Joint Detection and CFO Compensation in Asynchronous Muti-User MIMO OFDM Systems Vincent Kotzsch, Jörg Hofed and Gerhard Fettweis Vodafone Chair Mobie Communications Systems, TU-Dresden, Germany Emai: vincent.kotzsch; joerg.hofed}@ifn.et.tu-dresden.de Abstract It is we known that carrier frequency offsets caused by inaccuracies of oca osciators between transmitter and receiver stations destroy the orthogonaity among OFDM subcarriers and induce additiona intercarrier interference. In conjunction with MIMO transmission where different users interfere with each other, this effect strongy degrades the signa detection performance if it is not compensated beforehand. In the upink of muti-user systems different CFOs between a mobie terminas occur whereas its correction is more difficut. In this paper we consider the upink of a fuy asynchronous system with different transmitter and receiver CFOs which appears in distributed MIMO systems with separate users and base stations. We describe a combined scheme for joint CFO correction and spatia ayer detection in frequency domain. The detection performance is shown for some seected equaiser concepts. In this way we present interference canceation agorithms with ow and scaabe compexity. Finay, numerica simuation resuts are provided to compare the detection performance. I. ITRODUCTIO It has been shown in many pubications that the orthogona frequency division mutipex OFDM moduation scheme in mutipe-input mutipe-output MIMO systems is a promising candidate to fufi requirements for achieving high spectra efficiency at adequate computationa effort [1]. In recent standardisation processes, OFDM has been chosen as ceuar mobie communications system, namey orthogona frequency division mutipe access OFDMA. In conjunction with space division mutipe access SDMA techniques it is possibe to assign time-frequency-space resources to users fairy fexiby. A genera overview on state of the art MIMO OFDM/SDMA systems is given in []. In such systems, separate base stations and mobie terminas have to suffer from inaccuracies in terms of synchronisation mismatches in time and frequency [3]. Timing offsets are caused by propagation deays through transmission channes, but not considered throughout this paper. Carrier frequency offsets CFOs occur due to different unsynchronised oca osciators at each mobie termina in the network as we as Dopper shifts in reative movements to the base station respectivey. In ceuar systems the different mobies have to be frequency aigned to its serving base station such as in singe frequency networks. One approach is to use downink signas as reference to estimate and track the CFO in each termina reativey to the base station [4]. Thus it is possibe to de-rotate the phase on the upink stream to accompish a singe frequency network. Approaches to future mobie communication systems consist of more than one cooperative base station in a so caed network MIMO custer to improve the spectra efficiency in ceuar environments. In such distributed systems there are high requirements on the frequency aignment to achieve the anticipated gains. It is difficut to maintain the carrier frequency offset targets in such scenarios uness high effort is spent for base station synchronisation over sateite reference signas, ike goba positioning systems. Furthermore, it is probematic to ensure that the terminas in a muti ceuar network have a perfect synchronisation behaviour at a. Transmitter CFOs in OFDMA systems are aready treated in [4] and [5]. The main focus there was to mitigate the muti-user and mutipe access interference in the SISO case. In [6] the effects of different transmitter CFOs in an OFDM SDMA system are described with a ow compexity equaising approach for its compensation. In this paper, we provide a genera system mode where K asynchronous users transmit their data over the same channe resource and wi be detected by M asynchronous base stations where M K. We derive a convenient approximation for the intercarrier interference ICI power which is used in a new agorithm for the joint CFO compensation and user detection in such a network MIMO OFDM SDMA system where the base stations perform a cooperative signa processing at a centra entity. We aso consider different compexity eves for the interference canceation and show the trade-off between the signa processing effort and the user detection performance. The paper is organised as foows: In section II we derive our muti-user MIMO OFDM system mode and the CFO impact. Afterwards in section III we present an anaytica SIR anaysis. The combined CFO compensation and detection agorithm is described in section IV. Performance evauations and simuation resuts are given in section V, before concuding remarks are provided in section VI. II. SYSTEM MODEL We consider an OFDMA system where K active users simutaneousy transmit data on a subset of D subcarriers. The time domain representation of the base band signa for user k can be denoted as IDFT operation s k i [n] = 1 X k jπn i [] e, 0 n 1 1 D where X k i [] = 0 / D and represents the DFT size. The OFDM symbo index is given by i = 0,..., S.
