Outage Probability Analysis of Multipath Fading Channels in Long Term Evolution-LTE

Transcription

1 Proeedngs of Internatonal Conferene on Emergng Trends n Eletrons & Teleommunatons (ICETET) 9 th - 31 st May, 1 KUALA LUMPUR, MALAYSIA (MTEC1) ISS (onlne): 39- ISS (prnt): 39- Outage Probablty Analyss of Multpath Fadng Channels n Long Term Evoluton-LTE 1 Pattet Krshna, Tppart Anl Kumar and 3 Kaltkar Kshan 1, Department of ECE, SVS Group of Insttutons, Warangal,Telangana,Inda 3 Department of ECE, Vaagdev College of Engneerng, Warangal,Telangana,Inda kpattet@gmal.om,tvakumar@yahoo.o.n,prof_kkr@redffmal.om ABSTRACT 3 rd Generaton Partnershp Projets Long Term Evoluton (3GPP-LTE) s a new standard for moble broadband aess that wll meet the throughput and overage requrements of a fourth generaton ellular systems. The key goals for ths evoluton are nreased peak data rate, mproved spetrum effeny, mproved overage and redued lateny. There are two typal ways to mprove and measure a wreless ommunaton system performane, whh are bt error rate (BER and P (e)) and outage probablty (Pout). In ths paper, we fous on redung Pout to mprove our system performane. The outage performane method s based on hannel apaty and mutual nformaton. Keywords: LTE; BER; Fadng Channels; Outage Probablty. 1. ITRODUCTIO Fourth generaton (G) Long Term Evoluton-LTE wreless ellular ommunaton systems must provde bandwdth-effent, robust ommunaton wth low lateny and supportng multple users on broad band wreless hannels. Sne tme varyng hannel ondtons and thus tme-varyng hannel apaty s an mportant features of G moble ommunaton systems and any future wreless ommunaton systems, these systems should exhbt a hgh degree of adaptvely on many levels n order to reah these goals. LTE s provdes to mprove throughput and spetral effeny along wth redung the lateny. The peak data rate requrement of LTE s 1Mbps for downlnk and Mbps for uplnk. Ths an be aheved usng a salable bandwdth, multple antenna elements and lnk adaptaton. The bandwdth n LTE an vary from 1. MHz to MHz. LTE s also an Internet Protool (IP)-paket based system wth hgher data rates and lower paket delay than prevous generatons [1-3]. Outage Probablty s a key performane metr of wreless ommunaton systems under o-hannel nterferene (CCI). Outage ours when the hannel apaty s less than the transmsson rate R,.e. log 1SR h R hene, the man dea of the performane mprovement s nreasng the hannel apaty, whh an be aheved by several transmsson tehnques suh as LTE. In ths paper organzed as follows, Seton II explans about the statstal modelng of dfferent fadng hannels, outage Probablty analyss of fadng hannels explaned n Seton III and onluson n seton IV.. STATISTICAL MODELLIG OF FADIG CHAELS To understand wreless ommunatons, t s neessary to explore what happens to the sgnal as t travels from the transmtter to the reever. One of ICETET 1 MTEC1 P a g e 3

