Adaptation of Hybrid FSO/RF Communication System Using Puncturing Technique

Transcription

1 644 M. N. KHAN, M. JAMIL, M. HUSSAIN, ADAPTATION OF HYBRID FSO/RF COMMUNICATION SYSTEM USING PUNCTURING... Adaptaton of Hybrd FSO/RF Communcaton System Usng Puncturng Technque Muhammad Nasr KHAN, Mohsn JAMIL 2, Mazhar HUSSAIN 3 Department of Electrcal Engneerng, The Unversty of Lahore, Pakstan 2 Department of Electrcal Engneerng, The Islamc Unversty n Madnah, Saud Araba 3 Department of Computer Scence, Insttute of Southern Punjab, Pakstan muhammad.nasr@ee.uol.edu.pk, mohsn@u.edu.sa, mazhar.hussan@sp.edu.pk Manuscrpt receved June 4, 26 Abstract. Spectrum of rado frequency (RF) communcatons s lmted and expensve to nstall new applcatons. Free space optcal (FSO) communcaton s a vable technology whch offers enormous bandwdth, lcense free nstallaton, nexpensve deployment and error prone lnks. The FSO lnks degrade sgnfcantly due to the varyng atmospherc and weather condtons (fog, cloud, snow, haze and combnaton of these). We propose a hybrd FSO/RF communcaton system whch adapts the varyng nature of atmosphere and weather. For the adapton of varyng atmosphere and weather scenaros, we develop a novel optmzaton algorthm. The proposed algorthm s based on the well-known puncturng technque. We provde an extrnsc nformaton transfer (EXIT) chart for the bnary and quaternary mappng scheme for the proposed communcaton system. We smulate the proposed algorthm for the hybrd communcaton system and analyze the system performance. The proposed algorthm s computatonally less expensve and provde better performance gans over varyng atmosphere and weather condtons. The algorthm s sutable for fast speed applcatons. Keywords Free Space Optcal (FSO) communcaton, Low Densty Party Check (LDPC) code, Extrnsc Informaton Transfer (EXIT), Puncturng Optmzaton Algorthm (POA), Mnmum Postve Dfference (MPD). Introducton Communcatng over FSO, wth ts nearly boundless bandwdth, has been proposed as vable canddate for "last mle connectvty" []. But the meteorologcal condtons and scntllaton severely affect the FSO channel. FSO communcaton undergoes sgnfcant deteroraton whenever the vsblty of the laser beam s affected. It s mentoned n [2] that fog s the domnant parameter whch sgnfcantly affects the vsblty of the FSO laser beam. The atmospherc effects on the FSO beam propagaton can be dvded nto power attenuaton and laser power fluctuaton usually called scntllaton [2]. Atmosphere effects on the FSO lnk have been nvestgated n [2 4]. These channel varatons can be mproved by ntroducng the rate adaptng technque. We have nvestgated n the prevous chapters that we can acheve certan gans by mplementng the codng scheme over the sgnal ndependent Gaussan nose model. Prevously, we specfcally concentrated on the mproved performance of the system by mplementng LDPC codes. But we dd not nvestgate the rate adaptablty of the LDPC codes. Therefore, t s a good dea to nvestgate the mplcaton of rate adaptablty of LDPC codes by mplementng the puncturng technques. Prevous study on punctured LDPC codes can be found n [5], [6], consderng the bnary erasure (BEC) channels. Low densty party check (LDPC) code was frst ntroduced by Gallager [7] n 962 and ts performance s nearly close to the Shannon s lmts. The LDPC codes of any rate and block length can also be created easly by just changng the shape of the party check matrx. It means that the rate adaptablty n the LDPC codes can be obtaned easly compared to other codes. LDPC codes have the feature of parallelsm for supportng dfferent speeds, performances and memory consumpton. It s therefore better to desgn LDPC codes because of the capacty approachng performance and comparable easy mplementaton [8]. Extrnsc nformaton transfer (EXIT) chart [9] s a good approach to measure the code convergence performance. It conssts of two components decoder curves, varable and check node curves. We wll utlze ths approach as a performance measure n optmzaton problem. Recent research [2], [6] shows that the demerts of one communcaton lnks (FSO) can be overcome by ntroducng a parallel channel of other communcaton lnk (RF) named as hybrd FSO/RF communcatons system. But a true hybrdzaton can be made possble only when both channels collaboratvely compensate the dsadvantages of each other DOI:.364/re OPTICAL COMMUNICATIONS

