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Adaptive Array Processing for Time-Varying Interference Mitigation in IEEE 802.16 Systems

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Adaptive Array Processing for Time-Varying Interference Mitigation in IEEE 802.16 Systems
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  The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) ADAPTIVE ARRAY PROCESSING FOR TIME-VARYING INTERFERENCEMITIGATION IN IEEE 802.16 SYSTEMS M. Nicoli, M. Sala, O. Simeone L. Sampietro, C. SantacesariaDEI, Politecnico di Milano Siemens S.p.A. Com CRD MWPiazza L. da Vinci 32, I-20133 Milano, Italy S.S. 11 km 158, 20060 Cassina de’ Pecchi, Milano, Italye-mail: {nicoli, simeone}@elet.polimi.it e-mail: {luigi.sampietro, claudio.santacesaria}@siemens.comA BSTRACT In this work, we propose an adaptive technique for interfer-ence mitigation based on Minimum Variance DistortionlessResponse (MVDR) beamforming for the uplink of a WiMAX-compliant system. This method is designed to cope with time-varying interference due to the asynchronous access of users inthe neighboring cells. Channel parameters needed for beam-forming are obtained by exploiting both the preambles in thetransmitted frames and the pilot subcarriers embedded in eachinformation-bearing OFDM symbol. The effectiveness of the proposed technique is shown through numerical simulations of a standard WiMAX uplink over standard multipath channels.I. I  NTRODUCTION WiMAX (Worldwide Interoperability for Microwave Access)is a standard-based technology that provides  fi xed last mile broadband wireless access, intended as a cost-effective alter-native to existing wired technologies such cable and DigitalSubscriber Line (DSL). WiMAX-compliant systems conformto the IEEE 802.16-2004 or the ETSI HiperMAN standards [1][2]. In the uplink of a cellular WiMAX system, a major sourceof impairment is the out-of-cell interference. Array processingis a well studied technology for reducing interference from un-wanted terminals. In order to make array processing effective,the base station needs to update the spatial  fi ltering based on both the  fl uctuations of the channel of the desired user and thevariations of the spatial features of the interference. In a  fi xedaccess scenario, such as the one targeted by the  fi rst releaseof WiMAX [1], the channel coherence time is assumed to belarge enough to encompass the entire transmitted frame. How-ever, due to the asynchronicity between the access in differentcells, the spatial features of interference may vary within theframe. Therefore, the channel invariance and the noise non-stationarity need to be jointly accounted for when designingspatial processing for interference mitigation.In this work, we propose a solution to cope with time-varying interference based on Minimum Variance Distortion-less Response (MVDR) beamforming. This is coupled witha strategy to estimate both the desired user’s channel and thespatial covariance of the interference, assumed to be Gaussiandistributed. Themethod exploitsboth thepreamble within each burst and the pilot subcarriers embedded in each OFDM sym- bol, working in two steps: 1) Estimate of the desired user’schannel and the interference covariance matrix from the mea-surements of   L  preambles in the frame; the proposed estima-tion exploits the stationarity of the channel within the frame BS 0 TS 0 BS 1 BS 2 BS 3 TS 1 r  TS 2 TS 3 10 d  1 d  20 d  30 d  0 d  2 d  3 d  Figure 1: Uplink layout for a wireless cellular system. Shadedcells represent the fi rst ring of interference for reception of user TS 0  by base station