A DSSS Signal Detection Method Based on Wavelet Decomposition and Delay Multiplication Xiaolin Zhang, Sijia Li, Zengmao Chen College of Information and Communication Engineering Harbin Engineering University Harbin, China Email:
[email protected] Abstract—This paper proposes an improved method for direct sequence spread spectrum (DSSS) signal detection with low signal to noise ratio (SNR) in noncooperative field. To solve the problem that the correlative peaks appear discontinuously and unsteadily for DSSS signal with very low SNR, the wavelet decomposition-delay multiplication combined processing technique is proposed to improve the autocorrelation of signal under detection. The simulations indicate that this method can effectively achieve blind detection and pseudo-noise (PN) sequence period estimation of DSSS signal in low SNR scenarios. Keywords—signal detection; DSSS signal; PN sequence period estimation; wavelet decomposition
I. INTRODUCTION Detection and parameter estimation of direct sequence spread spectrum (DSSS) signal with low power spectral density has always been a hot research topic in recent years, especially when the signal to noise ratio (SNR) is very low. Facing this challenge, scholars put forward many methods, among which the autocorrelation detection method has been studied earlier and more often [1] [2]. It was first proposed by A. Polydoros in the 1980s, mainly using the characteristics of the independence of noise space at different time [3]. Although it has a fairly good detection performance, the obvious disadvantage is that the correlative peaks are not easy to extract when the SNR is low, which makes this detection scheme not viable in low SNR scenarios [4]. To solve the problem of the traditional autocorrelation detection scheme, the paper proposes a novel algorithm to improve the above mentioned autocorrelation method by using the wavelet decomposition-delay multiplication combined processing technique (called the proposed method), which is capable of making the final peaks more obvious. The simulations indicate that the proposed method can guarantee effective detection and pseudo-noise (PN) sequence period estimation of DSSS signal with low SNR. Moreover, it can also be applied in noncooperative fields. II. AUTOCORRELATION DETECTION METHOD Suppose the received signal uses binary phase shift keying (BPSK) modulation, it can be represented as [5]
x(t ) = s(t ) + n(t ) = Ad (t )cos(ωc t + ϕ0 ) + n ( t )
where s (t ) is the DSSS signals, n(t ) is the additive white Gaussian noise (AWGN) in the channel, A, ωc and ϕ0 represent the amplitude, carrier frequency and initial phase for the signal of interest, respectively. d (t ) is a composite sequence formed by source signals, which is modulated by a PN sequenceto spread its spectrum, it can be expressed by d (t ) = a ( t ) c ( t )
(2)
where a (t ) is the source signals and c (t ) is the PN sequence. Assume that N represents the length of the PN sequence, Tc denotes the chip width, Rc (τ ) is a periodic function with a period of NTc , it can be represented as °1 − τ (1 + N ) / NTc 0 ≤ τ < Tc Rc (τ ) = ® Tc ≤ τ < ( N − 1) Tc − 1/ N °¯
(3)
The sequence after spectrum spreading d (t ) is essentially a splicing sequence of ± c (t ) , so its autocorrelation function Rd (τ ) also has the characteristics of the PN sequence—having obvious correlative peaks value over a period and the distance between adjacent peaks is equal to the period of the pseudonoise sequence [6]. While the autocorrelation function of Gaussian white noise is a į-function, when τ ≠ 0, RN (τ ) ≈ 0 [7]. Therefore, we can detect DSSS signal and estimate the PN sequence period based on the autocorrelation difference of the sequence after spectrum spreading and Gaussian white noise. In practical applications, due to the randomness of source code sequence, positive and negative peaks may cancel out each other at certain integer times of PN period. What’s more, since the observation time is limited, the autocorrelation function of the signal is estimated by finite sample data, so the correlation characteristic of noise may not be ideal. Therefore, when the SNR is high, the correlative peaks are obvious and easy to extract; when the SNR is low, the correlative peaks are inundated by Gaussian white noise and it is impossible to distinguish and accurately extract. This problem makes it hard to detect the DSSS signal with low SNR.
This paper is funded by the International Exchange Program of Harbin Engineering University for Innovation-oriented Talents Cultivation.
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A. Wavelet decomposition To solve this problem of traditional method, we first use wavelet decomposition technique to denoise the received signals, which is mainly based on wavelet multi-resolution analysis theory [8] and Mallat algorithm [9]. Usually Gaussian white noise is mostly contained in the details with high frequency, so we can use a specific wavelet basis to divide the signals into low frequency part CA1 and high frequency part CD1, and then decompose low frequency part CA1 into low frequency part CA2 and high frequency part CD2, and continue this decomposition in this form until it reaches the scale we need. Finally, reconstruct the small signals together [10]. This method can achieve the purpose of reducing signal noise. The selection of wavelet basis is based on the mathematical properties of wavelet function and the scale function of wavelet. In this paper, we select the Daubechies (dbN) wavelet basis to decompose the received signals. The number of decomposition layers is determined by the carrier frequency f c and sampling rate f s . Since the sampling rate in the simulation is 40MHz and the carrier frequency is 4 MHz, the frequency band range of the signal decomposing in 3 layers is f s / 16 ~ f s / 8 [11] i.e. 2.5MHz ~ 5MHz , the carrier frequency of is exactly within this range. In other words, the CD3 part can reflect the characteristics of the received DSSS signal.