2 RADIOENGINEERING, VOL. 25, NO. 4, DECEMBER and provdng good performance mprovements of the communcaton system. To cope wth the channel varatons, we propose puncturng LDPC codes whch provdes better performance mprovement by makng the system adaptve over the non-adaptve (fxed) system [6]. The proposed algorthm shows a better flexblty over a slowly fadng channels. These codes have the flexblty of operatng over a wde range of code rate havng a same encoder and decoder par. Havng a sngle par of encoder and decoder s the man am of the hybrd code desgn whch can adapts the weather varatons by ntroducng the puncturng algorthm. We propose a novel optmzaton algorthm whch mplements rate adaptablty of LDPC code over a wde range of rates. It optmzes the puncturng fractons for dfferent weather condtons (clear sky, ran and fog). We show that transmsson relablty over a range of rate s possble usng the proposed algorthm as compared to a fxed system n [6]. We are provdng nvestgatons on how the puncturng algorthm adapts dfferent weather condtons n a flexble fashon usng quadrature modulaton scheme. Our objectve s to provde transmsson relablty over a wde range of rate for the hybrd communcaton system by adaptng the optmzed puncturng patterns for varyng meteorologcal condtons. Our puncturng scheme s dfferent from the exstng puncturng scheme [] that we are proposng the scheme whch can be applcable for a generalzed channel model (sngle, hybrd and block fadng). We nvestgate over dfferent weather scenaros n hybrd channel model usng the bnary and quaternary modulaton. The proposed algorthm provdes a better adaptaton over a wde range of rate for dfferent channels. 2. Irregular LDPC Codes Prelemnary Low densty party check (LDPC) codes have receved attenton by the research communty because of ther capacty approachng performance over a large range of data transmsson and storage channels. The orgnal Gallager codes are known to be regular LDPC codes [7]. For another class of codes known as rregular LDPC codes, Luby et al. [] demonstrated that the properly constructed codes can acheve better performance comparng to the regular ones. An LDPC code can be well represented by a bpartte graph known as Tanner graph []. The Tanner graph conssts of two sets of component nodes decoders known as varable nodes decoder (VND) and check nodes decoder (CND). The number of edges whch jon the VND and CND are equal to the number of s n the sparse party check matrx H. The teratve decodng of the LDPC code s performed by passng messages between the neghborng VND and CND. The flow of nformaton between the varable and check nodes s shown n Fg.. Irregular LDPC structures [2] are those for whch the degrees of each set of nodes are chosen accordng to some dstrbuton. For a rght regular also known as check-regular LDPC structure, ts all check nodes have the same degree. For I v,c σ 2 ch,2 V V 2 V 3 V 4 V n I v,cn I c,v σ 2 ch,2 I Ic,v3 c,v2 σ 2 ch,4 σ 2 ch,4 C C 2 C n σ 2 ch,2 Fg.. Tanner graph representaton of rregular LDPC codes and exchange of nformaton flow between the CND and VND. rregular LDPC code structure, we can defne a degree dstrbuton ensemble (λ, ρ) from edge perspectve way as [8] λ(x) = ρ(x) = dv max =d mn v dc max =d mn c λ x, () ρ x (2) where dv mn and dv max are the mnmum and maxmum varable node degrees respectvely, dc mn and dc max are the mnmum and maxmum check node degrees respectvely and the fracton of edges whch are connected to degree varable nodes s denoted by λ and the fracton of edges whch are connected to degree check nodes, s denoted by ρ. The set of varable (check) nodes of degree (equvalently columns(rows) of weght ) shall be desgnated by V (C ) and translatng from edge perspectve to node perspectve as V = λ d max v λ j j=dv mn j., (3) ρ C = d max v. ρ j (4) j=dv mn j Accordng to [3], for a fxed check node degree (rghtregular), f λ be the edge fracton ncdent to varable node of degree d v, then we can fnd the varable node fracton v of degree usng the followng expresson as well, v = ( R m)d c λ (5) d v where R m denotes the mother code rate. For the rest of the chapter we denote the block length by n, the number of check nodes by m, the number of edges by E. 3. Puncturng Prelamnares An error correctng code can be consdered to be the rate-adaptve codes when the nformaton rate of the code s dynamcally adapted to the communcaton channel requrement. We nvestgate the feature of rate-adaptablty of the rregular LDPC codes by ntroducng the puncturng technque. Puncturng ncreases the rate of orgnally constructed code, (.e., C(n, k)), by deletng a set of symbols from the codeword, where p < n. It then converts the code ensemble

