Frame Detection Based on Cyclic Autocorrelation and Constant False ...

CHANNEL CHARACTERIZATION AND MODELING

Frame Detection Based on Cyclic Autocorrelation and Constant False Alarm Rate in Burst Communication Systems Liu Guangzu, Wang Jianxin, Ban Tian* School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210014, China

Abstract: Frame detection is important in burst communication systems for its contributions in frame synchronization. It locates the information bits in the received data stream at receivers. To realize frame detection in the presence of additive white Gaussian noise (AWGN) and frequency offset, a constant false alarm rate (CFAR) detector is proposed through exploitation of cyclic autocorrelation feature implied in the preamble. The frame detection can be achieved prior to bit timing recovery. The threshold setting is independent of the signal level and noise level by utilizing CFAR method. Mathematical expressions is derived in AWGN channel by considering the probability of false alarm and probability of detection, separately. Given the probability of false alarm, the mathematical relationship between the frame detection performance and Eb/N0 of received signals is established. Experimental results are also presented in accordance with analysis. Keywords: frame detection; frame synchronization; cyclic autocorrelation; constant false alarm rate; burst communications

I. INTRODUCTION Frame synchronization is one of the critical

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operations in burst communication systems since it indicates the boundary of information data in the data stream. In order to realize frame synchronization at receiver, the preamble is transmitted at the head of each burst. A burst is usually composed of preamble word and information data, as shown in Fig. 1. The preamble word consists of two segments: bit-timing recovery (BTR) word and unique word (UW). They are used for bit-timing recovery and frame synchronization, respectively. There exist two categories of frame synchronization methods: correlation rule and maximum-likelihood (ML) rule [1-6]. Correlation rule has been popular because of its simplicity in implementation as well as acceptable performance, and the ML rule outperforms the correlation rule at the expense of additional computation. Both methods perform frame synchronization when transmitted signals have arrived at receiver. However, nothing else than noise exist during the guard time interval between two adjacent bursts. The probability of false alarm is thus so high that it may affect the demodulation of receiver. For example, the correlation rule evaluates correlation value between the sampled inputs and UW, frame synchronization is accomplished on condition that the correlation value exceeds threshold value. China Communications • May 2015

The probability of frame synchronization is sufficiently high as long as the threshold value is lower, at the same time the probability of false alarm is increased. To avoid such a tradeoff, frame detection should be performed prior to frame synchronization. The frame detection mentioned here is to detect the come forth of preamble while not to locate the information data. In such case, the threshold value of correlation rule can be adjusted to a lower value to improve the performance of frame synchronization with a negligible false alarm rate. This paper addresses the problem of frame detection in the presence of additive white Gaussian noise (AWGN) and frequency offset due to imperfect carrier frequency estimation. Energy detection is a good method for frame detection since it adopts matched filter to achieve optimized performance. It does not need any information of the received signals to be detected and thus attracts much attention in cognitive radio [7-8]. In our context, the received signals may have additional Doppler frequency offset which may lead to remarkable deterioration of matched filtering. In addition, energy detection is not a preferred option since it does not explore the information of preamble. Conventional statistical signal processing methods consider random signals being statistically stationary, in which case the parameters of the underlying physical mechanism that generate the signal are time invariant. However, most realistic signals in communication systems have periodically time-varying parameters. For example, BTR in the preamble is generally periodic in order to accomplish bit-timing recovery as fast as possible (e.g. a repeated bit sequences of “1100” for QPSK modulating scheme) [9]. Although in some cases this periodicity can be ignored by signal processors, such as receivers which must detect the presence of signals of interest, estimate their parameters, and extract their messages, in many cases there can be much to gain in terms of improvements in the performance of these signal processors by recognizChina Communications • May 2015

ing and exploiting underlying periodicity [10]. In wireless communication systems, there can be a considerable variation in the amplitude of incoming burst due to rain fading. Therefore, a desirable property of the frame detection is to have a constant false alarm rate (CFAR) [11]. This paper proposes a frame detection method which exploits the periodicity of BTR by using cyclic autocorrelation function. The cyclic autocorrelation values of the received signals are applied to a CFAR detector which detects the BTR without foreknowledge of signals and noise level. The proposed method is robust to the frequency offset and independent of the bit-timing recovery. This paper is organized as follows: Section II presents a burst model with π/4 differential quadrature phase shift keying (π/4-DQPSK) modulation. In Section III, the mathematical analysis of the proposed method is given. In section IV, simulation results on the probability of frame detection versus signal-to-noise ratio are presented. Section V outlines some concluding remarks.

