Super-Orhogonal Space-Time Trellis Codes for Virual Anenna Arrays Oludare Sokoya 1, Hongjun Xu and Fambirai Takawira 3, Member IEEE 1. Meraka Insiue, CSIR Preoria. dsokoya@csir.co.za. & 3. School of Elecrical, Elecronic and Compuer Engineering Universiy of KwaZulu-aal Durban 4041, Souh Africa {Xuh, fakaw}@ukzn.ac.za Absrac This paper invesigaes he performance of super-orhogonal space ime rellis codes when Virual Anenna Arrays () are employed. The concep of virual anenna arrays was developed o emulae Muliple-Inpu Muliple- Oupu (MIMO) schemes wih limied number of anennas. The emulaed MIMO sysems drasically increase daa hroughpu in erms of he bi error rae (BER) and he frame error rae (FER) when compared wih MIMO schemes where is no employed. Index Terms super orhogonal codes, anenna arrays, co-operaive diversiy, space ime codes, error rae, fading channel. I. ITRODUCTIO Wireless sysems which communicae over Single- Inpu Single-Oupu (SISO) wireless channel have limied capaciies in fading channels when compared o ransmission over MIMO wireless channels. Telaar [1] and Foschini e al [] have shown ha no only can MIMO overcome he limiaion of SISO sysems, bu he average capaciy of a r MIMO Gaussian channel grows linearly wih min (, r). The work in [1] and [] assume ha he fading beween pairs of ransmi-receive anenna elemens are independen and idenically Rayleigh for he MIMO (or mulielemen anenna) sysems o achieve heir large capaciy. However, in real propagaion environmens, he fading is no independen, due mainly o he insufficien spacing beween anenna elemens especially a he receiver side. I has been observed [3] ha when he fading is correlaed, he channel capaciy can be significanly smaller han when he fades are independenly idenically disribued. This inheren challenge of MIMO schemes This work is suppored by he African Advanced Insiue for Informaion & Communicaion Technology (Meraka Insiue) a he Council of Scienific and Indusrial Research (CSIR), Preoria Souh Africa. limis he number of anenna elemens ha can be deployed a various ends of a MIMO sysem i.e. he ransmi and he receive end. For a cellular nework, he deploymen of muliple anennas migh be possible a he Base Saion (Transmi end), bu i migh no be possible o have more han one anenna a he Mobile saion (MS) due o he compac naure of mobile devices. Virual anenna arrays [4] were recenly inroduced o allow he applicaion of MIMO capaciy enhancemen echniques, o mobile erminals wih a limied number of anenna elemens. aurally, he deploymen of MIMO echniques seems o be impossible where he number of anennas a he receiver is a limiing facor. However, one could view a cell no as a sysem of single poin communicaion links, bu raher as a nework wih cerain number of anenna elemens available in i, which hen allow i o communicae among each oher. Wih appropriae precauions, such deploymen could emulae MIMO sysems. The difference o he radiional MIMO anenna array is ha he anenna elemens are conneced hrough a wireless link. The configuraion of a Virual anenna array MIMO scheme is depiced in Figure 1. The paper is organized as follows. In Secion II, he concep of is presened. In Secion III, a brief review of space ime coding schemes is given wih emphasis on he SOSTTC scheme. Secion IV, he general ransmission model of he SOSTTC is given and laer on he emulaed MIMO scheme is expressed. Simulaion resuls are laer presened in Secion V. Finally, conclusions are drawn in Secion VI II. COCEPT OF VIRTUAL ATEA ARRAYS Dohler [4] summarized he concep of Virual Anenna Arrays as: Le a sufficien number of users wihin a communicaion sysem communicae wih he base saion and direcly wih each oher such ha a rade-off is found beween curren echnological limis and required capaciy increased. From ha simple design crierion various echnical implicaions follow.