3 646 M. N. KHAN, M. JAMIL, M. HUSSAIN, ADAPTATION OF HYBRID FSO/RF COMMUNICATION SYSTEM USING PUNCTURING... (.e., C(n, k)) nto a new code ensemble C(n p, k). The punctured codng rate R p s then ncreased to R p = k n p where (6) can be wrtten n the context of puncturng fracton as R p = R m (7) p where p represent the puncturng fracton and can be calculated for a gven code rate usng (7). We can further defned t wth new name "overall puncturng" because we are dvdng the puncturng dstrbuton nto the dfferent populaton type,.e., populaton type means dfferent varable node degree. Then the overall puncturng fracton P can be defned as (6) P = p v (8) ϱ where ϱ s varable node populaton types n the rregular LDPC code structure. In order to fnd the optmum puncturng fractons, we propose an effcent puncturng algorthm and verfy the results usng the Monte Carlo smulatons. 3. VND and CND EXIT Functons EXIT chart was frst ntroduced n [4] for measurng convergence behavor of teratvely decoded parallel concatenated codes and later on generalzed for LDPC codes analyss n [3], [5], [6]. The man components of the EXIT chart are the EXIT functons of the component decoders whch relates the a-pror mutual nformaton (MI) avalable to the component decoder whch then generates the extrnsc MI after teratve decodng. Consderng the Gaussan assumpton of the ncomng messages to a varable node v of degree, the EXIT functon for the code component nvolvng the varable nodes for rregular structure s gven by [3] ( ) ( ) I EV IAV, σch 2 = λ J ( )[J (I AV )] 2 + σch,v 2 where J has been defned n [9], [4], σch,v 2 = 4 for the σn 2 unpunctured varable node v (σn 2 denotes the channel nose varance), σch,v 2 = for the punctured varable nodes v and the Fg. s redrawn as Fg. 2. Smlarly the EXIT functon for the check node decoder nvolvng all the check nodes for rregular structure can be wrtten as I EC (I AC ) = ρ J ( J ( I AC ) ). () 3.2 Puncturng Optmzaton (PO) Algorthm Our objectve s to provde transmsson relablty over a wde range of rate by adaptng the optmzed puncturng patterns for varyng weather condtons. The crtera s to (9) I v,c σch,2 2 V V 2 V 3 V 4 V n I c,v I v,cn σ 2 ch,2 I I c,v2 c,v3 σ 2 ch,4 C C 2 C n Fg. 2. Tanner graph representaton of rregular LDPC codes wth punctured and unpunctured varable nodes. fnd the best threshold by optmzng the puncturng patterns for varyng weather condtons over a wde range of rates. In the proposed algorthm, Puncturng Optmzaton (PO), we defne the Mnmum Postve Dfference (MPD) rule whch calculates the mnmum postve value when the two EXIT curves obtaned usng (9) and () just touches. The PO algorthm can be summarzed n the followng algorthmc steps as. Defne γ and γ (.e., varyng weather condton n terms of κ) and puncturng code rate. 2. Intalze the fne/course grd search method and calculate p usng (7), calculate dfferent puncturng patterns usng (8) for each desred rate and ensure the puncturng fractons for varable nodes should be between and. Algorthm s flexble n terms of speed and effcency whch s dependent on the grd search method (fne/coarse). 3. Intalze average sgnal to nose rato (SNR) ( γ), whch gves the average MI. Then transmt the average MI through the communcaton channel (sngle/hybrd/block fadng) dependng on respectve weather condtons. 4. Perform numercal calculaton for EXIT curves usng (9) and () for each of the puncturng combnatons and gven SNR. 5. Calculate the MPD between the two curves, f we got the postve value MPD where the tunnel between the EXIT curves opens, we accept those values (puncturng patterns and correspondng thresholds) otherwse agan go to Step 3 to ncrease the average SNR. Ths step should run for each defned puncturng par n Step 2. The MPD can be expressed mathematcally as, { MPD : mniav ( IEV (I AV ) I EC (I AV ) ), s.t : MPD > ɛ thr () where we select the threshold ɛ thr = 2 3 whch s very small value to gve accurate enough results. 6. Select the best optmum puncturng pars P and the correspondng thresholds {(γ, γ)} over a partcular weather scenaros.

