Abstract A signal detection method is being indispensible in the cognitive radio
system for the ... modelled as cyclostationary processes that exhibit underly-.
社団法人 電子情報通信学会 THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS
信学技報 TECHNICAL REPORT OF IEICE.
Signal Detection Method based on Cyclostationarity for Cognitive Radio Kimtho PO† and Jun-ichi TAKADA† † Graduate School of Engineering, Tokyo Institute of Technology 2-12-1 O-okayama, Meguro-ku, Tokyo, 152-8550 Japan E-mail: †{kimtho,takada}@ap.ide.titech.ac.jp Abstract A signal detection method is being indispensible in the cognitive radio system for the coexistence with the primary users such as ISDB-T system. This paper presents the detection method based on spectral correlation by using cyclostationarity properties of ISDB-T signal. The detection of the presence and absence of ISDB-T signal is performed based on scanning the cyclic frequencies of its cyclic spectrum or its cyclic autocorrelation function. The decision is made very simple i.e. at a given cyclic frequency if the cyclic spectrum or its cyclic autocorrelation function is below the threshold level, the signal is absent otherwise signal is present. The detection performance is investigated under white Gaussian noise channel. Key words Cognitive Radio, IEEE 802.22, Signal Detection, spectral correlation, cyclostationarity
1. Background The IEEE 802.22 Wireless Regional Area Network
a cyclostationary signal. Despite the signal feature detection has been considered by the IEEE 802.22 WG, the analysis is yet to be done clearly.
(WRAN) has been proposed to increase the efficiency of spec-
In this paper, the signal feature detection based on spectral
trum utilization in radio spectrum currently allocated to the
correlation of cyclostationarity is studied. We also investi-
TV broadcast services. It is the first worldwide wireless stan-
gate the detection performance under additive white Gaus-
dard based on cognitive radio (CR) technique and it aims at
sian noise (AWGN) channel. Compared with the energy de-
providing the wireless broadband access to rural and remote
tector, the signal feature detection has better performance
area, with the performance comparable to those of existing
in low SNR environment.
fixed broadband access technologies such as DSL and cable modem [1] [2] [3].
The rest of this paper is organized as follows. In Section 2, the overview of cyclostationarity is described while Section
One of the key challenges of the IEEE 802.22 WRAN re-
3 presents the ISDB-T signal characteristic. Section 4 shows
quirement is to detect the presence or absence of the TV
the cyclic autocorrelation and cyclic spectrum density func-
signals at very low signal-to-noise ratio (SNR). To achieve
tion of ISDB-T signal. The statistical test for detection and
this context, the IEEE 802.22 Working Group (WG) has
the detection method are presented in Section 5 and section
considered several methods for signal detection such as sim-
6, respectively. Finally, Section 7 concludes this paper.
ple received signal strength indication (RSSI) measurements and signal feature detection [2].
2. Cyclostationarity Analysis
The energy detection method performs the signal measure-
It is known that most of the communication signals can be
ments and determine the unoccupied channel candidates by
modelled as cyclostationary processes that exhibit underly-
comparing the power estimated to the predefined threshold
ing periodicities in their signal structures [5]. A zero-mean
levels. However, this method is prone to false detections since
continuous signal x(t) is called second order (wide sense)
it only measures the signal power. When the signal is heavily
cyclostationary if its time varying autocorrelation function
fluctuated, it becomes difficult to discriminate between the
Rxx (t, τ ) defined as
absence and the presence of the signal [4]. On the other hand, the feature detection is basically per-
Rxx (t, τ ) = E{x(t)x? (t + τ )}
(1)
formed based on cyclostationarity. The ISDB-T signal which
is periodic in time t for each lag parameter τ and it can be
employs OFDM technique exhibits the underlying periodic-
represented as a Fourier series
ity in their structure, thus ISDB-T signal can be modelled as —1—
Rxx (t, τ ) =
∑
α Rxx (τ )ej2παt ,
(2)
In practice, the OFDM signal in (8) can be efficiently implemented by using IFFT. In this study, only one OFDM
α
where the sum is taken over integer multiples of fundamental
segment of ISDB-T mode 1 is used in order to reduce the
cyclic frequency α for which cyclic autocorrelation function
complexity of the simulation. Table 1 shows the parameters
(CAF) is defined as
of ISDB-T and Table 2 shows the simulation parameters used
α Rxx (τ )
1 = lim T →∞ T
∫
in this simulation.
