Signal Detection Method based on Cyclostationarity for Cognitive Radio

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1 THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. Signal Detection Method based on Cyclostationarity for Cognitive Radio Abstract Kimtho PO and Jun-ichi TAKADA Graduate School of Engineering, Tokyo Institute of Technology O-okayama, Meguro-ku, Tokyo, Japan 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 82.22, Signal Detection, spectral correlation, cyclostationarity 1. Background The IEEE Wireless Regional Area Network (WRAN) has been proposed to increase the efficiency of spectrum utilization in radio spectrum currently allocated to the TV broadcast services. It is the first worldwide wireless standard based on cognitive radio (CR) technique and it aims at providing the wireless broadband access to rural and remote area, with the performance comparable to those of existing fixed broadband access technologies such as DSL and cable modem [1] [2] [3]. One of the key challenges of the IEEE WRAN requirement is to detect the presence or absence of the TV signals at very low signal-to-noise ratio (SNR). To achieve this context, the IEEE Working Group (WG) has considered several methods for signal detection such as simple received signal strength indication (RSSI) measurements and signal feature detection [2]. The energy detection method performs the signal measurements and determine the unoccupied channel candidates by comparing the power estimated to the predefined threshold levels. However, this method is prone to false detections since it only measures the signal power. When the signal is heavily fluctuated, it becomes difficult to discriminate between the absence and the presence of the signal [4]. On the other hand, the feature detection is basically performed based on cyclostationarity. The ISDB-T signal which employs OFDM technique exhibits the underlying periodicity in their structure, thus ISDB-T signal can be modelled as a cyclostationary signal. Despite the signal feature detection has been considered by the IEEE WG, the analysis is yet to be done clearly. In this paper, the signal feature detection based on spectral correlation of cyclostationarity is studied. We also investigate the detection performance under additive white Gaussian noise (AWGN) channel. Compared with the energy detector, the signal feature detection has better performance in low SNR environment. The rest of this paper is organized as follows. In Section 2, the overview of cyclostationarity is described while Section 3 presents the ISDB-T signal characteristic. Section 4 shows the cyclic autocorrelation and cyclic spectrum density function of ISDB-T signal. The statistical test for detection and the detection method are presented in Section 5 and section 6, respectively. Finally, Section 7 concludes this paper. 2. Cyclostationarity Analysis It is known that most of the communication signals can be modelled as cyclostationary processes that exhibit underlying periodicities in their signal structures [5]. A zero-mean continuous signal x(t) is called second order (wide sense) cyclostationary if its time varying autocorrelation function R xx(t, τ) defined as R xx(t, τ) = E{x(t)x (t + τ)} (1) is periodic in time t for each lag parameter τ and it can be represented as a Fourier series 1

2 R xx(t, τ) = Rxx(τ)e α j2παt, (2) α where the sum is taken over integer multiples of fundamental cyclic frequency α for which cyclic autocorrelation function (CAF) is defined as T /2 Rxx(τ) α 1 = lim R xx (t, τ)e j2παt dt. (3) T T T /2 The Fourier transform of R α xx(t, τ) is called the cyclic spectrum (CS) which is defined as S α xx(f) = Rxx(τ)e α j2πfτ dτ. (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) N 1 Rxx(l) α 1 = lim x[m]x [m + l]e j2παm m, (5) N N m= where N is the number of samples of signal x[m] and m is the sampling interval. By applying the discrete Fourier transform to R α xx(l), the cyclic spectrum is given as S α xx(f) = l= R α xx(l)e j2πfl l. (6) For a signal which does not exhibit cyclostationarity, CAF or CS is below the threshold level for all α =. Anyway, if α = CAF and CS reduce to the conventional autocorrelation function and power spectral density function, respectively. The cyclic frequencies α are typically related to the symbol rate and the carrier frequency of the signal [5]. 3. ISDB-T Signal Characteristics Before employing the feature detection mechanism to identify 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)e j2πfct } (7) where f c is the center frequency and c(t) is the complex baseband OFDM signal which is given as c(t) = + n= k= K 1 d(n, k)g(t nt s) e j2π(k (K 1)/2) f(t nt s), (8) where d(n, k) is a complex symbol sequence corresponding to symbol number n and carrier number k. K is the total number of carriers, T s is the total symbol duration, f is the carrier spacing and g(t) is the unit rectangular pulse with duration T s centered at. In practice, the OFDM signal in (8) can be efficiently implemented by using IFFT. In this study, only one OFDM segment of ISDB-T mode 1 is used in order to reduce the complexity of the simulation. Table 1 shows the parameters of ISDB-T and Table 2 shows the simulation parameters used in this simulation. Magnitude (db) The spectrum of ISDB-T signal is shown in Figure ISDB T spectrum Frequency (MHz) Figure 1 Spectrum of ISDB-T signal Figure 1 shows that the ISDB-T signal occupies khz bandwidth. So, for the energy detector, the signal is absent or present can be done by measuring the power in this bandwidth and then compare with the power threshold. If the power is lower than the threshold, the signal is absent otherwise the signal is present. 4. CAF and CS of ISDB-T Signal 4. 1 Cyclic Frequencies Analysis In this section, the cyclic frequencies of OFDM signal Parameter QPSK Table 1 T u = 252 µs T /mathrmg = T u /4 T s = T u + T /mathrmg ISDB-T parameters Description QPSK modulation OFDM useful symbol duration OFDM guard interval OFDM total symbol duration f = khz Carrier separation (= 1/T u) K = 18 N o = 5 Table 2 Parameter f c = 1.16 MHz N F F T = 248 Number of sub-carriers Number of OFDM symbols Simulation parameters Description Center frequency Number of FFT samples f s = 4.64 MHz Sampling frequency (= 4f c) T = 8.192ms t = 64µs Length of observation data Window size 2