4 RADIOENGINEERING, VOL. 25, NO. 4, DECEMBER For each defned rate, pckup the best mnmum threshold and the correspondng puncturng patterns obtaned from Step 6 for varyng weather condtons. 8. Repeat all above steps for varyng weather condtons of δ. We extend (9) n the context of puncturng fracton and the new extrnsc MI can be expressed as, ( ) [ I EV IAV, σch 2 = λ p J ( ψ ) + ( p )ξ ] (2) where ψ = ( )[J (I AV )] 2 and ξ = J ( ) ψ + σch, 2. Snce we are puncturng the varable nodes so that () wll reman same. In order to fnd the optmum puncturng fracton and the correspondng threshold, we run the proposed algorthm defned n Sec. 3. Although we dd smulaton for a wde range of rate R p =.3.8 but we are showng one smulaton results n Fg. 3 for a gven rate of R p =.6. The pnk arrow over the varable node curve shows that the dstance between the two EXIT curves decreases and we end-up wth an optmzed results. We are presentng few puncturng patterns and the correspondng threshold obtaned usng the proposed algorthm n Tab. for three cases. IEV, IAC VNC CNC 4 = IAV, IEC Fg. 3. Code optmzaton usng EXIT functons of VND and CND usng the proposed algorthm. Puncturng Fractons p 2 =.5p 4, p 2 = p 4, p 4 =.5p 2 p 2 [.,.7,.23] R p =.3, p =.7, C =.62 db p 4 [.23,.7,.] γ [db] [.8,.75,.65] p 2 [.25,.38,.5] R p =.4, p =.38, C =.24 db p 4 [.5,.38,.25] γ [db] [.5,.3,.] p 2 [.34,.5,.66] R p =.5, p =.5, C =.9 db p 4 [.66,.5,.34] γ [db] [2.2,.8,.45] p 2 [.39,.58,.77] R p =.6, p =.58, C =.68 db p 4 [.77,.58,.39] γ [db] [3.4, 2.45,.9] p 2 [.43,.64,.85] R p =.7, p =.64, C =.23 db p 4 [.85,.64,.43] γ [db] [5.65, 3.2, 2.2] p 2 [.66,.69,.92] R p =.8, p =.69, C = 2.4 db p 4 [.72,.69,.46] γ [db] [6.95, 5.95, 3.8] Tab.. Optmum puncturng fracton. 4. Hybrd FSO/RF Channel We are mplementng the proposed algorthm over a hybrd channel (FSO/RF) and verfy that the proposed algorthm acheves transmsson relablty by adaptng the rate n each channel dependng the respectve channel weather scenaros. We dd not see such analyss before and by usng the proposed algorthm, we can ncrease system effectveness usng a sngle par of encoder and decoder. Our objectve s to decrease the computatonal complexty and cost of the communcaton system usng sngle par of encoder and decoder consderng a slow varyng channel. We are consderng the addtve whte Gaussan nose (AWGN) channel and varyng the channel condtons by δ, where the value of δ denotes the channel qualty.e., ether clear sky condton or bad channel condton. The detaled block dagram of the hybrd FSO/RF codng s shown n Fg. 4. At the transmtter sde, the system nputs k-length nformaton bts, whch are encoded by rate R p = R m P. 4. FSO Channel Model The FSO lnk employs ntensty modulaton wth drect detecton usng two level-pulse ampltude modulaton (2-PAM) transmsson scheme. The receved sgnal (y) after the optcal to electrcal converson s gven by y = ηpx + z (3) where η s the photodetector effcency whch s assumed to be unty for smplcty, x {, } s the transmtted optcal symbols after puncturng, P 2 s the optcal receved sgnal to nose rato (γ). Varous nose models are possble ncludng Posson, sgnal dependent Gaussan and sgnal ndependent Gaussan nose []. In ths paper, we use the sgnal ndependent Gaussan nose model, where z s the Gaussan dstrbuted random varable wth zero mean and unt varance. 4.2 RF Channel Model We consder a lne of sght (LOS) RF channel whch s modelled as a fadng free AWGN channel. Let P be the transmt RF power on the RF lnk, then the receved RF nosy sgnal ŷ ŷ = P x + ẑ (4) where x {+, } s the transmtted RF symbols after puncturng usng bnary phase shft keyng (BPSK), ẑ s the AWGN wth zero mean and unt varance. Quaternary mappng scheme s mplemented n Sec. 5. The receved RF SNR s defned as γ = P. 4.3 Puncturng Code Desgn In a hybrd FSO/RF communcaton system, our am s to transmt data bts over two ndependent parallel channels

