The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)
ADAPTIVE ARRAY PROCESSING FOR TIMEVARYING 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, I20133 Milano, Italy S.S. 11 km 158, 20060 Cassina de’ Pecchi, Milano, Italyemail: {nicoli, simeone}@elet.polimi.it email: {luigi.sampietro, claudio.santacesaria}@siemens.comA
BSTRACT
In this work, we propose an adaptive technique for interference mitigation based on Minimum Variance DistortionlessResponse (MVDR) beamforming for the uplink of a WiMAXcompliant system. This method is designed to cope with timevarying interference due to the asynchronous access of users inthe neighboring cells. Channel parameters needed for beamforming are obtained by exploiting both the preambles in thetransmitted frames and the pilot subcarriers embedded in eachinformationbearing 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 standardbased technology that provides
ﬁ
xed last mile broadband wireless access, intended as a costeffective alternative to existing wired technologies such cable and DigitalSubscriber Line (DSL). WiMAXcompliant systems conformto the IEEE 802.162004 or the ETSI HiperMAN standards [1][2]. In the uplink of a cellular WiMAX system, a major sourceof impairment is the outofcell interference. Array processingis a well studied technology for reducing interference from unwanted 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. However, 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 nonstationarity need to be jointly accounted for when designingspatial processing for interference mitigation.In this work, we propose a solution to cope with timevarying interference based on Minimum Variance Distortionless 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 measurements of
L
preambles in the frame; the proposed estimation 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 interference. 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 multipath channels.II. S
YSTEM AND SIGNAL MODEL
We consider the uplink of a IEEE 802.162004 cellular system[1]. Fig. 1 exempli
ﬁ
es the scenario of interest for a squaredlayout with frequency reuse
F
= 4
. In this example, the transmission by the terminal station TS
0
to its own base station BS
0
is impaired by the interference from
N
I
= 3
outofcell terminal 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 multipath 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 addition, each OFDM data symbol includes
K
p
pilot subcarriers.Within the
s
th OFDM symbol of the
th burst (
s
= 0
represents the preamble), the
M
×
K
signal received on the
K
1424403308/06/$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 WiMAXcompliant system.subcarriers can be written as
Y
(
,s
) =
HX
(
,s
) +
N
(
,s
)
,
(1)where
H
= [
h
1
···
h
K
]
is the
M
×
K
spacefrequency channel 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 outofcell interference. The noise is assumed to be zeromean complex (circularly symmetric) Gaussian, tem porally uncorrelated but spatially correlated, with spatial covariance
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 assumed 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 timevarying interferers. Activeinterferers may be indeed different in each OFDM symbol, asthe access is not synchronized between cells. In
ﬁ
g. 1, for instance, 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 spacefrequency matrix
H
,it is useful to write it as
H
=
e
HF
T
, in terms of the
M
×
W
spacetime channel matrix
e
H
that gathers by columns the
W
taps of the discretetime channel impulse response in the timedomain. The DFT matrix reads
F
k,w
= exp[
−
j
2
πn
k
(
w
−
1)
/N
]
,
with
n
k
∈
{
0
,...,N
−
1
}
denoting the frequency index for the
k
th useful subcarrier and
N
the total number of subcarriers. According to the multipath model [4] for the propagation channel between TS
0
and BS
0
, the spacetime matrix
e
H
is assumed to be the superposition of
N
R
paths’ contributions. 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 symbolspaced 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 powerdelayanglepro
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]
; thetransmitterreceiver antenna gain
G
=
G
(T)
+
G
(R)
[dB]
; the power loss
L
(
d
0
) [dB]
experienced over the distance
d
0
between TS
0
and BS
0
; the random
ﬂ
uctuations
S
0
∼
N
(0
,σ
s
)
due to shadowing. As recommended in [1], the pathloss isherein modelled according to the HataOkamura model [4]. Notice also that
P
(T)0
is limited by the maximum power available at the TS’s, i.e.
P
(T)0
≤
P
(T)max
.