Figure 1: A Virual Anenna MIMO Scheme The number of communicaing anenna elemens will dicae he maximum achievable capaciy. This number will depend on he acual number of available anenna elemens willing o communicae and he general echnology limi. Once he number of muually communicaing anennas are esablished, echnical realizaions have o be found o come close o he heoreical capaciy bound. The realizaion of a scheme will largely depend on he following; Access scheme (FDMA, TDMA and CDMA) Choice of main link echnology (GSM, UMTS) Choice of relaying echnology (Fixed, Selecive and Incremenal Relaying) Transceiver Complexiy umber of anennas wihin a given geographical area Synchronizaion To embed ino an exising echnology, such as GSM, he direc link beween he base saion and he mobile saion can be chosen o be based on 3G UMTS W-CDMA echnology and he relaying link can use a echnology ha is capable of direc mode communicaion e.g. HiperLA. A can be formed wih mobile erminals ha are close geographically o each oher and which require a beer QoS in ha hey sar supporing each oher via muual communicaion. For example, he mobile erminals can communicae wih he base saion using he W- CDMA link and a he same ime hey relay furher capured informaion o oher mobile erminals wihin he same group using HiperLA echnology. Concepual rules for forming a can be summarized as follows: Base saions and mobile erminals should be able o suppor a scheme; for he mobile erminal his means i mus be able o suppor boh he main link wih he base saion and also he relaying link o oher erminals and for he Base saion his means i mus be able o encode daa-sreams such as if i is communicaing o each mobile erminal hrough a MIMO sysem. Upon regisering ino a nework each mobile erminal mus inform he base saion of is abiliy o suppor wih is echnological realizaion and limiaions. The mobile saion should be able o rack each mobile saion o deermine is posiion wihin he nework. Whenever wo or more mobile saions ge close spaially ogeher o form a, he base saion should inform he mobile saion abou such possibiliy. Depending on he previously negoiaed agreemen, he nework iniiaes he formaion of a among hese mobile erminals. When he condiion of a relaying link deerioraes, he nework should iniiae a deachmen of he mobile erminal or erminae he enire group. III SPACE TIME CODIG The use of channel coding in combinaion wih a MIMO scheme achieves diversiy, bu he drawback is loss in bandwidh efficiency. Diversiy can be achieved wihou any sacrifice in bandwidh efficiency if he channel codes are specifically designed for muli-anenna ransmission scheme. Space ime coding is a bandwidh and power efficien mehod of communicaing over fading channels. I combines he design of channel coding, modulaion, ransmi diversiy, and receive diversiy. Space ime codes provide beer performance compared o an uncoded sysem. Some of he basic echniques of space ime code are reviewed below A. Layered Space Time Code Layered space ime (LST) codes are channel codes ha are designed according o he layered archiecure proposed by Foschini in [6]. The consrucion of he LST codes for an r sysem whose capaciy is linearly scaled wih is based on an separaely coded one-dimensional (1-D) subsysems of equal capaciy. The LST archiecure demuliplexes a sream
of daa ino layers and each layered daa is hen 1- D convoluionally encoded by he encoders and hen ransmied by anennas. The above described layered space ime archiecure is formally known as he horizonally layered space ime (HLST) archiecure. Daa can be rearranged amongs he layers such ha he coded daa are ransmied by ransmi anennas forming a diagonally layered space ime archiecure (DSLT) [7]. B Space Time Block Code Space ime block codes were firs presened by Alamoui [8] as a simple ransmi diversiy echnique. Tarokh e al [9], [10] generalized Alamoui s scheme by using he heory of orhogonal design and also exended i o wo or more ransmi anennas. The orhogonal design allows for he use of a simple maximum-likelihood decoding algorihm based on linear combining a he receiver. There are wo classes of space ime block codes generaed