Cyclic Autocorrelation based Blind OFDM Detection and ...

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Cyclic Autocorrelation based Blind OFDM Detection
and Identification for Cognitive Radio
Ning Han, Guanbo Zheng, Sung Hwan Sohn, Jae Moung Kim
INHA-WiTLAB, INHA University
253 Younghyun-dong, Nam-gu, 402-751
Incheon, Korea
neil_han@ieee.org, gbzheng@gmail.com, sunnyshon@gmail.com, jaekim@inha.ac.kr
Abstract—Cognitive radio is considered as a promising technique
to increase the utilization of limited spectral resource. The key
issue in cognitive radio is to design a reliable spectrum sensing
method that is able to detect the signal in the target channel as
well as to recognize different signals. In this paper, focusing on
classifying different OFDM signals, we propose a two-step
detection and identification approach. The key parameters to
separate different OFDM signals are the subcarrier spacing and
guard interval. A simple but reliable peak detection method is
adopted in the first step, while a peak searching method is used
to determine the length of guard interval. Simulations are
carried out in AWGN to verify the validation of the proposed
method. It is shown that our method can satisfy the detection
and identification requirement with a low false alarm
probability.
Keywords-cognitive radio; spectrum sensing; OFDM;
cyclostationary; signal detection and identification
I. INTRODUCTION (HEADING 1)
It is commonly believed that there is a scarcity of spectrum
availability at frequencies that can be economically used for
wireless communications, especially in the bands below 3 GHz
[1]. However, according to the measurements taken in [2], the
shortage is mainly caused by the spectrum policy under which
the spectrum is licensed to a limited number of
implementations. Cognitive radio provides the opportunity to
utilize the vacant spectrum resources while helping to prevent
interference to primary users that own the frequency bands. It
is defined as an intelligent wireless communication system that
is aware of its surrounding environment, and learns from the
environment and adapts its internal states to statistical
variations in the incoming RF stimuli by making
corresponding changes in certain operating parameters in real
time [3]. The new functionality (spectrum sensing) requires
that the radio is able to separate the vacant frequency bands
from those filled with primary user signals accurately.
It is well known that by splitting a single high-rate data
This work was supported by the Korea Science and Engineering
Foundation (KOSEF) through the National Research Lab. Program funded by
the Ministry of Education, Science and Technology (No. M10600000194-
06J0000-19410). This work was supported by the Korea Science and
Engineering Foundation (KOSEF) grant funded by the Ministry of Education,
Science and Technology (MEST) (No. R01-2006-000-10266-0(2008)).
978-1-4244-2108-4/08/$25.00 © 2008 IEEE
stream into a number of lower rate subcarriers, OFDM holds
several advantages including robustness against frequency
selective fading or narrowband interference [4]. Recently, due
to the booming of WiFi and WiMAX, OFDM based systems
are becoming the trend for next generation wireless
communications. Therefore, the detection method separating
OFDM signal from other single carrier signal or random noise
comes to the frontier. [5] proposed to exploit the embedded
periodicity among the subcarriers in OFDM signal. [6]
developed several criteria based on the time domain
periodicity introduced by the cyclic prefix in DVB-T OFDM
symbol. These approaches require either the number of
subcarriers or the spacing between consecutive subcarriers in a
priori. However, different OFDM systems usually own their
unique parameters due to various applications. Even in a single
OFDM system, there are several operation modes with
different parameters to achieve various transmission data rates.
These make the detector almost impossible to know the
information in advance. Thus, the existing methods are
impractical to detect OFDM signal blindly.
In this paper, by considering the uncertainties in the
detector, we proposed a time domain cyclostationarity based
approach to detect and identify OFDM signal from random
noise. The key parameters to discriminate different OFDM
signals are the subcarrier spacing and duration of guard
interval. The proposed approach consists of two steps. The first
step is to detect the OFDM signal from random noise simply
by recognizing the symmetric peaks in the autocorrelations,
which is a special case of the cyclic autocorrelation function.
The subcarrier spacing is calculated as long as the OFDM
signal is detected. In the second step, by searching the cycle
frequencies, the length of guard interval is calculated to
recognize different OFDM signals. The main advantage is that
the proposed method does not require the FFT process. Since
the number of subcarrier is unknown, the mismatch of FFT
parameters will reduce the performance of any FFT based
detection methods.