5 648 M. N. KHAN, M. JAMIL, M. HUSSAIN, ADAPTATION OF HYBRID FSO/RF COMMUNICATION SYSTEM USING PUNCTURING... k ENC (k, n) n o c no c no2 c no c no 2 Puncturng pattern c no D c no D D 2 Channel Inputs c no c no3 c no 2 c no c no Parallel FSO/RF Channel E O x FSO MAP RF MAP x z ẑ ŷ O E y APD Λ H VN Λ Λ 3 Λ no Λ nr2 Decodng CN n r CSI Λ nr Fg. 4. Detaled Block dagram of hybrd FSO/RF codng system. (hybrd FSO/RF). Prevously researchers [7] have suggested a separate error-correctng code for each channel. Here, however, our man goal s to desgn only one LDPC code as shown n Fg. 4. It s noted that the channel state nformaton (CSI) s avalable at the transmtter so that the approprate puncturng rato can be selected. We have shown an example of puncturng pattern n whch D denotes the poston of punctured (deleted) bts. The rato of the puncturng wll be determned by the CSI. Each n-bt codeword after puncturng s splt nto 2 streams of lengths n o and n r to be transmtted on FSO and RF lnks respectvely. The resultng blocks are sent through the respectve channel,.e., c no coded bts through the FSO lnk and bts through the RF lnks respectvely. Puncturng wll be sutable n order to ncorporate dfferent weather condtons. It wll puncture the bts dependng on weather condton and adapts the rate of transmsson n a flexble fashon. In hybrd channel case, we use the Tanner graph representaton to defne the ensemble C(Ψ, ρ) of bpartte graphs. We represent E be the set of edges n the graph and let E o and E r be the set of edges that are ncdent wth varable nodes correspondng to the optcal and RF channels, respectvely. We can extend () n terms of hybrd channel representaton as, λ o (x) = λ ox and λ r (x) = λ r x, where λ o(λr ) s the fracton of edges connected the optcal (RF) varable node of degree. We are consderng the rght regular LDPC code structure, so (2) wll reman same. Then the Ψ n the new code ensemble for the hybrd code desgn can be desgnated as Ψ = {λ o (x), λ r (x)}. In the hybrd code desgn, we assume that the number of RF punctured nodes s gven by n p, where p s the fracton of RF nodes that are punctured. In the same way, we denote the FSO punctured nodes by np and p s the fracton of punctured FSO varable nodes. 5. Implementng POA Usng Quaternary Modulaton We begn by dscussng how the EXIT chart based technques of [9], [3] can be used to optmze the LDPC code usng the bnary modulated AWGN channels. Our objectve here s to mplement the proposed algorthm usng quaternary modulatons (QPSK/4-PAM). The block dagram shown n Fg. 4 of the conventonal system can be extended to Fg. 5 to ncorporate the mapper/de-mapper constructon. The coded bts from the transmtter are then permuted usng nterleaver to generate the nterleaved codeword. The codeword vector s then fed to the mapper that converts the bts nto symbols. Each symbol s ether complex or real dependng on the type of mapper (QPSK/4-PAM). The symbols are normalzed to have average energy Ê s = M M= x 2 for QPSK and E s = M M= x for 4-PAM, where M = 2 m and m s the number of bts n each symbol. We then extend the algorthm for the quaternary modulatons scheme for the hybrd FSO/RF channel. For ths we analyze the demapper EXIT curves for dfferent mappng schemes (Gray and ant-gray). We provde nvestgatons for 4-PAM and QPSK EXIT over varyng channel condtons. Then we smulate the overall EXIT chart curve for the hybrd FSO/RF channel. Snce we consder the parallel channel, we also measure the best possble fracton of bts to be transmtted to the respectve channel. The man components of the recever are the demapper and the LDPC decoder, each of whch s mplemented usng the log lkelhood rato (LLR) values. Conventonally they are connected wth nterleavers and denterleavers [8] but n our smulaton, we dd not mplement the nterleaver and denterleavers because of the randomness created by the k-bts Transmtter ENC. (k, n) Recever ˆk-bts Channel Decoder CND VND Λ d,e Π X Y MAP. Z Λ d,a Λ Π dm,e D-MAP. Π Λ dm,a ω Channel Fg. 5. Implementaton of quaternary modulaton for the hybrd FSO/RF communcaton system.