from orhogonal designs. The firs class consiss of hose from real orhogonal designs for real consellaion such as Pulse Ampliude Modulaion (PAM) and he second consis of hose from complex orhogonal designs for complex consellaions such as Phase Shif Keying (PSK) and Qudraure Ampliude Modulaion (QAM). The exisence of real orhogonal designs for differen value of is known as he Hurwiz-Radon problem in mahemaics [11]. From he Hurwiz-radon heory, a full rae real orhogonal design exis only when, 4 or 8. The proposed scheme of Alamoui in [8] was laer shown in [9] as a space ime block code from complex orhogonal design of rae 1 for. C Space Time Trellis Code Space ime rellis coding was inroduced by Tarokh e al [1] as a means of combining signal processing and muliple ransmi anenna producing a sysem wih significan gain over he earlier ransmi diversiy schemes. Space ime rellis codes operaes on a one inpu symbol a a ime and hen produce a sequence of vecor symbols whose lengh represen he number of ransmi anennas. In [13], opimum space ime rellis codes were proposed using generaor marices, which provide maximum diversiy and coding gain for various numbers of saes and anenna wih PSK modulaion. I can be shown ha he space ime rellis codes presened by Tarokh in [1] provide he bes radeoff beween consellaion size, daa rae, diversiy advanage and rellis complexiy when compared wih oher codes [13], [14]. D Super-Orhogonal Space Time Trellis Code A new class of space ime codes called super orhogonal space ime rellis codes (SOSTTC), was inroduces in [15]. These codes combine se pariioning and a super se of orhogonal space ime block codes in a sysemaic way o provide full diversiy and improved coding gain when compared wih earlier space ime rellis consrucions [1], [13] and [14]. SOSTTC no only provide a scheme ha is an improvemen in coding gain when compared wih earlier consrucions, bu i also answers he quesion of a sysemaic design for any rae, number of saes and he maximizaion of coding gain. The orhogonal ransmission marix used in he design of SOSTTC is given in (1). 1 ( x x θ ) A,, 1 * jθ * x e x1 For an M-PSK modulaion wih consellaion signal a j represened by x i M e π, i 1,., a 0,1,, M-1, one can pick θ πá/m, where á 0,1,, M-1. In his case, he resuling ransmied signals of (1) are also member of he M-PSK consellaion and, herefore do no expand he consellaion signals. Since he ransmied signals are from a PSK consellaion, he peak-o-average power raio of ransmied signals is equal o one. The choice of θ 0, π for Binary PSK (BPSK) and θ 0, π/, π, 3π/ for Quaernary PSK (QPSK). I should be noed ha when θ 0, (1) becomes he code presened in [8]. The consrucion of he SOSTTC is based on he expansion of he orhogonal ransmission marices and sandard se pariioning mehod [16]. In [15], he se pariioning for he SOSTTCs is shown and also he way he code maximize coding gain, wihou sacrificing rae, in more deails. A ransmission sysem of jθ x e x IV Sysem Model ransmi anennas and (1) receive anennas is considered. The inpu binary daa sreams are firs fed ino an ouer rellis code modulaion encode o generae a sequence of complex modulaed symbols. The complex modulaed symbols x i (i 1,,, ) are hen fed ino an inner space ime block encoder o generae he orhogonal ransmied (n) code marix (1). x i is define as he complex value of he modulaed symbol ransmied from he h (n) ransmi anenna in he nh signaling inerval and h ij is he channel coefficien from he ih ransmi anenna r
o he jh receive anenna a he same signaling inerval, i (1,,., ) and j (1,,., r ). Assuming ha he channel sae informaion is know a he receiver, he corresponding se of successive signal sample a wo oupu ime is given by: ( ) where l 1,,, r and η n l are independenly idenical disribued complex zero mean Gaussian h 11 h 1 h 1 Base Saion h jθ l l1 1 l ηl θ * j * l r l1 l 1 ηl r noise samples, each sample wih σ per dimension. I is assume ha he channel elemens undergo Rayleigh Fading. A EMULATIO OF (, () r ) SOSTTC WITH In [15], Hamid e al. presened various example of he SOSTTC scheme wih more han one anenna a he receiver and various saes of