Interference Analysis in Time and Frequency Asynchronous Network MIMO OFDM Systems

Transcription

1 Interference Anayss n Tme and Frequency Asynchronous etwork MIMO OFDM Systems Vncent Kotzsch and Gerhard Fettwes Vodafone Char Mobe Communcatons Systems, TU-Dresden, Germany Ema: {vncent.kotzsch, fettwes}@fn.et.tu-dresden.de Abstract It s we known that symbo tmng offsets arger than the cycc prefx as we as carrer frequency offsets between transmtter and recever statons destroy the orthogonaty among OFDM subcarrers and nduce addtona nterference. In conjuncton wth MIMO transmsson on frequency seectve fadng channes where dfferent users nterfere wth each other, these effects strongy degrades the sgna detecton performance. In ths paper we consder fuy asynchronous spatay mutpexed transmsson wth dfferent symbo tmng and carrer frequency offsets on each transmtter-recever nk whch appear n dstrbuted MIMO systems wth mutpe users and base statons. We derve a factorzed system mode for sgna transmsson n frequency doman where the dfferent effects of nter-carrer, nter-symbo and nter-bock nterference are separated and anayzed n terms of sgna-to-nterference-nose-rato degradaton. Fnay, we evauate the nterference eves at a recever staton for dfferent nk-eve as we as system-eve smuaton setups. I. ITRODUCTIO It has been shown n many pubcatons that the orthogona frequency dvson mutpex OFDM moduaton scheme n mutpe-nput mutpe-output MIMO systems s a promsng canddate to fuf requrements for achevng hgh spectra effcency at adequate computatona effort e.g. [], []. In recent standardsaton processes OFDM has been chosen for appcaton n ceuar mobe communcatons, namey orthogona frequency dvson mutpe access OFDMA. In conjuncton wth space dvson mutpe access SDMA technques t s possbe to assgn tme-frequency-space resources to users fary fexby e.g. [3]. In such systems, separate base statons BS and user termnas UT suffer from naccuraces n terms of synchronzaton msmatches n tme and frequency e.g. [4], []. Symbo tmng offsets STO between users are caused by propagaton deays through transmsson channes. Carrer frequency offsets CFO occur due to unsynchronzed oca oscators at each UT n the network as we as Dopper shfts from reatve movements w.r.t to the BS respectvey. Approaches for future mobe communcaton systems ncude custers of base statons that work n a cooperatve manner n order to mprove the spectra effcency n ceuar envronments e.g. [3]. In such dstrbuted systems there are hgh requrements on the tme/frequency agnment of the users to the BS network to acheve the antcpated gans. There has been a ot of work n the fed of the nterference anayss n order to descrbe the effects of STOs and CFOs so far e.g. [], [5], [6], as we as to understand the effects of nsuffcent CP ength n the case of arge STOs e.g. [7], [8], [9], but often there are mtatons n such a way that t s dffcut to map a asynchronous network MIMO OFDM system to the exstng error modes. In ths paper, we provde a generazed frequency doman transmsson mode where K asynchronous users transmt ther data over the same channe resource and w be receved by M asynchronous base statons. We derve a convenent approxmaton for the overa nterference power that ncudes the effects of STOs, CFOs and nsuffcent CP ength, whch s used for an extensve nterference anayss. The