A Low-Complex Cyclostationary Signal Detector for

A Low-Complex Cyclostationary Signal Detector for Cognitive Radio Communications Shahriar Shirvani Moghaddam Faculty of Electrical Engineering Shahid Rajaee Teacher Training University Tehran, Iran, 1678815811 Email: [email protected]

Ehsan Abedi Digital Communications Signal Processing Research Lab. Shahid Rajaee Teacher Training University Tehran, Iran, 1678815811 Email: [email protected]

Keywords- Cyclostationary detection; cognitive radio; orthogonal frequency-division multiplex (OFDM); complexity; field programmable gate array (FPGA).

Cyclostationarity feature is more usual in different types of communication signals [8], which makes these algorithms applicable in many scenarios. Recently, the focus has been on detecting orthogonal frequency-division multiplex (OFDM) signals because OFDM is already a widely used modulation scheme and is expected to be employed in many future communication systems as well. Some implementations of cyclostationary feature detection algorithms can be found in [9]. A common approach to detect cyclostationary features has been the estimation of the cyclic autocorrelation function (CAF) of the received signal [7]. In the previous work, the application of the spatial sign function (SSF) to the received signal prior to the estimation of the CAF has been proposed in [10]. Recently, an angular domain implementation of the spatial sign cyclic correlation estimator has been presented [11]. The benefits of the angular domain processing are further reductions in implementation complexity, particularly in the size of the memory that is needed to implement the autocorrelation, which is usually a significant factor in both the implementation area and power consumption.

I. INTRODUCTION Cognitive radio (CR) is able to detect unoccupied licensed frequency bands to solve the problem of spectrum shortage and extra demand for spectrum [1]. Spectrum sensing (SS) is the key element of cognitive radio communications. SS methods mainly include energy detection (ED) [2], matched filtering [3], eigenvalue based detection [4] and cyclostationary detection [5].

In this paper, analysis of various detection algorithms based on energy detector and cyclostationary features are presented. The aim is to find appropriate algorithm for spectrum sensing both performance and computational complexity point of views. These algorithms are analyzed in an additive white Gaussian noise (AWGN) scenario considering an OFDM signal. The symbol structure of OFDM signals are examined for IEEE802.11a standard for WLAN and digital video broadcasting-terrestrial (DVB-T) system.

Abstract—The key enablers of opportunistic spectrum access in cognitive radio is finding white spaces which requires high sensitive along with low-complex detector. In this paper, different algorithms based on cyclostationary feature of orthogonal frequency division multiplex signal in both IEEE802.11 (wireless local area network) and terrestrial digital video broadcasting (DVB-T) standards are analyzed numerically in MATLAB software and synthesized on FPGA in order to suggest the best detector in terms of receiver operating characteristic (ROC) curve and computational complexity as well as power dissipation in a joint state. Simulations results in both MATLAB (for performance evaluations in the view of ROC curve and complexity analysis) and Xilinx ISE13.2 (for dissipated power analysis) show that the angular domain cyclostationary detector is the low-complex lowpower algorithm compared to energy detection (ED) as well as original and sign versions of cyclostationary algorithms which is not sensitive to noise uncertainty.

Energy detector is susceptive to noise uncertainty and its performance is poor at low signal to noise ratio (SNR) regimes. In addition, there is no difference between main and interference (undesired) signals in this method [6]. Matched filtering requires prior information, which renders it impractical for many CR scenarios. Eigenvalue based detection methods solve the first and second problems of ED but the third one is remained. In order to have a method which solves all of the above-mentioned problems, many researchers focused their attentions on cyclostationary feature detection due to its high accuracy in low SNRs, no need to priori information about primary signal, and also the ability to separate main and undesired signals. Cyclostationary signal detectors use periodicities in the second-order statistics for signal detection. Statistical tests for the presence of cyclostationarity were first presented in [7].

In general, specifications of detector performance is characterized by two metrics, probability of detection ( ) and probability false alarm ( ). Both of them are important, since low probability of detection increases the interference imposed on the primary users, whiles high false alarm rate increases the missed spectral opportunities in the secondary user. This paper is organized as follows. Section II, provides information about signal definitions and Neyman–Pearson hypothesis testing. The cyclostationary signal detector algorithms are described in Section III. In Section IV, analysis and comparison of different algorithms are simulated numerically and implemented on FPGA by respected software. Moreover, the best method in the terms of computational complexity and performance in a joint state. Finally, Section V concludes this investigation.