he rellis. Our ineres in his secion of he paper is he scheme wih wo ransmi anennas and wo receive anennas. The combined signals from he wo receive anennas are a simple addiion of he combined signal, which could have been made a each receive anenna. I can hence be concluded ha if signals received a each anenna are independen and if he combining is performed a each anenna, he same resuls should be obained by adding he wo signals. The (, ) SOSTTC scheme can be applied o a single anenna mobile erminal. The main idea is o use he oher (supporing) mobile erminal as a ransparen relay. This laer one acs as a second receiving anenna for he arge mobile erminal. The scheme is depiced in Figure. This scheme yield a diversiy gain of 4 under perfec condiion wih respec o non-diversiy scheme. The idea is o send boh orhogonal ransmission marix inended for he arge mobile saion (MS) from he wo ransmi anenna a he base saion (BS). Boh hese sreams are received by he relaying MS and he arge MS, hrough differen channels h 11, h 1, h 1, h. The relaying MS reransmis is received double sream o he arge MS using channel h 3, acing as a ransparen ransceiver. I should be noed ha he arge MS receives wo ses of orhogonal ransmied Figure : Base Saion Anennas (Tx) and One Relaying MS emulaion he (, ) SOSTTC scheme. signals i.e. he received signals as a resul of he BS /Targe MS link and also he received signal as a resul of he Relaying MS/Targe MS link. The echnological realizaion of separabiliy is no sraighforward and severely dependen on he underlying sysem assumpions and access echnology. I should be noed, however ha he separaion is echnically feasible and accomplished as noed in [17]. Since he wo signal sreams are separable, he combining akes place in he arge MS. The arge MS receives (3): jθ 1 11 1 1 η1 θ * j * 11 1 1 η a he nh signaling inerval from he base saion and he relaying MS receives (4): jθ 3 1 1 η3 θ * j * 4 1 1 η4 (3) (4) The relaying MS reransmis he received double sream hrough channel h 3. Thus, he arge MS receives finally: r h r η 5 3 3 5 jθ 5 3 1 1 3 3 η3 η5 () n () n () n () n 6 h3 r4 η6 * () n () n () n () n () n jθ () n () n () n * () n () n () n 6 3 1 3 1 3 η4 η6 r h h x e h h x h r Targe MS h 3 r h h x e h h x h Relaying MS (5) A he branch of he rellis of he SOSTTC scheme, he decoder compues an esimae of signals for boh he direc base saion/arge MS link and he relaying/ MS link using he maximum likelihood echnique.
Once he branch merics are compued he Vierbi Algorihm [5] is applied o search for he pah wih he lowes accumulaed meric. V SIMULATIO RESULTS The simulaion resuls shown in Figure 3-6 were based on he following assumpions. The enire wireless channels involved are quasi-saic non-frequency selecive Rayleigh channels wih average power of uniy. The oal power of he ransmied coded symbol was normalize o uniy. The receiver is assumed o have perfec knowledge of he channels. For he SOSTTC resuls, each frame consiss of 56 bis while for he STBC resuls, each frame consis of 4 bis. Figures 3 and 4 shows he bi error rae and he frame error rae of a 4-sae SOSTTC for a and non- sysems wih QPSK modulaion respecively, while Figure 5 and 6 shows he bi error rae and he frame error rae of a STBC scheme for a and non- sysems wih QPSK modulaion respecively. From he four figures, one can see ha he emulaed (, ) scheme performs worse ha he radiional (, ) MIMO schemes i.e. STBC and SOSTTC, however beer ha he (, 1) MIMO schemes. The performance degradaion wih respec o he (, ) MIMO schemes is due o he addiional noise in he relaying mobile saion. Figure 4: FER of 4-Sae SOSTTC scheme wih QPSK, and non - for a varying number of ransmi, relaying and arge mobile saion Figure 5: BER of STBC scheme wih QPSK, and non - for a varying number of ransmi, relaying and arge mobile saion Figure 3: BER of 4-Sae SOSTTC scheme wih QPSK, and non - for a varying number of ransmi, relaying and arge mobile saion Figure 6: FER of STBC scheme wih QPSK, and non - for a varying number of ransmi, relaying and arge mobile saion