paper s organzed as foows: In secton II we derve our network MIMO OFDM system mode. A SIR approxmaton for a subcarrers s gven n secton III. Performance evauatons and smuaton resuts are provded n secton IV, before n secton V concudng remarks summarze the man resuts. otaton: Bodface etters denote matrces and underned etters vectors respectvey. We use [.] for ndexng an eement of a vector or matrx. Lowercase etters descrbe varabes n the tme doman and uppercase etters varabes n frequency doman respectvey.. T s used as transpose and. H as conjugate transpose operator. The operator E. expresses the expectaton vaue. II. SYSTEM MODEL We consder the upnk of a ceuar system wth K actve users whch are connected to ther servng base staton each. For the jont mut-user detecton process we use a custer of base statons whch receve the user sgnas at an approprate power eve. The users smutaneousy transmt ther data on a set of OFDM subcarrers D n frequency doman. In order to avod OFDM nter-symbo nterference and sef ntercarrer nterference ICI we use a cycc prefx CP of CP sampes. As a resut one OFDM symbo bock conssts then of B = + CP tme doman sampes. The representaton of the base band sgna for user k s gven as IDFT operaton: x k [n] = X k jπn [] e, CP n D where X k [] = / Dand represents the DFT sze. The OFDM symbo ndex s denoted by =,..., S. After the transmsson over the channe wth the mpuse response vector h whch conssts of L dscrete channe taps, the sgna

2 # d d 3 # d R C # #3 # 3 d d 3 d 3 #3 UT #: UT #3: t= μ x CP Symbo - μ x μ x3 CP Symbo t Mut-user nterference MUI R Rx DFT Wndows: a R Inter-symbo nterference from prevous symbo b Fg. : Geometrca System Mode and Tmng Msmatches Inter-carrer nterference ICI from current wndowed symbo at the mth recever branch can be obtaned by: K r m [n] = L h m,k [λ]x k [n λ μm,k ] + v m λ= e jδϕm,k [n] [n] where v m [n] c,σv ncorporates spatay and temporay uncorreated AWG. Δϕ m,k = ϕ k ϕ m mpes the phase rotaton error between the up and the down converson process and μ m,k the nteger symbo tmng offset on the nk between the kth user termna and the mth base staton. If n λ μ m,k < the prevous sampes wthn x k are used. In our smuaton mode μ m,k many occurs due to the propagaton deays between the users and the base statons. Usuay n ceuar networks the base statons work n a synchronous manner and the users w be agned va a tmng advance whch s estmated user specfc by the base statons and transmtted va the downnk contro channes. Therefore the users can be agned wthn the range of the cycc prefx duraton mnus the maxmum channe excess deay w.r.t the sampe perod T S : TCP,eff TCP τ max CP,eff = = 3 T S whch s henceforth referred to as effectve CP ength. Snce we want to empoy a coherent recepton at a base statons ths constrant w ony hod n a certan area where the users are symmetrcay grouped. Otherwse a tmng behavour occurs as depcted n Fg. b. If tmng offsets arger than the CP ength occur μ > CP we w catch from the prevous OFDM symbo whch conssts of the channe decay effect and the tme doman wndowng of the prevous symbo. Due to the dstorton of the orthogonaty of the desred OFDM symbo subcarrers we w aso get ICI from current wndowed symbo. In Eq. Δϕ m,k [n] represents the CFO effect that aso caused ICI and corresponds to a near phase process for each T S nk: Δϕ m,k [n] =π Δf m,k nt S + ϕ m,k 4 In reduced unts the CFO Δf m,k s normazed to the subcarrer spacng B SC whch eads wth nt S = to: n B SC Δϕ m,k [n] =π Δε m,k n + ϕm,k 5 wth Δε m,k =Δf m,k /B SC. If OFDM symbos are transmtted consecutvey ϕ s gven as ϕ =Δϕ m,k [ ]. Uness otherwse stated we aways use the dfferenta CFO vaues n the foowng. Wthn ths work we assume tme nvarant channe mpuse responses CIR wth taps modeed as{ h m,k [λ] } c,σh[λ] βm,k PL wth varance σ h[λ] βm,k PL = E h m,k [λ] and a sum power of σ H = β m,k L m,k PL λ= σ h[λ]. In order to take the user postons and the resutng STOs nto account we ncude a smpfed dstance dependent path-oss on each nk whch can be approxmated by: d m,k ηpl = B PL 6 β m,k PL where η PL represents the path-oss exponent and B PL a constant that contans certan propagatons effects. Wth D the receved sgna at the th subcarrer n frequency doman s obtaned by the DFT operaton apped to the receved sampes r m [n] at the mth base staton: Y m [] = n= d r m [n] e jπn 7 If we use the matrx vector notaton we can rewrte the transmsson equaton for the synchronous case to: K Y m = FΞ Rx h m,k Ξ Tx F }{{ H k X } + FΞ Rx v m 8 V m where F C represents the Fourer matrx wth the entres F[, n] = e j π n /, h C B B ncudes

3 the CIR matrx n Toeptz structure wth the frst coumn [h h L ] T. Due to the nserton of the CP by usng the [ ] T CP addng matrx Ξ Tx = [ I CP ] T I B and the CP removng matrx Ξ Rx =[I ] B, h becomes crcuant and H C then represents a dagona matrx wth the SISO channe transfer functon CTF n frequency doman whch can aso be stated as H = dag F h. Consderng nk specfc STOs {μ m,k > CP sutabe shft } matrces ζ m,k =[I B ] μ m,k ; ζ m,k Prev =[I B ] B μ m,k B B are nduced where the operator [ ] μ m,k expresses a vertca downshft at whch on the upper part μ m,k zero rows are nserted and [ ] B μ m,k vce versa. Furthermore we nsert CFO phase dstortons on each nk whch are represented wthn dagona CFO matrces φ m,k = dage jδϕm,k [n] C B B. Wth these extensons we can rewrte Eq. 8 to: Y m = K FΞ Rx φ m,k ψ m,k ζ m,k h m,k Ξ Tx F H X k + FΞ Rx φ m,k ψ m,k Prev ζm,k Prev hm,k Ξ Tx F H X k + FΞ Rx v m 9 where ζ m,k Prev ncudes the of the prevous wndowed OFDM symbo. In Eq. 9 we aso ncuded ψ m,k, ψ m,k Prev as dagona nk wndow matrces wth ψ m,k = [ ] T [ ] ] T T B B [ I B μ and ψ m,k m,k Prev [ = [Iμ m,k ] ] T T T []. In ths case we are not restrcted to shft n zero rows wthn ζ m,k and ζ m,k Prev and can shft n rows wth arbtrary vaues as we. In order to soate the dfferent nterference effects n frequency doman we can spt Eq. 9 by nsertng the dentty matrx I B = Ξ Tx Ξ Rx + b: Y m = K FΞ Rx φ m,k ψ m,k Ξ Tx Ξ Rx ζ m,k h m,k Ξ Tx F H X k + F Ξ Rx φ m,k ψ m,k b ζ m,k h m,k Ξ Tx F H X k... Wthout prove we state that due to the structure of the used matrces the terms whch are couped va b are equa to zero. We can appy further spttngs to obtan: K Y m = FΞ Rx φ m,k ψ m,k Ξ Tx F H FΞ Rx ζ m,k Ξ Tx F H Θ m,k FΞ Rxh m,k Ξ Tx F H + FΞ Rx φ m,k ψ m,k Prev Ξ TxF H,P rev FΞ Rx ζ m,k Prev Ξ TxF H Θ m,k Prev k X FΞ Rx h m,k Ξ Tx F }{{ H } k X + FΞ Rx v m V m In Eq., besdes the known phase rotaton matrces Θ and the CTF matrces H, we can aso compute the ICI/ matrces and,p rev for μm,k CP by appyng the spectra theorem wth a coumn of the Fourer matrx f n : = [, p] = φ m,k n=μ m,k CP n=μ m,k CP e jδϕ [, p] = e jπ B + CP B μ m,k n= e jπn κm,k,p rev [, p] = e jπ B + CP or equvaenty as a Drchet kerne B μ m,k [, p] = πκm,k θ sn,p rev [, p] = e jπ μ m,k CP [n + CP,n+ CP ] f n f H n m,k [n+ CP ] e jπn p ε m,k e jπ μm,k CP κ m,k μ m,k CP ε m,k n= B μm,k sn πκ m,k e jπn κm,k κ m,k = otherwse κ m,k = e jπ πκm,k θ,p sn rev μm,k CP sn πκ m,k otherwse wth κ m,k =Δε m,k + p, p =... and: θ = B + CP ε m,k +κ m,k μ m,k CP + κ m,k B μ m,k θ,p rev = B + CP ε m,k + κ m,k μ m,k CP The probem n Eq. 8 s that the crcuarty of the effectve CIR matrx h m,k = Ξ Rx h m,k Ξ Tx ony hods for a channe ength of L CP +. Otherwse n the case that the maxmum excess deay τ max s arger than the CP L > CP +, h m,k s no onger crcuant and sef ICI and furthermore from the prevous OFDM symbo w occur. In order to ncude aso ths effect of n our transmsson mode we form [ a upper tranguar ] Toeptz matrx h m,k wth the frst row h m,k L hm,k. Wth h m,k xm we can mode the from the prevous OFDM symbo. Another goa s to keep h m,k crcuant. Therefore we add the part to the CIR matrx h wth respect to the CP ength such that Eq. 8 can be rewrtten to: K Y m = F Ξ Rx h m,k + h m,k Ξ Tx F H X k =dagfh m,k F Ξ Rx h m,k Ξ Tx F H X k + F Ξ Rx h m,k Ξ Tx F H X k +V m

4 where h m,k = ζ CP h m,k represents a eft shft to skp the effect of the CP add and remove matrces. If we combne Eq. and Eq. we get a equaton for the frequency doman transmsson of data symbos over frequency seectve channes wth dfferent STOs and CFOs on each nk: Y m = K Θ m,k FΞ Rx h m,k + h m,k Ξ Tx F H =dagfh m,k F Ξ Rx ζ m,k h m,k Ξ TxF H +,P rev Θm,k Prev FΞ Rx X k h m,k + h m,k Ξ Tx F H =dagfh m,k X k X k,p rev FΞ Rxζ m,k Prev hm,k Ξ TxF H X k + FΞ Rx ζ m,k h m,k Ξ TxF H X k +V m We can aso rewrte Eq. wth respect to the th subcarrer: K Y m [] = [, ] [, ]X k []e j π μm,k Y U K + [, p] [p, p]x k [p]e j π μm,k p p D,p Y ICI K +,P rev [, p]hm,k [p, p]x k [p]e j π μm,k CP p p D Y K [, q] [q, ] X k [p] p D q= + K p D q= Y ICI [, q] [q, ] X k [p] +V m [] Y III. SIR AALYSIS 3 For the SIR anayss of the receved sgna the focus of our nterest s on the nterference terms n Eq. 3 whch represent the mpact of nter-carrer and nter-symbo nterference. If we assume that we use an advanced recever where the spata nterference among users Y U can be canceed the SIR on the th subcarrer at the mth recever branch γ m s gven by: E { Y U } γ m = E { Y ICI + Y Y ICI + Y + V [] } K [, ] σ H σ = m,k X K 4 ςm,k + σv If we defne that a channes and data symbos are uncorreated can be denoted as: =σ σ X [, p] +,P rev [, p] p D,p p D + σxσ [, p] p D =σ σ X sn πε m,k η m,k sn πε m,k + σxσ η m,k 5 wth the defnton for η m,k : B μ m,k η m,k μ m,k > CP = CP,eff <μ m,k CP μ m,k CP,eff For the power caused by the channe decay we use the foowng approxmaton: σ = L λ ω σ h[λ] βm,k PL 6 λ=+ω { μ ω = m,k > CP CP μ m,k 7 CP,eff <μ m,k CP In the speca case where the STOs are n the range of the CP η m,k = Eq. 5 smpfes to the known souton: =σ σ X sn πε m,k 8 sn πε m,k In the other case of dea CFO synchronzaton ε m,k =Eq. 5 changes to: =σxσ H η m,k + σxσ η m,k 9 m,k For the nterference anayss the SR degradaton w aso be of nterest and can be stated as the rato: = γ dea γ rea Γ m Loss = σ H σ m,k X σici,m + σ V σv α m σ σ X Γ m Loss = K α m + σ ICI,m σv, α m = [, ] wth σ ICI,m = K ςm,k.

