Algorithm for Detecting the Number of Transmit Antennas in MIMO-OFDM Systems: Receiver Integration

Transcription

1 Algoith fo Detecting the Nube of Tansit Antennas in MIMO-OFDM Systes: Receive Integation Eckhad Ohle Ting-Jung Liang and Gehad Fettweis Vodafone Chai Mobile Counications Systes Technische Univesität Desden Geany eail: {eckhadohle liang Abstact Knowledge of the channel between all tansiteceive antenna pais is essential fo enabling the decoupling of spatial steas and coheent data detection in wieless MIMO- OFDM systes The design of the peable stuctue fo MIMO channel estiation in an ad-hoc syste depends on the nube of tansit antennas in the syste A challenge at the eceive is theefoe to accuately detect the nube of tansit antennas in ode to pefo MIMO channel estiation In this contibution we extend ou pevious algoith fo detecting the nube of tansit antennas as pesented in [] and show how to integate this algoith in a typical eceive flow Results show that ou algoith can be successfully applied in a ealistic syste if the unavoidable synchonization inaccuacies ae caefully taken into account I INTRODUCTION This wok focuses on an ad-hoc MIMO-OFDM syste opeating on a bust tansission basis In such a syste the initial acquisition of incoing packets is of citical ipotance Typically a eceive would fist pefo packet detection followed by tiing synchonization and subsequent fequency synchonization befoe estiating the MIMO channel and detecting the eceived data [2] Synchonization as well as channel estiation in MIMO- OFDM systes is usually achieved by eploying a peable coposed of a shot taining field (STF) piaily intended fo synchonization followed by a long taining field (LTF) piaily intended fo channel estiation Synchonization can be pefoed without knowledge of the actual nube of tansit antennas if the STF is caefully designed The LTF stuctue as well as the pilot sequences tansitted within the LTF typically depend on the nube of tansit antennas which eans that the nube of tansit antennas has to be known befoe the MIMO channel estiation A siple solution adopted in [3] is the tansission of additional signaling infoation befoe the MIMO-LTF but this appoach has the disadvantage of inceased ovehead and tansission latency In [] we poposed a novel algoith to detect the nube of tansit antennas befoe MIMO channel estiation based only on the MIMO-LTF and hypothesis testing We then evaluated its pefoance unde pefect synchonization conditions In this wok we extend the wok in [] by integating it into a eal wold counication syste This is not a staight fowad extension because the algoith is applied afte the fist coase synchonization stage and theefoe has to cope with unavoidable fequency and tiing synchonization isatches It tuns out that fo ou peviously poposed algoith ipefect tiing synchonization leads to sevee pefoance degadation wheeas ipefect fequency synchonization has little ipact on the algoith pefoance In this wok we popose a ethod to easue the esidual tiing synchonization inaccuacies and by applying this ethod show that the algoith fo detecting the nube of tansit antennas etains its obust pefoance even unde ipefect tiing synchonization conditions The algoith pefoance will be evaluated using a MIMO-OFDM syste based on IEEE802n paaetes The eainde of the pape is oganized as follows: In section II we intoduce the syste odel In section III we discuss eceive functions equied fo synchonization channel estiation and detection of the nube of tansit antennas In section IV we show how to integate ou algoith in a typical eceive flow The pefoance of the integated syste will be evaluated in section V Finally conclusions ae dawn in section VI II SIGNAL MODEL AND PREAMBLE DESIGN In this wok we conside the OFDM ulticaie odulation technique whee (in geneal coplex valued) tansit sybols ae odulated onto ultiple subcaies in the fequency doain Tansfoation to the tie doain is achieved by eans of a discete Fouie tansfo (DFT) Each tie doain OFDM sybol is potected against inte sybol intefeence by a cyclic pefix (CP) At the eceive afte deleting the CP the signal is conveted back into the fequency doain by an invese DFT opeation A Signal Model The eceived tie doain signal can be witten as [ N t NCIR ] yk = + v k () t= b=0 x t k bh t b