BS 0 . and takes into account the possible variations of the interfer-ence. 2) Tracking of the interference covariance matrix alongOFDM data symbols by using the  K  p  pilots included in eachOFDM data symbol.The effectiveness of the proposed technique is shownthrough numerical simulations of a standard WiMAX uplink over conventional multi-path channels.II. S YSTEM AND SIGNAL MODEL We consider the uplink of a IEEE 802.16-2004 cellular system[1]. Fig. 1 exempli fi es the scenario of interest for a squaredlayout with frequency reuse  F   = 4 . In this example, the trans-mission by the terminal station TS 0  to its own base station BS 0 is impaired by the interference from  N  I   = 3  out-of-cell termi-nal stations  { TS i } N  I i =1  that employ the same carrier frequency.In the  fi gure,  d i  denotes the distance of the  i th terminal fromits base station for   i  = 0 , ···  ,N  I  , while  d i 0  is the distance of the interferer TS i  (with  i  6 = 0 ) from the the base station BS 0 of the user of interest. BS 0  is assumed to be equipped with anantenna array of   M   antennas (covering a  90  degree sector in fi g. 1), while TS’s have a single omnidirectional antenna.The signal transmitted by TS 0  is organized into bursts (see fi g. 2) and it is received by BS 0  through a multi-path channel.A frame consists of   L  bursts, with each burst being made of   L s OFDM symbols: the fi rst OFDM symbol (preamble) contains atraining sequence for synchronization and channel estimation,whereas the subsequent symbols contain coded data. In addi-tion, each OFDM data symbol includes  K  p  pilot subcarriers.Within the  s th OFDM symbol of the   th burst ( s  = 0  rep-resents the preamble), the  M   ×  K   signal received on the  K  1-4244-0330-8/06/$20.00 c ° 2006 IEEE  The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)   Subcarrier    k  Time  (  s, l )(OFDMsymbols) 0 Burst l =1 Burst l =2 Burst l =L PilotData    P   R   E   A   M   B   L   E   P   R   E   A   M   B   L   E   P   R   E   A   M   B   L   E L   1  ⋅   ⋅   ⋅  s L S  ⋅   ⋅   ⋅  0   1  ⋅   ⋅   ⋅  s L S  ⋅   ⋅   ⋅  0   1  ⋅   ⋅   ⋅  s L S  ⋅   ⋅   ⋅ Figure 2: Frame structure for the uplink of a WiMAX-compliant system.subcarriers can be written as Y ( ,s ) = HX ( ,s ) + N ( ,s ) ,  (1)where  H = [ h 1  ··· h K  ]  is the  M   ×  K   space-frequency chan-nel matrix, whose element  ( m,k )  represents the channel gainfor the  m th receiving antenna on the  k th subcarrier; the K   ×  K   diagonal matrix  X ( ,s ) = diag { x 1 ( ,s ) ··· x K  ( ,s ) } contains the transmitted symbols (either pilot or data); N ( ,s ) = [ n 1 ( ,s ) ··· n K  ( ,s )]  models both the backgroundnoise and the out-of-cell interference. The noise is assumed to be zero-mean complex (circularly symmetric) Gaussian, tem- porally uncorrelated but spatially correlated, with spatial co-variance Q ( ,s )  (equal for all the subcarriers): E[ n k ( ,s ) n H k + n (  + m,s + t )] = Q ( ,s ) δ  ( n ) δ  ( m ) δ  ( t ) . Here  δ  ( · )  denotes the Dirac delta. The channel vector  h k  is as-sumed to be constant throughout the entire frame, whereas thecovariance Q ( ,s )  may generally vary on each OFDM symbol(i.e., as a function of   s ) due to time-varying interferers. Activeinterferers may be indeed different in each OFDM symbol, asthe access is not synchronized between cells. In  fi g. 1, for in-stance, the interferer TS 1  may stop at any given time and a newterminal may become active in the cell, generating an abruptchange in the signal interfering on user TS 0 .  