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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION 1
Improved Decoding of BICM-OFDM Transmissions
Plagued by Narrowband Interference
Michele Morelli, Senior Member, IEEE, and Marco Moretti, Member, IEEE
Abstract—We consider an OFDM system employing bit-
interleaved coded-modulation (BICM) and investigate the prob-
lem of reliable data detection in the presence of narrow-
band interference (NBI). Such a scenario may arise in many
practical contexts, including cellular applications and wireless
transmissions over unlicensed frequency bands. It is known that
conventional BICM decoding strategies suffer from significant
performance degradation when the received signal is plagued by
NBI. To overcome this difficulty, in the present work we model the
interference power on each subcarrier as a nuisance parameter
which is averaged out from the likelihood function. This approach
results into a novel bit-metric that makes use of a suitable
estimate of the NBI power obtained from previous data decisions.
Numerical simulations indicate that the error rate performance
of the proposed scheme is close to that of a maximum likelihood
(ML) Viterbi decoder having perfect knowledge ofthe NBI power
across the signal spectrum.
Index Terms—Orthogonal frequency division multiplexing,
narrowband interference suppression, BICM decoding.
I. INTRODUCTION
ORTHOGONAL frequency-division multiplexing
(OFDM) is an appealing technology for broadband
digital transmissions due to its remarkable advantages in
terms of spectral efficiency and robustness against multipath
fading. For these reasons, it has been selected as the air
interface in many communication standards, including the
wireless local area network (WLAN) [1] and the wireless
metropolitan area network (WMAN) [2].
On the other hand, OFDM is highly sensitive to narrow-
band interference (NBI), which may arise when operating
over unlicensed frequency bands where other communication
systems are present. A practical example is offered by the
IEEE 802.11g WLAN, which is allocated in the unlicensed
2.4 GHz band and may occasionally collide with a Bluetooth
user located in the same coverage area [3]. A severely in-
terfered scenario is also encountered in emerging spectrum-
sharing systems [4], where a broadband multicarrier network
opportunistically establishes a communication link by filling
existing gaps in the frequency spectrum without disrupting
operations of primary licensed users.
As pointed out in [5] and [6], the presence of NBI may
seriously degrade the error rate performance of an OFDM
system. The reason is that each data symbol is transmitted
over a unique subcarrier and is likely to be lost when the
corresponding subcarrier is strongly interfered. In [7], an
Manuscript received October 15, 2009; revised April 13, 2010 and August
17, 2010; accepted October 5, 2010. The associate editor coordinating the
review of this paper and approving it for publication was H. Nguyen.
The authors are with the Università di Pisa - Ingegneria dell’Informazione,
Via Caruso, Pisa 50126 Italy (e-mail: marco.moretti@iet.unipi.it).
Digital Object Identifier 10.1109/TWC.2010.12.091535
estimate of the interfering signal is obtained in the frequency
domain using a few measurement tones and it is next sub-
tracted from the received waveform. This requires some a-
priori information about the bandwidth and center frequency
of the interferer, which must be acquired in some manner.
A frequency-domain approach for NBI cancellation is also
presented in [8], where decisions on previously detected
symbols are exploited to predict the NBI contribution on
each subcarrier. In order to achieve satisfactory performance,
the decoding process should start from the most realiable
subcarriers, i.e., those experiencing the highest signal-to-noise
plus interference ratio (SNIR). Unfortunately, no indication is
provided in [8] as how to obtain such information.
It is shown in [9] that channel coding/decoding alone
provides poor immunity to NBI. A popular approach for
interference suppression in coded OFDM systems is based
on erasure insertion. In practice, this technique introduces
additional puncturing in the decoding process by deliberately
ignoring the jammed subcarriers [10], [11]. Although erasure
insertion dispenses from knowledge of the interference power,
it needs to know the NBI position in the frequency domain.
The latter can be estimated during the silent periods [12] or
in a decision-directed fashion [13]. Alternatively, joint erasure
marking and decoding can be accomplished as illustrated
in [14], where jammed subcarriers are erased automatically
during the decoding process without exploiting any a-priori
information about their position. A major drawback of this
approach is the heavy processing load, which increases with
the number of jammed subcarriers. To simplify the decoder,
a suboptimal algorithm is also presented in [14] according to
which an erasure is declared whenever the bit metric exceeds
a preset threshold.