5 TABLE I: Smuaton Parameters Parameter Vaue Carrer Frequency f C.5GHz System Bandwdth B S =/T S 5.36MHz FFT Sze 4 Used Subcarrer SC 4 CP Length CP 7 User Transmt Antenna o. BS Receve Antenna o. User Power σx 3dBm Pathoss Coeffcent η PL 3.86 Propagaton Envronment Factor ogb PL 4.dB ose Power per Subcarrer σv -3dBm SR=dB,L= SR=5dB,L= SR=dB,L= SR=5dB,L= SR=3dB,L= ε Fg. : SR Degradaton due to ncreasng CFO IV. SIMULATIO RESULTS In ths secton, we compare the effect of the dfferent nterference sources n a ceuar network MIMO system. The basc smuaton parameters are sted n Tab. I. In order to vary the channe ength and so the maxmum excess deay between the smuatons we use an parametrzabe exponenta channe power deay profe wth the foowng tap varances: σh[λ] = e λ σ λ, λ =...L. 3 σ λ wth L λ= σ h[λ] =. We defne the ast tap sha to be db beow the frst one by settng the RMS deay spread to σ λ = L n.. Frsty, we want to separate the effects of the CFO and the STO. Therefore we consder a SISO system wth one user K = and one base staton M = where we omt the path-oss β m,k PL = and ony ncrease μ and ε at dfferent SR eves. In Fg. we can see that the SR oss strongy depends on the current nose eve. In Fg. 3 the effect of the STO s depcted for dfferent channe engths L n order to ustrate the effect of from the prevous OFDM symbo. If the STO s not wthn the range of the effectve CP we observe the due to the channe decay effect. Lookng at the curve for a fat channe L = we ceary see the effect of due to the tme doman wndowng of the OFDM symbos n the case that the STO s arger than the CP ength. Furthermore we can see a strong dependence on the SR eve agan. Secondy, we ncude the effect of the path-oss wthn our smuatons and evauate the tmng dfferences due to propagaton deays, whch depend on the dstance between the user and the base staton. As a resut, the sgna attenuatons and aso the SR depend on the dstance eve. In ths context we frst anayze the scenaro when one user moves from a base staton away at certan dstances d, = d BS UT and the resutng tmng dfference s not compensated by any tmng advance mechansm. Based on the known dstance we can get the propagaton deay for the user nk, whch has to be samped w.r.t. the symbo perod T S by appyng: μ, d, = 4 c Lght T S 5 5 L=.75 CP L=.5 CP L=.5 CP L= SR=3dB SR=dB SR=dB.5 μ /.5 CP Fg. 3: SR Degradaton due to ncreasng STO As a resut we get a mappng of the user dstance d m,k to the resutng STO whch s evauated wthn the smuatons. A the propagaton and envronment effects are ncuded wthn B PL and based on the path-oss mode n []. We assume an average budng heght of m, a BS antenna heght of 35m, an UT heght of.5m and a street wdth of m at a reference dstance of d =m. We repeat ths transmsson for dfferent channe engths once wthout a CFO and once at a CFO eve of.5% of subcarrer spacng whch eads to the absout CFO of 75Hz. ote that we do not consder power contro at a such that arge SR eves near to the base staton can occur. The resutng SR oss s depcted n Fg. 4 where we normazed d BS UT w.r.t the dstance d CP = T CP c Lght whch s covered by the CP. As we aready dscussed above, cose to the base staton we can observe a hgher senstvty to the CFO because at hgh SR vaues the effect of the CFO s ampfed, whch s aso vsbe n Fg.. It shoud be noted that n the SISO case a tmng probems can be soved by smart tmng advance agorthms. In the network MIMO case where we assume coherent recepton n the UL ths s usuay not the case. Therefore n the next scenaro we assume a system wth three users K = 3 and three base statons M = 3 as depcted n Fg. a. ow the users move from the ce corner towards