6 RADIOENGINEERING, VOL. 25, NO. 4, DECEMBER varable node decoder tself. The receved symbols are passed nto the demapper, whch demaps the symbols and produce a vector Λ dm,e known as the extrnsc LLR of the demapper. The vector Λ dm,e s then denterleaved by Π and the resultng vector Λ d,a s fed n to the LDPC decoder known as LDPC a pror LLR whch works on standard sum product algorthm. The output of the LDPC decoder Λ d,e s then fed back to the nterleaver and the resultng vector Λ dm,a s ntroduced as the nput to the demapper known as demapper a pror LLR. Ths s known as the teratve process between the demapper and the LDPC decoder and shown n Fg Demapper Soft Value The demapper s based on soft value operaton and t extracts the soft value of each coded bt. In the softdemapper, the channel symbols Z {y, y } for the FSO channel are demapped n the form of LLR Λ dm,e. Here n our analyss, we are consderng both the QPSK(Gray/ant- Gray) and 4-PAM(Gray/ant-Gray), each symbol represented by two coded bts (.e., for FSO channel x, x and for RF channel x, x ), the demapper needs to calculate the LLR of the coded bts for each ncomng channel symbol. For the sake of smplcty and to save space, we provde formulaton only for the FSO coded bts (x, x ). The LLR value of x condtoned on the matched flter output Z can be calculated usng the Bayes s rule as Λ(x Z) = Λ a (x )+ ln p(z x =, x = ) + p(z x =, x = ).e (Λ a (x )) p(z x =, x = ) + p(z x =, x = ).e (Λ a (x )). (5) For an arbtrary number of M coded bts x x,,m per symbol Z, we can wrte the LLR values of k-bts as [9] Λ(x k Z) = Λ a (x k ) } {{ } a pror + 2 M = 2 M p(z x k =, x j, j=,,m, j k ).e M Λ a (x j ) j=, j k M Λ a (x j ) j=, j k p(z x k =, x j, j=,,m, j k ).e = } {{ } extrnsc (6). 5.2 Transfer Characterstcs of Demapper The shape of the transfer characterstcs of the demappers QPSK/4-PAM depends on the channel SNR and bt labelng pattern pattern (Gray/ant-Gray) [2]. We then proceed by showng the performance comparsons of the demappers dependng on the bt mappng by calculatng the EXIT curves. We measured the demappers s EXIT curve by runnng a number of Monte Carlo smulaton [8]. The demappers s EXIT functon can be represented as I E,dm ( IA,dm, γ ). The results of the Monte Carlo smulatons for the demapper transfer curves are shown n Fg. 7. From the smulaton results n Fg. 7, t s notced that Gray mappng doesn t show any mprovement whle the ant- Gray mappng s showng mprovement after a number of teraton. The nformaton transfer curve for Gray mappng s not gong to change for ncreasng a pror knowledge and t stays farly constant. It shows the strong mpact of selectng the mappng scheme teratve process. However the ant-gray mappng scheme s showng some slope wth ncreasng the a pror knowledge. 5.3 Overall EXIT Chart Usng POA In our work we proposed the adaptaton of POA over the jont channel condtons (e.g., we consder two stuatons, clear sky condton for delta (δ stands for the channel qualty) equals to zero and bad weather condton for delta equal to.25) and try to mnmze the postve dfference between the two EXIT chart curves. The POA elaborate for the hybrd FSO/RF communcaton system. We evaluate the POA over a wde range of rate and t shows from the results that the algorthm s adaptve over all the rates. Furthermore the algorthm s adaptve over varyng channel condtons. We propose POA and measure the EXIT chart for the gven code rate. The EXIT chart measures the mutual MI jontly and gves an estmate of code convergence. Whle measurng the MI, we ntroduce a new parameter named as delta and say that the qualty of both channels wll be controlled by delta. In ths way, we use two values of delta n smulatons whch ncorporate dfferent weather condtons QPSK ant Gray mappng QPSK Gray mappng 4 PAM Gray mappng 4 PAM ant Gray mappng VN I EV IE,dm.5.4 D-MAP I E,dm I A,dm I AV d v d c CN IA,dm Fg. 6. Iteratve graph of demapper and LDPC decoder. Fg. 7. EXIT chart curves for QPSK/4-PAM demappers for SNR =. db usng the AWGN a-pror channel approxmaton.