To realize frame detection in the presence of additive white Gaussian noise (AWGN) and frequency offset, a constant false alarm rate (CFAR) detector is proposed through exploitation of cyclic autocorrelation feature implied in the preamble.

II. SYSTEM MODEL The proposed method takes advantage of the cyclostationary property of the preamble, which is generated by the periodicity of BTR. The proposed frame detection method is validated on π/4-DQPSK modulation scheme. In π/4-DQPSK digital burst communication system, symbols are transmitted as the changes of phase rather than the absolute phase. Specifically, the bit stream, denoted as d(k)(k=1,2, ...), is converted into a pair of parallel bits before modulation denoted as dI(k)dQ(k),k=1,2,..., then the phase difference Δθ(k) is determined by

Information of previous burst

DATA

Guard time

Preamble

BTR

UW

Information

DATA

Fig.1 Frame format

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∆θ(k)  = θ(k) − θ(k − 1)  π/4, dI (k)dQ (k) = ”11”      dI (k)dQ (k) = ”01”   3π/4, =   −3π/4, d I (k)dQ (k) = ”00”     −π/4, dI (k)dQ (k) = ”10”

respectively. (1)

The complex envelope of the transmitted signal can be expressed as  s g(t − kT )e jθ(k) (2) a (t) = k

where g(∙) denotes the square root raised cosine function, T is the symbol duration, and θ(k) is the phase of the transmitted signal at the k-th symbol interval. Assuming that sa(t) is only corrupted by complex Gaussian white noise process za(t), then the complex envelope of the received signal can be expressed as ra (t) = sa (t)e j(2π f t+θ ) + za (t) (3) where fd is the carrier frequency offset; θ0 is a random phase. Substituting (2) into (3), the received signal can be written as  ra (t) = g(t − kT )e jθ(k) e j(2π f t+θ ) + za (t) (4) d

0

d

0

k

III. MATHEMATICAL DERIVATION Assuming that the BTR is a repeated bit series of “1100”, the workflow of proposed frame detection method is shown in Fig.2, where \ fs=1/Ts is the sampling frequency of the analog-to-digital converter (ADC). Generally speaking, fs is chosen to satisfy M=T/TS, where M∈Z, i.e., there are exactly M samples in a symbol interval. The frame detection method is divided into two steps. In the first step, the cyclic autocorrelation values, denoted as Y(k), of the received signals at a fixed delay M is calculated. In the second step, the CFAR detector is used to decide whether the BTR exists or not. The mathematical analysis of these steps will be presented in Sections 3.1 and 3.2,

3.1 Cyclic autocorrelation function The output of the ADC can be expressed as r(n) = s(n) + z(n) (5) where  s(n) = g(n − kM)e jθ(k) e j(2π∆ f n+θ ) (6) 0

k

s(n) is the received signal sample sequence without noise, and ∆ f = fd / fs is the normalized Doppler frequency. z(n) is the AWGN noise with zero mean and variance σ2, denoted as z(n)~N(0,σ2). Following the ADC, both r(n) and M-sample delayed r*(n−M) are sent to the complex multiplier. The output of complex multiplier can be expressed as y(n) = r(n)r∗ (n − M) = s(n)s∗ (n − M) + z(n)z∗ (n − M)  (7) +s(n)z∗ (n − M) + z(n)s∗ (n − M) = yss (n) + yzz (n) + ysz (n) where the differential results y ss(n) and yzz(n) are defined as yss (n) = s(n)s∗ (n − M) (8) yzz (n) = z(n)z∗ (n − M) (9)

