Anti-interference Wi-Fi synchronization method

Abstract

The invention belongs to the technical field of synchronization algorithms of wireless communication, and particularly relates to an anti-interference Wi-Fi synchronization algorithm. For an L-STF sequence specified by a Wi-Fi protocol, a received signal is modeled into a random variable obeying F distribution in a frequency domain based on a specific frame structure of the L-STF sequence, a corresponding detection threshold is obtained through a quantile table of the F distribution under a given false alarm probability, and threshold judgment is performed by using the threshold so as to realize constant false alarm probability (CFAR) detection. The false alarm probability of an estimator adopted by the constant false alarm probability detection algorithm only depends on the setting of a threshold value and is irrelevant to noise power, channel state and the like; simulation results show that the method still keeps good synchronization performance even under bad conditions of channel change, low signal-to-noise ratio and the like. According to the method, the actual application scene of Wi-Fi is considered, the algorithm has the anti-interference capability, and compared with a traditional algorithm, the synchronization performance is better.

Description

Technical Field

[0001] The present invention belongs to the technical field of synchronization algorithms for wireless communications, and in particular relates to an interference-resistant Wi-Fi synchronization method. Background Art

[0002] Wi-Fi technology is one of the representative technologies of modern communications. It has the advantages of high speed, wide coverage and low threshold, so it is favored by governments and enterprises. It can be widely used in offices, homes and mobile environments, making it convenient for people to connect to the high-speed Internet anytime and anywhere. With the development of communication technology, the Wi-Fi series of protocols has been iterated to the seventh generation of IEEE802.11be standard. The goal of the Wi-Fi series of protocol standards is to further improve the throughput of WLAN networks and provide low-latency access guarantees, which puts forward new requirements for its synchronization performance and anti-interference capabilities.

[0003] For the Wi-Fi physical layer, the receiver uses a constant false alarm probability detection algorithm to greatly improve the synchronization accuracy, which is a very practical issue. Summary of the invention

[0004] The object of the present invention is to provide a Wi-Fi synchronization method that is resistant to interference and has high synchronization accuracy.

[0005] The present invention targets the L-STF sequence specified in the Wi-Fi protocol, models the received signal as a random variable obeying the F distribution in the frequency domain based on its specific frame structure, obtains the corresponding detection threshold through the quantile table of the F distribution under a given false alarm probability, and uses the threshold to make a threshold decision to achieve constant false alarm probability (CFAR) detection. Since the false alarm probability of the estimator used in the constant false alarm probability detection algorithm only depends on the setting of the threshold, it has nothing to do with the noise power, channel state, etc.; simulation results show that even under adverse conditions such as channel changes and low signal-to-noise ratio, the method of the present invention still maintains good synchronization performance. The present invention takes into account the actual application scenarios of Wi-Fi, the algorithm has anti-interference ability, and has better synchronization performance than traditional algorithms.

[0006] Symbols used in this article: Bold uppercase letters are matrices, bold lowercase letters are column vectors. I is the unit matrix. (·) T , (·) * and(·) H They are transpose, conjugate, and conjugate transpose, respectively. (·) -1 Indicates the inverse, represents the pseudo-inverse. diag(A) represents the column vector consisting of the diagonal elements of A, and diag(a) represents the diagonal matrix with the elements in a as the diagonal elements. vec(·) represents column vectorization. ‖·‖2 represents the Euclidean norm, ‖·‖F represents the Frobenius norm. E{·} represents the expectation. FFT(a) represents the fast Fourier transform of vector a, IFFT(a) represents the inverse fast Fourier transform of vector a,

[0007] The anti-interference Wi-Fi synchronization algorithm provided by the present invention has the following specific steps:

[0008] The first step is to define the synchronization sequence specified by the Wi-Fi protocol as s, where s is the FFT transform of the first sixty-four sampling points of the L-STF sequence, and the length is N = 64. Since there are values ​​on 12 subcarriers of the s sequence, and the amplitude of the other 52 subcarriers is 0, let the coordinate set corresponding to the subcarriers with subcarrier amplitude 0 be T1, and the coordinate set corresponding to the subcarriers with signals be T2. Consider the hypothesis test: H0 means that the receiver does not receive the target signal, and H1 means that the receiver receives the target signal. The received signal is defined as y(n), which is expressed as follows:

[0009] H0∶y(n)=z(n)#(1)

[0010] H1:y(n)=s(n)+z(n)#(2)

[0011] Where z(n) is additive complex Gaussian white noise, satisfying the distribution is the noise variance. Consider the number of receiving antennas is M r ,definition:

[0012]

[0013]

[0014]

[0015] In the formula, Indicates M r A complex matrix with N rows and N columns, Indicates M r Line M r A complex matrix of columns, Indicates M r -dimensional column vector.