Although erasure insertion can reveal useful in many ap-
plications, it might be inadequate in a severely interfered
scenario [5]. The reason is that a strong narrowband interferer
can hit a substantial number of adjacent subcarriers due to
spectral leakage. This results into a large number of erasures,
which may compromise the error correcting capability of
the employed code. One possible solution to this problem
is presented in [9] by modeling the interfering signals as
complex sinusoids and using a set of PLLs to estimate their
frequencies. The estimated parameters are next used to design
a notch filter which is applied before the discrete Fourier
transform (DFT) operation so as to prevent the occurrence
of spectral leakage. A similar approach is employed in [15],
where a prediction-error filter is introduced in the time-domain
for interference suppression. Unfortunately, both methods are
unable to hanlde bursty interference that can unexpectedly
appear in the middle of a data packet.
1536-1276/10$25.00 c
2010 IEEE
2 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION
Convolutional
encoder
OFDM
modulator
OFDM
demodulator
Propagation
channel
+
+
AWGN
NBI
Interleaver Symbol
mapping
BICM encoder
Viterbi
decoder
Bit metric
generator
Deinterleaver
BICM decoder
p
X
Fig. 1. Block diagram of the considered BICM-OFDM transceiver.
In this work we present an improved decoding strategy
for OFDM transmissions affected by NBI. In doing so, we
apply maximum likelihood (ML) methods and consider a bit-
interleaved coded-modulation (BICM) [16], which is currently
adopted in some commercial standards to provide the system
with a form of code diversity. Following the same approach
employed in [17], we treat the NBI power on each subcarrier
as a nuisance parameter which is averaged out from the
likelihood function. Unfortunately, the exact ML solution does
not lend itself to a practical implementation. Therefore, we
propose an alternative suboptimal scheme where the NBI
power is estimated on the basis of previous data decisions
and is next employed to properly weight the bit metrics in
the currently decoded OFDM block. Compared with erasure
decoding, our scheme can achieve better performance as it
does not simply discard information from jammed subcarriers,
but rather reduces the weight of those bits that have been
impaired by NBI. Numerical simulations indicate that the
error-rate of the proposed method is close to that of a genie-
aided Viterbi decoder having perfect knowledge of the NBI
power.
The rest of the paper is organized as follows. In Sect. II
we describe the signal model and introduce basic notation.
Sect. III illustrates the proposed ML-based scheme for BICM
decoding in the presence of NBI. We present simulation results
in Sect. IV, while some conclusions are drawn in Sect. V.
II. SIGNAL MODEL
We consider the OFDM-based BICM system illustrated in
Fig. 1. The information bits are first convolutionally encoded
and interleaved by means of a standard block interleaver.
A set of consecutive m= log2Minterleaved bits is then
mapped onto M-ary symbols taken from a PSK or QAM
constellation Ausing a mapping function χ{·}. After par-
titioning the M-ary symbol sequence into adjacent segments
of Nelements, we use each segment to modulate Navailable
subcarriers by means of a conventional OFDM modulator.
The latter comprises an inverse discrete Fourier transform
(IDFT) operation and the insertion of a cyclic prefix (CP)
longer than the channel impulse response (CIR) to avoid
interblock interference (IBI). Transmission takes place over
a multipath fading channel. We consider low mobility appli-
cations (such as indoor communications) where the channel
keeps approximately constant over short frames and denote by
h= [h(0), h(1),...,h(L−1)]Tthe corresponding CIR vector,
with [·]Tindicating the transpose operation. At the receiver
side, the incoming waveform is down-converted to baseband
and sampled at a rate fs=N∆f, where ∆fis the frequency
spacing between adjacent subcarriers. After discarding the CP,
a set of Nsamples corresponding to an OFDM block is fed to
a DFT device. Let Xp= [Xp(0), Xp(1),...,Xp(N−1)]Tbe
the DFT output from the pth received OFDM block and ap=
[ap(0), ap(1),...,ap(N−1)]Tthe vector of corresponding
data symbols. Due to possible coexistence with other com-
munication systems operating over the same frequency band,
some subcarriers may be jammed by NBI. Thus, assuming
ideal frequency and timing synchronization, we have
Xp(n) = H(n)ap(n) + ηp(n)(1)
where H(n)is the channel gain at the nth DFT output, which
is related to the discrete-time CIR by
H(n) =
L−1
X
ℓ=0
h(ℓ)e−j2πnℓ/N (2)
while ηp(n)is a disturbance term that accounts for both
thermal noise and NBI. Following [14], we model ηp(n)as
a Gaussian random variable with zero mean and variance
σ2(n) = σ2
w+σ2
I(n), where σ2
wis the thermal noise con-
tribution, while σ2
I(n)represents the average NBI power on
the nth subcarrier. For the time being, σ2
I(n)is assumed to be
constant over the observation period. To further simplify the
derivation, the random variables ηp(n)are treated as statisti-
cally independent for different values of nand p. Although this
assumption is reasonable when applied to thermal noise, some
correlation is expected between the interference contribution
over closely spaced subcarriers. Since such correlation could
be exploited to improve the resilience of the system to NBI,
we use the independence assumption to describe a worst-case
scenario.
Returning to Fig. 1, we see that the quantities Xp(n)at the
output of the OFDM demodulator are employed to generate
suitable metrics for each coded bit. These metrics are then
deinterleaved and passed to a conventional Viterbi decoder.
Our goal is to design the bit metrics so as to improve the
error-rate performance in the presence of NBI. In doing so we
employ ML methods and assume that the channel response
H(n)is perfectly known at the receiver. In practice, H(n)
can be estimated by exploiting a preset number Kof training
blocks placed at the frame’s beginning and carrying known
symbols. A powerful scheme for accurate channel estimation
in the presence of NBI has recently been proposed in [17].
For simplicity of exposition, in this work we only consider
the traditional non-iterative decoding architecture of Fig. 1. As
discussed later, however, our approach can also be extended to
more complex implementations such as BICM receivers with
iterative or turbo-decoding [18].
MORELLI and MORETTI: IMPROVED DECODING OF BICM-OFDM TRANSMISSIONS PLAGUED BY NARROWBAND INTERFERENCE 3
To proceed further, we denote by bp(n) =
{b(1)
p(n), b(2)
p(n),...,b(m)
p(n)}the sequence of mbits
mapped onto the M-ary symbol ap(n). Then, for any Xp(n)
the BICM receiver generates 2mmetrics corresponding to
each of the mbinary hypotheses b(i)
p(n) = b, with b= 0 or
1 and i= 1,2,...,m. At large signal-to-noise ratios (SNRs),
these metrics can be approximated as [16]
γ(i)
p(n, b)≃max
˜a∈Ω(i)(b){ln [p(Xp(n)|˜a)]}(3)
where p(Xp(n)|˜a)is the probability density function (pdf)
of Xp(n)conditioned on a given value ˜a∈ A, while
Ω(i)(b)is the subset of 2m−1symbols ˜asuch that the bit
sequence ˜
bmapped onto ˜ahas the ith entry equal to b, i.e.,
Ω(i)(b) = {χ{˜
b(1),˜
b(2),...,˜
b(m)}
˜
b(i)=b}. The quantities
in (3) are then deinterleaved and used as branch metrics in
a conventional Viterbi processor, which eventually selects the
codeword with the best accumulated metric.