The cross differential result between s(n) and z(n) is defined as ysz (n) = s(n)z∗ (n − M) + z(n)s∗ (n − M) (10)

It can be seen from Eq. (7) that y(n) is the summation of three terms, where y zz(n) and ysz(n) are unfavorable, they will be discussed in detail in section 3.2. Substituting Eq. (6) into Eq. (8), yss(n) can be rewritten as  yss (n) = g(n − lM)g (n − (k + 1)M) l k  (11) e j(θ(l)−θ(k)) e j2π∆ f M Thus, yss(N+2M) can be expressed as  yss (n + 2M) = g (n − (l − 2) M) l

=

 l

ra (t )

A/D Convert

f s = 1 / Ts

y (n)

r (n)

Z −M

*

DFT

Y (k )

⋅

2

r * (n − M )

u (k )

CFAR

Y/N

k

g (n − (k − 1) M) e j(θ(l)−θ(k)) e j2π∆ f M k

g (n − lM)

g (n − (k + 1) M) e j(θ(l+2)−θ(k+2)) e j2π∆ f M

(12) Notice that θ(l + 2) − θ(k + 2) = θ(l) − θ(k) (13) Eq. (12) can be rewritten as

Fig.2 Block diagram of the proposed frame detection method

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China Communications • May 2015

 l

k

g(n − lM)g (n − (k + 1)M)

e j(θ(l)−θ(k)) e j2π∆ f M = yss (n)

(14) Therefore the autocorrelation function Rs(n;M) of s(n) is periodic with 2M because of the periodicity of yss(n). s(n) is cyclostationary and its cyclic autocorrelation funcα tion Rs (M) is nonzero at cyclic frequencies α=kfs/2M,k=1,2,... To simplify description, we α define Y(k) = Rs (M) . In the case of N=1024, M=8, the magnitude of Y(k) is depicted in Fig. 3, where N denotes the length of s(n). We N observe that |Y(k)| with k = possesses a 2M majority of the total power, which is very desirable for frame detection. The above analysis also indicates that the proposed method is insensitive to frequency offset fd because of the differential operation. To reduce the computational complexity and facilitate the mathematical analysis for threshold setting, we define u(k) = |Y(k)|2 .   N u If is detected to exceed a threshold 2M value, the BTR word is presumed to exist, otherwise the noise is presumed. A thorough analysis of CFAR detector is discussed in the following section.

3.2 Mathematical analysis of CFAR detector In this section, the mathematical analysis of CFAR detector based on Neyman-Pearson Observer is presented. Case 1: Mere presence of noise Without s(n), the output of the complex multiplier y(n) is equal to yzz(n), which can be expressed as: yzz (n) = z(n)z∗ (n − M) = yzzI (n) + jyzzQ (n) (15) where z(n) = zI (n) + jzQ (n) (16) I yzz (n) = zI (n)zI (n − M) + zQ (n)zQ (n − M) (17) yzzQ (n) = zQ (n)zI (n − M) − zI (n)zQ (n − M) (18)

In our design, ADC is preceded by an anti-aliasing low-pass filter with cutoff frequen-

China Communications • May 2015

cy M/2T, and M=8 is chosen to accommodate some frequency offset fd. Consequently z(n) and z(n−M) is uncorrelated, therefore, we have       E yzz (n) = E yzzI (n) = E yzzQ (n) = 0 (19)       E yzz (n) = E yzzI (n) = E yzzQ (n) = 0 (20)  2  E yzz (n) = σ4 (21)

Let us consider the statistical property of Yzz(k), which is a N point DFT of yzz(n), and it can be expressed as N−1  − j 2πkn Yzz (k) = 1 yzz (n)e N = YzzI (k) + jYzzQ (k) N n=0 (22) where N−1  