A. Channel model  In order to model (and estimate) the space-frequency matrix H ,it is useful to write it as  H  =  e HF T , in terms of the  M   ×  W  space-time channel matrix  e H  that gathers by columns the  W  taps of the discrete-time channel impulse response in the time-domain. The DFT matrix reads  F  k,w  = exp[ −  j 2 πn k ( w  − 1) /N  ] ,  with  n k  ∈  { 0 ,...,N   − 1 }  denoting the frequency in-dex for the  k th useful subcarrier and  N   the total number of subcarriers. According to the multipath model [4] for the prop-agation channel between TS 0  and BS 0 , the space-time matrix e H  is assumed to be the superposition of   N  R  paths’ contribu-tions. Each path, say the  r th, is described by a direction of arrival (DOA) at the receiving array ( θ 0 ,r ), a delay ( τ  0 ,r ) and acomplex fading amplitude ( α 0 ,r ): e H = 10 P  (R)020 N  R X r =1 α 0 ,r a ( θ 0 ,r ) g T ( τ  0 ,r ) = SAG T .  (2)The  M   ×  1  vector   a ( θ 0 ,r )  denotes the array response to thedirection ofarrival θ 0 ,r , while the W  × 1  vector  g ( τ  0 ,r ) collectsthe symbol-spaced samples of the waveform  g ( t − τ  0 ,r ) , thatis the cascade of transmitter and receiver   fi lters shifted by thedelay τ  0 ,r . The fading amplitudes  { α 0 ,r } N  R r =1  are assumed to beuncorrelated and to have normalized power-delay-angle-pro fi le Λ 0 ,r  = E[ | α 0 ,r | 2 ]  so that P N  R r =1 Λ 0 ,r  = 1 . The matrices  S  =[ a ( θ 0 , 1 ) ··· a ( θ 0 ,N  R )] ,  G  = [ g ( τ  0 , 1 ) ··· g ( τ  0 ,N  R )]  and  A  =diag( α 0 , 1 ,...,α 0 ,N  R )  in (2) gather the channel parameters for the whole multipath set.The received power   P  (R)0  [dBm]  in (2) is given by P  (R)0  =  P  (T)0  + G − L ( d 0 ) + S  0 ,  (3)and it depends on: the transmitted power   P  (T)0  [dBm] ; thetransmitter-receiver antenna gain  G  =  G (T) +  G (R) [dB] ; the power loss  L ( d 0 ) [dB]  experienced over the distance  d 0  be-tween TS 0  and BS 0 ; the random  fl uctuations  S  0  ∼  N  (0 ,σ s ) due to shadowing. As recommended in [1], the path-loss isherein modelled according to the Hata-Okamura model [4]. Notice also that  P  (T)0  is limited by the maximum power avail-able at the TS’s, i.e.  P  (T)0  ≤ P  (T)max .  B. Interference model  As previously explained, due to the asynchronicity of the ac-cess in different cells, at any given time instant (here as-sumed to be a multiple of the OFDM symbol time), the po-sition and therefore the power of the terminals interfering fromneighboring cells may change. As a consequence, the non-stationary process vector   n k ( ,s )  has time-varying covariance Q ( ,s )= Q n  + Q I  ( ,s ) , sum of the background noise matrix Q n  =  σ 2 n I M   and the contribution Q I  ( ,s )  from the N  I   out-of-cell active interferers.We assume that the signal from each interferer TS i ,  i  =1 ,...,N  I  , is received by BS 0  through a multipath channelwith the same characteristics as in (2). It follows that the i th interferer spatial covariance (averaged with respect to thefast fading) depends on the DOA’s  { θ i,r ( ,s ) } N  R r =1 , the nor-malized power-angle-pro fi le  { Λ i,r ( ,s ) } N  R r =1  and the received power   P  (R) i 0  ( ,s )  [dBm], according to: Q I  ( ,s )= N  I X i =1 10 P  (R) i 0 ( ,s )10 N  R X r =1 Λ i,r ( ,s ) a ( θ i,r ( ,s )) a H ( θ i,r ( ,s )) .