User #1 j U,1 j ϕ U,1 BS,1 j ϕ U, K BS, M j ϕ U,1 BS, M j ϕ U, K BS,1 j BS,1 BS #1 User #K BS #M j U, j K BS, M Joint Receiver Processing Entity CFO CFO FFT FFT Ch. Ch. Joint Detection and CFO Comp. User #1 User #K Fig. 1. System Data Fow To avoid intersymbo interference among OFDM symbos, a cycic prefix CP is prepended by copying the ast CP time domain sampes of an OFDM symbo before the beginning. After the transmission over the channe with the impuse response vector h which consists of CIR discrete channe taps, the signa at the mth receiver branch can be obtained by r m i [n] = K CIR λ=1 h m,k [λ]s k i [n λ] e jδϕm,k [n] i +w m i [n] where w incorporates additive white Gaussian noise. Δϕ m,k = ϕ k ϕ m impies the phase rotation error between the up and the down conversion process on the ink between the kth user and the mth base station. ϕ is in genera referred to as phase noise, but in our mode we ony investigate the CFO impact such that Δϕ m,k i [n] can be defined as a inear phase process for each ink: Δϕ m,k i [n] =π Δf m,k nt S + ϕ m,k 0 3 For a genera system mode the CFO Δf m,k is normaised to subcarrier spacing B SC which eads with nt S = to n B SC Δϕ m,k i [n] =π Δɛ m,k n + ϕm,k 0 4 with Δɛ m,k = Δf m,k /B SC. If OFDM symbos are transmitted consecutivey ϕ 0 is given as ϕ 0 = Δϕ m,k i 1 [ 1]. The channe impuse response h m,k is modeed as zero-mean compex Gaussian variabe with variance σh = E h m,k λ }. For the sake of simpicity the OFDM symbo index i is omitted for the rest of this section. With Dthe received signa at the th subcarrier in frequency domain is obtained by a DFT operation Y m [] = 1 1 r m [n] e jπn 5 Subsequenty we use vector matrix notation to simpify the transmission mode. With the Fourier transform matrix F and the ink CFO matrix Φ m,k = diage jδϕm,k [n] where Φ m,k C, 5 can be rewritten as K Y m = F Φ m,k h m,k s k + w m Y m = K and in stacked form FΦ m,k F H }} E m,k Fh m,k F H }} H m,k 6 X k + Fw m 7 Y m = [ E m,1 H m,1...e m,k H m,k] X + W m 8 Y = E H X + W 9 with E, H C M K, the user symbo vector X = [X 1...X K ] T and the receiver vector Y = [Y 1...Y M ] T. With FF H = I, the unitary simiarity transformation of Φ m,k is used and the eements in E m,k are stated as 1 e jδϕm,k [n] e jπn p 10 E m,k [, p] = 1 or equivaenty as Dirichet kerne 1 for κ =0 E m,k [, p] = 1 ejπκ otherwise 1 sinπκ sin πκ 11 with κ =Δɛ m,k + p, p =1... Based on this mode, the frequency domain transmission of 6 can be rewritten for the th subcarrier to K Y m [] = E m,k [, p]h m,k [p, p] X k [p] }} + W [] Y m [] = p D H m,k [,p] K H m,k [, ] X [] k + K p D,p H m,k [, p] X k [p] +W [] 1 } } Y ICI in which H m,k [, p] represents the effective transmission channe in frequency domain. The first term of Eq. 1 represents the ICI free spatia mutipexing signa transmission with a
user common phase error CPE terme m,k [, ] which causes an additiona phase increment of the channe of one OFDM symbo. The second term Y ICI incudes sef and muti-user ICI which destroys the orthogonaity of the subcarrier symbos X k [] and eads to ampitude and phase errors of the received symbos. III. SIR AALYSIS For the SIR anaysis of the received signa the focus of our interests is on the Y ICI term in Eq. 1 which represents the impact of the intercarrier interference. As it is aready stated in [7] and [8] in the case of randomized transmit symbos the first term in 1 is uncorreated to Y ICI. Thus, the SIR on the th subcarrier at the mth receiver is given by K E SIR m E m,k [, ] } σh σ X = E E m,k [, p] } σhσ X K p D,p } } +σ W 13 In the numerator the CPE term in Eq. 13 is fuy compensated by the receiver agorithms. For the ICI power estimation of we use resuts from [9] with the adaptation to the CFO can be expressed as E Y ICI YICI} H as E = E m,k [, p] } σhσ X context. p D,p = σhσ X With 11 Eq. 14 can be written as = σ Hσ X 1 E E m,k [, ] } 14 1 1 sin πδε m,k sin π/δε m,k 15 With sinπ/δε m,k π/δε m,k for arge the ICI power can be approximated with = σhσ X [1 sinc πδε m,k ] sinc πδε m,k = 1 r πδεm,k r k + 1! r=0 1 πδεm,k 3! σhσ X πδε m,k /3. 