YzzI (k) = 1 N

n=0

yzzI (n) cos 2πkn + yzzQ (n) sin 2πkn N N



(23) YzzQ (k) = 1 N

N−1    yzzQ (n) cos 2πkn − yzzI (n) sin 2πkn N N n=0

(24) I From Eq. (23, 24), it is obvious that Yzz (k) Q and Yzz (k) are weighted linear combination

of statistically independent random variables. I Based on the central limit theorem, Yzz (k) and YzzQ (k) are approximately normally distributed

random variables with zero mean and variance σ2zz . Define uzz(k) as  2  2 uzz (k) = YzzI (k) + YzzQ (k) (25)

consequently, uzz(k) is an exponential distrib2 uted random variable with mean equal to 2σzz .

0 -5

Y(k)/dB

yss (n + 2M) =

-10 -15 -20 -25

0

50

100

150 k

200

250

300

Fig.3 Magnitude of Y(k) for N=1024 and M=8

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The probability density function of uzz(k) can be expressed as uzz − 2 f (uzz ) = 1 2 e 2σzz (26) 2σzz If the noise variance σ is known, we can 2 zz

2 make the variable replacement vzz = uzz /σzz in

Eq. (25). Eq. (25) is changed to v − zz f (vzz ) = 1 e 2 (27) 2 Suppose λ0 is the decision threshold, then, the probability of false alarm can be expressed as +∞ λ0 − Pf = f (vzz )dvzz =e 2 (28) λ0

or, equivalently, λ0 = −2 ln P f (29) 2 In practice, σzz is unknown, but it can be estimated from a block of the observed data, i.e. N −1  σ ¯ 2zz = 1 u (k) (30) Nc k=0 zz c

where Nc is the number of samples used for estimating noise power. Correspondingly, the probability of false alarm for threshold λ0 is given as below [12]   λ −N Pf = 1 + 0 (31) Nc c

Case 2: presence of preamble and noise In this case, the output of complex multiplier can be expressed as y(n) = yss (n) + yzz (n) + ysz (n) (32) where  ysz (n) = sI (n)zI (n − M) + sQ (n)zQ (n − M)  +zI (n)sI (n − M) + zQ (n)sQ (n − M)  + j sQ (n)zI (n − M) − sI (n)zQ (n − M) (33)  +zQ (n)sI (n − M) − zI (n)sQ (n − M) I Q = ysz (n) + jysz (n). Similarly, as derived in case 1, the following results can be obtained       E ysz (n) = E yIsz (n) = E yQsz (n) = 0 (34)   2  2  σ2 B(n) E yIsz (n) = E yQsz (n) = (35) 2   E (ysz (n))2 = σ2 B(n) (36) where B(n) = s2I (n) + s2Q (n) + s2I (n − M) + s2Q (n − M).

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as

The N points DFT of ysz(n) can be expressed

Ysz (k) = 1 N

N−1 

ysz (n)e

−j

2πkn N = YszI (k) + jYszQ (k)

n=0

(37) According to the central limit theorem, YszI (k) and YszQ (k) are approximately normally Q distributed random variables. Ysz (k) and Ysz (k)

are statistically independent and identically distributed Gaussian random variables with N−1  σ2 2 B(n) . zero mean and variance σsz = 2N n=0

We define ysz+zz (n) = ysz (n) + yzz (n) , the DFT of ysz+zz (n) can be expressed as 2πkn N−1 1  ysz+zz (n)e− j N Ysz+zz (k) = N (38)  n=0 I Q = Ysz+zz (k) + jYsz+zz (k) I Q Then, Ysz+zz (k) and Ysz+zz (k) are statistically

independent and identically distributed Gaussian random variables with zero mean and variN−1  4 σ2 2 B(n) + σ . ance σsz+zz = 2N n=0 2 Since Y(k) is the DFT of y(n), it can be expressed as Y(k) = DFT {yss (n) + ysz (n) + yzz (n)} = DFT {yss (n)} + DFT {ysz (n) + yzz (n)} I Q = YssI (k) + Ysz+zz (k) + j YssQ (k) + Ysz+zz (k) I Q = Y (k) + jY (k)

