The Comparisonal Analysis of the Concept of Rectangular and Hexagonal Pilot in OFDM

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1 Communicaions and ework, 2009, doi: /cn Published Online Augus 2009 (hp:// The Comparisonal Analysis o he Concep o Recangular and Hexagonal Pilo in OFDM Jeanbapise YAMIDI 1, Muqing WU 2 Broadband Communicaion ework Laboraory, Beijing Universiy o Poss and Telecommunicaions, Beijing, China 1 jbyamindi@yahoo.r, 2 wumuqing@bup.edu.cn Absrac: Channel esimaion in coheren OFDM by insering pilo-symbols ino wo-dimensional ime- requency laice is a promising candidae or improving channel ransmission capaciy in uure wireless communicaion sysems. This paper proposes a new Caresian mahemaical concep o he Hexagonal Pilo Paern, Hexagonal Pilo wih Virual and Recangular Pilo Paern. The main ocus o his work is o compare beween he wo pilos and by virue o simulaion conclusion which o he wo pilos yields a beer perormance. Keywords: hexagonal pilo paern, hexagonal pilo wih virual, recangular pilo paern, esimaion, inerpolaion, exrapolaion 1. Inroducion One o he mos imporan echniques applied in Physical layer o WiMAX is known as Orhogonal Frequency -Division Muliplexing (OFDM), which is he sysem or daa ransmission and he suppor or channel esimaion and synchronizaion. Many auhors proposed he concep o pilo ones o inerpolae he channel response in [1] and [2], recenly some lieraure proposed mehods o pilo symbols apar rom he exising equi-spaced pilo paern or OFDM sysem as described in [4] and [5]. In his paper, we are ocusing on a speciic pilo subcarriers by doing he analyical descripion and srucural pilo o he wo dieren pilos known as Hexagonal and Recangular. The res o his paper is organized as ollows: The graphical represenaion o Recangular and Hexagonal Pilo Paern in Secion 2, The Simulaion resuls o he Hexagonal Pilo Paern, Hexagonal wih Virual and Recangular Pilo Paern in Secion 3. The analyical evaluaion and comparison in Secion 4 and he paper is concluded in Secion The Recangular and Hexagonal Pilo Paern Represenaive 2.1 The Recangular Pilo Grid Represenaion The recangular Pilo grid marix can be expressed by rec p 0 0 p where Δp is he disance in requency and Δp is he disance in ime direcion and his recangular marix can be wrien as: (1) where 0 V VRECT (2) 0 subcarriers in he requency direcion and he OFDM symbols in he ime direcion ha can be arranged as a se given by: P n, k, n, k,..., n, k. (3) ap ap And he number o pilo subcarriers in he inpu block is expressed by p de rec (4) The esimaion o block conains p number o OFDM symbols each hosing p pilo posiions. The oal number o pilo posiions o a recangular pilo grid is given by prec, Under he condiion o 1 2(1 ) prec, p p (5) 2 D,max and. (6) CP The graphical represenaion o he recangular pilo in he coordinae sysem is depiced below. C