(4)As in (3), the received power is obtained from the power  P  (T) i  ( ,s )  transmitted by TS i , taking into account the path-lossover the distance  d i 0 ( ,s )  and the shadowing effect  S  i 0 ( ,s ) ∼  N  (0 ,σ s )  over the link TS i -BS 0  (see  fi g. 1) P  (R) i 0  ( ,s ) =  P  (T) i  ( ,s ) + G − L ( d i 0 ( ,s )) + S  i 0 ( ,s ) . (5)Some further comment is in order about the transmitted power. Since adaptive modulation and coding is adopted to sat-isfy a  fi xed bit error rate (BER  = 10 − 6 ), the modulation/codingschemeselected(amongthesevenpossibletransmissionmodeslisted in [1]) by the  i th user ( i  6 = 0 ) and the correspondingtransmitted power will be functions of the path loss (over thedistance  d i ( ,s ) ) and the shadowing (over the link TS i -BS i ).  The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) III. I  NTERFERENCE MITIGATION THROUGH ARRAYPROCESSING On the signal (1), the base station BS 0  performs the MVDR [5]spatial  fi ltering  ˆ x k ( ,s ) = w H k  (  ) y k ( ,s )  with: w k ( ,s ) = Q − 1 ( ,s ) h k ¡ h H k Q − 1 ( ,s ) h k ¢ − 1 .  (6)Implementation of such a beamforming requires an estimate of the channel on each subcarrier, i.e. of the whole stationary ma-trix  H and the current interference covariance matrix  Q ( ,s ) .In this Section, two techniques suited for the estimation of such parameters are proposed: a  fi rst one estimates the parametersfrom the preambles (Sec. III-A) and a second one tracks thevariations of the interference covariance matrix along the datasymbols (Sec. III-B).As a preliminary observation, notice that from (1) the re-ceived signal can be written in terms of the space-time channelmatrix  ˜H as Y ( ,s ) =  ˜H˜X ( ,s ) + N ( ,s ) ,  (7)where  ˜X ( ,s ) = F T X ( ,s )  is the  W   ×  K   convolution matrixwith the transmitted signal in the time-domain. The alternativesignal model (7) is useful for deriving the channel estimator asdiscussed in the following.  A. Multi-preamble estimation in time-varying noise Given the signal received on the preamble ( s  = 0 ) of any burst,the conventional approach for the estimation of   H ( , 0)  is theLeast Squares (LS) technique [6]: H LS ( , 0) = [ Y ( , 0) ˜X ( , 0) † ]  · F T =  ˜H LS ( , 0)  · F T ,  (8)where  ˜H LS ( , 0) = Y ( , 0) ˜X ( , 0) † is the LS estimate of thespace-time channel  ˜H ( , 0) , and  ( · ) † denotesthe pseudoinverseoperator. Moreover, the estimate of the covariance Q ( , 0)  can be obtained from N LS ( , 0) = Y ( , 0) − H LS ( , 0) X ( , 0)  as Q LS ( , 0) = 1 K  N LS ( , 0) N HLS ( , 0) .  (9)The long coherence time of the channel H , not considered inthe preamble-by-preamble estimation above, can be exploited by simply averaging the LS estimates over the preambles (i.e.,over   ). This approach will be referred to as the multi-preambleLS estimate (MLS): H MLS  = 1 L L X  =1 H LS ( , 0)  (10) Q MLS ( , 0) = 1 K  N MLS ( , 0) N HMLS ( , 0) ,  (11)with N MLS ( , 0) = Y ( , 0) − H MLS X ( , 0) . Even though the MLS estimate (10) is consistent (the esti-mate error goes to zero for   L  → ∞ , due to the independenceof the  L  measures), it is suboptimal as it does not account for the non-stationarity of the noise. A weighting should be intro-duced in the average (10) to account for time-varying second-order statistics of noise. To this aim, let us perform a spatial pre-whitening before channel estimation: Y w ( , 0) = Q − H / 2LS  ( , 0) Y ( , 0) . This, for   K   → ∞ and thus  Q LS ( , 0)  →  Q ( , 0) , makes thenoise  N w ( , 0) =  Q − H / 2LS  ( , 0) N ( , 0)  be stationary over the preambles (i.e., over    ). However, it has to be noticed thatthe whitened channel  ˜H w ( , 0) =  Q − H / 2LS  ( , 0) ˜H ( , 0)  is nowtime-varying. More speci fi cally, only the spatial componenthas been modi fi ed, from (1), into  S w ( , 0) =  Q − H / 2LS  ( , 0) S ,and it is now varying from preamble to preamble. The tempo-ral component is still constant over the whole frame. The op-timal estimate for such a channel structure, characterized