[0016] The design statistic θ(k) is as follows:

[0017] θ(k)=r(k) H Q(k) -1 r(k) #(6)

[0018] If there is no target signal in the received signal, that is, y(n) = z(n);

[0019] For r(k) H Q(k) -1 r(k), it is known that r(k) and Q(k) are independent of each other.

[0020] Define R(k) to satisfy:

[0021] r(k)~CN(0,R(k))#(7)

[0022] make but And there exists a unitary matrix U(k) such that:

[0023]

[0024] but

[0025] make

[0026] You can get:

[0027]

[0028] because For the numerator of θ(k), we have:

[0029] For the denominator The following lemma is known:

[0030] For the matrix Its elements obey the standard complex Gaussian distribution with independent and identical distribution, that is, h ij ~N(0,1),1≤i≤M,1≤j≤N, define h n is the nth column of H, H n Delete h from matrix H n The sub-matrix after , then is:

[0031]

[0032] For the matrix H whose elements obey the distribution specified above, we have:

[0033]

[0034] For have

[0035]

[0036] make Then we have:

[0037]

[0038] Therefore, from formula (12) in the lemma, we can see that Where L is the number of elements in set T1, L = 52, M r =4.

[0039] Therefore, for the estimator θ(k), we have:

[0040]

[0041] Substitute L = 52, M into formula (15) r =4, we can get, It obeys the F distribution with a degree of freedom of (8.98). In order to facilitate the threshold judgment, consider Right now It follows an F distribution with (8.98) degrees of freedom.

[0042] When the estimated Receiving H0, it is considered that the receiver does not receive the target signal, so the false alarm probability is given by R 2 satisfy:

[0043]

[0044] According to the above analysis, the processed estimator obeys a specific F distribution, so the false alarm probability is set According to the quantile table of F distribution, we can get R 2 Table 1 gives the value of different false alarm probabilities. The corresponding threshold R when taking the value 2 .

[0045] Table 1 Quantile table of F distribution with degrees of freedom (8.98)

[0046]

[0047] Since this synchronization algorithm is performed in the frequency domain, its core is that when y(n) = z(n), the estimated quantity have:

[0048]

[0049] It should be noted that when the received signal is a signal plus noise (without the target signal), if the interference also obeys the Gaussian distribution, then for the estimated quantity, the distribution it obeys does not change, and the above CFAR detector can play an anti-interference role.

[0050] In the second step, according to the random variable obeying the F distribution modeled by the received signal in the first step, constant false alarm probability (CFAR) detection can be implemented to synchronize the received signal.

[0051] In the second step, the received signal is synchronized through constant false alarm probability (CFAR) detection. The specific process is as follows:

[0052] (1) Based on the given false alarm probability The corresponding detection threshold R is obtained by using the F distribution quantile table shown in Table 1 2 ;

[0053] (2) Calculate the estimated value of the received signal modeling according to the first step

[0054] (3) Compare the estimated value with the threshold. If the estimated value is less than the threshold, calculate the estimated value corresponding to the next sampling point.

[0055] (4) Repeat steps (2) to (3). When the estimated value is greater than the threshold, it indicates that the target signal is detected. The sampling position at this time is output, and the synchronization process is completed.

[0056] Advantages of the method of the present invention:

[0057] (1) Compared with the traditional Schmidl&Cox synchronization algorithm, the constant false alarm probability detection algorithm significantly improves the synchronization accuracy.

[0058] (2) When the received signal is a signal plus noise (no target signal), if the interference also obeys the Gaussian distribution, then for the estimated quantity, the distribution it obeys does not change, and this algorithm can play an anti-interference role. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 The figure is a flowchart of the method of the present invention.

[0060] Figure 2 is the quantile-quantile plot of the estimator and the F-distributed random variable.

[0061] Figure 3 This is a performance comparison curve between the constant false alarm probability detection algorithm and the traditional synchronization algorithm.