2 whee yk denotes the signal at eceive antenna xt k is the signal tansitted fo tansit antenna t vk denotes coplex valued zeo ean additive white Gaussian noise (AWGN) and k is the saple index The channel ipulse esponse (CIR) h t b between the eceive-tansit antenna pai t has a length of N CIR taps with powe σh 2 k at tap k and su powe σh 2 The DFT (o invese DFT) of soe abitay vecto b (B) of diension [N ] in the tie (fequency) doain is defined by B = Fb b = N FH B and FF H = NI N (2) whee F epesents the [N N] Fouie atix with eleents {F} nk = exp( j2πnk/n) ( ) H is the heitian opeato and I N is the [N N] identity atix Unde the assuption of pefect eceive synchonization the N eceived tie doain saples belonging to the -th OFDM sybol ae stacked into a colun vecto y Left-sided ultiplication of y with F yields the fequency doain epesentation of the eceived signal in vecto-atix notation Y 0 Y N Y = X X N t T }{{}}{{} X H H N t H + V V N R V (3) Siila to () Y denotes the signal at eceive antenna X is the signal tansitted fo all tansit antennas t = [ N t ] H denotes the channel between tansiteceive antenna pai t and V denotes AWGN The tansitted signal is defined by X t = diag{x0 t XN t } whee diag{ } ceates a diagonal atix fo the coplex valued sybols Xn t odulated onto subcaies n = [0 N ] Finally a single channel vecto is given ] T Given by H t = [ H0 t HN t t= σ2 X σ 2 t V σh 2 = N k=0 σ2 h k = σh 2 = as the eceived signal noise and channel powe pe subcaie the signal-to-noise atio (SNR) at the eceive is SNR = N t t= σ2 X /σ 2 t V B Peable Design In packet based OFDM systes the tansitted data is typically peceded by a bipatite peable The geneic stuctue fo this peable that we will conside in this wok is depicted in Fig The uppe and lowe indices in Fig such as LTF t denote tansit antenna t and OFDM sybol Tx Tx NT a a STF a a Fig LTF LTF LTF LTF LTF MIMO peable stuctue Data Data Lowecase and uppecase lettes denote the tie and fequency doain signal epesentation Noal and boldface lettes denote the saple and atix (vecto) signal epesentation The fist pat the STF has a length of N STF saples and copises L identical sequences a of length N a = N STF /L The STF is tansitted in an othogonal anne eg fo only one antenna o cyclically shifted fo all antennas The second pat the LTF copises N t OFDM sybols each guaded by a cyclic pefix as adopted in [3] Evey LTF-OFDM sybol contains pilot sequences fo channel estiation In ode to iniize the channel estiation eo pilot sequences tansitted fo diffeent antennas ae designed to be utually othogonal [4] Othogonality can be achieved by tansitting sequences sepaated in the tie (TO) fequency (FO) o code (CO) doain In [] we discussed all thee designs although in this wok we will estict ouselves to the TO design without loss of geneality In a TO design antenna t tansits pilot sequences only duing the t (th) LTF sybol ie only within LTF t =t III INDEPENDENT RECEIVER FUNCTIONS A Packet Detection and Coase Tiing Fo packet detection using the STF pesented in the pevious section we eploy a schee pesented in [5] which exploits the epetitive stuctue of the STF At each tie instant k the eceived signal yk within a window [k k + N STF ] is assued to be the eceived STF Subsequently a etic Ω k is calculated so that the coelation between all possible cobinations of eceived sequences a within that window aveaged ove all eceive antennas is calculated and noalized by the powe of the eceived sequences a Noalization ensues that Ω k can only take values between zeo and one Expessing a cetain eceived sequence a by the vecto yi = [y k+n a i y k+n a (i+) ]T Ω k can be calculated accoding to: Ω k = ( Na N l= ) Na N a i= i = Na l i=0 (yi )H yi+l ( N ) (4) Na = i= (y i )H yi Once Ω k exceeds a cetain theshold T c at tie index ˆk PD the eceive assues a packet has aived and seaches fo the axiu Ω k in a window of length N STF +N CP stating fo ˆk P D The saple index ˆk SCT at which the axiu Ω k is detected is egaded as the stat of the packet In ultipath fading envionents ˆk SCT will typically have a positive delay wt the exact packet stat Theefoe we popose to shift the estiated packet stat by N CT saples backwads to obtain the final estiate as ˆk SCT = ˆk SCT N SCT We define a packet to be detected coectly if ˆk SCT lies within a window of ±N CP aound the exact packet stat k S [6] B Fequency synchonization If the caie fequencies f ct x at the tansitte and f crx at the eceive ae unsynchonized then the eceived signal y k expeiences a linea phase otation φ k = 2πεk/N in tes of paaete k whee ε = (f ctx f crx )/f sc epesents the caie fequency offset (CFO) elative to the subcaie spacing f sc