2 Proeedngs of Internatonal Conferene on Emergng Trends n Eletrons & Teleommunatons (ICETET-1) 9th 31st May -1, KAULALAMPUR, MALAYSIA; ISS (onlne): 39-, ISS (prnt): 39- the mportant aspets of ths path between the transmtter and reever s the ourrene of fadng. The RF (rado frequeny) sgnals wth approprate statstal propertes an readly be smulated. Statstal testng an subsequently be used to establsh the valdty of the fadng models frequently used n wreless systems. Capaty of ommunaton hannels s the maxmum data rate that an be transmtted over the hannels suh that arbtrary tolerable small error probabltes an be aheved. The hannel apaty onept was ntally defned by Shannon. Shannon defned the apaty n terms of mutual nformaton as the maxmum mutual nformaton that an be aheved between the nput and output of the hannel. ow let us onsder the system apaty of the faded hannel n the hannel model s yn hnxn wn (1) Where hn represents the fadng gan n the hannel. Fadng gan s modeled dependng on dfferent fadng hannels. xn Represent the transmtted sgnal and wn a zero mean gaussan nose wth varane and dentally and ndependently dstrbuted (d) wth respet to tme. The apaty of the AWG Channel s Cawgn log 1 SR Bts/s/Hz () In Raylegh fadng hannels fadng gan s assumed to be random but onstant over tme and delay onstrant s small ompared to the hannel oherene tme, the apaty of the hannel an be wrtten C log 1 h SR Bts/s/Hz (3) A system s sad to be outage f the transmtter sends data rate R s larger than the Channel apaty. Hene outage Probablty s defned as follow Pout Pr C R Pr log 1 h SR R () A. Raylegh Fadng The moble antenna, nstead of reevng the sgnal over one lne-of-sght path, reeves a number of refleted and sattered waves, as shown n Fg.1. Beause of the varyng path lengths, the phases are random, and onsequently, the nstantaneous reeved power beomes a random varable. In the ase of an un modulated arrer, the transmtted sgnal at frequeny reahes the reever va a number of paths, the th path havng an ampltude a, and a phase. If we assume that there s no dret path or lne-of sght (LOS) omponent, the reeved sgnal s(t) an be expressed as s t a os( t ) 1 The phase depends on the varyng path lengths, hangng by when the path length hanges by a wavelength. Therefore, the phases are unformly dstrbuted over [, ]. When there s relatve moton between the transmtter and the reever, eqn. () must be modfed to nlude the effets of moton ndued frequeny and phase shfts. Let the th refleted wave wth ampltude a and phase arrve at the reever from an angle relatve to the dreton of moton of the antenna. The Doppler shft of ths wave s gven by d v os where v s the veloty of the moble, s the speed of lght (3x1 m/s), and the s are unformly dstrbuted over [,]. The reeved sgnal s(t) an now be wrtten as s(t) = a os( t t ) 1 d Expressng the sgnal n phase and quadrature form, eqn. (3) an be wrtten as s( t) I( t)os t Q( t) sn t () () (7) () where the n phase and quadrature omponents are respetvely gven as I(t) = a os( t ) 1 d Q(t) = a sn( t ) 1 d (9) (1) ICETET 1 MTEC1 P a g e 3

3 Proeedngs of Internatonal Conferene on Emergng Trends n Eletrons & Teleommunatons (ICETET-1) 9th 31st May -1, KAULALAMPUR, MALAYSIA; ISS (onlne): 39-, ISS (prnt): 39- The envelope R s gven by R I t Q t (11) When s large, the n phase and quadrature omponents wll be Gaussan []. The probablty densty funton (pdf) of the reeved sgnal envelope, f(r), an be shown to be Raylegh gven by r r exp, r (1) Where the onstant kd s the strength of the dret omponent, d s the Doppler shft along the LOS path, and d are the Doppler shfts along the ndret paths gven by equaton (). The envelope n ths ase has a Ran densty funton gven by [] r r k d rkd exp I o, r (1) Where I() s the th order modfed Bessel funton of the frst knd. The umulatve dstrbuton of the Ran random varable s gven as k F r) 1 Q r ( d,, r (1) Fg.1. Mehansm of rado propagaton n a moble envronment. A number of ndret paths and a lneof-sght path are shown Varyng the number of paths, t an be seen that the fadng envelope n the absene of a lne-of-sght path fts the Raylegh dstrbuton for as few as sx paths. Ths was establshed by ondutng h-square tests for dfferent values of. Fgure shows the RF sgnals and envelopes for the ase of a statonary moble unt (=1). The Raylegh faded RF sgnal (Fgure a) and envelope (Fgure ) show that the sgnal strengths an fall below the average value (shown by the horzontal lne n Fgure ). B. Raan Fadng The Ran dstrbuton s observed when, n addton to the multpath omponents, there exsts a dret path between the transmtter and the reever. Suh a dret path or lne-of-sght omponent s shown n Fg.1. In the presene of suh a path, the transmtted sgnal gven n eqn. (3) an be wrtten as 1 1 s(t)= a os( t t ) k os( t t) d d d (13) Where Q(.) s the Marum s Q funton * &+. The Ran dstrbuton s often desrbed n terms of the Ran fator K, defned as the rato between the determnst sgnal power (from the dret path) and the dffuse sgnal power (from the ndret paths). K s usually expressed n debels as k K ( db) 1log d 1 (1) In equaton (1), f kd goes to zero (or f kd / «r / ), the dret path s elmnated and the envelope dstrbuton beomes Raylegh, wth K(dB) = -. To smulate the presene of a dret omponent, the reeved sgnal was modeled by eqn. (9). Ths meant that a term wthout any random phase needs to be added to the sgnal generated n the ase of Raylegh fadng. The rest of the smulaton was arred out as n the ase of Raylegh fadng. The RF sgnal and the envelope orrespondng to = 1 are shown n Fgure b and Fgure d. It s seen that the flutuaton n the envelope for Ran s muh smaller than for the Raylegh ase (Fgure ). The horzontal lne n Fgures () and (d) orrespond to the mean value of the Raylegh envelope. The RF sgnals and demodulated envelopes for both Raylegh and Ran ases for a moble veloty of m/s are ompared n Fgure 3. It s seen that the ICETET 1 MTEC1 P a g e 37