II.

SIGNAL STRUCTURE AND DETECTION TEST

A. Signal Structure The signal ( ) is a zero mean complex signal with Gaussian distribution. A common structure of an OFDM symbol is depicted in Fig. 1. The OFDM symbol with a length consists of the data with a length and a cyclic prefix with a length . The cyclic prefix is a transcript of samples from the end of the symbol, added to the front of the symbol in order to alleviate inter-symbol-interference (ISI) and enhance the system performance in multipath propagation channels. The cyclic prefix can also be utilized for timing and frequency attainment [12].

under however the probability of detection as a function of SNR can be analyzed by simulations. The performance of the algorithms can be compared by evaluating the detection sensitivity as a function of SNR. III. CYCLOSTATIONARY SIGNAL DETECTORS The signal is said to be cyclostationary if its time varying expectation of covariance or autocorrelation is periodic, i.e., can be presented with some set of Fourier coefficients [14]. If the autocorrelation is periodic for some delay, as is the case for the OFDM signal as presented in Fig. 1, then its frequency component at some cyclic frequency, is nonzero. This component, cyclic autocorrelation, can be estimated as with observations as [14]. ( . )=

Fig. 1. OFDM symbol structure including data and cyclic prefixes

As shown in Fig. 1, if we have a sequence containing some OFDM symbols and the delay value is = , the autocorrelation of the cyclic prefix and its corresponding complex conjugate which is at the end of the OFDM symbol will result in a positive-mean pulses with a period of and a duration of samples. Outside the similar parts, the expectation value of ( ) ∗ ( − ) remains zero as depicted in Fig. 1. If the received signal is random Gaussian white noise, i.e., the real and imaginary parts are Gaussian random and also are uncorrelated with each other, the result of the autocorrelation will be zero. This is the null condition of Neyman–Pearson hypothesis test [13]. B. Neyman-Pearson Test for Signal Detection In the following analyses, Neyman–Pearson criterion is applied as hypothesis testing for all algorithms in order to awareness of signal. We can define the Neyman–Pearson hypothesis testing as follows, ∶

=

(1)

∶

= +

(2)

where is the estimate of the signal detection test statistics produced as a result of the algorithm under consideration, is the contribution of noise to the test statistics and, is the corresponding test statistics for the signal. The requirement for prospering test is that the presence of a signal changes the value of the test statistics and thus algorithms can detect signal. For all of the algorithms considered in this investigation, the probability distribution and the cumulative distribution function ( < ) of the test statistics under the hypothesis are known (only noise present). Therefore, the decision threshold for the can be calculated as, = (1 − ) providing a constant false-alarm rate for detection. In signal decision making, the null hypothesis is rejected when, ≥ and is assumed. Knowledge of distribution under is not required for testing, even though it can be specified at least for some of the algorithms. These results in an absence of welldefined a priori knowledge of the probability of detection ( )

1

( ) ∗( − )

(3)

The estimate is a single frequency part from the discretetime Fourier transform (DTFT) of ( ) ∗ ( − ) at a single frequency = ( )=

1

( )

∗(

− ) (4)

= X(k) + jY(k)

The statistical test for the existence of cyclostationary signal can be accomplished with test statistics computed in the frequency domain as presented in [15]. First, the imaginary and real parts of the cyclic autocorrelation estimate are classified as a vector, ( . )

̂=

( . )

(5)

The test statistic is then computed as =

̂Σ

(6) ̂

where Σ is the covariance matrix of ( ) . Under the null hypothesis, the test statistics is distributed [14], and therefore the decision threshold is obtained from =

(1 −

)

(7)

Although the cyclostationary signal detector with frequencydomain test statistics is practical, and could prepare a means for observation of multiple cyclic frequencies simultaneously, it can be apperceived that fundamentally there is no need to calculate the FFT, which makes a major portion to power loss. The concern feature in the cyclostationary signal detector with frequency-domain is the relative intensity of a cyclic frequency component of the autocorrelation to the average variance of the autocorrelation signal. However, all the information required to calculate this is already available in the time domain. For a single cycle frequency, the cyclic autocorrelation function in (3) is a frequency shifted autocorrelation of the input signal. Frequency shift can be efficiently performed with the CORDIC algorithm, [16-18] and thus there is no need to calculating FFT. Other cyclostationary based detector has been presented in [19]. This detector is based on the observation that the cyclic frequency components are also present in the autocorrelation of

the sign function of the complex input data. The sign function of the input signal ( ) is calculated as ( ) . ( ) = | ( )| 0.