(39) According to the analysis in Section 3.1, the energy of Y(k) is centered at k=N/2M. Eq. (39) can be rewritten as     I Q N .  (k) + j YssQ (k) + Ysz+zz (k) , k = 2M  YssI (k) + Ysz+zz Y(k) ≈   Y I (k) + jY Q (k),  otherwise. sz+zz sz+zz

(40)     N N I Q Y Y That is, and are sta2M 2M tistically independent random variables with 2 identical variance equal to σsz+zz , and mean equal to YssI (k) and YssQ (k) , respectively. Define u(k) as  2  2 u(k) = Y I (k) + Y Q (k) (41)   2 u N  Then,  is a non-central chi-square 2M  distributed random variable with 2 degrees of freedom. Thus, the probability density func-

China Communications • May 2015

tion of u can be expressed as √  A2 − u+ uA 1 2σ2sz+zz f (u) = e I0 (42) 2σ2sz+zz σ2sz+zz  2  2 w h e r e A2 = YssI ( N ) + YssQ ( N ) , a n d 2M 2M I0(∙) denotes the modified zero order Bessel function of the first kind. Given the threshold λ0, the detection probability function can be written as √  +∞ +∞ A2 − u+ uA 1 2σ2sz+zz du Pd = f (u)du = e I0 2σ2sz+zz σ2sz+zz λ0

λ0

(43) 2 Define v = u/σsz+zz , the probability of detection can be rewritten as   +∞ 1 e− v + 2S NR I0 √vS NR dv Pd = 2 λ /σ λ /σ   (44)  1 e− v + 2S NR I0 √vS NR dv = 1− 2 0 0

2 sz+zz

0

2 sz+zz

2 2 where S NR = A /σsz+zz is the input signal-to-

noise ratio of the CFAR detector, and it satisfies the following equation S NR = S NRin + S NRDFT − S NRloss (45) where SNRin denotes the signal-to-noise ratio of the received signal, SNRloss denotes the signal-to-noise ratio reduction of the differential operation, SNR DFT denotes signal-to-noise ratio enhancement of the DFT operation, and all terms in (45) are in dB. Notice that SNRloss is not a constant, the relationship between

S NRloss

SNRloss and SNRin will be discussed in the next section. Thus we obtain a CFAR detector based on the sequence Y(k) as follows: (1) Given the probability of false alarm Pf and the samples number Nc used for estimating the noise power, the threshold λ0 is calculated through   λ −N Pf = 1 + 0 ; Nc c

(2) Calculate u(k) = |Y(k)|2 ; (3) Estimate the noise power using following expression  k −1  k +N /2    1   σ2n = u(k) + u(k)  Nc  0

0

k=k0 −Nc /2

c

k=k0 +1

N where k0 = ; 2M (4) Make a decision on the presence of burst frame if u (k0 ) ≥ λ0 σ2n

3.3 Signal-to-noise ratio analysis Differential operation is a nonlinear process, the loss of SNR due to differential operation is not readily determined analytically. Through simulation, the loss of SNR is determined for SNRin values ranging from -40dB to 30dB, and it can be approximated as below

  S NRin < −10dB f or |S NRin |    f or S NRin > 10dB 2.2 = (46)    0.02244 · S NR2 − 0.3594 · S NR + 3.983 −10dB ≤ S NRin ≤ 10dB f or in in

In Fig. 4, the relationship between SNRloss and SNRin is plotted. SNRloss decreases linearly when SNRin10dB and conforms to the rule of quadratic fit in the other case. Let us now consider the effect of DFT on SNR enhancement. After DFT operation, we notice that the noise power be distributed equally into N parts and the signal power be   N distributed almost equally into u and 2M   u − N . Considering that the detection of 2M China Communications • May 2015

 N , the SNR en2M hancement of DFT can be expressed as S NRDFT = 10 lg N − 3 (47) So far, the relationship between SNR and SNRin has been given, then a curve of Pd versus SNR in can be drew. However, the final aim is to give a plot of Pd versus normalized signal-to-noise ratio Eb /N0, so the relationship between SNR and Eb /N0 must be given. Based on the definition of normalized signal-to-noise ratio, the following equation can be given

BTR only depends on u



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S NRin = Eb /N0 − 10 lg (M/2) (48)

Then SNR can be expressed as

S NR = Eb /N0 − 10 lg (M/2) + 10 lg N − 3 − S NRloss

(49) Fig. 5 plots the curve of SNR versus Eb /N0 according to (49).