T /2
−j2παt
Rxx (t, τ )e
dt.
(3)
The spectrum of ISDB-T signal is shown in Figure 1.
−T /2
ISDB−T spectrum
α The Fourier transform of Rxx (t, τ ) is called the cyclic spec-
trum (CS) which is defined as ∞
α Sxx (f ) =
α Rxx (τ )e−j2πf τ dτ .
0 (4)
−∞
A discrete cyclic autocorrelation function of discrete time signal x(n) with a fixed lag l is defined in the similar manner as (3) α (l) = lim Rxx
N →∞
N −1 1 ∑ x[m]x? [m + l]e−j2παm∆m , N
Magnitude (dB)
∫
−5
−10
(5)
m=0
where N is the number of samples of signal x[m] and ∆m is the sampling interval. By applying the discrete Fourier
−15 0.7
0.8
α transform to Rxx (l), the cyclic spectrum is given as
α Sxx (f ) =
∞ ∑
0.9 1 1.1 Frequency (MHz)
1.2
1.3
Figure 1 Spectrum of ISDB-T signal α Rxx (l)e−j2πf l∆l .
(6) Figure 1 shows that the ISDB-T signal occupies 428.57 kHz
l=−∞
For a signal which does not exhibit cyclostationarity, CAF
bandwidth. So, for the energy detector, the signal is absent
or CS is below the threshold level for all α = | 0. Anyway,
or present can be done by measuring the power in this band-
if α = 0 CAF and CS reduce to the conventional autocorre-
width and then compare with the power threshold. If the
lation function and power spectral density function, respec-
power is lower than the threshold, the signal is absent oth-
tively. The cyclic frequencies α are typically related to the
erwise the signal is present.
symbol rate and the carrier frequency of the signal [5].
4. CAF and CS of ISDB-T Signal
3. ISDB-T Signal Characteristics
4. 1 Cyclic Frequencies Analysis
Before employing the feature detection mechanism to iden-
In this section, the cyclic frequencies of OFDM signal
tify the ISDB-T signal, it is important to show the characteristic of this signal. The signal format of ISDB-T in the RF band is given as follows x(t) = Re{c(t)ej2πfc t }
Table 1 ISDB-T parameters Parameter QPSK
(7)
Tu = 252 µs T/mathrmg = Tu /4
where fc is the center frequency and c(t) is the complex baseband OFDM signal which is given as c(t) =
+∞ K−1 ∑ ∑
Ts = Tu + T/mathrmg ∆f = 3.968 kHz K = 108
d(n, k)g(t − nTs )
No = 5
Description QPSK modulation OFDM useful symbol duration OFDM guard interval OFDM total symbol duration Carrier separation (= 1/Tu ) Number of sub-carriers Number of OFDM symbols
n=−∞ k=0
· ej2π(k−(K−1)/2)∆f (t−nTs ) ,
(8)
Table 2 Simulation parameters Parameter
where d(n, k) is a complex symbol sequence corresponding to
fc = 1.016 MHz
symbol number n and carrier number k. K is the total num-
NF F T = 2048
ber of carriers, Ts is the total symbol duration, ∆f is the carrier spacing and g(t) is the unit rectangular pulse with
Description Center frequency Number of FFT samples
fs = 4.064 MHz Sampling frequency (= 4fc ) T = 8.192ms ∆t = 64µs
Length of observation data Window size
duration Ts centered at 0. —2—
is computed as follows.