16 with Δε m,k as an approximatey quadratic factor. Equation 16 gives an convenient term to be evauated in CFO compensation agorithms. From Eq. 13 we derive that in the proposed muti-user MIMO system the interference power of each ink superimpose each other and the resuting approximated ICI power at one receiver branch can be obtained by σici,m = K γm,k 17 A coser ook at Eq. 13 yieds that the joint noise and interference term at each subcarrier consists of σy,m = σ ICI,m +σ W. From Eq. 16 we know that σici,m can vary according to the Δε m,k distribution. This means that for each receiver station m there is another effective noise term σy,m. IV. RECEIVER PROCESSIG The steps to be done at the receiver processing entity are depicted in Fig. 1. In this section, we wi concentrate on the joint CFO compensation and detection process. A short overview over CFO estimation is given beforehand. A. Frequency Error Estimation For the upcoming ayer detection, the frequency errors have to be known at the receiving entity. The muti-user CFO estimation is treated in [3] and the resuts can be reused here. [5] aso introduces a muti-user CPE estimation scheme for asynchronous OFDMA systems. According to Eq. 10, the CPE can be interpreted as a mean phase rotation during one OFDM symbo. With Eq. 4 and 10 the CPE Δθ of the ith OFDM symbo with respect to the CP on each ink can be denoted as } 1 Δθ m,k i = E m,k 1 [, ] = e jδϕm,k [n] i = 1 m,k 1 sinπδɛ m,k ejπδɛ sin e jπδɛm,k i 1+ CP πδɛ m,k }} Δϕ m,k [0]=Δϕ m,k i i 1 [ 1] 18 As a resut for every ink on different subcarriers an equa but over more than one OFDM symbo a changing CPE occurs. ormay, this is an additiona phase offset on each OFDM symbo which wi be inherenty estimated by the channe estimation process and wi aso be taken into account during the equaisation process by estimating the spatia decorreation fiter G. Aternativey, the CPE impact on the channe can directy be obtained from the muti-user CFO estimates and can be deveoped into the time series as it is done in 18. For the rest of this etter we assume that each CFO and CPE vaue is perfecty known for each ink. B. Muti-User Spatia Layer Detection Based on Eq. 1, we describe two possibe user ayer detection strategies in the seque. Uness otherwise stated, the foowing derivations are aways denoted for the th subcarrier and for K users and M receiver stations. 1 Layer Detection with CPE Correction: As we have identified in section III, the intercarrier interference can be interpreted as additiona noise with σici,m. It is cear that in the case of ow ICI the therma noise foor is much stronger than the part caused by the interference. In ceuar systems we suppose that the CFO is partiay precompensated at termina side, such that the ow ICI assumption hods. However, the CPE phase de-rotation cannot be negected because the phase error eads to performance degradations. With 18 we coud form a matrix which contains a ink CPEs in the ith OFDM symbo derived from the measured CFOs: e jδθ1,1 i e jδθ1,k i ΔΘ i =..... 19 e jδθm,1 i e jδθm,k i
ΔΘ i is inherenty superimposed eading to the effective channe H. Due to the nature of the phase difference matrix, the time variant channe can be decomposed in a static part and a dynamic phase rotation part. Then we can simpify the channe inversion such that a continuousy tracking because of the static part is not necessary. With the foowing equations H i = Θ i,r H Θ i,t = H.ΔΘ i 0 H 1 i = Θ 1 i,t H 1 Θ 1 i,r = H 1.ΔΘ H i 1 = G.ΔΘ H i we are abe to invert the effective channe in a ow compexity manner. ote that. means the eement wise matrix product. Hence, we can appy known muti-user detection fiters with the restriction to the couped channe mode shown in the foowing transmission equation X i = G.ΔΘ H i Y i = G.ΔΘ H i ΔΘ i.h X i + W i 3 where W is the effective noise vector. It is known that the Maximum-Likeihood detector yieds the optimum resuts by minimizing the error Y HS. Therefore we get the optimum detector by using the foowing equation: X i = X i + W i = arg min Y i H.