IV. SIMULATION RESULTS

Fig.4 SNR loss due to the differential operation

Fig.5 SNR versus Eb /N0 with N=256 and M=8

Fig.6 Theoretical and simulation results of Pd versus SNR (in dB) with M=8, N=256, L=32 and Nc=16

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In this section, three simulation results are presented. To validate the derivation in this paper, Pd of Eq. (44) which is called theoretical result here and the simulated detection probability are drawn in Fig. 6 to compare with each other. To evaluate the performance of proposed method in this paper, Pd versus Eb /N0 is drawn in Fig. 7. The comparison of detection probability between the proposed method and the energy detection method under the conditions of constant false detection probability is given at the end of this section. Fig. 6 compares theoretical and simulation results of Pd versus SNR in dB. L=N/M is the number of symbols involved in the simulation. From Fig. 6 we can see that the curve of theoretical and that of simulation overlap each other, it shows that the mathematical analysis of the proposed method is correct. We also notice from Fig. 6 that SNR greater than 15 dB is required for the probability of detection approaching unity, it seems that the method is imperfect at low signal-to-noise ratio. However, there is signal-to-noise ratio enhancement in the method, thus, the method can work well at low Eb /N0. The following simulation results indicate such a conclusion. Fig. 7 plots the curves of Pd versus E b / N0 with with M=8, N=256, L=32 and Nc=16. When Eb /N0 great than 6dB, the probability of detection approaches unity while the probability of false alarm can be less than 10-6. Such a performance could satisfy requirements of almost all burst communication systems. Furthermore, if the number of symbols are doubled, i.e. L=64, the required Eb /N0 could be reduced to 3dB without a performance deterioration.

China Communications • May 2015

Fig. 8 plots the detection probability of the proposed method and the energy detection method under the conditions that false detection probability is equal to 10-3. Energy detection method requires the estimation of noise power. If the noise power estimation is inaccurate, the detection performance of energy method is significantly degraded. When Eb /N0 is equal to 4dB, the detection probability of the proposed method approaches unity, while the detection probability of the energy detection method with 1dB noise power estimation uncertainty is approximately equal to 0.87. Therefore, the performance of the proposed method is better than that of the energy detection method.

Fig.7 Curves of Pd versus Eb /N0 with M=8, N=256, L=32 and Nc=16

V. CONCLUSION

ACKNOWLEDGEMENT This work was supported by National Science Foundation of China under Grant No. 61401205.

References [1] B. Ramakrishnan, Matched nonlinearities for frame synchronization in presence of frequency offsets[J], Electronics Letters, 2009, Vol.45, No.4, pp.236-237. [2]  R. Pedone, M. Villani, A. Vanelli-Coralli, et al., Frame Synchronization in Frequency Uncertainty[J], IEEE Transactions on Communications, 2010, Vol. 58, No. 4, pp. 1235-1246. [3] Zae Yong Choi and Yong H. Lee, Frame Syn-

China Communications • May 2015

1 0.9 0.8

Proposed ED with 1dB uncertainty ED with 2dB uncertainty ED with 3dB uncertainty

0.7

d

0.6 P

A new method based on cyclic autocorrelation and the CFAR detector is proposed to detect frame in burst communication systems. The closed-form expressions for false detection probability and detection probability are derived in the additive white Gaussian noise channel. The computer simulations validate the derivation. The proposed method is robust to frequency offset and independent of bit timing. Furthermore, this method can work well at very low signal-to-noise ratio without any penalty in regard to implementation complexity and its false alarm rate is constant.

