Inenaional Jounal of Wieless Communicaions, ewoking and Mobile Compuing 07; 4(6): 44-50 hp://www.aasci.og/jounal/wcnmc ISS: 38-37 (Pin); ISS: 38-45 (Online) MIMO Cogniive adio Capaciy in Fla Fading Channel Mohan Pemkuma, Muhappa Peumal Chia Depamen of Eleconics and Communicaion Engineeing, Panimala Insiue of Technology, Chennai, India Email addess empemkuma@yahoo.co.in (M. Pemkuma), chi_mp003@yahoo.co.in (M. P. Chia) Keywods Capaciy, MIMO, Cogniive adio, Fla Fading Channel eceived: Ocobe 30, 07 Acceped: ovembe 3, 07 Published: Decembe 6, 07 Ciaion Mohan Pemkuma, Muhappa Peumal Chia. MIMO Cogniive adio Capaciy in Fla Fading Channel. Inenaional Jounal of Wieless Communicaions, ewoking and Mobile Compuing. Vol. 4, o. 6, 07, pp. 44-50. Absac In his pape capaciy of a niive adio (C) sysem enabled wih muliple inpu muliple oupu (MIMO) echnology is deived and simulaed unde fla fading channel siuaion. Muliple inpu muliple oupu niive adio sysem povides effecive specum uilizaion along wih inceased divesiy gain as moe numbe of anennas ae used in he ansmiing and eceiving eminals. Deivaion of capaciy is done in fla fading channel siuaion following ayleigh disibuion. Fom he deived capaciy fomula, simulaion is pefomed fo diffeen ansmiing and eceiving anennas and i is analyzed fo he amoun of infomaion bis which a fla fading channel can pocess. This analysis will conibue fo designing and developing MIMO C sysems which can be employed fo wieless applicaions in sma ciies.. Inoducion As digiizaion of wieless communicaion sysems is inceasing a a fase ae fo caeing day o day wieless applicaions, specum allocaion gains impoance. Specum allocaion is done effecively by niive adio (C) sysem [] and [] which senses he availabiliy of whie space o fee specum holes and ansfes digiized infomaion beween a ansmie and a eceive [3]. oweve, o povide fuhe enhancemen of C sysems, muliple inpu muliple oupu (MIMO) echnology can be an opimal soluion. MIMO echnology povides inceased divesiy gain, specal efficiency due o usage of moe numbe of anennas in ansmission and ecepion [4]. Divesiy gain povided by MIMO echnology is he poduc of he numbe of ansmi and eceive anennas employed in he MIMO sysem which efes o usage of ansmi divesiy and eceive divesiy conceps. Specal efficiency efes o capaciy consideed along wih fequency in ez epesened as bis/sec/z. Combining MIMO echnology fo C sysems can esul in MIMO C sysems which aain moe significance fo evolving wieless applicaions which ae digiized and hence, analysis of such sysems needs o be done. Analyzing capaciy [5] fo MIMO C sysems can povide valuable insighs fo wieless applicaions developmen fo 4G and 5G sysems. Capaciy analysis of MIMO C sysems [6]-[8] gives he possible amoun of infomaion bis which can be handled depending on he wieless channels. Basically, capaciy of a C sysem incopoaed wih single inpu single oupu (SISO) echnology efes o insananeous capaciy epesened in bis/sec which also epesens he maximum daa ae. Deeminaion of capaciy can be calculaed fo an Addiive Whie Gaussian oise (AWG) channel and fading channels. Fo AWG channel he channel capaciy is calculaed as he logaihm of base fo a given bandwidh and signal o noise aio (S). The capaciy of an AWG channel does no involve he fading
45 Mohan Pemkuma and Muhappa Peumal Chia: MIMO Cogniive adio Capaciy in Fla Fading Channel channel coefficien and i is non fading channel whee he bes example can be noise due o movemen of elecons in he pined cicui boad (PCB) of a pesonal digial assisan (PDA). On he ohe hand, capaciy of a fading channel fo a C sysem involves incopoaion of a fading channel coefficien o give a eal impac of he fading channel in line of sigh (LOS) o non line of sigh (LOS) scenaio. The mahemaical epesenaion of capaciy of a fading channel fo a C sysem needs o be obained eihe fo a fla fading channel o a fequency selecive fading channel duing daa ansmission. Simila o SISO sysems, MIMO C sysems [9] ae pobably subjeced o opeae in fequency fla fading channels and fequency selecive fading channels. Moeove, MIMO C capaciy [0] and [] analysis can conibue o digial daa deecion in digial wieless sysems and a numbe of eseach woks have been deal as given fom [6]-[]. eseach papes fom [6]-[] give he eseach woks elaing o capaciy analysis of MIMO C and hei gaphical esuls. In he wok of [6] egodic