III. IMPROVED BICM DECODING
In a genie-aided receiver having perfect knowledge of the
NBI powers σ2= [σ2(0), σ2(1),...,σ2(N−1)]T, the metric
in (3) takes the form
γ(i)
p,KIV(n, b) = min
˜a∈Ω(i)(b)(|Xp(n)−˜aH(n)|2
σ2(n))(4)
and is referred to as bit-metric with known interference
variance (KIV). As mentioned previously, however, vector
σ2is typically unknown, thereby preventing the practical
implementation of KIV. One possible strategy consists of
computing the metric without taking NBI into account. This
amounts to setting σ2(n) = σ2
win (4) for n= 0,1,...,N−1,
and leads to the following bit metric for an interference-free
scenario (IFS)
γ(i)
p,IFS(n, b) = min
˜a∈Ω(i)(b)n|Xp(n)−˜aH(n)|2o(5)
where the denominator σ2
whas been skipped because it appears
as an irrelevant factor for all candidate codewords. As IFS
is known to exhibit poor performance in a highly interfered
scenario [9], in the sequel we present an alternative approach
where σ2is treated as a nuisance random vector and is aver-
aged out from the likelihood function. It is worth mentioning
that a similar Bayesan idea has been recently employed in [19]
to get bit metrics with increased robustness against channel
estimation errors.
A. Metric computation in the presence of NBI with unknown
power
In the presence of NBI with unknown power, the KIV
cannot be used as it exploits the variances σ2(n)which are
actually unknown. To overcome this difficulty, we temporarily
neglect the bit interleaving operation and concentrate on
the ML estimation of the modulation symbols in a frame
composed by P+KOFDM blocks. The first Kblocks
of the frame, which are commonly used for synchronization
and channel estimation purposes, are modulated by a training
sequence [dT
−K+1 dT
−K+2 ··· dT
0]Tof known symbols,
with dp= [dp(0), dp(1),...,dp(N−1)]T. The last Pblocks
represent the payload section and convey the sequence a=
[aT
1aT
2··· aT
P]Tof coded modulation symbols that must
be detected. For notational simplicity, we collect the DFT
outputs into a vector X= [XT
−K+1 XT
−K+2 ··· XT
P]T, with
[XT
−K+1 XT
−K+2 ··· XT
0]Tcorresponding to the training
sequence.
Given the unknown parameters (a,σ2), from (1) it follows
that the entries of Xare statistically independent and Gaus-
sian distributed with mean ap(n)H(n)and variance σ2(n).
Accordingly, their joint pdf takes the form shown in (6), where
ξ(n)is a known quantity defined as
ξ(n) =
0
X
p=−K+1
|Xp(n)−dp(n)H(n)|2.(7)
As anticipated, we model σ2as a random vector that is
subsequently averaged out from the likelihood function. This
calls for the adoption of some a-priori pdf for σ2. Due to its
mathematical tractability, a convenient choice is the inverse-
gamma [20] pdf
p(σ2) = η
σ4exp n−η
σ2o,for σ2>0(8)
which has been suggested to characterize the power of the sea
clutter in radar signal processing [21] and is also employed in
[17] in the context of channel estimation for OFDM systems.
To further simplify the analysis, in the following derivations
we consider the entries of σ2as statistically independent.
Thus, averaging p(Xa,σ2)in (6) with respect to p(σ2)
and letting δ(n) = η+ξ(n), yields the marginal likelihood
function for ain the form shown in (9), or equivalently in (10).
The marginal log-likelihood function (LLF) is obtained by
taking the logarithm of p(X|a). Skipping additive constants
and irrelevant factors independent of a, this produces
Λ(a) = −
N−1
X
n=0
ln "δ(n) +
P
X
p=1
|Xp(n)−ap(n)H(n)|2#.
(11)
At this stage we use the identity
ln "P
X
p=0
αp#= ln(α0) +
P
X
p=1
ln 1 + αp
Pp
k=1 αp−k,(12)
which holds true with any set {α0, α1,...,αP}of real
positive numbers. Then, letting α0=δ(n)and αp=
|Xp(n)−ap(n)H(n)|2for p= 1,2,...,P, after neglecting
the irrelevant term ln[δ(n)] we may rewrite (11) as
Λ1(a) =
N−1
X
n=0
P
X
p=1
λ1[ap(n),←−
ap(n)] (13)
with ←−
ap(n) = [ap−1(n), ap−2(n),...,a1(n)]Tand the value
of λ1[ap(n),←−
ap(n)] as shown in (14). Unfortunately, the
quantity λ1[ap(n),←−
ap(n)] cannot be used as a branch metric
in a Viterbi processor because it depends not only on the
current symbol ap(n), but also on past symbols ←−
ap(n)
modulating previously transmitted OFDM blocks. A possible
way out is based on the assumption that the interleaver size
is equal to one OFDM block so that, when decoding the pth
4 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION
p(Xa,σ2) =
N−1
Y
n=0
1
[πσ2(n)]P+Kexp (−1
σ2(n)"ξ(n) +
P
X
p=1
|Xp(n)−ap(n)H(n)|2#) (6)
p(X|a) =
N−1
Y
n=0
∞
Z
0
η
σ4(πσ2)P+Kexp (−1
σ2"δ(n) +
P
X
p=1
|Xp(n)−ap(n)H(n)|2#)dσ2(9)
p(X|a) =
N−1
Y
n=0
η
πP+K
(P+K)!