The rest of our paper is organized as follows; Section II
describes the time domain cyclostationarity of OFDM signal in
terms of cyclic correlation function (CAF). Section III presents
the proposed detection procedure and criteria based on the
blind assumption. Simulation results are discussed in Section

IV to show the feasibility and advantages of the proposed
method. Finally, we conclude the paper in Section V.
II. CYCLOSTATIONARITY OF OFDM SIGNAL
Cyclostationary random process has been studied since the
1980s. It is well known that the signal in wireless
communications can be modeled as a cyclostationary random
process instead of stationary one. It gives us another view to
analyze the unique characteristics embedded in signals. The
basic concept of cyclostationary random process is reviewed in
this section and the characteristics in the CAF of OFDM signal
is exploited and discussed as the preliminary of the proposed
detection and identification method.
A. Definition of CAF
A process, for instance x(t), is said to be cyclostationary in
the wide sense if its mean and autocorrelation are periodic with
some period, say T [7]:
( ) ( )
m t+ T = m T
(1)
x x
τ τ τ τ
Rxt+ T + , t+ T − = Rxt+ , t−
2 2 2 2
where R ( t τ 2, t τ 2)
x + − , the function of two independent
variables t and , is periodic in t with period T for each value of
( τ 2, τ 2)
Rxt+ t−
is polyperiodic in t for each . The
associated Fourier series for this function is
τ τ
R t t R e
( τ )
(2)
α i2παt x + , − =
x
2 2
{ α}
(3)
for which { Rx } α are the Fourier coefficients,
T 2
α 1
−i2παt
x ( τ) x(
, τ)
T −T
2
R = R t e dt (4)
and the sum over includes all integer multiples of the
reciprocal of the fundamental period T. is the cycle
frequency, which could be used to separate different signals.
B. CAF of OFDM signal
The CAF of baseband OFDM signal can be calculated as
follows [6]:
( πN∆fτ) ( π∆τ) α A sin
n Rx= e
T sin f
s
∞
πα ( ) τ
−i2n−f N −1
i2π∆f τ
2
( ) ( α )
⋅ e G f G − f df
−∞
Where G(f) is the Fourier transform of the rectangular pulse
shape g(t). A is the variance of the symbol sequence. Ts = Tu
+ Tg is the symbol duration, where Tu = 1/f is the useful
n
(5)
978-1-4244-2108-4/08/$25.00 © 2008 IEEE
symbol duration, Tg is the duration of the guard interval and
f is the subcarrier spacing. The typical CAF magnitude of
OFDM signal is shown in Fig. 2, in which is normalized to
1/Ts and is normalized to useful symbol duration. The signal
exhibits discrete cyclic autocorrelation surfaces for the cycle
1
frequencies n = n/Ts, which peak at τ =± =± T where
u
∆f
sin ( πN∆fτ) the factor
takes its maximum value. It is
sin ( π∆fτ) clear that is selected as the integer number of 1/Ts, and when
τ =± T , the CAF values exhibit peak properties. As the
u
value increases the peak decreases. If the value of Ts and Tu is
known in the detector, we are able to design the detection
process to catch the peaks exhibited in the CAF functions.
However, in blind detection and identification, the parameters
of received signal is unknown by the detector of cognitive
radio. It means the values of at which CAF exhibit peaks are
unable to obtain a priori.
Figure 1. CAF with step between equals integer number of 1/Ts
Figure 2. CAF with step between equals fraction number (1/20) of 1/Ts

In order to detect all possible OFDM signals, a step size of
that is smaller than subcarrier spacing should be selected to
calculate the CAF of received signal as shown in Fig. 3. Thus,
we can observe the changes in the CAF of OFDM signal in
details, as illustrated at u T τ =± , the pattern of which is better
for us to understand the characteristic of CAF of OFDM
signal. It is clear that the peak values decrease when takes
the integer number of 1/Tu. However, there are other smaller
peaks between them. Since the information of Tu is unknown,
the detector has to check the CAF with a step size that is
smaller than the subcarrier spacing.