capaciy and ouage capaciy of MIMO niive adio channel is discussed by consideing he inefeence empeaue. Conibuion [7] gives MIMO niive adio newoks capaciy balancing in wieless channels. [8] addesses houghpu fo MIMO sysems wih maximum and minimum consains. Maximizaion of channel capaciy fo space division access muliple access MIMO niive newoks is deal in [9]. In eseach pape [0] i discusses MIMO along wih C specum shaing fo he pefomance enhancemen of C. [] povides infomaion abou niive adio senso newoks in lage scale mulicluse MIMO. In [] muli-use MIMO niive adio sysems fo simulaneous specum sensing and daa ansmission is poposed. Though excellen eseach woks fom [6]-[] ae available, his wok pesens capaciy analysis of MIMO C sysems in wieless fla fading channels as an addiion o exising eseach woks. The consideed MIMO wieless fla fading channel coefficiens in his eseach pape follow ayleigh disibuion epesening a non line of sigh (LOS) scenaio. The capaciy of wieless channel [5] is deived in pefec channel scenaio and impefec channel scenaio whee he impefec channel esimaes can be found ou using esimaion algoihms [6]. The commonly available esimaion algoihms ae leas squaes (LS), minimum mean squae eo (MMSE), maximum likelihood (ML) algoihms [6]. Leas squaes esimaion algoihm poduces a leas value of he paamee which needs o be esimaed which ae he MIMO wieless channel coefficiens. Leas squaes algoihm is a simple compuaional algoihm. Minimum mean squae eo (MMSE) esimaion algoihm poduces an esimae of he paamee using pobabiliy densiy funcion (PDF) fo a given condiion, pobabiliy of he inpu and oupu paamees. MMSE algoihm is complex bu a he same ime poduces bee pefomance in ems of mean squae eo (MSE) fo a paamee which needs o be esimaed fom he acual value of he paamee. Maximum likelihood is also anohe esimaion algoihm which poduces an esimaion paamee using PDF by maximizing he value. Among LS, MMSE and ML esimaion algoihms, ML poduces a supelaive appoach in compaison o MMSE and LS appoach in ems of mean squae eo (MSE). MMSE esimaion algoihm oo pefoms well unde condiions given he PDF. The ask of his pape is o use a simple algoihm such as LS and obain capaciy of MIMO C wieless channel. Also, simulaions esuls ae done o suppo he deivaions of capaciy of MIMO C sysem. Ouline of his pape is ha secion gives he inoducion abou MIMO niive adio and capaciy. Secion pesens sysem model fo MIMO niive adio sysem in fla fading and fequency selecive fading channels. Secion 3 deives capaciy of a MIMO niive adio in a wieless fla fading channel. Secion 4 pesens MIMO capaciy of C sysem wih impefec channel esimaes. Secion 5 pesens simulaion esuls fo capaciy analysis of MIMO niive adio. Conclusion of he pape is given in secion 6. epesenaion I efes o an ideniy maix used in he conex of his pape.. Mimo Cogniive adio Sysem Model MIMO niive adio sysem model consideed in his pape has a pimay ansmie wih P ansmiing anennas and a pimay eceive wih P eceiving anennas which is licensed specum. Also, a niive ansmie (seconday ansmie) has S ansmiing anennas and a niive eceive (seconday eceive) has S eceiving anennas. In a siuaion, whee a niive ansmie having S anennas inends o access a eceive wih P eceive anennas hough P S MIMO channel maix i epesens a niive adio communicaion scenaio. A niive ansmie afe acquiing he fequency specum of pimay uses hough sensing [3], if i inends o ansmi a S S daa maix Dundegoing binay phase shif keying (BPSK) [4] modulaion scheme, he P S eceived signal maix a he pimay eceive akes he epesenaion = D+ () whee is he P S MIMO wieless channel maix wih fla fading having ayleigh disibuion. is he P S noise maix a he pimay eceive and i is a complex Gaussian noise maix. Similaly a C sysem in MIMO fequency selecive fading channel is epesened as [ ] = ( ; τ) D[ ] + [ ] ()