VI COCLUSIO This paper deal primarily wih he performance of 4- sae SOSTTC scheme wih sysems wih deployed Virual Anenna Arrays. I could be shown ha successfully emulaes a radiional MIMO sysem by leing adjacen mobile saion communicae among each oher. Simulaions resuls show clearly ha a deploymen clearly ouperforms a sysem wihou by several db, which jusifies he increase in complexiy due o he required relaying procedure. REFERECES [1] Telaar I.E., Capaciy of Muli-Anenna Gaussian Channels European. Transacion on Telecommunicaion. vol 10, no 6, pp. 585-595, ov./dec. 1999. [] G.J. Foschini and M.J. Gans, On limis of wireless communicaions in a fading environmen when using muliple anennas, IEEE Wireless Communicaion Magazine, vol. 6, pp. 311-335, Mar. 1998. [3] C. Chuan, J.M. Kahn, and D. Tse, Capaciy of muli-anenna array sysems in indoor wireless environmen, in Globecom 98, Sydney, 1998. [4] M. Dohler and H. Aghvami, A sep oward MIMO: Virual Anenna Arrays, Cenre for Telecommunicaion Research, King s College London UK. [5] A.J. Vierbi, Error bounds for convoluional codes and an asympoically opimum decoding algorihm, IEEE Transacion on Communicaion, vol. 13, pp. 60-69, April 1967. [6] G.J. Foschini, Layered space-ime archiecure for wireless communicaion in a fading environmen when using muli-elemen anenna, Bell Labs Technical Journal, vol.1, no., pp 41-59, Auumn 1996. [7] D. Shiu and J. Kahn, Layered space ime codes for wireless communicaion using muliple ransmi anennas, Proc. of IEEE ICC 99, Vancouver, BC, June 6-10, 1999. [8] S. Alamoui, Space-ime block coding: A simple ransmier diversiy echnique for wireless communicaions, IEEE Journal on Seleced Areas in Communicaion, vol. 16, pp. 1451-1458, Oc 1998. [9] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, Space-ime block codes from orhogonal designs, IEEE Transacion on Informaion Theory, vol. 45, pp. 1456-1467, July 1999. [10] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, Space ime block code for high daa raes wireless communicaions: Performance resuls, IEEE Journal on Seleced Areas in Communicaion, vol.17, pp. 451-460, Mar. 1999. [11] A.V. Geramia and J. Seberry, Orhogonal Designs, Quadraic Forms and Hadamard Marices, Lecure oes in Pure and Applied Mahemaics, vol. 43, Marcel Dekker: ew York and Basel, 1979. [1] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, Space ime codes for high daa rae wireless communicaion; Performance analysis and code consrucion, IEEE Transacion Informaion Theory, vol.44, no., pp. 744-765, March 1998. [13] S. Baro, G. Bauch, and A. Hansmann, Improved codes for space-ime rellis-coded modulaion, IEEE Communicaion Leers, pp. 0-, January 000. [14] Z. Chen, J. Yuan, and B.Vuceic, An Improved space-ime rellis coded modulaion scheme on slow Rayleigh fading channels, IEEE Inernaional Conference on Communicaion, pp. 1110-1116, Mar. 001. [15] H. Jafarkhani and. Seshadri, Super-orhogonal space-ime rellis codes, IEEE Transacion on Informaion Theory, vol.49, pp. 937-950, April 003. [16] G. Ungerboeck, Channel Coding wih Mulilevel/Phase signals, IEEE Transacion on Informaion Theory, vol.8, pp. 55-67, Jan. 198. [17] M. Dohler, e al., for ho-spos wih applied STC, M-VCE Inernal Repors I, II, III and IV, 1999-00. Oludare A. Sokoya compleed his BSc. Eng degree in Augus 001 in he School of Elecronic and Elecrical Engineering a he Obafemi Awolowo Universiy, Ile- Ife, igeria and M.Eng from Universiy of KwaZulu aal in 005. He worked wih Philips Projec Cenre, igeria from 00 o lae 003 as a Telecommunicaion Engineer. He is currenly wih Meraka Insiue as a suden wih he Wireless Africa group. Dr. Hong-Jun Xu received he BSc degree in 1984 from he Universiy of Guilin Technology and he M Sc degree from he Insiue of Teleconrol and Telemeasure in Shi Jian Zhuang, 1989, and he PhD degree from he Beijing Universiy of Aeronauics and Asronauics in 1995. His research ineress are in he area of digial and wireless communicaions and digial sysems. Professor Fambirai Takawira is head of he School of Elecrical, Elecronic and Compuer Engineering a he Universiy of KwaZulu-aal. His research ineress are in he general areas of adapive signal processing, digial communicaions and daa neworks