The Effect Of Transmitter Channel State Information (CSIT ) On The MIMO Capacity Performance

Transcription

1 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS The Effect Of Transmtter Channel State Informaton (CSIT ) On The MIMO Capacty Performance Lect. Ghanm Abd AL Kareem Electrcal Engneerng Department College of Engneerng Al-Mustansrya Unversty Asst. Prof. Dr. Raad.H.Thaher Electrcal Engneerng Department College of Engneerng Al-Mustansrya Unversty Abstract Wreless communcaton systems employng multple antennas at both the transmtter and recever have been shown to offer sgnfcant gans over sngle-antenna systems. It s shown that the ergodc capacty and outage capacty ncreases lnearly wth respect to RT. It s also shown that the capacty s mproved when the channel state nformaton (CSI) s known at the transmtter for MIMO system and for all values of SR. In ths work, MIMO system has been studed n detal and smulated for dfferent cases and concentrated on the capacty performance when the channel state nformaton s known (Water fllng ) and when the CSI s unknown to TX (Equal power allocaton ).MIMO system was descrbed and smulaton results ( usng MATLAB computer smulaton program) were presented and dscussed. Keywords; Sngle Input Sngle Output (SISO), Multple Input Multple output (MIMO). SR, Ergodc and Outage Capacty, CSIT. الملخص أنظمة االتصاالت الالسلكية التي تستخدم هوائيات متعددة في االرسال واالستتباال أعطت مكاستك يايتمة مبارنتة م ظتام الهوائي الواحد. وتاين أن استيعاب قدرة اريودك واستيعاب قتدرة االنبطتا تتزداد خطيتا نستاة الت. R T وتظهتم أضاتا أن استيعاب البدرة تتحسين ع دما ضعمف معلومات حالتة الب تاة )CSI فتي االرستال ل ظتام اادختال وااختمات المتعتدد MIMO system ولكت قتي نستاة االاتارة الت الاو تا.SR فتي هت ا الاحت نظتام MIMO درس مالتفصتي وتت عمت محايتاة لحتاالت مختلفتة تميتزت علت ادا قتدرة االستتيعاب ع تدما ضعتمف معلومتات حالتة الب تاة تعائتة الميتا ) fllng (Water وع دما ال ضعمف معلومات حالة الب اة تخصيص البدرة المتساوي ) allocaton (Equal power. لبد تت عتمو وم اق تة ال تائج ل ظام MIMO ماستخدام ممنامج المحاياة الحاسومي. MATLAB 9a 149

2 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS Introducton The feld of wreless communcaton systems and networks has experenced explosve growth and wreless communcatons has become an mportant part n every day lfe. To overcome the lmted capacty of conventonal SISO systems, by the use of multple antennas a multple nput multple output (MIMO) systems, offers greater capacty than SISO counterparts. The multple antennas can be used to ncrease the communcaton realblty by dversty or to ncrease the data rate by spatal multplexng or a combnaton of both. Multple antenna has performance and capacty enhancements wthout the need for addtonal power spectrum [1].. The MIMO (Multple Input Multple Output) System.1 Conventonal Antenna System.1.1 SISO (Sngle Input Sngle Output) System SISO refers to antenna system wth sngle antenna at both the transmtter and recever. Ths system can reach 1 Gb/S transmsson rates by employng suffcently hgh bandwdth along wth codng and modulaton that acheves the requred spectral effcency. However, there are some lmtatons assocated wth the varous phenomena that occur n outdoor wreless wde area networks (WWA) [,3]..1. SIMO(Sngle Input, Multple Output), MISO( Multple Input,Sngle Output) systems In these systems multple antennas at the recever and/or the transmtter n a wreless network. It promoses hgher data rates at longer ranges wthout consumng extra bandwdth or transmts power [1], such technology popularly known as smart antenna, offers a varety of advantages whch f expoted correctly can enable multplcatve gans n network performance. Fgure (1) shows dfferent antenna systems.