Inenaional Jounal of Wieless Communicaions, ewoking and Mobile Compuing 07; 4(6): 44-50 46 whee ( ; τ ) epesens he MIMO channel wih ime delay epesened by using a mulipah powe delay pofile. A mulipah powe delay pofile (PDP) is a plo of ime delay in µ s and coesponding powe value in decibel. 3. Deivaion of Mimo Cogniive adio Capaciy To deive he capaciy of MIMO niive adio sysem, capaciy is consideed as maximizaion of muual infomaion [4] and [5]. I is epesened as C = max I( ; ) (3) D f D ( D ) whee I ( D; ) is muual infomaion and i is given as whee ( ) is diffeenial enopy of he eceived signal maix, ( / D) is condiional enopy. The diffeenial enopy is given as σ ( ) = log Π eσ (5) is vaiance of eceived signal maix given by; σ = E[ ] ; whee is emiian and also known as complex conjugae and i is σ = E[( D + )( D + ) ]. Fuhe i is ewien as σ = E[( D + )( D + )] (6) I ( D; ) = ( ) ( / D) (4) E DD D D σ = [ + + + ] (7) DD D D E E E E σ = [ ] + [ ] + [ ] + [ ] (8) Second and hid ems in (8) ae independen of each ohe and i is zeo. Consideing fis and fouh ems i is σ = DE[ ] D + E[ ] (9) whee D is daa maix, is MIMO channel maix which is fla fading channel, = E[ ] is he P P channel coelaion maix and is P P noise coelaion maix, which is andom and follows Gaussian disibuion ( ) = log Π e[ D D + ] (0) Fuhe, condiional enopy is ( / D) = ( ) = log Π e[ ] () Also, muual infomaion is wien by subsiuing (0) and () in (4) I( D: ) = log Π e D D + log Πe () On fuhe simplificaion i is πe D D + I( D; ) = log πe (3) channel is obained by subsiuion of (5) in (3) and i is given as C = max log ( I + D D ) (6) f ( D) D πe D D I( D; ) = log + πe (4) 4. Mimo Cogniive adio Capaciy wih Impefec Channel Esimaes Muual infomaion on simplificaion of (4) is I( D; ) = log ( D D + ) (5) The P S eceived signal maix imp a he pimay eceive wih leas squaes (LS) [6] impefec channel esimaes is fomulaed as Capaciy of MIMO niive adio sysem in fla fading
47 Mohan Pemkuma and Muhappa Peumal Chia: MIMO Cogniive adio Capaciy in Fla Fading Channel whee LS imp LS = D ( + E ) + (7) epesens P S MIMO wieless channel maix obained by LS channel esimaion algoihm [6], E is he P S eo veco maix which is E = LS (8) whee values of eo maix ae complex Gaussian having zeo mean and vaiance σ. The capaciy of MIMO C E sysem wih impefec channel esimaes using LS is C whee I( D; imp ) imp fd( D ) = max[ I( D; imp )] (9) is he aveage muual infomaion beween D and imp. The muual infomaion of MIMO C sysem wih impefec channel esimaes using LS is defined as ( ) I ( D; ) = ( ) D (0) imp imp imp whee ( imp ) is diffeenial enopy of he P S MIMO eceived signal maix wih impefec channel esimaes and ( D) imp is condiional diffeenial enopy wih impefec channel esimaes. Diffeenial enopy ( imp ) is whee σ imp ( imp ) = log πe σ () imp is he vaiance of P S MIMO coelaion maix of he eceived signal maix wih LS channel esimaes a he pimay eceive wih epesenaion σ = E[ impimp ] () imp Subsiuing (7), () akes he fom imp imp LS LS E[ ] = E[( D( + E ) + ) ( D( + E ) + ) ] (3) As signal and noise ae independen, consideing mahemaical consains (3) is simplified as E[ impimp ] = D D + DE D + (4) LS ˆ ˆ whee ˆ = E[ LSLS ] is he P P channel coelaion maix wih impefec channel esimaes, E LS is he LS P P eo coelaion maix and σ = = E[ ] is P P coelaion maix of he noise. Fuhe, imp subsiuing (4) in () he diffeenial enopy of he P S MIMO eceived signal maix is ( imp ) Condiional diffeenial enopy ( D) ( imp / D) is D D + D log ˆ ELSD + = πe LS (5) imp is ( ). Due o following Gaussian disibuion, noise enopy ( ) imp / D = ( ) = log πe DELSD + (6) Also, muual infomaion is I( D: imp ) = log Π e D ˆ D + DE D log D LS + Π e ELSD + LS (7) Fuhe, on solving (7)
Inenaional Jounal of Wieless Communicaions, ewoking and Mobile Compuing 07; 4(6): 44-50 48 πe D ˆ D + D ELSD + DELSD + LS = + πe DELSD + DE D LS + I( D; ) log The muual infomaion on simplificaion of (8) is (8) I( D: imp ) = log (( D ˆ D + DE D ) ( DE D ) ) LS LS + LS + + (9) Capaciy of MIMO niive adio sysem wih leas squaes impefec channel esimaes is obained by subsiuing (9) in (9) and i is log ( ( I + D ˆ D + D ELSD + LS ) C = max fd( D) ( DELSD + ) ) (30) 5. Simulaion esuls Simulaion esuls ae given fo MIMO C sysem fo Fla fading channel. Capaciy in bis/second is obseved beween seconday ansmie, he niive use and pimay eceive. The niive use is also he seconday ansmie whee i.5 epesens he unlicensed band of communicaion and he pimay ansmie and pimay eceive fom he licensed band of communicaion. Simulaion is done by vaying he signal powe and keeping he noise powe as consan and vaious values of capaciy of MIMO C sysems ae obained fo diffeen ansmiing and eceiving anennas. Fla Fading S=8;S=8 Fla Fading S=4;S=4 FlaFading S=;S= Capaciy( bis/sec/z).5 0.5 0 0 5 0 5 S(dB) Figue. Capaciy vs S (db) in MIMO C fla fading wieless channel.