hδ(n) + PP
p=1 |Xp(n)−ap(n)H(n)|2iP+K+1 (10)
λ1[ap(n),←−
ap(n)] = −ln "1 + |Xp(n)−H(n)ap(n)|2
δ(n) + Pp−1
k=1 |Xp−k(n)−H(n)ap−k(n)|2#(14)
block, decisions about the past symbols ←−
ap(n)have already
been taken and are available at the receiver. Hence, if the
error rate is adequately small, we may reasonably replace
λ1[ap(n),←−
ap(n)] in (14) by
λ2[ap(n)]
=−ln "1 + |Xp(n)−H(n)ap(n)|2
δ(n) + Pp−1
k=1 |Xp−k(n)−H(n)ˆap−k(n)|2#
(15)
where ˆap−k(n)is the decision on ap−k(n). It is worth
observing that λ2[ap(n)] only depends on the current symbol
ap(n)and, in consequence, it may now be used as a branch
metric in a Viterbi processor.
A close inspection of (15) reveals that the denominator
in the argument of the logarithm is the sum of ηplus an
estimate of σ2(n)(up to a scaling factor) computed on the
basis of the DFT outputs up to time p−1. The fact that all
past OFDM blocks are employed for estimating σ2(n)is a
direct consequence of our basic hypothesis that the average
interference power keeps constant over the entire frame [13].
This assumption is commonly adopted in the related literature,
even though in practice it may be unrealistic due to the bursty
nature of the interference. Therefore, assuming that the aver-
age NBI power is constant only over a limited time window
spanning KOFDM blocks and neglecting the presence of η,
we propose to replace λ2[ap(n)] with
λ3[ap(n)] = −ln "1 + |Xp(n)−H(n)ap(n)|2
βˆσ2
p(n)#(16)
where βis a design parameter and
ˆσ2
p(n) = 1
K
K
X
k=1
|Xp−k(n)−H(n)ˆcp−k(n)|2(17)
is an estimated value of σ2(n)at the pth OFDM block, with
ˆcℓ(n) = dℓ(n)
ˆaℓ(n)
−K+ 1 ≤ℓ≤0
1≤ℓ≤P.(18)
This way, any abrupt variation of the NBI average power
caused by the presence of bursty interference originates a
transient phase in the estimation of σ2(n)which terminates
after KOFDM blocks.
Since we may interpret λ3(˜a)as a scaled version of
ln [p(Xp(n)|˜a)], the set of 2mbit metrics corresponding to
Xp(n)are eventually computed from (16) in the form
γ(i)
p,UIV(n, b) = min
˜a∈Ω(i)(b)(ln "1 + |Xp(n)−H(n)˜a|2
βˆσ2
p(n)#)
(19)
and are referred to as bit metrics with unknown interference
variance (UIV).
B. Remarks
1) From (19) it appears that UIV reduces the influence of
jammed subcarriers by properly weigthing the corresponding
metrics on the basis of the estimated NBI power. This strat-
egy should result into improved error rate performance with
respect to simple erasure insertion. It is worth observing that
erasure decoding can be seen as a special case of UIV when
ˆσ2
p(n)approaches infinity for some n.
2) Compared to a conventional BICM decoder employing
the IFS metric in (5), the proposed UIV only introduces little
additional complexity due to the need for estimating the NBI
power as in (17). However, it should be observed that UIV is
much simpler to implement than the sequential joint erasure
marking and decoding scheme illustrated in [14], which entails
iterative application of the decoding process with one single
bit erasure being marked at each new iteration.