Figure 3. CAF when =Tu with step size between equals fraction number
(1/20) of 1/Ts
III. BLIND DETECTION AND IDENTIFICATION OF OFDM
SIGNAL
OFDM has been selected for most of the future wireless
communication standards. For various operation environments
and applications, different values of parameters are selected to
implement the system with the purpose of achieving optimum
capacity. These parameters include number of subcarriers,
subcarrier spacing, the length of guard interval, etc. Even in
the same standard, there are several operation options in which
the parameters are setup differently to achieve various
transmission data rates. Thus, when detecting the incoming
signal, it is impossible to select the detection criteria based on
the known OFDM parameters as in [6]. Therefore, in order to
fit into the practical application, the parameters of OFDM
signal should be treated as unknown factors at the detector. In
this paper, we propose a blind detection and identification
method for cognitive radio, which consists of two steps: the
simple but reliable peak detection method that calculates the
subcarrier spacing in the first step and a peak searching
method employed to determine the length of guard interval in
the second step. We assume that the observation time is longer
than one OFDM symbol and the step size between each is
selected as the fractional value of subcarrier spacing such as
1/20, 1/10.
A. OFDM Signal Detection
The blind detection of OFDM signal could be considered
as a binary hypotheses test:
1
() = ()
() = () + ()
H 0 : r t w t signal absent
H : r t s t w t signal present
where r(t) is the received signal, s(t) and w(t) represent the
OFDM signal and noise respectively. As described previously,
the peaks in the CAF of OFDM signal are mainly due to the
cyclic prefix in OFDM symbol. This feature is employed as
the main criterion to separate OFDM signal from noise.
In the first step of the proposed scheme, we employ the
simple peak detection method that detects the symmetric peaks
when = 0, as demonstrated in Fig. 4. Based on the
characteristic of OFDM symbol with cyclic prefix, we
consider that the time period between the major peaks should
be equal to Tu, the effective symbol duration.
Figure 4. CAF when =0 as a function of
In order to catch these symmetric peaks, we formulate the
amplitude of CAF with equal to 0 as the test statistic, which
is expressed as follows:
Z = R
1
0
r
( τ )
2
( πN∆fτ) ( π∆τ) A sin
= ⋅ −
T sin f
s
( ) sin ( N∆f )
T sin ( π∆fτ) 978-1-4244-2108-4/08/$25.00 © 2008 IEEE
N −1
i2π∆f τ
2 e
∞
i2π fτ
e G( f ) G( −∞
f ) df
δ τ π τ
= A + N0
s
From the theoretical analysis, Z1 takes the largest peak
when = 0 and two other peaks when u T τ =± , which agrees
with our expectation. Since the subcarrier spacing is
determined, it could be used for signal identification.
2
2
(6)

B. OFDM Signal Identification
As explained before, different OFDM signals can be
classified by the parameters such as the length of guard
interval, subcarrier spacing and so on. In the first step of the
proposed scheme, subcarrier spacing has been calculated after
the OFDM signal is detected. Therefore, another parameter,
length of guard interval is the target of identification in second
step.
Since the duration of useful symbol has been determined in
the first step, we can observe the CAF for =Tu, as shown in
Fig. 1 and Fig. 3. By inserting the =Tu to (5), the test statistic
could be expressed as a function of n, as described in the
following:
2
( )
Z = R T
αn
x u
2
( π N∆fTu) ( π∆
)
N −1
∞
A sin
i2π∆f Tu
2
−i2π( αn−
f ) Tu
= e ⋅ e G( f ) G( α n − f ) df
T sin fT
s u
−∞
The only term determining Z2 is the integration term of
pulse signal. In order to observe the more detail pattern of
CAF, we employ the step size of each as the fractional value
of subcarrier spacing. The smaller step size of each is the
more detailed pattern we can observe. In our simulation, step
size identical to 1/20 of subcarrier spacing is utilized, while the
peaks of CAF are shown in Fig. 3. Therefore, our purpose is to
determine the distance of two maximum peaks in domain,
which is equal to the reciprocal of Ts. We proposed to employ
the cycle frequency searching scheme to determine the two
maximum peaks in the CAF pattern. After calculating the Ts,
we can easily obtain the length of guard interval as Ts-Tu.