7 65 M. N. KHAN, M. JAMIL, M. HUSSAIN, ADAPTATION OF HYBRID FSO/RF COMMUNICATION SYSTEM USING PUNCTURING... Hybrd channel EXIT chart δ = Hybrd channel EXIT chart δ = IEV, I AC IEV, I AC I AV, I EC (a) EXIT Chart at δ = and (R p =.7) I AV, I EC (b) EXIT Chart at δ =.25 and (R p =.7). Fg. 8. Best Threshold (.e., optmzed puncturng par for the best value of SNR). Our objectve s to optmze the code usng the puncturng technque and we provde example for the bnary mappng. We know that the optmzaton crtera n our proposed algorthm requres two EXIT curves to be generated, one that corresponds to the VND, we call IEV and another that corresponds to the CND, we call IEC. The goal s then ft the two curves together by pckng the approprate puncturng ratos (patterns). It s seen from Fg. 5, that the VND curve characterzes not only the varable nodes of the LDPC code, but also the characterstcs curve of the mappng. The overall VND EXIT curve s created by frst generatng the transfer characterstcs curve for the mapper at the gven SNR whch s known as the demapper EXIT curve. The demapper curve can be generated usng Monte Carlo smulaton [4], [8] under the assumpton that the demapper s a pror nput s condtonally Gaussan [9]. We can extend (9) n the form of overall quaternary modulaton VND EXIT functon as IEV (IAV, γ, d v ) = pj κ! q 2 IE,dm (IA,dm, γ) ]. + ( p)j κ + [J (7) (I )]2, I where v )[J AV E,dm (IA,dm, γ) = q κ = (d 2 2 J dv.j (IA,dm ) + σch (γ)) and we can model the a-pror LLR,.e., IA,dm (IAV, d v ) = J dv.j (IAV ), for the demapper whch s the output of the VND and s assumed as Gaussan random varable [3]. It s noted that (7) represents the regular LDPC code VND curve. In case of an rregular curve, we can extend (7) as dv max X IEV (IAV, γ) = ν p IEV IAV, γ, d v (8) = + ( p )IEV IAV,, d v. It s notced from Fg. 7, that QPSK wth Gray mappng, we cannot have any mappng gan and therefore, we can utlzed (8) for analytcal smulatons. The smulaton results δ Puncturng Optmzaton Algorthm Results (QPSK) Rp p2 p4 p D2 p D4 γ [db] γ D [db] Tab. 2. Puncturng fracton for each rate n hybrd FSO/RF channel (QPSK). showng the behavor of EXIT chart varatons (optmzaton) for varable puncturng ratos. The results obtaned for the hybrd channel are shown n Fg. 8 and presented n Tab. 2. If δ = as gven n Tab. 2, weather s consdered to be clear and t wll not affect the MI of the system. On the other hand, f the value of δ, (delta =.25 as gven n Tab. 2), t means that the weather s not clear and the MI s affected by a gven amount of delta. So ths s the way, we can ncorporate dfferent weather condton n smulaton. It s also techncally very clear that f the weather s clear, the system performs well wth maxmum MI and on the other way around for bad weather, the performance of the system s also worse wth low MI. 6. Concluson We propose a novel puncturng optmzaton algorthm for rate adaptaton and analyse ts performance for the hybrd FSO/RF channel case. We see that the propose algorthm well adapted the dfferent weather scenaros by provdng the best threshold and the correspondng puncturng patterns. It dstrbute the amount of channel bts n an effcent way under equal and unequal channel condtons n a flexble fashon. We see that our proposed algorthm performs well under all channel condtons and provde better performance. New results for the hybrd EXIT chart have been derved for the bnary and quaternary modulaton schemes as well whch present the behavor of EXIT chart n the hybrd channel. We also develop the analyss for the quaternary modulaton and provde the smulaton results of the correspondng mappers. The new research results wll help n mplementng the proposed algorthm for hgh speed communcaton applcatons. The algorthm s computatonally less complex and effcent.