B. Interference model
As previously explained, due to the asynchronicity of the access in different cells, at any given time instant (here assumed to be a multiple of the OFDM symbol time), the position and therefore the power of the terminals interfering fromneighboring cells may change. As a consequence, the nonstationary process vector
n
k
(
,s
)
has timevarying 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
outofcell 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 normalized poweranglepro
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 pathlossover 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 satisfy 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 matrix
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. IIIA) and a second one tracks thevariations of the interference covariance matrix along the datasymbols (Sec. IIIB).As a preliminary observation, notice that from (1) the received signal can be written in terms of the spacetime 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 timedomain. The alternativesignal model (7) is useful for deriving the channel estimator asdiscussed in the following.
A. Multipreamble estimation in timevarying 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 thespacetime 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 preamblebypreamble 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 multipreambleLS 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 estimate error goes to zero for
L
→ ∞
, due to the independenceof the
L
measures), it is suboptimal as it does not account for the nonstationarity of the noise. A weighting should be introduced in the average (10) to account for timevarying secondorder statistics of noise. To this aim, let us perform a spatial prewhitening 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 nowtimevarying. 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 temporal component is still constant over the whole frame. The optimal estimate for such a channel structure, characterized by anonstationaryspatialcomponentandaconstanttemporalcom ponent, can be derived following the maximum likelihood ap proach[6]. Werefertotheresultingestimateasmultipreamblespacetime 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 multipreamble 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 interference 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
pilots 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 correlation 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 estimate can be re
ﬁ
ned by a sample average, otherwise it needsto be reinitialized 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 802.162004 compliantsystem [1] is considered with a cellular layout as in
ﬁ
g. 1 andcell side
r
= 1
km. The main system parameters used for simulations are listed in Table 1. A uniform linear array (ULA) of
M
= 4
elements is adopted by BS
0
with interelement spacingof
d
= 1
.
8
λ
[3]. The receiver at BS
0
consists of MVDR
ﬁ
ltering, soft demodulation, LogMAP convolutional decoding andReedSolomon 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 transmission mode are adaptively selected based on the spatial positionand the shadowing effects as described in Sec. IIB.Delays and amplitudes of the multipath channel (2) are selected according to the SUI3 model. Directions of arrival of both user and interferers are drawn from a Gaussian distribution
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
dBiPathloss exponent
γ
4
Reference pathloss 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 powerangle 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 distance
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 interference and the channel estimate accuracy. This is shown brie
ﬂ
yin the following. Denoting by
∆
h
k
(
) =
ˆh
k
(
)
−
h
k
the channel 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 interference 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 signi
ﬁ
cantly larger than MST. We can thus conclude that MST is better suited to be used for MVDR beamforming (6).In
ﬁ
g. 4top we compare the estimation techniques withthe ideal case of known channel in terms of average BER (after 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)
45403530252015105010
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)
4540353025201510500.880.920.961
TS
0
main DOA (deg)
Figure 4: Average BER (with minimal allowed BER
= 10
−
3
)
for MVDR receiver with different parameter estimation techniques (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 asynchronously within each burst. In particular, we consider
L
= 3
bursts of
L
s
= 10
symbols and the user TS
0
placed in broadside at a distance
d
= 0
.
8
km from BS
0
. The interference scenario 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); reestimation 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 timevarying interference mitigation.V. C
ONCLUSION
In this work, an adaptive technique based on MVDR beamforming that copes with outofcell 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 function of the time index over the frame.in the uplink of a WiMAXcompliant system has been pro posed. The method exploits both the preambles and the pilot subcarriers embedded in each data OFDM symbol in order to estimate the timeinvariant wireless channel of the desired use and track the variations of spatial characteristics of interference. Performance of the discussed technique has beenvalidated through numerical results of a multicell 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 ofIEEE802.162004 systems.R
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[2]
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[3]
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A. Goldsmith,
Wireless communications
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H. L. Van Trees,
Optimum array processing
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[6]
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