0.5 0.4 0.3 0.2 0.1 0 -4

-2

0

2

Eb/N0 (dB)

4

6

8

10

Fig.8 Detection probability of proposed and energy method with M=8, N=256 and Pf=10-3 chronization in the Presence of Frequency Offset[J], IEEE Transactions on Communications, 2002, Vol.50, No.7, pp.1062-1065. [4] M. Chiani and M. G. Martini, On sequential frame synchronization in AWGN channels[J], IEEE Transactions on Communications, 2006, vol. 54, no. 2, pp. 339-348. [5] X. Luo and M. K. Howlader, Noncoherent decoder-assisted frame synchronization for packet transmission[J], IEEE Transactions on Wireless

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Communications, 2006, vol. 5, no. 5, pp. 961966. [6] A. Korpansky and M. Bystrom, Detection of aperiodically embedded synchronization patterns[J], IEEE Transactions on Communications, 2004, vol. 3, no. 5, pp. 1386-1392. [7] Tevfik Yucek, Huseyin Arslan, A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications[J], IEEE Communications Surveys & Tutorials, 2009, Vol.11, No.1, pp.116-130. [8] Ebtihal Haider Gismalla, Emad Alsusa, Performance Analysis of the Periodogram-Based Energy Detector in Fading Channels[J], IEEE Transactions on Signal Processing, 2011, Vol.59, No.8, pp.3712-3721. [9] Matsumoto, Y., Umehira, M., High Performance Coherent Demodulator for Wireless ATM Systems-offset-QPSK simultaneous carrier and bit-timing recovery scheme[C] , Vehicular Technology Conference, 1997 IEEE 47th, Vol. 1, pp. 290-294. [10] William A. Gardner, Antonio Napolitano, Luigi Paura, Cyclostationarity: Half a century of research[J], Signal Processing , 2006, pp.639-697. [11] M. R. Soleymani and H. Girard, The Effect of the Frequency Offset on the Probability of Miss in a packet Modem Using CFAR Detection Method[J], IEEE Transactions on Communications, 1992, Vol. 40, NO. 7, pp. 1205-1211,. [12] Mark A. Richards, “Fundamentals of Radar Signal Processing”, McGraw-Hill Companies, Inc., 2005.

Biographies Liu Guangzu, studied electronic and information engineering at Nanjing University of Science and Technology, Nanjing, P.R. China, and received his

63

M.S. degrees from Shandong University, Jinan, China in 2003. Since 2003 he has been with the School of Electronic and Optical Engineering at Nanjing University of Science and Technology as a teaching assistant, lecturer. His main research areas are communications signal processing and software radio. Wang Jianxin, studied electronic and information engineering at Nanjing University of Science and Technology, Nanjing, P.R. China, and received his M.S. and Ph.D. degrees in 1987 and 1999, respectively. Since 1987 he has been with the School of Electronic and Optical Engineering at Nanjing University of Science and Technology as a teaching assistant, lecturer, associate professor, and since 2001 as a professor. He was a visiting researcher at the Institute of Telecommunications, University of Stuttgart, Germany in 2000, December 2011, and December 2012, respectively. His main research areas are communications signal processing and software radio. Ban Tian, received the M.S. degree in signal and information processing from Southeast University, Nanjing, China in 2009, and the Ph.D. degree in communications and electronics from Telecom ParisTech, Paris, France in 2012. Since November 2012 he has been with the School of Electronic and Optical Engineering, Nanjing University of Science and Technology, China, where he is currently an assistant professor. During 2009/2012, Dr. Ban worked at the “Laboratoire de Traitement et Communication de l’Information’’ (LTCI), the joint research laboratory between Telecom ParisTech and the ‘‘Centre National de la Recherche Scientifique (CNRS), UMR 5141. His current research interests include fault tolerant techniques in digital designs and digital signal processing.

China Communications • May 2015