2 2 THE COMPARISOAL AALYSIS OF THE COCEPT OF RECTAGULAR AD HEXAGOAL PILOT I OFDM Recangular Hexagonal V 2 V 2 V 1 V 1 Figure 1. The recangular pilo grid. Figure 2. The hexagonal pilo grid. 2.2 Modiicaion o Recangular Pilo Paern The applicaion o Cogniive Radio or opimum channel esimaion by using pilo paern can aec he requency band by he presence o Licensed User. The pilo paern in he presence o Licensed User can be classiied according o he Bandwidh ino arrowband Licensed User and Wideband Licensed User. 1) The arrowband Licensed User: I can exchange easily he posiion o he pilo symbols wih daa pars. This exchange o he pilo subcarrier is conneced o he daa subcarrier o he previous or he nex subcarrier and we assumed ha he applicaion o pilo symbols in he channel esimaion process canno modiy he pilo symbol bu only one daa subcarrier and can lose some hroughpu so his narrowband inererence is depiced. 2) The Wideband Licensed: There are similariies in he process o arrowband and Wideband, he only dierence is on he edge locaion o he License User signal exchange o wo pilo subcarriers wih daa subcarriers and he number o deacivaed subcarriers is depending upon he Licensed User Band. 2.3 The Hexagonal Pilo Grid Represenaion The implemenaion o Hexagonal Pilo is aciliaed by he Virual Pilo in reducing he Pilo Densiy by he annulmen o u 2 =0 and he Pilo Densiy becomes dp= u 1 v 2 and he represenaion o he srucure is according o he Hexagonal Pilo spacing. The equaion o he Hexagonal Pilo is expressed by V VH (7) And graphically i can be represened as below. In boh o he wo dieren ypes o Pilo, he Iner-Symbol Inererence is sill a big challenge during he process o pilo ransmission. This challenge can be resolved by he ollowing echniques. 2.4 Modiicaion o Hexagonal Pilo Paern The process o exchanging he posiion o he pilo subcarrier wih he daa subcarrier conneced o he previous subcarrier and he nex subcarrier is done by exchanging he pilo subcarrier wih he daa subcarrier which lies in he previous subcarrier or in he nex subcarrier. By doing his we can sill be able o keep he pilo symbols o be used in he channel esimaion process, bu on he oher side we will have o sacriice one daa subcarrier and hus lossing some hroughpu. This process is almos similar as in Recangular process, he only dierence, a he receiver, he received pilo symbols are processed using he ieraive algorihm in order o obain he virual pilo symbol. This ieraive algorihm inroduces he concep o inerpolaion opion which is applied via simple averaging beween he received shied pilo symbols and he received pilo symbols. The received shied pilo symbols in he nex subcarrier or exrapolaing he virual pilo symbols on he posiion o he Licensed User by he eec o he received pilo symbols. 2.5 The Virual Pilo The Virual Pilo symbols are ieraive o he inerpolaion o coniguous pilo o he posiion o he virual. I is deined a irs by he pilo spacing in requency axis, which is smaller han he channel coherence bandwidh, and he second is pilo spacing in ime axis, which is smaller han he channel coherence ime on he iniial compuaion o he received pilo symbols or each OFDM. The OFDM rames during each ime slos, and subcarriers in he requency domain respecively. oe ha his operaion mus be processed only a he pilo posiions as: H H k n (8) k, n,, k n k n, Sk, n S k,n is he ransmied symbol, he indexes k, and n indicaes he posiion o each pilo symbol wihin he OFDM rame. The symbol W is he se o pilo posiions wihin he OFDM sub rame. C

3 THE COMPARISOAL AALYSIS OF THE COCEPT OF RECTAGULAR AD HEXAGOAL PILOT I OFDM 3 Figure 3. Inerpolaions processes, (a) he DFT principle or requency domain inerpolaion, (b) linear inerpolaion process over he ime domain. These Inerpolaions processes are illusraed by he igure above. By he iniial compuaion o he channel he value can be linearly inerpolaed i.e. he value o he virual pilo symbols is expressed by 1 H n, k Hn, k1 Hn, k 2 1 (9) n k n k Where H, 1 and H, 1 are iniial esimaes respecively o he previous and he nex pilo a his poin. The ieraive algorihm processing o pilo symbols is expressed as or n =1: ( p 1) pilos in ime direcion, number o subcarriers and he number o OFDM symbols per rame. A he posiions close o Licensed User's carriers. The esimaion process isel is divided ino wo pars assume ha i we can assume ha i can also be divided ino more han wo depending on he number o Licensed User ha exis. The irs par is he upper par and he second is he lower par. The par o he specrum which is occupied in he middle is discarded and no included in he channel esimaion calculaion. By deploying he virual pilo concep on cerain case or good undersanding le us illusrae by band less han 2x disance o pilos, he edge eec o he sliding window can be avoided, hence beer channel esimae can be obained, while he Channel Transer Funcion a he posiion o he Licensed User are discarded. or k =1: ( q 1) 1 H H H 2 n, k n, k1 n, k1 end end c s p 1,2,... and q 1, 2,... Where,,, are respecively he disance s c beween pilos in requency direcion, disance beween Figure 4. Transmied modiied hexagonal pilo paern or he wideband Licensed User case. Figure 5. Receiver side hexagonal pilo paern wih virual pilo symbols obained rom he ieraive processing algorihm. C