3) Inspection of (19) and (4) reveals that UIV differs from
KIV into two aspects, i.e., the presence of the logarithmic
function and the use of the estimate ˆσ2
p(n)in place of the
true noise-plus-interference power σ2(n). In order to show the
impact of the logarithmic function on the system performance,
in Sect. IV we compare the UIV with a BICM decoder
employing the following ad-hoc (AH) bit metrics
γ(i)
p,AH(n, b) = min
˜a∈Ω(i)(b)(|Xp(n)−H(n)˜a|2
ˆσ2
p(n))(20)
where ˆσ2
p(n)is still computed as in (17) and parameter β
appearing in (19) has been neglected as it represents an
irrelevant scaling factor for all codewords.
MORELLI and MORETTI: IMPROVED DECODING OF BICM-OFDM TRANSMISSIONS PLAGUED BY NARROWBAND INTERFERENCE 5
4) Parameter Kis expected to have a strong impact on
the performance of UIV and AH. On one hand, increasing
Kimproves the accuracy of the estimated NBI power in (17)
due to the larger observation window, but on the other hand it
reduces the capability to track abrupt variations of σ2(n)that
may occur in case of bursty interference. Simulation results
indicate that letting K= 4 provides a reasonable trade-off
between these conflicting requirements.
5) A basic assumption in the derivation of UIV is that
the interleaver size is equal to the number of coded bits
transmitted in a single OFDM block since otherwise the
decisions ˆcp−k(n)employed in (17) are unavailable when
decoding the pth block. This situation is typical of some
commercial standards including the IEEE 802.11a-n WLAN,
where bit interleaving is only performed in the frequency
direction and is not applied across adjacent OFDM blocks due
to the slowly fading characteristics of the propagation channel
[22]. However, the UIV can also be used in applications where
interleaving is accomplished over a subframe composed by
B > 1OFDM blocks. In such a case, the quantity ˆσ2
p(n)in
(17) is replaced by
ˆσ2
p(n;B) = 1
K
|p|B+K−1
X
k=|p|B
|Xp−k(n)−H(n)ˆcp−k(n)|2(21)
where |p|Bdenotes the remainder of the integer division p/B.
Clearly, for large values of Bthe NBI tracking capability of
UIV is reduced since the estimated NBI power ˆσ2
p(n;B)is
computed from the previous subframe and might be outdated
when used to detect the pth OFDM block. A possible way
out is illustrated in [23], where the expectation-maximization
(EM) algorithm is employed for joint bit decoding and NBI
power estimation. This solution avoids the use of outdated
information even in the presence of fast variations of the NBI
power as the latter is estimated by exploiting the DFT outputs
obtained in the current subframe rather than in previously
transmitted subframes. The price for this advantage is an
increase of the processing load since the EM-based scheme
in [23] operates in an iterative fashion and achieves conver-
gence in approximately three iterations, thereby requiring a
computational load three times larger than UIV.
6) Albeit derived for a conventional non-iterative receiver
architecture, the UIV can also be applied to BICM receivers
with iterative decoding (ID). Assume that the convolutional
encoder is periodically terminated by means of some tailing
bits, so that decoding can be independently performed over
subframes of Badjacent OFDM blocks. In such a case, the
metric of bit b(i)
p(n)being one of the two binary values
b= 0 or 1 is given by (22), where {˜
b(1),˜
b(2),...,˜
b(m)}is
the sequence of mbits mapped onto ˜aand Pr(˜
b(k))denotes
the a priori probability of ˜
b(k). These metrics are deinterleaved
and fed to a soft-input soft-output (SISO) decoder, which
eventually delivers the probabilities Pr(˜
b(k))to be used in the
next iteration as extrinsic information for recomputing the bit
metrics. Since the a priori probabilities are unavailable when
the decoding process starts, on the first iteration they are set
to 1/2.
IV. NUMERICAL RESULTS
Computer simulations have been run to assess the perfor-
mance of the detection algorithms illustrated in the previous
section. The system parameters are compliant with the IEEE
802.11g standard for WLAN and are summarized as follows.
