16] C. N. Georghiade and J. C. Han, Sequence etimation in the preence of random parameter via the EM algorithm, IEEE Tran. on Commun., vol. 45, no. 3, pp , Mar [17] C. Cozzo and B. L. Hughe, Joint channel etimation and data detection in Space-Time communication, IEEE Tran. on Commun., vol. 51, no. 8, pp , Aug [18] Y. Li, C. N. Georghiade, and G. Huang, Iterative maximum-likelihood equence etimation for pace-time coded ytem, IEEE Tran. on Commun., vol. 49, no. 6, pp , Jun [19] M. Safari and M. Uyal, Do we really need OSTBC for free-pace optical communication with direct detection? IEEE Tran. Wirele Commun., vol. 7, no. 11, pp , Nov [0] S. Karp, R. Gagliardi, S. E. Moran, and L. B. Stott, Optical Channel. New York: Plenum, [1] D. J. T. Heatley, D. R. Wiely, I. Neild, and P. Cochrane, Optical wirele: the tory o far, IEEE Commun. Mag., vol. 36, no., pp. 7 74, Dec [] J. G. Proaki, Digital Communication, 4th ed. New York: Mc Graw Hill, 000. Netor D. Chatzidiamanti S 08) wa born in Lo Angele, USA, in He received the Diploma of Electrical and Computer Engineering from the Aritotle Univerity of Thealoniki, Greece, in 005, and ince 008, he i puruing a Ph.D degree in the ECE department. Hi reearch area include performance analyi over fading channel, and freepace optical communication Murat Uyal wa born in Itanbul, Turkey in He received the B.Sc. and the M.Sc. degree in electronic and communication engineering from Itanbul Technical Univerity, Itanbul, Turkey, in 1995 and 1998, repectively, and the Ph.D. degree in electrical engineering from Texa A&M Univerity, College Station, Texa, in 001. Since 00, he ha been with the Department of Electrical and Computer Engineering, Univerity of Waterloo, Canada, where he i now an Aociate Profeor. He i currently on abbatical leave at Özyeğin Univerity, Itanbul, Turkey. Hi general reearch interet lie in communication theory and ignal proceing for communication with pecial emphai on wirele application. Specific reearch area include MIMO technique, pace-time coding, diverity technique and coding for fading channel, cooperative communication, and free-pace optical communication. Dr. Uyal i an Aociate Editor for IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS and IEEE COMMUNICATIONS LETTERS. He wa a Guet Co-Editor for Wiley Journal on Wirele Communication and Mobile Computing Special Iue on MIMO Communication publihed in 004. He i currently erving a a Guet Co-Editor for IEEE Journal on Selected Area in Communication Special Iue on Optical Wirele Communication to be publihed in 010. Over the year, he ha erved on the technical program committee of more than 50 international conference in the communication area. He recently co-chaired IEEE ICC 07 Communication Theory Sympoium and CCECE 08 Communication and Networking Sympoium. Dr. Uyal i a Senior IEEE member. Theodoro A. Tifti S 0-M 04) wa born in Lamia, Greece, in He received the degree in Phyic from the Aritotle Univerity of Thealoniki, Thealoniki, Greece, in 1993, and the M.Sc. degree in Digital Sytem Engineering from the Heriot-Watt Univerity, Edinburgh, Scotland, U.K., in Alo, he received the M.Sc. degree in Deciion Science from the Athen Univerity of Economic and Buine AUEB), Athen, Greece, in 000, and hi Ph.D. degree in Electrical Engineering from the Univerity of Patra, Patra, Greece, in 006. He i currently an Aitant Profeor in the Department of Electrical Engineering at the Technological Educational Intitute TEI) of Lamia, Lamia, Greece. Hi current reearch interet include cooperative diverity ytem, wirele communication theory, digital communication over fading channel and freepace optical communication.

8 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. X, NO. XX, XXXXX George K. Karagiannidi M 97-SM 04) wa born in Pithagorion, Samo Iland. He received the Univerity and Ph.D. degree in electrical engineering from the Univerity of Patra, Greece, in 1987 and 1999, repectively. From 000 to 004, he wa a Senior Reearcher at the Intitute for Space Application and Remote Sening, National Obervatory of Athen, Greece. In June 004, he joined Aritotle Univerity of Thealoniki, Greece, where he i currently Aociate Profeor of Digital Communication Sytem in the Electrical and Computer Engineering Department. Hi current reearch interet include digital communication theory, wirele optical communication and underwater communication. He i the author or coauthor of more than 100 technical paper publihed in cientific journal and preented at international conference. He i alo a coauthor of three chapter in book and author of the Greek edition of a book on Telecommunication Sytem. He erve on the editorial board of the EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING. Dr. Karagiannidi ha been a member of Technical Program Committee for everal IEEE conference. He i a member of the editorial board of the IEEE TRANSACTIONS ON COMMUNICATIONS, IEEE COMMUNICATIONS LETTERS and Lead Guet Editor of the pecial on Optical Wirele Communication of the IEEE JOURNAL ON SELECTED AREAS IN COMMU- NICATIONS. He i co-recipient of the Bet Paper Award of the Wirele Communication Sympoium WCS) in IEEE International Conference on Communication ICC 07), Glagow, U.K., June 007.