3 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS Fgure(1) SISO,SIMO,MISO,and MIMO system 3. The MIMO (Multple Input Multple Output) System The use of multple antennas at transmtter and recever sdes popularly known as Multple Input Multple Output (MIMO) wreless s an emergng cost effectve technology that offers hgh data rates wreless communcatons, near 1 Ggabt/second transmsson rate, Moreover ths technology resolve many lmtatons assocated wth SISO system [1,4]. MIMO s a communcaton concept of havng antennas at both the recever and the transmtter of rado lnk as shown n Fgure () Fgure () The MIMO channel 1

4 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS The dea behnd MIMO s that sgnals on the transmt antennas at one end and that at the recevng end antennas outstandng are combned n such a way that the qualty of the sgnal (Bt Error Rate) or the data rate (Bt/sec) of the communcaton system wll be mproved [4]. MIMO system can ncrease the transmsson capacty wth the number of antennas, as wll be seen from the smulaton results. 3.1 MIMO Capacty The system s descrbed by the matrx equaton y E T S HS n...( 1) Where Es s the total energy avalable at the transmtters y s the R * 1 vector of sgnals receved on the R antenna S s the T * 1 vector of sgnals transmtted on the T antenna n s the R * 1 nose vector consstng of ndependent complex Guassan dstrbuted element wth zero mean and varance σ H s the R * T channel matrx When the channel s known at the transmtter, the maxmum capacty of a MIMO channel can be acheved usng the water fllng prncple []. On the transmt convarance matrx, the capacty s then gven by C E H k 1 log 1 T...( ) And for R T C log ( 1)...( 3) EH denotes that the excepton s taken wth respect to resemble statstcs of H. Where Є s a scalar representng the porton of the avalable transmt power gong nto the sub channel. ρ s average SR. And when the channel s unknown to the transmtter (no CSIT).

5 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS C E w {log det( I r T w )}...( 4 ) where HH w H * * H r r t t Where Ir = the dentty recever matrx. If our bandwdth s W Hz, the maxmum achevable data rate over ths bandwdth usng MIMO technques s WC bts/s [6]. 3. Ergodc Capacty Ths s the tme-averaged capacty of a stochastc channel. It s found by takng the mean of the capacty values obtaned from a number of ndependent channel realzaton [7,8]. 3.3 Outage Capacty The q% outage capacty s defned as the capacty that s guaranteed for (1- q )% of the channel realzaton. It represents another measure of the channel capacty hence the nstantaneous capacty []. C ns 1 ln( 1 P ) t...( ) where λ s the egen value matrx. 4. Equal Transmt Power Allocaton In ths case, the power allocated to sub channel s gven by P = P/t, = 1,,, t, and Pr s gven by [7]. P r P t...( 6 ) Thus the channel capacty () can be wrtten as C r o r o P ln 1 ln 1 t 1 1 P t nats / s / Hz...( 7 ) 3

6 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS Water- Fllng Prncple Consder a MIMO channel where the channel parameters are known at the transmtter. The water-fllng prncple can be derved by maxmzng the MIMO channel capacty under the rule that more power s allocated to the channel that s n good condton and less or none at all to the bad channels. To determne ths optmal energy allocaton teratvely through the water-fllng prncple []. Set the teraton count p to 1 and calculate the constant μ: ( r M T 1 p 1) E o s r p ( 8 ) Usng ths value of μ, the power allocated to the th subchannel s calculated as M T E s o r p 1 1 1, 1,,..., r p 1...( 9 ) If the power allotted to the channel wth the lowest gan s negatve (.e., λr-p+1<), we dscard ths channel by settng λr opt -p+1= and rerun the algorthm wth the teraton count p ncremented by. The optmal power allocaton strategy, therefore, allocates power to those spatal subchannels that are non-negatve. 6. Smulaton Results and Dscusson The common approach whch has been done to nvestgate the promses of MIMO capacty s to buld a MATLAB capacty program that nclude the basc capacty equatons for the system wth related dfferent channel equatons n a Raylegh fadng channel and smulate the actual capacty performance. Fgure (3) shows a plot of the capacty versus SR for SISO, MIMO systems. We note that ergodc capacty ncreases wth ncreasng SR (db) and wth ncreasng t or r. It s observed that at SR=dB the capacty vares from 7 bts/s/ Hz for SISO to 1 bts/s/hz for MIMO (r=t=4). Hence t s concluded that the capacty growth acheved by MIMO system s the hghest compared to other systems yeldng remarkable mprovement (especally for Hgh SR). Fgure (4) shows the effect of the number of transmttng antennas when the number of recevng antennas s 4 on the capacty for fxed SR values (,,1,)dB. Fgure () shows the effect of 4