( . )=

(8)

( )=0

( ) ∗( − )

(9)

Because of the normalization, the covariance matrix is replaced by a constant, resulting in simplified computation of the test statistics and therefore the testing of the hypotheses, the test statistics can be calculated from the sign cyclic correlation estimator as ( . )

=2

( . )

+

The test statistics is decision threshold like (7).

(10)

distributed [19], resulting in the

In [11], angular domain of sign cyclic correlation was presented. In angular domain sign cyclic correlation, the sign function is rewritten using exponential presentation of complex numbers as ∅ ( ) . ( )≠0 ( )= , ∅ ( ) =< ( ) (11) ( )=0 0. Using the notation of (11), the sign cyclic correlation estimator (10) can be written as ( . )=

=

=

1

∅ ( )

1

∅ ( )

1

∅ ( )

∅ (

∅ (

)

1

)

(16)

Assuming Gaussian distribution, the applied to test statistics as (

=

−

) (17)

is threshold for the =

(1 −

approximately distributed, the decision test can be calculated as (18)

)

If the threshold exceed the test statistics assumed to be uniform, and is rejected. IV.

test can also be

, then ∅ ( ) is

PERFORMANCE AND C OMPLEXITY ANALYSES

A. Performance Analysis The signal used in this investigation is an OFDM signal with similar symbol structures to IEEE802.11 standard [21] or DVBT system [22] considering the parameters depicted in Table I. Selecting the subcarrier modulation depends on the bit error rate (BER). Fig. 2 shows the bit error rate for different subcarrier modulations. As shown, in high regimes, the system uses respectively 64 and 16 but for low respectively and are the best choices [21,22].

Table I: Parameters of IEEE802.11a and DVB-T standards

2

(13) Standard Parameter

To test the uniform distribution, the angle ∅ ( ) ∈ [0.2 ] is categorized in even-sized bins, resulting in binomially distributed random variables 1

(1 −

(12)

Under the null hypothesis of the Neyman–Pearson test, the input signal contains only Gaussian white noise. For Gaussian noise ∅ ( ) is uniformly distributed, ∅ ( )~(0.2 ).

.

=

For evaluating the performance of IEEE802.11a standard, the signal under detection utilizes OFDM modulation with = 64 and = /4 = 16 samples. = 32000 samples per each detection are used for detection, resulting in a constant detection time equals 1.6 . False alarm rate is assumed to be 0.05.

)

∅ ( )=∅ ( )−∅ ( − )−

∅ ( ) ~

are (15)

=

( )≠0

The sign cyclic correlation estimator can be calculated as 1

Considering a sufficiently large , the elements of approximately ( . )–distributed where

.

∈ [0.

− 1]

IEEE 802.11a

DVB-T

N-FFT (size)

64

2048 , 8192

Cyclic Prefix Length

1/4 symbol length

1/8 symbol length

Subcarrier Modulation

BPSK, QPSK, 16QAM ,64QAM

QPSK, 16QAM, 64QAM

Bandwidth

20 MHz

8 MHz

T-FFT (µs)

3.2

224, 896

(14)

where is the total number of samples used for the current test and from the implementation point of view = 4 is optimal [20].

Fig. 2: Bit error rate vs SNR for different subcarrier modulations in OFDM systems

Fig. 4: Probability of detection vs SNR for different detection algorithms in WLAN ( = 0.05)

In the next parts, 16 subcarrier modulation is applied for simulation of ED algorithm and three cyclostationary-based algorithms, original, sign and angular were introduced in section III. Fig. 3 shows the performance of ED algorithm for IEEE802.11a standard in two different distributions. As depicted in this figure, ED under distribution offers higher performance than Gaussian. Therefore, we use distribution in all simulations for ED algorithm.