B. Delay multiplication Due to the randomness of source sequence, the positive and negative peaks cancel out each other at some integer times of PN period, which leads to the situation that some large peak may not occur. In order to make the correlative peaks appear more clearly, the delay multiplication technique can be used. If the delay time is t0 , the autocorrelation function of the baseband part of the delay multiplication signals is
Delay Multiplication
Detection and Estimation
Correlative Peaks Searching
Autocorrelation
Fig. 1. The flow chart of the proposed method
Firstly the signal received by the receiver is decomposed using the db6 wavelet basis in 3 layers to obtain CD3 part as the next processing signals. Then the signals is multiplied by the delayed signals, and processed by autocorrelation function. Finally the DSSS signal is detected by searching the correlative peaks, and the distance between adjacent peaks is the period of the PN sequence. IV. SIMULATION RESULTS To demonstrate the performance of the proposed method, simulations are implemented by MATLAB to compare its performance with the traditional autocorrelation method and improved method only processed by wavelet decomposition. The parameters of simulation are shown as follows: f c = 4MHz , f s = 40 MHz , Rc = 2Mbit / s , N=127, the length of source code sequence is 10. The following figure is a contrast of autocorrelation function of the DSSS signal obtained by three method when SNR= -10dB. The abscissa of the waveform in Fig. 2 is the delay time τ represented by sampling points, and the amplitude coordinate is the normalized amplitude. 1 0.8 0.6 0.4 0.2 0
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(a) Traditional method
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The information contained in the autocorrelation function is Ra (τ ) Ra (τ + t0 ) Rc 2 (τ ) , where Rc 2 (τ ) is still a pulse sequence with a period of NTc . Because the source code sequence is not stable, the autocorrelation function of the delay signals is not equal to the original signals. The value of the autocorrelation at this time is the result of Ra (τ ) and Ra (τ + t0 ) , so when the delay time is equal to the chip
width, i.e. τ = Tc the autocorrelation can be boosted to a larger value after the delay multiplication. C. The proposed method Based on the theoretical analysis above, this paper propose a method using wavelet decomposition-delay multiplication
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Wave Decomposition
1 Normalized amplitude
= Ra (τ ) Ra (τ + t0 ) Rc 2 (τ )
Received Signals
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(b) Method with wavelet decomposition. 1 Normalized amplitude
Rdm (τ ) = R {a ( t ) c ( t ) a ( t + t0 ) c ( t + t0 )}
combined processing technique to improve the traditional autocorrelation method. The steps of the proposed method is shown in Fig. 1.
Normalized amplitude
III. THE PROPOSED METHOD
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(c) Proposed method Fig. 2. Comparison of the three methods
As it is shown in Fig. 2 (a), the autocorrelation function of the signal obtained by the traditional method has no obvious peak value, the correlative peaks are submerged by the strong noise. However, after applying the wavelet decomposition,
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some stronger correlative peaks can be observed in Fig. 2 (b). It is worth noting that some weaker peaks are still submerged, which means that they are unable to be detected accurately. In Fig.2 (c), the autocorrelation of the signal obtained by the proposed method has much larger and more obvious correlative peaks at each integer times of PN period. Moreover, the peaks are clearer and easier to extract. Therefore, the proposed method has a better effect in the detection of DSSS signal and the estimation of the PN period. Fig.3 shows the detection performance of traditional method, improved method with wavelet decomposition and the proposed method further incorporating delay multiplication. The decision criteria is whether equal-width peaks with intervals of PN sequence occur. The condition that the relative error of the PN sequence period is less than 1% is considered as the correct detection. Each method perform 100 times Monte Carlo simulation with SNR ranging from -15dB to -5dB.
Computer simulations show that the proposed method has a better performance than the traditional method in terms of effectively detecting the DSSS signal and accurately estimating the PN sequence period at low SNR, which makes the proposed method a competitive option for the detection of DSSS signal in noncooperative fields. ACKNOWLEDGMENT This paper is funded by the International Exchange Program of Harbin Engineering University for Innovationoriented Talents Cultivation. The authors acknowledge the support from the National Natural Science Foundation of China (Grant No. 61401196) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20140954), and also acknowledge the support from the Central University Basic Operating Expenses Project of Harbin Engineering University (Grant No. 201749).
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REFERENCES
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Fig. 3. Detection performance of three methods
As it is shown in Fig. 3, the traditional method can detect DSSS signal with a correct rate of 90% or more when the SNR is larger than -7dB; the improved method with wavelet decomposition can achieve the same performance when the SNR is -9dB. Compared to the above two methods, the proposed method can retain the same performance with SNR being as low as -13dB. When SNR is higher than -11dB, the correct detection rate can reach 100%. Therefore, the proposed method achieves effective detection of DSSS signal with lower SNR. Meanwhile, the estimation performance of the PN sequence period can also be guaranteed at lower SNRs. V. CONCLUSIONS In this paper, an improved autocorrelation method based on the combination of wavelet decomposition and delay multiplication is proposed, in view of the problem that correlative peaks in traditional autocorrelation method are not continuous and unstable. The proposed method is aimed at reducing the influence of the randomness of source code sequence on the correlative peaks, and solving the problem that the peaks are submerged by noise when the SNR is too low.
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