7 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS the number of recevng antennas when the number of transmttng antennas s 4 on the capacty for fxed SR values (,,1,)dB. However, In both graph t s ndcated that the capacty ncreases wth T & R and the best value for the case of 4 4 system because t s not practcal to use hgh values of R & T. Fgure (6) shows the ergodc capacty versus number of recevng antenna (1,,3,4) and the number of transmttng antennas (,4,6,8,16) at SR=1 db when the CSI s known at the transmtter and when the channel s unknown. It s concluded that the capacty s mproved when the CSI s known to TX and ncreasng number of recevng antennas for a (4 4) system whch gves 1 bps/hz where as the correspondng value s 11 bps/hz when the CSI s unknown to TX. The effect of CSIT(Known & Unkown) on the outage capacty for (1,,1,)% are consdered n fgure (7). It s concluded that the outage capacty for (4 4)system and CSIT s known s the best. At SR=16dB and for Known CSIT. The maxmum capacty 14. bps/hz for 1% outage capacty,bps for % outage capacty,16bps for 1% outage capacty, 17 bps for % outage capacty. The ergodc and outage capacty for any number of T and R of a MIMO n a Raylegh fadng channel consderng no CSIT(equal power allocatons) and perfect CSIT (water fllng allocaton) s shown n fgures (8,9,1,11) respectvely. It s concluded that ergodc capacty and outage capacty s better when CSIT s known ( water fllng) and generally the ergodc capacty s better and the approxmately conceded for (4 4)as shown n fgure (11) {-e bps/hz at SR=18dB). Fgure(1) compares the capacty of MIMO system when the CSIT s known and CSIT s unknown. It s observed that the capacty ncreases lnearly wth (R T) and the capacty s better for water fllng algorthm {maxmum capacty 1bps/Hz for (4 4) case }at SR=dB. Fgure(13) shows the 3-dmensonal surface of capacty versus SR versus the bandwdth. Fgure (14) shows the outage probablty versus SR for bps/hz capacty for SISO,MISO,SIMO,MIMO and t s observed that the outage probablty s better for MIMO(4 4) water fllng. 7. Concluson From our work t can be concluded that MIMO system offers sgnfcant gan n performance over tradtonal wreless communcaton system. MIMO system gve better capacty mprovement for all values of SR, and T R {from fgure (3) 1 bps/hz for 4 4 system, 7bps/Hz for SISO system }and t s also ndcated that MIMO system wth 4 4 s the best one.the effect of CSI at Tx was nvestgated and t was showed (proven) that the MIMO system offer better performance when the CSI s known for all values of SR and all values of (R T). It was also concluded that the ergodc capacty and outage capacty for water fllng case (-e CSI s Known to TX) gves better capacty than the equal power allocaton (CSI s unknown to TX)

8 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS counter part. From our results t s recommended to use the MIMO system wth 4 4 to get better performance. 8. References: [1]A.J.Panlraj, D.Gore,R.V. abar and H.Boleske, An Overvew of MIMO communcatons", A Key to Ggabt wreless, IEEE Transacton on Communcaton. ov3. []Raad.H.Thaher, Envronmental Analyss of MIMO channel Capacty under Varable Factors,ERJ, Vol.3, o.3, July 9. [3]Sheedhar.A.Joshetal., Modellng and capacty Analyss of Correlated MIMO Channels. Internatonal Journal of Engneerng Scence & Technology Vol.,1. [4]Wllam.C.Y.Lee, wreless and cellular Telecommuncatons, 3 rd edton, MCGrow- Hll, 6. []T.M Cover, J.A, Thomas, Elements of Informaton Theory, edtons, John Wely & Sons, Inc [6]Panlraj, Arogyaswam, Roht abar, and Dhananjay Gore, "Introducton to space-tme wreless communcatons", Cambrdge, UK: Cambrdge Unversty press, 3. [7]Yang Wen Lang, Ergodc and outage capacty of narrow band MIMO Gaussan channels, Department of Electroncal and computer Engneerng.The Unversty of Brtsh Columba,Aprl 19 th,. [8]Gesbert,M,Shaf,D.s Shu and A.agub, From Theory to Practce, An overvew of MIMO space-tme coded wreless system. IEEE J.Slect Area Commun. Vol.1,o.1,PP81-3, Aprl 3. 6