IV. SIMULATIONS AND DISCUSSIONS
Simulations are carried out to evaluate the performance of
the proposed blind detection and identification method. OFDM
signal used in the simulations belongs to four modes with
different subcarrier spacing and guard interval. The subcarrier
spacing is expressed in terms of the number of subcarriers in
the same band, such as 1k and 2k. The length of guard interval
is select from 1/4 and 1/8 of useful symbol duration. The
detection and identification performances are evaluated among
these OFDM signals under AWGN.
A. Signal detection performance
Since the first step of signal detection determines the
success of the whole detection and identification process, the
reliability of detection is the main concern when designing the
detection criteria. Peak detection by checking the symmetric
peaks is a good method with low false alarm probability.
Detection performance using the peak detection is evaluated in
terms of the detection and false alarm probabilities under
different SNRs. The results are shown in Fig. 4. It is clear that
larger amount of subcarrier results in better detection
performance. Therefore, 2k subcarrier with 1/4 length of guard
interval achieves the best performance. However, the detection
time should be longer. For the target detection probability of
90%, even the OFDM with shortest symbol duration is able to
be detected below -1dB. This detection performance could be
improved by increasing the observation time, since its symbol
2
(7)
978-1-4244-2108-4/08/$25.00 © 2008 IEEE
duration is shorter than that of other cases. It is also notable
that the false alarm probabilities which are indicated by the
blue curve are almost zeros for all the OFDM signal detection.
It proves that the method by detecting the symmetric peaks is
reliable for the first step.
Figure 5. Simulation results of OFDM signal detection
B. Signal Identification Performance
If the OFDM signal is detected in the first step,
identification is carrier out to determine the symbol duration
using the method described in the previous section. The
performance is evaluated through the probability of successful
identification. Successful identification means the ratio of
guard interval to useful symbol belongs to a certain range of
possible ratio. An example is shown in Fig. 5 with 2 different
OFDM signals. Both of them have 2k subcarriers but different
length of guard interval. In order to guarantee the fairness of
detection with different guard interval, a threshold is select by
6/32 to separate OFDM signals with 1/4 guard interval from
that with 1/8. Meanwhile, a threshold is select by 3/32 to
separate OFDM signals with 1/8 guard interval from that with
1/16. Therefore, the degradation of identification of 1/8 is
mainly due to the shorter symbol duration as well as the
narrower threshold of identification compared to that of 1/4.
Furthermore, this performance could also be improved by
increasing the observation duration.
V. CONCLUSION
Although there are some existing detection methods
proposed for OFDM signal, they require the knowledge either
the number of subcarrier or the spacing between consecutive
subcarriers as a priori. In this paper, we focus on the signal
detection and identification scheme for OFDM system with
unknown parameters. The key parameters to discriminate
different OFDM signals are the subcarrier spacing and length
of guard interval In order to classify different OFDM signals,
a time domain cyclostationarity based approach is proposed
which consists of two steps: first, detect the OFDM signal
from random noise simply by recognizing the symmetric
peaks in the autocorrelations and calculate the subcarrier
spacing; second, by searching the cycle frequencies, the

length of guard interval is calculated to recognize different
OFDM signals. Simulations are carried out in AWGN and
verified our method can satisfy the detection and
identification requirement with a low false alarm probability.
Figure 6. Simulation results of OFDM signal identification with 2k number
of subcarrier
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[2] D.Cabric, S.Mishra, and R.W. Brodersen, “Implementation issues in
spectrum sensing for cognitive radios”, in Proc. Asilomar Conf. On
Signals, Systems and Computers, vol. 1, Nov. 2004, pp.772-776.
[3] Simon Haykin, “Cognitive radio: brain-empowered wireless
communications”, IEEE J.Commun.Mag., vol.23, no.2, Feb 2005.
[4] Richard D.J. van Nee, OFDM for Wireless Multimedia
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[5] S.H. Sohn, N. Han, G.Zheng, J.M. Kim, "Pilot Periodicity Based
OFDM Signal Detection Method for Cognitive Radio System", to
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[6] L.P. Goh, Z. Lei, F. Chin, "DVB Detector for Cognitive Radio" in Proc.
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[7] W.A. Gardner, Cyclostationarity in Communications and Signal
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978-1-4244-2108-4/08/$25.00 © 2008 IEEE