4 4 THE COMPARISOAL AALYSIS OF THE COCEPT OF RECTAGULAR AD HEXAGOAL PILOT I OFDM By deploying his scheme, we can sill esimae he channel opimally despie o he unloaded subcarriers caused by he Licensed User. A he receiver, he received pilo symbols are processed using he Ieraive algorihm o obain he virual pilo symbols like in he case o he arrowband Inererence. The scheme isel can be seen in Figure The Simulaion Resul In his secion we are going o do he comparison beween he Hexagonal Pilo Paern wih he Recangular Pilo Paern and he Hexagonal Pilo wih Virual symbols wih he Recangular Pilo Paern wih Virual Pilo symbols disribuion. For his simulaion, we consider he dieren parameers such as subcarriers per OFDM symbol, OFDM symbols per esimaor rame and he disance o subcarriers in he requency direcion and he ime direcion, he oal number o pilo subcarrier posiions is excessive o be direcly employed in he esimaion o all he channel ranser acors. Figure 6. The perormance comparison o hexagonal pilo paern and he recangular pilo paern in uncion o BER in Eb/0 in db scale. Figure 7. The perormance comparison o Hexagonal Pilo wih Virual symbols compared wih Recangular Pilo Paern wih Virual Pilo symbols in uncion o BER in SR in db scale. 4. The Comparisonal Analysis This secion presens he main goal o our work by making he analyical evaluaion and comparison o he Hexagonal Pilo Paern and Recangular Pilo Paern. Analysis o he eec o having several scaered inererences and he eeciveness o he proposed hexagonal pilo paern scheme o comba he inererences eecs. Here we analyze he eec o increasing number o inererers by using he ieraive and exploiing he channel coherence bandwidh propery. The Hexagonal Pilo Paern is more complicaed o be implemened using he 2xl-D Wiener iler. The implemenaion o Hexagonal Pilo Paern is easy due o he echnique o Hexagonal Pilo Paern wih he Virual Pilo symbols. The Hexagonal Pilo Paern is an opimum sampling. I is he main mehod which requires 13.3% less samples when compared o he Recangular Pilo Paern ha represens he same signal and gives a beer BER perormance, and hereore he Hexagonal Pilo Paern perorms beer and more eicien sampling mechanism when compared o he Recangular Pilo Paern as shown in Figure 6. The perormance comparison o he Hexagonal Paern wih virual pilos a high SR ouperorms signiicanly he oher hree, he Recangular, Hexagonal, and Hexagonal wih Virual pilos and inerpolaion/exrapolaion process. Recangular Paern wih Virual Pilos ouperorms he Recangular and Hexagonal Pilo Paern a high SR, while a low SR perormance degradaion occurs caused by he error o inerpolaing he noisy iniial channel esimaes. 5. Conclusions The simulaion shows ha Hexagonal Pilo design is beer han he recangular and oher pilo design paerns. This beer perormance is due o he eec o increasing number o inererers by using he ieraive and exploiing he channel coherence bandwidh propery o Hexagonal Pilo. The echnique o combining wih Virual Pilo symbols in he low SR space is due o he error caused by inerpolaion o he heavily noisy pilos and he Cogniive Radio is he bes suppor o perorm channel esimaion. The Hexagonal Pilo is become he mos useul in he sysem o Wireless ework communicaion hank o he compaibiliy o he Hexagonal Pilo and ework coniguraion. 6. Acknowledgmens Special hanks o Engineers rom Beijing Universiy o Poss and Telecommunicaions: Mr. Fena Adinew, Mr. Mala Umar, my proessor Wu Mu-qing and Beijing Universiy o Poss and Telecommunicaions or he assisance. C

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