by anon-stationaryspatialcomponentandaconstanttemporalcom- ponent, can be derived following the maximum likelihood ap- proach[6]. Werefertotheresultingestimateasmulti-preamblespace-time estimate (MST) given by H MST ( , 0) = h ˜H LS ( , 0) R − H / 2˜ x ˜ x  PR − H / 2˜ x ˜ x i  · F T (12)where R ˜ x ˜ x  =  ˜X ( , 0) ˜X H ( , 0) ,  and P is the projector onto the r 0  dominating eigenvectors of the temporal correlation R = 1 L L X  =1 R − 1 / 2˜ x ˜ x  ˜H HLS ,w ( , 0) Q − 1LS ( , 0) ˜H LS ,w ( , 0) R − H / 2˜ x ˜ x (13) Notice that the estimation of the temporal part of the channelis obtained from (13) based on a multi-preamble observation,while the estimate of the spatial part is updated within each preamble. The noise covariance estimate is again obtained as Q MST ( , 0) =  1 K  N MTS ( , 0) N HMST ( , 0) , with N MST ( , 0) = Y ( , 0) − H MST X ( , 0) .  B. Tracking of the interference covariance from data symbols The discussion above covered the computation of the channeland interference covariance matrices on the preamble of each burst. However, these estimates cannot be used for evaluatingthe MVDR beamformer (6) within the data burst since the in-terference covariance matrix Q ( ,s )  may also vary within the burst (i.e., along  s ). Therefore, a technique should be devisedin order to track the variations of   Q ( ,s )  by using the  K  p  pi-lots included in each data OFDM symbol. Given any channelestimate  ˆH  and labeling by the subscript  p  the signals on the K  p  pilot subcarriers, a preliminary estimate of  Q ( ,s )  can beobtained as Q p ( ,s ) = 1 K  p N p ( ,s ) N Hp ( ,s ) ,  (14)from N p ( ,s )= Y p ( ,s ) −  ˆHX p ( ,s ) . The estimate (14) can be compared with the estimate in the previous OFDM sym- bol in order to decide whether the interference has changed or   The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) not. This operation is herein performed by computing the cor-relation between the noise covariance matrix at two successiveinstants as: ρ ( ,s ) = tr[ Q p ( ,s ) Q p ( ,s − 1)] || Q p ( ,s ) || · || Q p ( ,s − 1) || where  ||·||  denotes the Frobenius norm of the argument matrix.If the correlation  ρ ( ,s )  is larger than a given threshold  ¯ ρ  (to be determined experimentally), the interference covariance es-timate can be re fi ned by a sample average, otherwise it needsto be re-initialized according to the new estimate value (14) as ˆQ ( ,s ) = ½  [ Q p ( ,s ) + ( T   − 1) ˆQ ( ,s − 1)] /T  ,  ρ ≥ ¯ ρ Q p ( ,s ) ,  ρ <  ¯ ρ where  T   ≤ s + 1  is the number of averaged matrices at the  s thOFDM symbol.IV. N UMERICAL RESULTS In this Section, the uplink of a IEEE 802.16-2004 compliantsystem [1] is considered with a cellular layout as in  fi g. 1 andcell side  r  = 1 km. The main system parameters used for sim-ulations are listed in Table 1. A uniform linear array (ULA) of  M   = 4  elements is adopted by BS 0  with inter-element spacingof   d  = 1 . 8 λ  [3]. The receiver at BS 0  consists of MVDR   fi lter-ing, soft demodulation, Log-MAP convolutional decoding andReed-Solomon decoding. The user TS 0  transmits at maximum power   P  ( T  )0  =  P  ( T  )max  with transmission mode QPSK- 12  (QPSK modulation and coding rate  1 / 2  [1]). Interferers  { TS 0 } 3 i =1  areuniformly distributed in their cells. Their power and transmis-sion mode are adaptively selected based on the spatial positionand the shadowing effects as described in Sec. II-B.Delays and amplitudes of the multipath channel (2) are se-lected according to the SUI-3 model. Directions of arrival of  both user and interferers are drawn from a Gaussian distrib-ution  θ i,r  ∼  N  ( θ i ,σ θ )  with mean  θ i  uniformly distributedin the 90 deg  sector and standard deviation  σ θ  = 5deg .  