Assuming that the symbol se-
On the other hand, we also simulate the cyclic spec-
quences d(n, k) are centered and i.i.d with the variance
trum of ISDB-T signal by using FFT accumulation method
σd2 = E{d(n, k)d? (n, k)}. Therefore, by using (1), (7) and
(FAM) [6]. The implementation model of FAM is illustrated
(8), the time varying autocorrelation of OFDM signal can
in Figure 3. It works as follows:
be simplified to Rxx (t, τ ) = σd2 Re{
+∞ K−1 ∑ ∑
g(t − nTs )g(t − nTs + τ )
n=−∞ k=0
· e−j2πfc τ e−j2π(k−(K−1)/2)∆f τ }.
(9)
Let assume that
∑
K−1
A(τ ) =
e−j2π(k−(K−1)/2)∆f τ ,
Figure 3 FFT accumulation method (FAM)
k=0
sin(π∆f Kτ ) −jπ∆f (K+1)/2τ = e . sin(π∆f τ )
(10)
Therefore, the time varying autocorrelation in (9) can be written as
•
The complex envelopes XT (k) are estimated efficiently
by means of a sliding N 0 -point FFT, followed by a downshift in frequency to baseband signal. •
In order to allow for an even more efficient estima-
tion, the N 0 -point FFT is applied to the data in blocks of L samples.
Rxx (t, τ ) = A(τ )σd2 Re{e−j2πfc τ
∑
•
∞
·
g(t − nTs )g(t − nTs + τ )}.
(11)
n=0
The product sequence between complex envelopes and
its conjugate are formed, then the cyclic spectrum is accomplished by means of a P -point FFT. The value of N 0 is determined according to the length of
It is seen that Rxx (t, τ ) is periodic in time t with the pe-
observation data T and sampling frequency fs which is given
riod equal to Ts , thus OFDM signal exhibits second order
by
cyclostationarity with the cyclic frequencies m α=± Ts
N 0 = fs T. (12)
where m is an integer.
(13)
The value of L is chosen to compromise between maintaining computational efficiency and minimizing cycle leakage
4. 2 Simulation of CAF and CS
and cycle aliasing, and is given by
A fast implementation of cyclic autocorrelation function
N0 . (14) 4 The number of sampling points of second FFT P is deter-
in (5) is computed via FFT algorithm. With τ varying from −2 µs to 2 µs and FFT length of 8192 points, the CAF of ISDB-T signals is shown in Figure 2.
L=
mined according to the window size ∆t, and in this simulation it is chosen as fs ∆t. (15) L Based on FAM, the cyclic spectrum of ISDB-T signal is
P =
simulated. In this simulation, the length of observation data T = 8.192 ms and the window size ∆t = 64 µs. Notably, for a reliable estimation of cyclic spectrum it is necessary to have T À ∆t. The cyclic spectrum of ISDB-T is shown in Figure 4. Figures 2 and 4 show that the CAF and CS of ISDB-T signal exhibits cyclic autocorrelation at cyclic frequencies α = ±m/Ts as given in (12). Figures 5 and 6 show the cyclic spectrum of ISDB-T signal in AWGN channel for the SNR = 0 dB and SNR = −5 dB, respectively. As seen in these Figures, the signal feature deFigure 2 CAF of ISDB-T signal
tection based on spectral correlation has better performance in low SNR environment. —3—
of the ISDB-T signal. The statistical test of the cyclostationarity which has been developed in [7] is adopted here. In [7], the test checks for a given cyclic frequency α the presence of cyclostationarity from a data sequence of length N , using a consistent and asymptotically normal estimator for the cyclic autocorrelation function. The consistent estimation of α ˆ xx the cyclic autocorrelation function R (l) is given by N −1 1 ∑ α ˆ xx x[m]x? [m + l]e−j2παm∆m R (l) = N m=0
α = Rxx (l) + ²α xx (l),
(16)
where ²(l) is the estimation error. Considering the widesense cyclostationarity, where the presence of cyclic frequency has to be checked for a given lag l, we define the Figure 4 CS of ISDB-T signal
row vector consisting of cyclic autocorrelation function estimation α α α ˆ xx ˆ xx (l)}], (l)}, Im{R rˆxx (l) = [Re{R
(17)
Similar to (17), the row vector of the true (asymptotic) value α (l) is defined by of the cyclic autocorrelation function rxx α α α rxx (l) = [Re{Rxx (l)}, Im{Rxx (l)}].