accumulation method (FAM) [6]. The implementation model of FAM is illustrated in Figure 3. It works as follows: R xx(t, τ) = σ 2 dre{ + n= k= K 1 g(t nt s)g(t nt s + τ) e j2πfcτ e j2π(k (K 1)/2) fτ }.

3 is computed as follows. Assuming that the symbol sequences d(n, k) are centered and i.i.d with the variance σ 2 d = E{d(n, k)d (n, k)}. Therefore, by using (1), (7) and (8), the time varying autocorrelation of OFDM signal can be simplified to On the other hand, we also simulate the cyclic spectrum of ISDB-T signal by using FFT accumulation method (FAM) [6]. The implementation model of FAM is illustrated in Figure 3. It works as follows: R xx(t, τ) = σ 2 dre{ + n= k= K 1 g(t nt s)g(t nt s + τ) e j2πfcτ e j2π(k (K 1)/2) fτ }. (9) Let assume that K 1 A(τ) = e j2π(k (K 1)/2) fτ, k= = sin(π fkτ) sin(π fτ) e jπ f(k+1)/2τ. (1) Therefore, the time varying autocorrelation in (9) can be written as R xx (t, τ) = A(τ)σdRe{e 2 j2πf cτ g(t nt s)g(t nt s + τ)}. (11) n= It is seen that R xx(t, τ) is periodic in time t with the period equal to T s, thus OFDM signal exhibits second order cyclostationarity with the cyclic frequencies α = ± m T s (12) where m is an integer Simulation of CAF and CS A fast implementation of cyclic autocorrelation function 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. Figure 3 FFT accumulation method (FAM) The complex envelopes X T (k) are estimated efficiently by means of a sliding N -point FFT, followed by a downshift in frequency to baseband signal. In order to allow for an even more efficient estimation, the N -point FFT is applied to the data in blocks of L samples. 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 is determined according to the length of observation data T and sampling frequency f s which is given by N = f s T. (13) The value of L is chosen to compromise between maintaining computational efficiency and minimizing cycle leakage and cycle aliasing, and is given by L = N 4. (14) The number of sampling points of second FFT P is determined according to the window size t, and in this simulation it is chosen as Figure 2 CAF of ISDB-T signal P = f s t. (15) L Based on FAM, the cyclic spectrum of ISDB-T signal is simulated. In this simulation, the length of observation data T = ms and the window size t = 64 µs. Notably, for a reliable estimation of cyclic spectrum it is necessary to have T 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/t s as given in (12). Figures 5 and 6 show the cyclic spectrum of ISDB-T signal in AWGN channel for the SNR = db and SNR = 5 db, respectively. As seen in these Figures, the signal feature detection based on spectral correlation has better performance in low SNR environment. 3