For Table 1: System parameters Carrier frequency f  c  3.5GHzChannel bandwidth 4MHz N. of subcarriers N   256 N. of useful subcarriers K   200 N. of pilot symbols per OFDM symbol K  p  8 TS maximum power  P  (T) max  27 dBmTS omnidirection antenna gain G (T) 2 dBiBS directional antenna gain (broadside) G (R) 16 dBiPath-loss exponent γ   4 Reference path-loss distance d ref   100 mShadowing standard deviation σ s  8 dB N. of paths for each interfer  N  R  3 Temporal channel support W   32 Cyclic pre fi x length 32 159131721    M   S   E 10 -3 10 -2 10 -1 MSTMLSMSE of the channel estimateMSE of the decisionvariableNumberof preamble l 159131721    M   S   E 10 -3 10 -2 10 -1   MSTMLSMSE of the channel estimateMSE of the decisionvariable 159131721    M   S   E 10 -3 10 -2 10 -1   MSTMLSMSE of the channel estimateMSE of the decisionvariableNumberof preamble l Figure 3: Normalized MSE for the channel estimate and thedecision variable, for MLS and MST, versus the number of  preamble   .each interferer a uniform power-angle delay pro fi le is adopted( Λ i,r  = 1 /N  R , for   i  6 = 0 ).The system performance is  fi rst evaluated for the case wherethe interference covariance matrix varies at the beginning of each burst but it is constant within each burst:  Q ( ,s ) = Q (  ) , ∀ s  (symbol index is dropped). The user TS 0  is placed at dis-tance  d 0  = 0 . 8 km from BS 0  with DOA  θ 0  = 0 deg. Wecompare the mean square error (MSE) on the channel estimateMSE h (  ) = E[ || ˆH (  ) − H || 2 ]  and the MSE on the decisionvariableMSE x (  ) = E[ | ˆ x k ( ,s ) − x k ( ,s ) | 2 ] versusthepream- ble number     for the different estimation techniques. The error on the decision variable clearly depends on both the interfer-ence and the channel estimate accuracy. This is shown brie fl yin the following. Denoting by ∆ h k (  ) =  ˆh k (  ) − h k  the chan-nel estimate error on the  k th subcarrier, from (1) and (6) it is MSE x (  ) = w H k  (  ) Q (  ) w k (  )  |    {z    }  MSE x, 1 (  ) + w H k  (  )Cov( ∆ h k (  )) w k (  )  | {z    }  MSE x, 2 (  ) (15)where  w k (  )  is the MVDR   fi lter calculated as in (6) fromthe channel estimate  ˆh k (  )  and for known spatial covariance ˆQ (  ) =  Q (  )  (as for for   K   → ∞ ). To simplify, wehave assumed uncorrelation between the channel estimate error  ∆ h k (  )  and interference n k ( ,s ) , and also E [ | x k ( ,s ) | 2 ] = 1 .We notice that the  fi rst term in (15) depends on the interfer-ence only, while the second one is also affected by the channelestimate covariance  Cov( ∆ h k (  )) . Fig. 3 compares the twosquared errors  MSE h (  )  (top  fi gure) and  MSE x, 2 (  )  (bottom fi gure) for MLS and MST. It can be seen that, even thoughthe MLS estimate is more convenient than MST in terms of  MSE h (  ) , its error on the decision variable  MSE x, 2 (  )  is sig-ni fi cantly larger than MST. We can thus conclude that MST is better suited to be used for MVDR beamforming (6).In  fi g. 4-top we compare the estimation techniques withthe ideal case of known channel in terms of average BER (af-ter channel decoding) versus the angular position of the user  placed at a distance  d  = 0 . 