ΔΘ i Y i } 4 X i Furthermore we derive the we known MMSE fiter with the ICI extension G = H H HH H + 1 σs diag σ 1 Y,m 5 where σ Y,m represents an effective noise vector with eements for each receiver station. With 3 after extraction of the kth row of G and the kth coumn of Θ H i, it is possibe to equaise the transmit symbos of the kth user X i k with X k i = G T [k, :] ΔΘ H i [:,k] Y i 6 The ast equation directy eads to the successive interference canceation SIC approach where aready detected symbos Xi k are removed from the received signas iterativey. Y i = Y i H[:,k]ΔΘ i [:,k] Xk i 7 X = Q X reaises the symbo decision of the current user data to avoid error propagation at the interference reduction stage. This can be accompished by decoding the information bits and remoduate the estimated symbos. In this context robust decoding techniques can be expoited to increase the system performance [10]. As a reference the GEIE approach is used here where aways the perfect known symbos are canceed. Furthermore, depending on the argest ayer SIR, the order of the detection process can be modified which resuts in an additiona permutation of the user ayers. Layer Detection with ICI Correction: Based on the first signa detection step it is further possibe to reduce the remaining interference. Aready detected symbos wi be remoduated and feed back in order to estimate the intercarrier interference Y ICI which wi be subtracted before the channe equaization is appied again. In a system with imited feedback processing resources ony adjacent, but strongest interfering, subcarriers are incuded depending on the ratio α m,k = σici,m α max 8 where α m,k =0, 1,..., / 1 and α max [0:1:/ 1 KM ]. Considering Eq. 1 and 3, the iterative scaabe decision feedback equaization DFE scheme can be written as X t i = Gt.ΔΘ H i Y i Ŷ t 1 ICI,i 9 with Ŷ m,t 1 ICI,i = K p=+α m,k p= α m,k p D,p H m,k [, p] X k,t 1 i [p] 30 as the ICI estimate on the th subcarrier and t as iteration numbering. For further simpification the processing entity can evauate and σici,m fairy easiy if the inear approximations derived to section III are used. ote that the noise variance in G t changes to σ w σ I M in the interference s reduction steps. V. PERFORMACE EVALUATIO In this section, we evauate the system performance under various CFO impairments. Therefore, we consider a set-up with three mobie stations K =3 and three base stations M =3, where we continuousy increase the CFO at each station. The simuation parameters are isted in tabe I. Within this simuation set-up we compare the introduced inear MMSE and the SIC detection schemes ony with CPE correction and further the decision feedback equaiser with an increasing number of adjacent subcarriers. Our ower bound is the case where no CFO correction is appied. In Fig., the uncoded bit error rate degradation for a Rayeigh fat channe and in Fig. 3 the uncoded bit error rate degradation for a Rayeigh channe weighted with the denoted power deay profie is pictured, whereas the normaised CFO ɛ is continuousy increased in a range from 10 3,..., 0.. Theɛ distribution at the users and base stations is appied as it is stated in tabe I. We can see in both figures that without any correction of the CFO impact the BER strongy degrades after a few percent s of subcarrier spacing. The initia CPE correction with inear detection yieds good resuts. This shows us that we can significanty increase the system performance if we appy this first correction step. As it was mentioned before in ceuar mobie networks the mobie terminas can pre-compensate its coarse CFOs such that ony residua frequency offsets occur at the receiver sides. In such scenarios the CPE correction often achieves sufficient