9 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS nt = 1, nr = 1 nt =, nr = nt = 3, nr = nt =, nr = 3 nt = 4, nr = 4 Capacty bts/s/hz SR n db Fgure(3) Ergodc capacty based WaterFllng algorthm for dfferent antenna confguratons MIMO system n a Raylegh Fadng Channel 3 3 SR1= SR1= SR1=1 SR1= Capacty(bt/s/Hz) t Fgure(4) Capacty of MIMO system when the number of recevng antenna s 4 and ncreasng the number of transmttng antenna [ ] 3 3 SR1= SR1= SR1=1 SR1= Capacty(bt/s/Hz) r Fgure() Capacty of MIMO system when the number of transmttng antenna s 4 and ncreasng the number of recevng antenna [ ] 7

10 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS Ergodc Capacty versus number of receved antennas r = 1 Ergodc Capacty versus number of receved antennas r = Ergodc Capacty(bps/Hz) 1 Ergodc Capacty(bps/Hz) umber of transmt antennas t umber of transmt antennas t Ergodc Capacty versus number of receved antennas r = 3 Ergodc Capacty versus number of receved antennas r = 4 Ergodc Capacty(bps/Hz) 1 Ergodc Capacty(bps/Hz) umber of transmt antennas t umber of transmt antennas t Fgure(6) Ergodc Capacty versus number of transmt and receved antennas when the channel s known and unknown to the transmtter when SR=1 db Outage Capacty of MIMO Channel for 4*4 Outage Capacty of MIMO Channel for 4*4 1 Percent Outage Capacty(bps/Hz) Es/(dB) Percent Outage Capacty(bps/Hz) Es/(dB) Outage Capacty of MIMO Channel for 4*4 Outage Capacty of MIMO Channel for 4*4 1 Percent Outage Capacty(bps/Hz) Es/(dB) Percent Outage Capacty(bps/Hz) Es/(dB) Fgure(7) [1,, 1 and ] Percent Outage Capacty of 4*4 MIMO system when the channel s known and unknown to the transmtter 8

11 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS ergodc Waterfllng capacty outage Waterfllng capacty ergodc Equal power capacty outage Equal power capacty capacty b/s/hz SRdB Fgure(8) Ergodc and Outage Capacty of a SISO system Raylegh channel consderng no CSIT (equal power allocaton) and perfect CSIT(waterfllng power allocaton) ergodc Waterfllng capacty outage Waterfllng capacty ergodc Equal power capacty outage Equal power capacty capacty b/s/hz SRdB Fgure(9) Ergodc and Outage Capacty of a 4*1 MISO system Raylegh channel consderng no CSIT (equal power allocaton) and perfect CSIT(waterfllng power allocaton) ergodc Waterfllng capacty outage Waterfllng capacty ergodc Equal power capacty outage Equal power capacty capacty b/s/hz SRdB Fgure(1) Ergodc and Outage Capacty of a 1*4 SIMO system Raylegh channel consderng no CSIT (equal power allocaton) and perfect CSIT(waterfllng power allocaton) 9

12 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS ergodc Waterfllng capacty outage Waterfllng capacty ergodc Equal power capacty outage Equal power capacty capacty b/s/hz SRdB Fgure(11) Ergodc and Outage Capacty of a 4*4 MIMO system Raylegh channel consderng no CSIT (equal power allocaton) and perfect CSIT(waterfllng power allocaton). 4 water fllng algorthm allocaton known channel state nformaton Average allocaton unknown channel state nformaton 4 3 Capacty bts/s/hz 3 1*1 8*8 6*6 4*4 1 * SR n db Fgure(1) MIMO Capacty for t equal to r wth known channel state nformaton (waterfllng algorthm) and unknown channel state nformaton (Average allocaton power) Capacty bts/s/hz 1 4 SRdB - 4 BW [Hz] Fgure(13) three dmensonal plot of Capacty versus bandwdth and SRdB 16

13 Journal of Engneerng and Development, Vol. 16, o.3, Sep. 1 ISS Outage Probablty x4 MIMO WF 4x4 MIMO 1-4x1 MISO 1x4 SIMO 1X1 SISO SRdB Fgure(14) Outage probablty versus SRdB for bps/hz n a Raylegh Fadng channel. 161