8 km from the BS. The probability  The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) -45-40-35-30-25-20-15-10-5010 -7 10 -6 10 -5 10 -4 10 -3 ST (L=1)MST LS (L=1) MLS    B   E   R Known channel    S  e  r  v   i  c  e  p  r  o   b  a   b   i   l   i   t  y TS 0  main DOA (deg) -45-40-35-30-25-20-15-10-500.880.920.961 TS 0  main DOA (deg) Figure 4: Average BER (with minimal allowed BER  = 10 − 3 ) for MVDR receiver with different parameter estimation tech-niques (top); probability of service (bottom).of service, calculated as  1 − P  out  from the outage probability P  out , is also shown on the bottom of the  fi gure. The outage probability is here de fi ned as  P  out  = Pr © P  b  ≥  ¯ P  b ª  where theminimum BER is set to  ¯ P  b  = 10 − 3 and the reference BER   P  b is computed for a MVDR receiver with known channel. Theaverage BER is obtained by averaging only over the channelinstances that satisfy  P  b  <  ¯ P  b .  The results show that MST cangain a decade in terms of BER with respect to MLS.We now let the interference covariance matrix vary asyn-chronously within each burst. In particular, we consider  L  = 3  bursts of   L s  = 10  symbols and the user TS 0  placed in broad-side at a distance  d  = 0 . 8 km from BS 0 . The interference sce-nario changes at the third and seventh symbol of each burst,with positions of the three interferers selected uniformly withintheir cell. The threshold is set to  ¯ ρ  = 0 . 8 . Fig. 5 showsthe BER (top) and the interference correlation  ρ ( ,s )  (bottom)over the OFDM symbols. The estimation of the interferencematrix  Q ( ,s )  is obtained as in Sec. III using three differentapproaches: estimation only from the preamble of the current burst (thick line); re-estimation within each OFDM symbolwithout tracking (dashed line); tracking in each OFDM sym- bol by the method in Sec. III with change detection (thin line).The BER results con fi rm that the proposed tracking method isan effective approach for time-varying interference mitigation.V. C ONCLUSION In this work, an adaptive technique based on MVDR beam-forming that copes with out-of-cell asynchronous interference 51015202530    B   E   R 10 -3 10 -2 10 -1 Interference estimation: from preamble only from current pilots (no memory) with detection/trackingSymbol index    C  o  r  r  e   l  a   t   i  o  n   ρ  0.5151015202530 Symbol index ρ Figure 5: BER (top) and correlation value ρ (bottom) as a func-tion of the time index over the frame.in the uplink of a WiMAX-compliant system has been pro- posed. The method exploits both the preambles and the pi-lot subcarriers embedded in each data OFDM symbol in or-der to estimate the time-invariant wireless channel of the de-sired use and track the variations of spatial characteristics of interference. Performance of the discussed technique has beenvalidated through numerical results of a multi-cell system in astandard multipath propagation environment.VI. A CKNOWLEDGEMENTS The authors would like to thank the former students D. Archettiand A.Bonfanti fortheircontribution to the simulation ofIEEE802.16-2004 systems.R  EFERENCES [1]  IEEE 802.16-REVd/D5-2004, “IEEE Standard for Local andMetropolitan Area Networks - Part 16: Air Interface for FixedBroadband Wireless Access Systems,” May 2004. [2]  ETSI, “Broadband Radio Access Networks (BRAN); HIPER-MAN; Physical (PHY) Layer,” Standard TS 102 177, 2003. [3]  S. Savazzi, O. Simeone, and U. Spagnolini, “Optimal design of linear arrays in a TDMA cellular system with Gaussian interfer-ence,”  Proc. IEEE SPAWC  , June 2005. [4]  A. Goldsmith,  Wireless communications , Cambridge UniversityPress, 2005. [5]  H. L. Van Trees,  Optimum array processing  , Wiley, 2002. [6]  M. Nicoli, O. Simeone, and U. Spagnolini, “Multi-slot estima-tion of fast-varying space-time communication channels,”  IEEE Trans. Signal Processing  , vol. 51, no. 5, pp. 1184-1195, May2003.
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