4 envelope (volt) envelope (volt) rf sgnal (volt) rf sgnal (volt) envelope (volt) envelope (volt) rf sgnal (volt) rf sgnal (volt) Proeedngs of Internatonal Conferene on Emergng Trends n Eletrons & Teleommunatons (ICETET-1) 9th 31st May -1, KAULALAMPUR, MALAYSIA; ISS (onlne): 39-, ISS (prnt): 39- sgnal envelope goes below the threshold (ndated by the horzontal lne) n Fgures (3) and (3d) more often than n Fgures () and (d). Ths nreases the hanes of loss of sgnal determned by the appearane of the envelope below the threshold when the moble unt s n moton. The envelope hstogram and the Raylegh ft to the envelope are shown n Fgure. The Raylegh densty funton was reated by alulatng the Raylegh parameter from the moments of the envelope data orrespondng to eqn. (9). The ft of the hstogram of the data to Ran an be undertaken smlarly tme (ns) 1 (a) () 1 1 tme (ns) tme (ns) 1 (b) (d) 1 1 tme (ns) Fg.. RF sgnals and envelopes for statonary moble (a) Raylegh faded sgnal (b) Ran faded sgnal () Raylegh envelope (d) Ran envelope C. akagam M-Dstrbuton It s possble to desrbe both Raylegh and Ran fadng wth the help of a sngle model usng the akagam dstrbuton []. The fadng model for the reeved sgnal envelope, proposed by akagam, has the pdf gven by m m m r ( m) 1 mr exp 1 m tme (ns) 1 (a) () 1 1 tme (ns) 1, r (17) tme (ns) 1 (b) (d) 1 1 tme (ns) Fg. 3. RF sgnals and envelopes for moble movng at a veloty m/s (a) Raylegh faded sgnal (b) Ran faded sgnal () Raylegh envelope (d) Ran envelope Where (m) s the Gamma funton and m s the shape fator (wth the onstrant that m ½) gven by m E r E r Er (1) The parameter ontrols the spread of the dstrbuton and s gven by r E (19) The orrespondng umulatve dstrbuton funton an be expressed as mr F( r), m () Where P(.) s the nomplete Gamma funton. In the speal ase m = 1, akagam redues to Raylegh dstrbuton. For m > 1, the flutuatons of the sgnal strength redue ompared to Raylegh fadng, and akagam tends to Ran. o speal smulaton was neessary to test for the valdty of akagam fadng. Sne akagam dstrbuton enompasses both Raylegh and Ran, the sgnal envelopes were tested aganst the akagam dstrbuton usng the h-square test. The akagam dstrbuton seems to be a good ft for Raylegh fadng wth an average value of the parameter m = 1 []. It also seemed to ft the Ran dstrbuton between 1 m. Results for the Raylegh and akagam ft are shown n Fg.. 3. OUTAGE PROBABILITY In a fadng rado hannel, t s lkely that a transmtted sgnal wll suffer deep fades that an lead a omplete loss of the sgnal or outage of the sgnal. The outage probablty s a measure of the qualty of the transmsson n a moble rado hannel. Outage s sad to our when the reeved sgnal power goes below a ertan threshold level [3, ]. It ICETET 1 MTEC1 P a g e 3

5 Proeedngs of Internatonal Conferene on Emergng Trends n Eletrons & Teleommunatons (ICETET-1) 9th 31st May -1, KAULALAMPUR, MALAYSIA; ISS (onlne): 39-, ISS (prnt): 39- an be alulated as the ntegral of the reeved sgnal power p (t) as out P th p( t) dt Where Pth s the threshold power. (1) The proedure to fnd the outage probablty s as follows: 1. Calulate the reeved sgnal power as gven n equaton. r r 1 exp exp () ln d Moble veloty M/se Outage Probablty (Raylegh) Outage Probablty (Raan ) Table I. Comparson of outage probablty for Raylegh and Ran fadng for a number of values of moble velotes Where s the mode or the most probable value of the Raylegh dstrbuton, s the shape parameter of the lognormal dstrbuton. 3. Set a threshold power level for the reeved sgnal relatve to the average sgnal power.. Count the number of tmes n the sample nterval that the reeved sgnal power goes below ths threshold.. Usng the bas onept of probablty, the outage s then alulated by takng the rato of the ount n step 3 to the total number of samples. For one reeved sgnal, we alulated the outage probabltes for varous thresholds, and ompared these values to those alulated analytally. The outage probabltes alulated analytally and through smulatons were found to tally qute well. Fg. shows the urves for the outage probablty, alulated analytally and through smulatons, for the Raylegh fadng ase. As observed from Table I, the outage probablty (averaged over smulatons) n a Ran hannel s lower than that n a Raylegh hannel, whh an be attrbuted to the presene of a lne-of-sght path. Moreover, the probablty of outage nreases as the moble veloty, or resultng Doppler shft, nreases. Fg.:The hstogram of the smulated data and the orrespondngly mathed densty funtons Fg. : Outage probablty for Raylegh fadng and statonary moble. Smulated values are ompared aganst theoretally omputed outage values. ICETET 1 MTEC1 P a g e 39