(18)
Then using (16), we can write α α rˆxx (l) = rxx (l) + ²α xx (l),
(19)
α α where ²α xx (l) = [Re{²xx (l)}, Im{²xx (l)}] is the estimation
error. It can be shown that √ D α lim N ²α xx (l) = N (0, Σxx (l)),
(20)
N →∞
Figure 5 CS of ISDB-T signal with SNR = 0 dB
D
where = denotes the conversion in distribution [7] and N (0, Σα xx (l)) is a multivariate normal distribution with mean 0 and asymptotic covariance matrix Σα xx (l). The covariance matrix can be expressed as
[
Σα xx (l) =
xx (l) Re{ Dxx (l)+C } 2
xx (l) Im{ Dxx (l)−C } 2
xx (l) Im{ Dxx (l)+C } 2
xx (l) Re{ Cxx (l)−D } 2
] ,(21)
where Cxx (l) and Dxx (l) are given as α Cxx (ln , lm ) =
1 NL
∑
(L−1)/2
s=−(L−1)/2
· FN,lm (α + α Dxx (ln , lm ) =
1 NL
2πs ) N
2πs ) N
∑
(L−1)/2 ? W (s)FN,l (α + n
s=−(L−1)/2
· FN,lm (α +
Figure 6 CS of ISDB-T signal with snr = −5 dB
W (s)FN,ln (α −
2πs ) N
(22) 2πs ) N (23)
where W (s) is a spectral window of length L (odd), ln and
5. Statistical Test for Detection 5. 1 Statistical Test Overview This paper also shows the statistical test for the presence
lm are the fixed set of lags. FN,l (ω) is defined as
∑
N −1
FN,l (ω) =
x[m]x[m + l]e−jωm∆t
(24)
m=0
—4—
Given that hypothesis H0 represents the case where the 150
primary signal is not present, and the hypothesis H1 represents the case where the primary signal is present, the following binary hypothesis testing problem can be formulated 100
as follows α H0 : rˆxx (l) = ²α xx (l),
signal is absent
(25) 50
α α H1 : rˆxx (l) = rxx (l) + ²α xx (l),
signal is present
(26)
α α Since rxx (l) is not random, the distribution of rˆxx (l) un0 −2
der both hypothesis differs only in mean. The asymptotic
−1.5
−1
−0.5 0 0.5 Cyclic frequencies (MHz)
1
1.5
2
complex normality of the cyclic autocorrelation estimate alFigure 7 Statistical Test
lows the formulation of the following generalized likelihood function as the test statistic for the binary hypothesis test. −1
150
T
α α ˆα (l)Σ rxx (l) T α (l) = N rˆxx xx (l)ˆ
(27)
ˆα where Σ xx (l) is the estimated covariance matrix. In [7] it 100
has been shown that under hypothesis H0 , regardless of the distribution of the input data, the distribution of T (l) conα
verges asymptotically to a central X 2 distribution with de50
grees 2. This makes it possible to analytically calculate the probability of false alarm for large enough observation length N for a given threshold, leading to an asymptotically con-
0 −0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.02 Cyclic frequencies (MHz)
stant false alarm rate test. One can write, under H0 : D
lim T α (l) = X22
(28)
N →∞
0.03
0.04
0.05
Figure 8 Zoom of Statistical Test
Under H1 , the distribution of the test statistics T (l) conα
some cyclic frequencies cannot be detected since they are
verges to a normal distribution −1
below the threshold level (red line) as indicated in this Fig-
T
D α α ˆα lim T α (l) = N (N rˆxx (l)Σ rxx (l), xx (l)ˆ
ure.