3 In the pesence of CFO the eceived signal on subcaie n can be expessed as: Y n = Ψ nn T n }{{} useful signal whee T i = t= Ht i X t i + N s=0s n Ψ ns T s + Vn (5) ICI Ψ ns = N ejπ( N )(s n+ε) sin (π(s n + ε)) sin ( π (6) N (s n + ε)) and we have dopped the OFDM sybol index Note that ICI is the intecaie intefeence and Ψ ns epesents the fequency doain influence of CFO In this contibution we ae only inteested in how the esidual CFO ε es afte an initial estiation and copensation (again a linea phase otation of the eceived tie doain signal) ight degade the pefoance of ou algoith fo detecting the nube of tansit antennas We theefoe assue that an estiato based on the STF as poposed in [7] is eployed Additionally we can odel ε es as a zeo ean Gaussian ando vaiable The vaiance of ε es is given by [7]: E [ ε 2 ] 3N 2 SNR es = 2π 2 N STF (NSTF 2 N a) 2 (7) C Peable Based Channel Estiation Stacking the N t LTF-OFDM sybols eceived at antenna into a colun vecto and using (3) the eceived signal can be ewitten as Y Y N t YLTF = X X }{{}}{{} X LTF H H N t H + V V N t VLTF (8) Note that in (8) the channel is assued to be constant duing the LTF If X LTF is of full ank which can be ensued by an appopiate peable design the least squaes channel estiate is calculated as Ĥ = X LTF Y LTF (9) whee X LTF = (XH LTF X LTF) X H LTF denotes the pseudo invese of the pilot sequences tansitted within the LTF A copehensive oveview on peable based channel estiation in MIMO-OFDM can be found in [8] D Detection of the Nube of Tansit Antennas In [] we deived an algoith which eploys the LTF in ode to detect the nube of tansit antennas in a MIMO- OFDM syste We now highlight the ipotant esults of this wok Specifically the deived algoith is based on caying out channel estiation fo each possible nube of tansit antennas u belonging to the set { N tax } allowed in the syste whee N tax is typically sall Coect and incoect hypothetical nubes of tansit antennas can be distinguished by eploying the etic Θ u { ]} NCP k=0 E [ĥu ĥ H u kk Θ u = { ]} (0) E [ĥu ĥ H u N k=0 whee ĥu is the estiated channel ipulse esponse belonging to a cetain hypothesis u Note that ĥu is the discete Fouie tansfo of (9) If u the nube of tansit antennas assued in MIMO channel estiation is incoect Θ u yields a constant value which equals the atio N CP /N accoding to the length of the suation intevals in (0) If u is coect Θ u only depends on the SNR and is always geate than the sae etic Θ u fo an incoect assuption on N t Theefoe the hypothesis that axiizes Θ u is assued to be coect ie kk ˆN t = ag ax u {Θ u} () Note that we assued fo each nube of tansit antennas allowed in the syste a unique LTF is tansitted IV RECEIVER INTEGRATION A MIMO-OFDM eceive incopoating the algoith fo detecting the nube of tansit antennas is depicted in Fig 2 PD Tiing Sync Feq Sync DFT Window Adjust Fig 2 DFT N N t ˆt Detect Receive flow Channel Est MIMO Detecto Fistly the eceive pefos packet detection (PD) and coase tiing synchonization accoding to sec III-A Note that a potential CFO does not degade the coase tiing synchonization This esults fo the fact that the diffeential phase otation between yi and y i+l in the nueato of (4) due to the CFO is the sae i and a cetain l Secondly the CFO is estiated and copensated The esidual CFO afte copensation can be chaacteized as discussed in sec III-B Afte convesion of the coasely synchonized signal to the fequency doain the nube of tansit antennas has to be detected (accoplished by the N t detection block) befoe MIMO channel estiation The N t detection block essentially ipleents (0) and needs to copute an estiate ĥ of the CIR Befoe we show how to copute (0) the effects of ipefect synchonization on the estiated CIR need to be discussed Fig 3 illustates the effect of ipefect tiing synchonization on ĥ The gey shaded aeas epesent the pat of the estiated CIR which contibutes to the su Σ nu in the nueato of (0) In the case of pefect coase tiing synchonization (Fig 3b)) the nonzeo pat of the estiated