6 Proeedngs of Internatonal Conferene on Emergng Trends n Eletrons & Teleommunatons (ICETET-1) 9th 31st May -1, KAULALAMPUR, MALAYSIA; ISS (onlne): 39-, ISS (prnt): 39-. COCLUSIO In ths paper, we shows the smple and straghtforward onept of multpath fadng hannels and t easy to vsualze the ntraes and understand the relatonshp between the dfferent parameters nvolved n fadng. Redung outage probablty (Pout) s to mprove system performane. The outage performane method s based on hannel apaty and mutual nformaton. REFERECES [1] Erk Dahlman, Stefan Parkvall, Johan Sköld. G LTE/LTE-Advaned for Moble Broadband. Aadem Press. 11. ISB: [] Stefana Sesa, Issam Toufk, Matthew Baker. LTE The UMTS Long Term Evoluton: From Theory to Prate. John Wley & Sons, 1st Edton, 9. ISB: [3] Farooq Khan. LTE for G Moble Broadband. Cambrdge Unversty Press.9. ISB: [] H. Hashem, The Indoor Rado Propagaton Channel, Proeedngs of the IEEE, Vol. 1, o. 7, pp. 93-9, July [] A. Papouls, Probablty, Random Varables, and Stohast Proesses, 3rd Edton, MGraw Hll, ew York, [] M. akagam, The m-dstrbuton. A General Formula of Intensty Dstrbuton of Rapd Fadng, n Hoffman, W. C., Statstal Methods n Rado Wave Propagaton, Pergamon Press, 19. [7] H. Suzuk, A Statstal Model for Urban Rado Propagaton, IEEE Tran. on Communatons, Vol. COM, o. 7, pp. 73-, July [] W. C. Y. Lee, Estmate of Loal Average Power of a Moble Rado, IEEE Trans. on Veh. Teh., Vol. VT-3, o. 1, pp. -7, February 19. [9] P. M. Shankar and B. A. Esensten, Projet based Instruton n Wreless Communatons at the Junor Level, IEEE Trans. on Eduaton, Vol. 3, o. 3, August, pp. -9 Tppart Anl Kumar s urrently a Professor n Eletrons and Communaton Engneerng Department, SR Engneerng College, Warangal. He reeved hs B.E. Degree from Osmana Unversty n 199 and M.Teh degree from atonal Insttute of Tehnology; Kurukshetra n.he obtaned hs PhD from Osmana Unversty n 9. He a senor member of IEEE and fellow of IETE, Hs researh nterests are Sgnal proessng for Communatons, Sgnal Proessng Applatons and Image Proessng. Kanthkar.Kshan Rao s urrently a Dretor n Vswambhara Eduatonal Soety and Professor n Department of Eletrons & Communaton Engneerng. He reeved hs B.E. and M.E. degrees from Osmana Unversty n 19 and 197. He obtaned hs PhD degree from Indan Insttute of Tehnology, Kanpur n 1973.He worked as Dretor and Prnpal for atonal Insttute of Tehnology, Warangal and Kakatya Insttute of Tehnology and Sene, Warangal. He a senor member of IEEE and fellow of IETE, He guded 3 PhD sholars and Master Projets. Hs researh nterests are Wreless Communatons, Sgnal Proessng Applatons and Cooperatve Moble Communatons. BIOGRAPHIES Pattet Krshna: Completed B.Teh degree n Eletrons and Communaton Engneerng and M.Teh degree wth spealzaton of Dgtal Systems & Computer Eletrons from JT Unversty, Hyderabad n and. He s havng 9 years of teahng experene and publshed papers n varous Internatonal & atonal journals. At present Krshna s pursung PhD n wreless Communatons under the faulty of Eletrons & Communaton Engneerng. Hs researh nterests are Sgnal proessng for wreless ommunatons, MIMO Communatons and Multuser MIMO Communatons. He s a Member of IEEE, ISTE and IETE. ICETET 1 MTEC1 P a g e 33