N →∞
−1 α αT ˆα 4N rˆxx (l)Σ rxx xx (l)ˆ
(l))
(29)
5. 2 Statistical Test Simulations This section provides the simulation results for the performance of the statistical test of (27) for the detection of the presence or absence of the ISDB-T signal. In order to compute (27), firstly, the row vector in (17) is computed by using (16). Secondly, the covariance matrix in (21) is computed. Finally, (27) can be computed by using (23) and (23). In this simulation, (23) and (23) are computed by using a
6. Detection Method The conventional energy detection corresponds to testing α the energy levels obtained from Sxx (f ) at α = 0 for the
presence and absence of signal, whereas the signal feature detection based on spectral correlation of cyclostationarity is based on scanning of a peak cyclic spectrum magnitude of the signals at one of their cyclic frequencies. If the peak cyclic spectrum magnitude is found the signal is present, otherwise the signal is absent. The decision flow is shown in Figure 9.
Kaiser window with L = 101 points and β = 10 while the lag l is set to 0. The cyclic frequency α is varied from 0 to 2fc and the FFT length is 1024 points. In this simulation, the probability of false alarm is set to 1%, then the threshold can be computed by using (28). Figure 7 plots the statistical test for the presence of ISDB-T signal vs. the cyclic frequencies for the probability of false alarm 1%.
Figure 9 Detection decision flow
We zoom Figure 7 in order to see the cyclic frequencies that present in this statistical test. Figure 8 shows this result. Figure 8 clearly shows that the cyclic frequencies are multiple of 1/Ts . They are {0, 0.39, 0.78,. . . } kHz. However,
For example, the detection of the presence of the ISDB-T signal reduces to the detection of the presence of its cyclic spectrum at cyclic frequencies α = ±m/Ts . —5—
7. Conclusion Signal detection mechanism is the most important in the cognitive radio system. In this paper, the signal feature detection based on cyclostationarity has been studied for the detection of the presence or absence of ISDB-T signal. This detector has better performance in the low signal to noise ratio environment. This paper also evaluates the statistical test for the presence of ISDB-T signal. In this test the cyclic frequencies can be detected if they are greater than the threshold level. The use of FFT for the efficient computation of CAF and CS is not appropriate due to the the necessity of the large size of the samples for OFDM signal, therefore the DFT will be considered in the future work. References [1] “Notice of Proposed Rule Making and Order — In the Matter of Facilitating Opportunities for Flexible, Efficient, and Reliable Spectrum Use Employing Cognitive Radio Technologies Authorization and Use of Software Defined Radios,” FCC ET Docket, No. 03-322, Dec. 2003. [2] “IEEE 802.22 Working Group on Wireless Regional Area Network,” http://www.ieee802.org/22/. [3] C. Cordeiro, K. Challapali, D. Birru, Sai Shankar, “IEEE 802.22: the first worldwide wireless standard based on cognitive radio” 2005 First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN 2005), pp. 328–337, Nov. 2005. [4] K. Po and J. Takada, “Signal detection for analog and digital TV signals for cognitive radio,” IEICE Technical Report, SR2006-54, November 2006. [5] A. Gardner, Cyclostationarity in Communications and Signal Processing, IEEE Press, 1994 [6] A. William, H. Herschel, “Digital implementations of spectral correlation analyzers” IEEE Transactions on Signal Processing, pp. 703–719, No.2, vol. 41, Feb. 1993. [7] V. Dandawate, B. Giannakis, “Statistical Tests for Presence of Cyclostationarity” IEEE Transactions on Signal Processing, pp. 2355–2369, No.9, vol. 42, Sept. 1994.
—6—