49 Mohan Pemkuma and Muhappa Peumal Chia: MIMO Cogniive adio Capaciy in Fla Fading Channel In Figue, capaciy analysis is done fo MIMO C fla fading wieless channels. A capaciy value of 0.05 bis/sec/z fo signal o noise aio (S) value of 5 db, a value of 0.5 bis/sec/z fo S value of 0 db, and a capaciy value of 0.37 bis/sec/z fo S value of 5 db fo ansmiing and eceiving anennas. Fo 4 ansmiing and eceiving anennas i has 0.4 bis/sec/z as capaciy fo 5dB, 0.39bis/sec/z fo 0dB and.0bis/sec/z capaciy fo 5dB. Also, fo 8 ansmie and eceive anennas i has 0.4bis/sec/z fo 5dB,.8bis/sec/z fo 0dB and.3bis/sec/z as capaciy fo 5dB. Capaciy efes o he insananeous capaciy of MIMO niive adio sysem. Capaciy inceases as he numbe of ansmiing and eceiving anennas inceases. This is due o he fac ansmiing and eceiving anennas povide an addiional divesiy gain. The capaciy epesened in ems of fequency is also specal efficiency which is in bis/sec/z fo a specific fequency. Table. Capaciy vs S (db) in fequency fla fading channels fo MIMO Scenaio. S (db) umbe of Tansmiing and eceiving Anennas and Capaciy in bis/sec/z S=; S= S=4; S=4 S=8; S=8 5 db 0.05 0.4 0.4 0 db 0.5 0.39.8 5 db 0.37.0.3 0 Mean Squae Eo(MSE) 0.05 0. 0.5 LS;S=;S= LS;S=4;S=4 LS;S=8;S=8 0. 0 5 0 5 0 5 30 S(dB) Figue. Mean Squae Eo vs Signal o oise aio fo MIMO C using LS algoihm. Figue, shows mean squae eo (MSE) and signal o noise aio fo ansmiing and eceiving anennas fo known aining sequence maices using leas squaes (LS) channel esimaion algoihm in fla fading channel. When he numbe of anennas inceases fo inceasing S values, mean squae eo value educes which signifies he impoance of impefec channel esimae scenaio analysis fo MIMO C sysem. MSE educes fo inceasing anennas as anennas conibue divesiy gain which govens he impoance of MIMO echnology wih niive adio sysems. 6. Conclusion By deiving capaciy and pefoming simulaion, capaciy of MIMO C sysem is analyzed in fla fading channel wih ayleigh disibuion. The obained simulaion esuls fo MIMO C sysem povide ha capaciy inceases as he numbe of ansmiing and eceiving anennas inceases. Incopoaion of MIMO echnology wih C can povide a new pah fo applicaions o be developed which equie vey high daa aes o cae day o day equiemens. Fuhe, obained esuls can used fo developmen of wieless applicaions elaing o C wih MIMO echnology and his in un can conibue fo developmen of digiized wieless poducs fo usage in sma ciies. efeences [] J. Miola III Cogniive adio, Liceniae Poposal, KT Sockhom, Sweden 998. [] J. Miola III and G. Q. Maguie J., Cogniive adio: Making Sofwae adios moe pesonal, IEEE Pesonal Communicaions, vol. 6. no. 4, pp-3-8, Augus 999. [3] S. aykin, Cogniive adio: Bain-empoweed wieless communicaions, IEEE J. Sel. Aeas Commun., vol. 3, no., pp. 0-0, Feb 005.
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