The OFDM terminals employ IDFT/DFT units of length
N= 64 and communicate over a bandwidth of 20 MHz.
The sampling period is 50 ns and a CP of length Ng= 16
samples is used to eliminate the IBI. The encoder uses the
industry-standard convolutional code with rate Rc= 1/2and
generator polynomials [133] and [171] (in octal). After block
interleaving, the coded bits are Gray-mapped onto a sequence
of 16-QAM symbols with average energy σ2
s=E{|ap(n)|2}
and encompassing P= 50 OFDM blocks. As mentioned
previously, K= 4 is employed throughout simulations. The
discrete-time CIR is composed by nT= 8 channel taps,
which are modeled as independent and circularly symmetric
Gaussian random variables with zero mean (Rayleigh fading)
and an exponentially decaying power delay profile
E{|h(ℓ)|2}=σ2
h·exp(−ℓ/nT)ℓ= 0,1,...,nT−1.
(23)
The constant σ2
hin (23) is chosen such that the channel
power is normalized to unity, i.e., E{khk2}= 1. In addition
to background noise with variance σ2
w, the received signal
is also affected by NBI which adds a Gaussian disturbance
term of variance σ2
Ito Mcontiguous subcarriers. Unless
otherwise stated, we assume that NBI is present during the
overall received frame. The signal-to-interference ratio over
the jammed subcarriers is defined as SIR =σ2
s/σ2
I, while
Eb/N0is the ratio between the average received energy per
information bit and the one-sided noise power spectral density.
Observing that Eb=σ2
s/(2mRc)and N0=σ2
w/2with m= 4
and Rc= 1/2, it follows that Eb/N0=σ2
s/(2σ2
w).
We begin by assessing the impact of parameter βon the
accuracy of UIV. Fig. 2 illustrates the bit-error-rate (BER)
vs. βfor Eb/N0= 12 dB, M= 4 and SIR= 0 or 5 dB.
As it is seen, for each SIR level there exists an optimum
value of βminimizing the BER. Since β= 1 seems a good
choice irrespective of the SIR level, this value is adopted in
all subsequent simulations. In practice, the design of βis
demanded to numerical simulations as the value that optimizes
the system performance in a specific operating scenario cannot
be mathematically predicted.
Fig. 3 presents BER results vs. Eb/N0for all investigated
schemes as obtained with SIR= 5 dB and M= 4. The curve
labeled GAE refers to a genie-aided erasure marking receiver
that has perfect knowledge of the NBI position across the
signal bandwidth and is able to erasure all jammed subcarriers.
As expected, the best performance is achieved by KIV due to
its ideal side information about the NBI power. The proposed
UIV performs similarly to GAE and is 0.5 dB far from KIV.
Compared to UIV, the AH entails a loss of approximately 0.5
dB, while larger degradations are observed with IFS which
does not take NBI into consideration.
Fig 4 illustrates the BER performance when the number of
jammed subcarriers is M= 1 and the SIR is still fixed to 5
dB. These results are in line with those in Fig. 3 and confirm
that UIV is approximately 0.5 dB far from KIV, while IFS
6 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION
γ(i)
p,UIV(n, b) = min
˜a∈Ω(i)(b)
ln "1 + |Xp(n)−H(n)˜a|2
βˆσ2
p(n;B)#+
m
X
k=1,k6=i
ln hPr(˜
b(k))i
(22)
10−2 10−1 100101102
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10−3
β
BER
SIR = 5 dB
SIR = 0 dB
Eb/N0 = 12 dB
Fig. 2. BER of UIV vs. βfor Eb/N0= 12 dB and SIR = 0 or 5 dB.
7 8 9 10 11 12 13 14 15
10−5
10−4
10−3
10−2
10−1
Eb/N0 (dB)
BER
IFS
AH
GAE
UIV
KIV
SIR 5 dB
Fig. 3. BER vs. Eb/N0with SIR = 5 dB and M= 4 jammed subcarriers.
is plagued by a large error floor at SNR values of practical
interest. Obviously, all considered schemes exhibit a lower
error rate as compared to the simulation set-up of Fig. 3 due
to the reduced number of jammed subcarries.