8 RADIOENGINEERING, VOL. 25, NO. 4, DECEMBER Acknowledgments The author would lke to thank Prof. Bll Cowley and Dr. Khoa D. Nguyen from the Insttute for Telecommuncaton Research, South Australa for provdng helpful support and useful suggestons durng the course of nvestgaton. References [] GAGLIARDI, R. M., KARP, S., Optcal Communcatons. 2nd ed. New York (USA): John Wley & Sons, Inc., 995. ISBN: [2] KHAN, M. N., COWLEY, W., NGUYEN, K. Lnk adaptaton of FAHOR communcaton system. In Proceedngs of the Australan Communcatons Theory Workshop (AusCTW). Wellngton (New Zealand), 22, p DOI:.9/AusCTW [3] MAKKI, B., SVENSSON, B., ERIKSSON, T., et al. On the performance of RF-FSO lnks wth and wthout Hybrd ARQ. IEEE Transactons on Wreless Communcatons, 26, vol. 5, no. 7, p DOI:.9/TWC [4] KHAN, M. N. Importance of nose models n FSO communcatons. EURASIP Journal of Wreless Communcaton and Networkng, Feb. 24, vol. 24, no. 2, p.. DOI:.86/ [5] PISHRO-NIK, H., FEKRI, F. Results on punctured low densty partycheck codes and mproved teratve decodng technques. IEEE Transactons on Informaton Theory, 27, vol. 53, no. 2, p DOI:.9/TIT [6] KHAN, M. N., JAMIL, M. Maxmzng throughput of free space communcatons system usng puncturng technque. Araban Journal for Scence and Engneerng, Nov. 24, vol. 39, no. 2, p DOI:.7/s [7] GALLAGER, R. Low-densty party-check codes. IRE Transactons on Informaton Theory, 962, vol. 8, no., p DOI:.9/TIT [8] JOHNSON, S. Iteratve Error Correcton: Turbo, Low-Densty Party-Check and Repeat-Accumulate Codes. New York: Cambrdge Unversty Press, 2. ISBN: [9] HAGENAUER, J. The EXIT chart-ntroducton to extrnsc nformaton transfer n teratve processng. In Proceedng of the 2th European Sgnal Processng Conference (EUSIPCO). Venna (Austra), Sep. 24, p ISBN: [] ESLAMI, A., VANGALA, S., PISHRO-NIK, H. Hybrd channel codes for effcent FSO/RF communcaton systems. IEEE Transacton on Communcaton, Oct. 2, vol. 58, no., p DOI:.9/TCOMM [] LUBY, M., MITZENMACHER, M., SHOKROLLAHI, M., et al. Improved low-densty party-check codes usng rregular graphs. IEEE Transactons on Informaton Theory, Feb. 2, vol. 47, no. 2, p DOI:.9/ [2] RICHARDSON, T., URBANKE, R. The capacty of low densty party-check codes under message-passng decodng. IEEE Transactons on Informaton Theory, 2, vol. 47, no. 2, p DOI:.9/ [3] TEN BRINK, S., KRAMER, G., ASHIKHMIN, A. Desgn of lowdensty party-check codes for modulaton and detecton. IEEE Transactons on Communcatons, Apr. 24, vol. 52, no. 4, p DOI:.9/TCOMM [4] TEN BRINK, S. Convergence behavor of teratvely decoded parallel concatenated codes. IEEE Transactons on Communcatons, Oct. 2, vol. 49, no., p DOI:.9/ [5] SHARON, E., ASHIKHMIN, A., LITSYN E. Analyss of lowdensty party-check codes based on EXIT functons. IEEE Transactons on Communcatons, Jul. 26, vol. 54, no. 7, p DOI:.9/TCOMM [6] ASHIKHMIN, A., KRAMER, G., TEN BRINK, S. Extrnsc nformaton transfer functons: model and erasure channel propertes. IEEE Transactons on Informaton Theory, Nov. 24, vol. 5, no., p DOI:.9/TIT [7] TAPSE, H., BORAH, D. Hybrd optcal/rf channels: characterzaton and performance study usng low densty party check codes. IEEE Transactons on Communcatons, 29, vol. 57, no., p DOI:.9/TCOMM [8] RAKIA, T., YANG, H.-C., ALOUINI, M.-S., et al. Outage analyss of practcal FSO/RF hybrd system wth adaptve combnng. IEEE Communcatons Letters, Aug. 25, vol. 9, no. 8, p DOI:.9/LCOMM [9] TEN BRINK, S., SPEIDEL, J., YAN, R.-H. Iteratve demappng and decodng for multlevel modulaton. In Proceedngs of the Global Telecommuncatons Conference. 998, vol., p DOI:.9/GLOCOM [2] TEN BRINK, S. Desgnng teratve decodng schemes wth the extrnsc nformaton transfer chart. AEU Internatonal Journal of Electroncs and Communcatons, 2, vol. 54, no. 6, p About the Authors... Muhammad Nasr KHAN was born n Salkot, Pakstan. He receved hs M.Sc. from TU Delft n 29 and Ph.D. from the Insttute for Telecommuncaton Research, South Australa. Hs research nterests nclude sgnal processng for communcaton, channel codng and detecton. Mohsn JAMIL was born n Gujranwala, Pakstan. He receved hs M.Sc. from NUS, Sngapore and Ph.D. from Unversty of Southampton, UK. Hs research nterests nclude control system and robotcs. Mazhar HUSSAIN was born n Multan, Pakstan. He receved hs Ph.D. from France. Hs research nterests nclude mage and sgnal processng.