Fig. 5: ROC curve for different detection algorithms in WLAN (SNR=-12dB)

Fig. 3: Probability of detection vs SNR for ED algorithm in IEEE802.11a standard for two distributions ( = 0.05)

Fig. 4 shows the probability of detection for different algorithms and receiver operating characteristic (ROC) curve is shown in Fig 5. As shown in Figures 4 and 5, we can find that the cyclostationary signal detector offers higher detection performance but in terms of complexity has the worst case. Not only the energy detector provides lower performance in detecting OFDM signal, but it is supposed that noise variance is fully determined which is not required for cyclostationary-based algorithms. The angular domain detector is low sensitive. However, the sensitivity of all the cyclostationary based algorithms change 2 , which can be considered small from practical point of view. The reduced performance of angular

Fig. 6: Probability of detection vs SNR for angular domain detector in various sensing times compared to usual cyclostationary detector ( = 0.05)

Fig. 7: Probability of detection vs SNR for energy detection algorithm for different noise uncertainty ( = 0.05)

Fig. 8: Probability of detection vs SNR for different detection algorithms in DVB-T ( = 0.05)

version of cyclostationary algorithm can be compensated by using larger sensing time as shown in Fig. 6. Fig. 7 shows the energy detector performance considering the noise uncertainty. It is obvious that increasing the noise uncertainty (from 0 to 2 ) results decreasing on probability of detection (from 0 to 17 ) which should not be considered in cyclostationary-based algorithms. For evaluating the performance of different detection algorithms in DVB-T standard, the OFDM signal is assumed to have = 8192 and = /8 = 1024 samples. = 262144 samples per each detection is used, resulting in a constant detection time 28.6 . It is supposed that false alarm rate is 0.05. Fig. 8 shows the probability of detection versus SNR for different algorithms and also ROC curves for different algorithms are shown in Fig. 9. The performance of all abovementioned algorithms is somewhat like WLAN standard but in order to increasing detection time, signal detection of all algorithms is 2 to 3 better than WLAN. B. Complexity Analysis Complexity of different algorithms are compared with each other by simulation in MATLAB software and evaluating the respected running times. Table II shows the running time of different algorithms. It is obvious that the energy detector has the lowest running time but in terms of performance and also sensitivity to noise is not reliable. After energy detector, the angular domain sign cyclic correlation detector has the lowest running time, since it just uses angular domain of the signal and furthermore has no need to two real and imaginary parts like other cyclostationary feature detectors. From Fig. 6 it is clear that if samples of angular domain sign cyclic correlation detector increases, even the performance could be better than cyclostationary detector. Table III shows the running time of angular domain sign cyclic correlation detector for different samples compared to cyclostationary detector. Although the number of angular domain samples has been manifold nevertheless its running time is lower than cyclostationary detector.

Fig. 9: ROC curve for different detection algorithms in DVB-T ( = −14 )

For determining the computational complexity and power dissipation, these algorithms were described with VHDLlanguage and synthesized on Spartan3 (XC3S400-4pq208) FPGA of Xilinx with ISE13.2 software. The hardware complexity and power loss of the algorithms were evaluated with the design tool that has been provided by the manufacturer of FPGA. The complexity comparison is based on the information of datasheet [23] and power estimation tool that has been presented in [24]. The power dissipation estimates of various detector implementations are presented in Table IV. In the view of implementation in FPGA, computational complexity and power dissipation of the cyclostationary signal detector is the highest. ED algorithm can be implemented by two multipliers, one adder, accumulator adder and one divider, furthermore it has the simplest implementation but in terms of probability of detection in low SNRs is the worst. The optimal detector in terms of computational complexity and power dissipation is angular domain sign cyclic correlation detector witch has good probability of detection and also low power dissipation.

Table II: Running time of various detectors under IEEE802.11a standard (SNR = −5dB) Type of detector Run time (ms)

ED

Cyclo.

Sign

Angular

42.351

1021

600.251

198.322

[6]

[7]

[8]

Table III: Running time of angular and original cyclostationary detectors under IEEE802.11a standard (SNR = −5dB) Type of detector

Cyclo.

[9]

Angular

Number of samples

M

M

2M

4M

Running time (ms)

1021

198.322

250.331

401.11

Table IV: The estimation of dissipated power for various detector implementations under IEEE802.11a standard Type of detector

ED

Cyclo.

Sign

Angular

Power consumption (mw)

1.35

32.25

12.32

3.92

[10]

[11]

[12] [13]

[14]

V. CONCLUSION In this paper, analysis of various detection algorithms based on energy detector and cyclostationary features presented. These algorithms simulated in MATLAB under IEEE802.11a and DVB-T standards and implemented on FPGA. Based on the simulations and implementation results, angular domain sign cyclic correlation detector is the low-complex detector that uses cyclostationary features and doesn’t need the variance of noise like energy detector. Furthermore, increasing the number of samples in angular detection offers higher performance compared to cyclostationary detector meanwhile both the power consumption and running time of angular one is more efficient than cyclostationary one. [1]

[2]

[3]

[4]

[5]

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