TABLE I SIMULATIO SETTIGS 10 0 LD MMSE without CPE Corr. Parameter Vaue User CFOs [ɛ/ 0 ɛ/] Base Station CFOs [ɛ 0 ɛ] CFO Range ɛ =10 3,..., 0. SR 0 db Channe Type IID Rayeigh Power Deay Profie Pedestrian A [11] Moduation Order 16-QAM Subcarrier umber = 51 User Subcarrier Aocation D = [106...6] umber of OFDM Symbos S =7 CP Length CP =40 BER 10 1 10 10 3 10 4 0 0.0 0.04 0.06 0.08 0.1 0.1 0.14 0.16 0.18 0. ε Fig.. LD MMSE with CPE Corr. SIC MMSE with CPE Corr. SIC MMSE with CPE Corr. and DFE α = 1,3,5 BER degradation for fat Rayeigh channes resuts with the advantage of a ow compexity effort. In the other cases as expected the system performance can be improved by appying the successive interference canceation schemes. Furthermore, the performance of both detection techniques can be increased by reducing further the ICI at each detection step. There we can see that if we incude ony a sma number of adjacent subcarriers into the ICI reduction process the BER performance can be improved. BER 10 0 10 1 LD MMSE without CPE Corr. LD MMSE with CPE Corr. SIC MMSE with CPE Corr. VI. COCLUSIO In this paper we presented how to cope with asynchronous muti-user MIMO systems. We have shown the compete system mode for such systems which we used for further evauation of signa detection and CFO compensation processes. The proposed muti-user detection techniques are evauated in a simuation environment and performance evauations show good improvements for our approaches. One advantage of the described agorithm is the channe decomposition into a static and a dynamic part. At this, with the knowedge of the estimated CFOs it is not necessary to track the time invariant channe in the case that time variations are ony caused by these CFOs. A parameters for the CFO compensation process can be derived from the CFO estimates. With the ICI power approximation we are aso abe to correct the intercarrier interference terms. The proposed scaabe detection agorithm compensates both ow and high ICI with proportiona processing effort. The given resuts can be used as an overview for the synchronisation poicies which have to be taken into account at ceuar network MIMO panning. REFERECES [1] G. L. Stöber, J. Barry, S. W. McLaughin, Y. G. Li, M. A. Ingram, and T. G. Pratt, Broadband MIMO-OFDM Wireess Communications, Proceedings of the IEEE, vo. 9, no., pp. 71 94, 004. [] M. Jiang and L. Hanzo, Mutiuser MIMO-OFDM for ext-generation Wireess Systems, Proceedings of the IEEE, vo. 95, no. 7, pp. 1430 1469, 007. [3] M. Morei, Timing and Frequency Synchronization for the Upink of an OFDMA System, IEEE Transactions on Communications, vo. 5, no., pp. 96 306, 004. [4] D. Huang and K. B. Letaief, An Interference-Canceation Scheme for Carrier Frequency Offsets Correction in OFDMA Systems, IEEE Transactions on Communications, vo. 53, no. 7, pp. 1155 1165, 005. SIC MMSE with CPE Corr. and DFE α = 1,3,5 10 0 0.0 0.04 0.06 0.08 0.1 0.1 0.14 0.16 0.18 0. ε Fig. 3. BER degradation for Rayeigh channes weighted with PDP [5] Y.-C. Liao and K.-C. Chen, Mutiuser Common Phase Error Estimation for Upink OFDMA Communications, in Proc. IEEE Wireess Communiations and etworking Conference, Hong Kong, March 007. [6] M. Schemann and V. Jungnicke, Effects of mutipe users CFOs in OFDM-SDMA up-ink an interference mode, in Internationa Conference on Communications ICC, Istanbu, Turkey, Jun. 006. [7] J. Lee, H.-L. Lou, D. Toumpakaris, and J. M. Cioffi, SR Anaysis of OFDM Systems in the Presence of Carrier Frequency Offset for Fading Channes, IEEE Transactions on Wireess Communications, vo. 5, no. 1, pp. 3360 3364, 006. [8] M. Krondorf, T. J. Liang, and G. Fettweis, Symbo Error Rate of OFDM Systems with Carrier Frequency Offset and Channe Estimation Error in Frequency Seective Fading, in Proc. IEEE Internationa Conference on Communication, UK, June 007. [9] D. Petrovic, W. Rave, and G. Fettweis, Properties of the Intercarrier Interference due to Phase oise in OFDM, in Proc. IEEE Internationa Conference on Communication, Korea, May 005. [10] S. Bittner, E. Zimmermann, W. Rave, and G. Fettweis, Performance Anaysis of Iterative MIMO-OFDM Receivers Under the Presence of Phase oise, in Proc. Internationa ITG/IEEE Workshop on Smart Antennas, Austria, February 007. [11] 3GPP TR 5.996, Spatia channe mode for Mutipe Input Mutipe Output MIMO simuations, 3GPP - 3rd Generation Partnership Project, 650 Route des Lucioes - Sophia Antipois; Vabonne - France, September 003, v6.1.0.