4 hˆk Fig 3 0 NCP- k ˆS CT hˆk < k S hˆk k ˆS CT > k S k k k N- 0 NCP- N- 0 NCP- N- a) b) c) Effect of ipefect tiing synchonization on the estiated CIR CIR is located exactly within Σ nu as long as N CIR N CP holds; a typical assuption in OFDM systes If the estiate fo the packet stat ˆkSCT is salle (Fig 3a) ) o bigge (Fig 3c) ) than the actual packet stat k S the estiated CIR expeiences a left o ight cyclic shift espectively Thus in the case of ipefect coase tiing synchonization Σ nu does not cove the coplete CIR This esults in a sevee degadation in the pefoance of the poposed algoith Consideing ipefect fequency synchonization we evaluate the ICI te in (5) The ICI te is assued to be an additive zeo ean coplex Gaussian ando vaiable Fo ε es using an appoxiation siila to [9] the ICI vaiance can be stated as ( σici 2 π2 ε 2 ) 2 es (2) 6 Since the STF is designed to ensue σici 2 σv 2 in the SNR egie of inteest the effect of ipefect fequency synchonization on the poposed algoith can be neglected Anothe way to view the condition σici 2 σ2 V is that the vaiance of ε es in (6) is sufficiently sall Fistly to calculate (0) we exploit that in a MIMO syste estiates of the CIR between all eceive-tansit antenna pais t ae available and appoxiate {E[ĥuĥH u ]} kk by N t= = ĥt ku 2 = ĥku 2 Secondly to account fo the ipefect coase tiing synchonization Σ nu needs to be adjusted to copletely cove the estiated CIR We theefoe eplace N CP k=0 by N k=ˆk FP in (0) whee ˆk FP is an estiate of the position of the fist path fo the estiated CIR Finally N = (ˆk FP + N CP ) od N is the (potentially) cyclic uppe liit of the suation window Eploying those changes (0) can now be appoxiated by: Θ u N k=ˆk FP ĥku 2 N k=0 ĥku 2 (3) To obtain an estiate ˆk FP fo the position of the fist path k FP of the estiated CIR we eploy a ethod oiginally poposed fo fine tiing in [0] The fist path of the CIR is found by the theshold decision: { } ˆk FP = in ĥku 2 > Γ and ĥku 2 > ĥk+u 2 (4) k whee k = [0 N ] The fist citeion ensues that the fist path is not chosen fo a noise only saple while the second citeion selects only local axia of the estiated CIR The theshold Γ depends on the instantaneous ealization of ĥku and is coputed accoding to { } Γ = ax ĥku 2 ax 0 Γ /0 ĥku 2 in 0Γ 2/0 (5) In [0] the authos popose to choose Γ = 0 db and Γ 2 = 8 db To ensue that k FP can be found in case of ˆk SCT > k S (see Fig 3c)) we additionally intoduce a cyclic ight shift of N SFT saples to ĥku 2 befoe the estiation of k FP Note that ˆk FP which has been estiated in conjunction with the tue nube of tansit antennas can be eused to adjust the DFT window as depicted in Fig 2 This allows fo a eduction in coputational ovehead A Siulation Setup V PERFORMANCE EVALUATION An OFDM syste with IEEE802n physical laye paaetes [3] is consideed The DFT size and cyclic pefix length wee N = 28 and N CP = 32 A ultipath Rayleigh fading channel with a powe delay pofile decaying with exp( k 036) and k = [0 5] has been chosen The syste copises N t { 2 4} tansit and N { 2 4} eceive antennas The STF has a length of N STF = 320 saples and is coposed of L = 0 identical sequences a of length N a = 32 as poposed in [3] Additionally the LTF consists of N t OFDM sybols (see section II-B) and all antennas tansit the sae ando BPSK odulated base sequences Diffeent base sequences have been used depending only on the nube of tansit antennas Fo packet detection (see section III-A) a theshold T c = 02 has been found to axiize the packet detection pobability Shifts of N SCT = 8 and N SFT = 0 saples have been chosen based on the distibution of coase tiing estiates at SNR = 0 db To odel the situation when a packet is detected in the noise befoe the actual packet stat (efeed to as a false ala) we pepend thee epty OFDM sybols which at the eceive will appea only as noise to each packet If a packet is detected in the noise the eceive is assued to be blocked and the packet is lost [] Finally the spectal ask accoding to [3] has been adopted esulting in the outeost and DC subcaies being set to be zeo B Pefoance Measues Fou easues ae eployed to chaacteize the pefoance of ou algoith The fist A is the pobability that N t has not been coectly detected given pefect packet detection The second D is the pobability of incoectly detecting a packet ie a false ala o the case whee k S N CP ˆk SCT k S + N CP does not hold The thid pefoance easue A/D is the pobability of incoectly detecting N t given a coect packet detection Finally D = (P D P A/D ) easues the ove all detection pefoance including packet detection and subsequent detection of N t C Results ) Pefect Synchonization: The figue of eit to benchak the poposed etic is the pobability of detecting the incoect nube of tansit antennas denoted by A