6 ther servng base statons n a symmetrca manner. Wthn ths symmetrca setup the users are aways on a crce wth radus R C. The dstance from the drect user to hs servng base staton can be obtaned by: d k,k = R R C, k = m 5 The dstance between one user to the non servng base staton can be cacuated by takng the hexagona ce structure nto account and can be stated as: d m,k = R + R C R + R C, k m. 6 R In order to have a more reastc smuaton we assume that the base statons now appy a tmng advance mechansm where the propagaton deays caused by the drect nk can be compensated. In ths context we ony consder the tmng dfferences between the drect user nk and the nks from the other two users at one base staton whch can not be compensated by the tmng advance. The tmng dfferences between the drect and non drect nk can be obtaned by: Δμ = μ, μ, 7 whch s then used as effectve STO. In Fg. 5 the resuts are shown for ncreasng R C. We omt the CFO n ths smuaton because from Fg. 4 we can derve that the CFO s not the domnant effect at the ce border. An mportant resut of Fg. 5 s that even n the fat channe case L = the CP can ony cover 6% of ts actua range du to the non-compensabe tmng dfferences between the users. As expected, we can see that the user radus where we can appy a coherent recepton at the base statons s strongy mted by the channe maxmum excess deay and the CP ength. V. COCLUSIO In ths paper we present a network MIMO OFDM system mode whch ncudes the effects of carrer frequency offsets as we as the effects of symbo tmng offsets n frequency seectve channes wth a fnte channe ength. We derve a cosed form expresson for cacuatng the SIR for severa scenaros. We anayze the SIR eve under dfferent channe condtons wth and wthout ncudng the effect of the channe path-oss. We seen that the regon where coherent recepton can be apped s mted by channe ength and the cycc prefx and that the man nterference s caused by the tmng msmatches between the user and the base statons. In a further work we w evauate smart tmng advance agorthm on whch we can extend the user radus where network MIMO s benefca. VI. ACKOWLEDGEMET The authors acknowedge the exceent cooperaton wth a project partners wthn the EASY-C project and the support by the German Federa Mnstry of Educaton and Research BMBF. Thanks aso to E. Ohmer and W. Rave for nsprng dscussons. 4 3 ε=,l=.75 CP ε=,l=.5 CP ε=,l=.5 CP ε=,l= ε=.5,l=.75 CP ε=.5,l=.5 CP ε=.5,l=.5 CP ε=.5,l=.5.5 d BS UT / d CP Fg. 4: Interference Power n a Ceuar SISO Setup.5.5 ε=,l=.75 CP ε=,l=.5 CP ε=,l=.5 CP ε=,l= R C / d CP Fg. 5: Interference Power n a Ceuar etwork MIMO Setup REFERECES [] G. Stuber, J. Barry, S. McLaughn, Y. L, M. Ingram, and T. Pratt, Broadband MIMO-OFDM Wreess Communcatons, Proceedngs of the IEEE, vo. 9, no., Feb 4. [] M. Speth, S. Fechte, G. Fock, and H. Meyr, Optmum Recever Desgn for Wreess Broad-Band Systems Usng OFDM. I, Communcatons, IEEE Transactons on, vo. 47, no., ov 999. [3] M. Jang and L. Hanzo, Mutuser MIMO-OFDM for ext-generaton Wreess Systems, Proceedngs of the IEEE, vo. 95, no. 7, 7. [4] M. More, C.-C. Kuo, and M.-O. Pun, Synchronzaton Technques for Orthogona Frequency Dvson Mutpe Access OFDMA: A Tutora Revew, Proceedngs of the IEEE, vo. 95, no. 7, Juy 7. [5] M. Konstantnos, A. Adams, and P. Constantnou, SR Degradaton due to Tmng and Frequency Synchronzaton Errors for OFDMA systems wth Subband Carrer Aocaton, n 4th European Wreess Conference, June 8. [6] Y. Mostof and D. Cox, Mathematca Anayss of the Impact of Tmng Synchronzaton Errors on the Performance of an OFDM System, Communcatons, IEEE Transactons on, vo. 54, no., Feb. 6. [7] S. Chen and C. Zhu, ICI and Anayss and Mtgaton for OFDM Systems wth nsuffcent Cycc Prefx n Tme-Varyng Channes, Consumer Eectroncs, IEEE Transactons on, vo. 5, no., Feb. 4. [8] M. Wang, L. Xao, T. Brown, and M. Dong, Optma Symbo Tmng for OFDM Wreess Communcatons, Wreess Communcatons, IEEE Transactons on, vo. 8, no., October 9. [9] Z. Wang and G. Gannaks, Wreess Mutcarrer Communcatons, Sgna Processng Magazne, IEEE, vo. 7, no. 3, May. [] 3GPP TR 36.84, Further Advancements for E-UTRA: Physca Layer Aspects, 3GPP - 3rd Generaton Partnershp Project, 65 Route des Lucoes - Sopha Antpos; Vabonne - France, February 9, v.4..