The interference rejection capability of the considered met-
rics are shown in Fig. 5 in terms of the error rate performance
vs. the SIR level. The SNR is fixed to 12 dB and M= 4.
The poor performance of IFS at low SIR values is a clear
evidence of the vulnerability of this method in the presence
of interference. In contrast, the other schemes exhibit a weak
dependence upon the SIR thanks to their intrinsic resilience
to NBI. It is worth observing that, since GAE ideally erases
all jammed subcarriers, its performance is theoretically inde-
pendent of the SIR level.
It is interesting to compare the performance of the inves-
7 8 9 10 11 12 13 14 15
10−5
10−4
10−3
10−2
10−1
Eb/N0 (dB)
BER
IFS
AH
GAE
UIV
KIV
SIR 5 dB
Fig. 4. BER vs. Eb/N0with SIR = 5 dB and M= 1 jammed subcarrier.
−5 −4 −3 −2 −1 0 1 2 3 4 5
10−4
10−3
10−2
10−1
100
SIR (dB)
BER
IFS
AH
GAE
UIV
KIV
Eb/N0 12 dB
Fig. 5. BER vs. SIR for Eb/N0= 12 dB and M= 4 jammed subcarriers.
tigated schemes in the presence of bursty interference. For
this purpose, in Fig. 6 we provide BER results vs. Eb/N0as
obtained with an interfering signal hitting four adjacent sub-
carriers and abruptly changing its frequency position during
the received OFDM packet. In practice, this situation may
arise in an IEEE 802.11g WLAN system interfered-with by
a Bluetooth signal, which is based on a frequency-hopping
protocol with a rate of 1600 hops per second. Comparing the
results of Fig. 6 with those in Fig. 3, we see that KIV, GAE
and IFS have virtually the same error-rate performance as in
the absence of any frequency hop. The reason is that KIV and
GAE are provided with istantaneous information as to which
subcarriers are actually jammed and can thus ideally track the
interfering signal as it moves in the frequency domain. As for
IFS, it does not attempt any NBI mitigation and, accordingly,
MORELLI and MORETTI: IMPROVED DECODING OF BICM-OFDM TRANSMISSIONS PLAGUED BY NARROWBAND INTERFERENCE 7
7 8 9 10 11 12 13 14 15
10−5
10−4
10−3
10−2
10−1
SNR (dB)
BER
IFS
AH
GAE
UIV
KIV
SIR 5 dB
Fig. 6. BER vs. Eb/N0with SIR = 5 dB and M= 4 jammed subcarrier.
its performance is independent of the NBI position. On the
other hand, since both UIV and AH exploit an estimate of
the NBI power obtained as in (17), any frequency hop of the
interfering signal will originate a transient phase during which
σ2(n)is poorly estimated and the error rate is correspondingly
increased. This explains the performance loss experienced by
these schemes when passing from the scenario of Fig. 3 to that
in Fig. 6. However, since the loss of UIV is much smaller than
that exhibited by AH, we conclude that the presence of the
logarithmic function in the UIV metric greatly reduces the
sensitivity of the decoder to the bursty nature of interference.
V. CONCLUSIONS
We have presented a novel scheme for BICM decoding in
an OFDM-based system affected by NBI. The interference is
assumed to be Gaussian distributed in the frequency domain
and ML methods are employed to solve the detection problem
by treating the average NBI power on each subcarrier as an un-
known nuisance parameter. Approximations have been made
to arrive at a practical decoding scheme where data decisions
are exploited to get an estimate of the NBI power and a Viterbi
processor is used to detect the transmitted codeword. Since the
proposed algorithm relies on a modification of the bit-metrics
employed in a standard BICM receiver, the overall complexity
is close to that of a conventional Viterbi decoder.
Simulations indicate that the proposed scheme is inherently
robust to NBI and can effectively be employed in a severely
interfered scenario. Its error rate performance is close to that
of genie-aided schemes relying on ideal erasure marking or
having perfect knowledge of the NBI power across the signal
spectrum. The new bit metric can also be used in advanced
BICM receivers with iterative or turbo decoding.
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