5 pef sync eal feq pef tiing pef feq eal tiing eal feq eal tiing D ' D D / A A x 2x2 D D x 2x x SNR [db] Fig 4 Pobability of detecting the incoect nube of tansit antennas Results ae plotted in Fig 4 (solid black lines) It can be seen that unde pefect synchonization conditions P A is aleady less than 0 4 at an SNR of 0 db Note that this is the wost case scenaio (ie a SISO tansission) Inceasing the nube of tansit and eceive antennas esults in pefoance gains of oughly 5 db in a 2x2 MIMO syste and 8 db in a 4x4 MIMO syste espectively fo A = 0 4 as copaed to a SISO syste 2) Effect of Tiing Synchonization: Unde eal packet detection and coase tiing synchonization conditions (Fig 4 A/D solid gey lines) a pefoance loss of oughly 3 db copaed to the foe case of pefect synchonization appeas The eason fo this is due to the inaccuacy of both the coase tiing synchonization and the estiation of the fist path of the estiated CIR (see section IV) in the low SNR egie 3) Effect of Fequency Synchonization: The effect of ipefect fequency synchonization on ou algoith is shown in Fig 4 fo pefect tiing synchonization (black cosses) and eal tiing synchonization (gey cosses) It can be seen that the algoith pefoance is as expected not affected by ipefect fequency synchonization 4) Oveall Detection Pefoance: We now show that the poposed algoith is suitable fo pactical ipleentation Specifically we copae the oveall issed packet detection pobability P D with the issed packet detection pobability P D Results ae given in Fig 5 Note that P D includes ipefect fequency synchonization It can be seen that in the wost case (ie a SISO syste) the pefoance loss is as low as 075 db at D = 0 4 In a 2x2 and 4x4 MIMO syste alost no pefoance loss is visible because A/D is salle than D (copae to the gey cuves in Fig 4) VI CONCLUSION In this wok we showed how ou peviously pesented algoith fo detecting the nube of tansit antennas in MIMO-OFDM systes [] can be integated into a typical MIMO-OFDM eceive In paticula we addessed the cucial issue of detecting the nube of tansit antennas 0-4 4x SNR [db] Fig 5 Missed packet detection pobability unde ipefect synchonization conditions It was found that ipefect tiing synchonization has a significant ipact on the algoithic pefoance while the effects of ipefect fequency synchonization ae negligible It was also shown that the oveall packet detection pefoance achieved by applying ou algoith is alost the sae as copaed to the case when the eceive has pefect knowledge of the nube of tansit antennas Consequently we believe that ou algoith can be consideed fo pactical application in next geneation ad-hoc obile wieless standads in ode to educe signaling ovehead and tansission latency REFERENCES [] E Ohle T-J Liang and G Fettweis Algoith fo Detecting the Nube of Tansit Antennas in MIMO-OFDM Systes in Vehicula Technology Confeence 2008 VTC2008-Sping IEEE 67th accepted fo publication 2008 [2] H Minn V Bhagava and K Letaief A Robust Tiing and Fequency Synchonization fo OFDM Systes IEEE Tansactions on Wieless Counications vol 2 no 4 pp Jul 2003 [3] IEEE 802n/D004 - Pat : Wieles LAN Mediu Access Contol (MAC) and Physical Laye (PHY) Specifications: Enhanceents fo Highe Thoughput Tech Rep 2006 [4] T-LTung and K Yao Channel Estiation and Optial Powe Allocation fo a Multiple-Antenna OFDM Syste EURASIP Jounal on Applied Signal Pocessing 2002 [5] K Shi and E Sepedin Coase Fae and Caie Synchonization of OFDM Systes: a New Metic and Copaison IEEE Tansactions on Wieless Counications vol 3 no 4 pp July 2004 [6] T-J Liang X Li R Ie and G Fettweis Synchonization in OFDM-Based WLAN with Tansit and Receive Divesities in IEEE 6th Intenational Syposiu on Pesonal Indoo and Mobile Radio Counications 2005 PIMRC 2005 vol 2-4 Sept 2005 pp Vol2 [7] M Moelli and U Mengali Caie-Fequency Estiation fo Tansissions Ove Selective Channels IEEE Tansactions on Counications vol 48 no 9 pp Sept 2000 [8] I Bahui G Leus and M Moonen Optial Taining Design fo MIMO OFDM Systes in Mobile Wieless Channels IEEE Tansactions on Signal Pocessing vol [9] MSpeth S A Fechtel G Fock and H Mey Optiu Receive Design fo Wieless Boad-Band Systes Using OFDM - Pat I IEEE Tansactions on Counications vol [0] B Yang K B Letaief R S Cheng and Z Cao Tiing Recovey fo OFDM Tansission IEEE Jounal on Selected Aeas in Counications vol 8 pp [] T-J Liang W Rave and G Fettweis On Peable Length of OFDM- WLAN in Vehicula Technology Confeence 2007 VTC2007-Sping IEEE 65th Apil 2007 pp