4 Figure 4 CS of ISDB-T signal 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 the cyclic autocorrelation function ˆR α xx(l) is given by ˆR α xx(l) = 1 N 1 x[m]x [m + l]e j2παm m N m= = R α xx(l) + ɛ α xx(l), (16) where ɛ(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 row vector consisting of cyclic autocorrelation function estimation ˆr α xx(l) = [Re{ ˆR α xx(l)}, Im{ ˆR α xx(l)}], (17) Similar to (17), the row vector of the true (asymptotic) value of the cyclic autocorrelation function r α xx(l) is defined by r α xx(l) = [Re{R α xx(l)}, Im{R α xx(l)}]. (18) Then using (16), we can write ˆr α xx(l) = r α xx(l) + ɛ α xx(l), (19) where ɛ α xx(l) = [Re{ɛ α xx(l)}, Im{ɛ α xx(l)}] is the estimation error. It can be shown that lim Nɛ α xx (l) = D N (, Σ α xx(l)), (2) N Figure 5 CS of ISDB-T signal with SNR = db where D = denotes the conversion in distribution [7] and N (, Σ α xx(l)) is a multivariate normal distribution with mean and asymptotic covariance matrix Σ α xx(l). The covariance matrix can be expressed as [ Re{ D xx (l)+c xx (l) Σ α } Im{ D xx(l) C xx (l) ] } 2 2 xx(l) = Im{ D xx(l)+c xx (l) } Re{ C xx(l) D xx (l),(21) } 2 2 where C xx(l) and D xx(l) are given as Figure 6 CS of ISDB-T signal with snr = 5 db 5. Statistical Test for Detection 5. 1 Statistical Test Overview This paper also shows the statistical test for the presence C α xx(l n, l m) = 1 NL D α xx(l n, l m ) = 1 NL (L 1)/2 s= (L 1)/2 W (s)f N,ln (α 2πs N ) F N,lm (α + 2πs N ) (22) (L 1)/2 s= (L 1)/2 W (s)f N,l n (α + 2πs N ) F N,lm (α + 2πs N ) (23) where W (s) is a spectral window of length L (odd), l n and l m are the fixed set of lags. F N,l (ω) is defined as N 1 F N,l (ω) = x[m]x[m + l]e jωm t (24) m= 4

5 Given that hypothesis H represents the case where the primary signal is not present, and the hypothesis H 1 represents the case where the primary signal is present, the following binary hypothesis testing problem can be formulated as follows H : ˆr α xx(l) = ɛ α xx(l), signal is absent (25) H 1 : ˆr α xx(l) = r α xx(l) + ɛ α xx(l), signal is present (26) Since r α xx(l) is not random, the distribution of ˆr α xx(l) under both hypothesis differs only in mean. The asymptotic complex normality of the cyclic autocorrelation estimate allows the formulation of the following generalized likelihood function as the test statistic for the binary hypothesis test. T α (l) = N ˆr xx(l)ˆσ α α 1 xx (l)ˆr xx αt (l) (27) where ˆΣ α xx(l) is the estimated covariance matrix. In [7] it has been shown that under hypothesis H, regardless of the distribution of the input data, the distribution of T α (l) converges asymptotically to a central X 2 distribution with degrees 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 constant false alarm rate test. One can write, under H : lim T α (l) = D X2 2 (28) N Under H 1, the distribution of the test statistics T α (l) converges to a normal distribution lim N T α (l) = D N (N ˆr xx(l)ˆσ α α 1 xx (l)ˆr xx αt (l), 4N ˆr xx(l)ˆσ α α 1 xx (l)ˆr xx αt (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 Kaiser window with L = 11 points and β = 1 while the lag l is set to. The cyclic frequency α is varied from to 2f c and the FFT length is 124 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%. 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/T s. They are {,.39,.78,... } khz. However, Cyclic frequencies (MHz) Figure 7 Statistical Test Cyclic frequencies (MHz) Figure 8 Zoom of Statistical Test some cyclic frequencies cannot be detected since they are below the threshold level (red line) as indicated in this Figure. 6. Detection Method The conventional energy detection corresponds to testing the energy levels obtained from S α xx(f) at α = 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. Figure 9 Detection decision flow 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/t s. 5

6 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 , Dec. 23. [2] IEEE Working Group on Wireless Regional Area Network, [3] C. Cordeiro, K. Challapali, D. Birru, Sai Shankar, IEEE 82.22: the first worldwide wireless standard based on cognitive radio 25 First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DyS- PAN 25), pp , Nov. 25. [4] K. Po and J. Takada, Signal detection for analog and digital TV signals for cognitive radio, IEICE Technical Report, SR26-54, November 26. [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 , No.2, vol. 41, Feb [7] V. Dandawate, B. Giannakis, Statistical Tests for Presence of Cyclostationarity IEEE Transactions on Signal Processing, pp , No.9, vol. 42, Sept

CycloStationary Detection for Cognitive Radio with Multiple Receivers

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