[0062] Figure 4 This is a performance comparison curve between the constant false alarm probability detection algorithm and the traditional synchronization algorithm in the presence of interference. DETAILED DESCRIPTION

[0063] The present invention uses a computer to simulate the process of synchronizing the received signal by a Wi-Fi receiver, sets a non-target sequence in the transmitted signal, that is, applies the algorithm of the present invention when receiving a pure noise signal, and calculates the received signal to obtain an estimated value. And by extracting the estimator The Quantile-Quantile plot is drawn using the sample data of a random variable drawn from an F distribution with (8.98) degrees of freedom. Figure 2 It is a quantile-quantile plot of the estimator and the random variable that obeys the corresponding F distribution. The quantile-quantile plot can determine whether the sample is close to a certain distribution, or verify whether two sets of data come from the same distribution. Figure 2 The horizontal axis represents the estimated The quantile of the sample data, the ordinate represents the quantile of the random variable that obeys the F distribution. From the figure, we can see that the scattered points are basically distributed near the straight line y=x, and to a certain extent, it can be considered that the two belong to the same distribution. Figure 2 It can be concluded that the statistics obtained by the simulator when there is no signal The quantiles are basically consistent with those of random variables that obey the theoretical corresponding F distribution, which verifies the theoretical accuracy and effectiveness of the CFAR detector.

[0064] The present invention uses a computer to simulate the process of synchronizing the received signal of the Wi-Fi system receiver, sets a target sequence in the transmitted signal, and respectively applies the traditional S&C algorithm and the algorithm of the present invention to synchronize the received signal to determine whether the target signal is received. The simulation is set under the Rayleigh channel, the number of receiving antennas is 4, the threshold of the traditional S&C algorithm is set to 0.8, and the false alarm probability of the algorithm of the present invention is set to 10 -7 , the corresponding threshold is 7.4609, and 10,000 Monte Carlo experiments are performed. Based on the number of times the target signal is received, the reception probability is calculated to draw a performance comparison curve to judge the synchronization ability of different algorithms. Figure 3 This is a performance comparison curve between the constant false alarm probability detection algorithm and the traditional synchronization algorithm. Figure 3 The traditional S&C algorithm (the red dotted line on the right) calculates the cross-correlation value of the repeated pilots and realizes synchronization by determining the normalized cross-correlation value and the size of the threshold. The CFAR detection algorithm (the black dotted line on the left) corresponds to the algorithm of the present invention. It can be seen that the synchronization performance of the constant false alarm probability detection algorithm proposed by the present invention is improved by 8-9dB compared with the traditional S&C algorithm. Since the Schmidl&Cox algorithm sets the threshold according to experience, and the calculation of the cross-correlation value is affected by factors such as noise power and channel state, synchronization is inaccurate. The statistics used by the constant false alarm probability detection algorithm proposed by the present invention obey a specific distribution, and its false alarm probability only depends on the setting of the threshold, and is independent of noise power, channel state, etc., so better synchronization performance can be achieved than the traditional algorithm.

[0065] Figure 4The performance comparison curve of the constant false alarm probability detection algorithm and the traditional synchronization algorithm in the case of interference. The simulation is set in Rayleigh channel, the threshold of the traditional S&C algorithm is set to 0.8, and the false alarm probability of the algorithm of the present invention is set to 10 -7 , the corresponding threshold is 7.4609, and an interference signal obeying a Gaussian distribution is applied, the signal-to-interference ratio is set to -5dB, 10,000 Monte Carlo experiments are performed respectively, and the reception probability is calculated based on the number of times the target signal is received to draw a performance comparison curve. Comparing the traditional S&C algorithm (the red dotted line with dots on the right) and the CFAR detection algorithm proposed in the present invention (the brown dotted line with dots on the left), it can be seen that the synchronization performance of the constant false alarm probability detection algorithm proposed in the present invention is improved by 11-12dB compared with the traditional S&C algorithm. Because when the received signal receives interference plus noise (no target signal), if the interference also obeys a Gaussian distribution, the distribution obeyed by the estimator does not change. Therefore, in the presence of interference, the synchronization performance of the algorithm proposed in the present invention is not greatly affected, while the performance of the traditional S&C algorithm is significantly deteriorated by interference. Figure 4 The change of synchronization probability verifies this conclusion and reflects the superiority of the algorithm proposed in the present invention.

[0066] References:

[0067] [1]Y.Jiang, B.Daneshrad and GJPottie, "A Practical Approach to JointTiming, Frequency Synchronization and Channel Estimation for ConcurrentTransmissions in a MANET," in IEEE Transactions on Wireless Communications, vol.16, no.6,

[0068] pp.3461-3475.

[0069] [2] Y.Jiang, MKVaranasi and J.Li, "Performance Analysis of ZF and MMSEEqualizersfor MIMO Systems: An In-Depth Study of the High SNR Regime," in IEEETransactionson Information Theory, vol.57, no.4, pp.2008-2026.

[0070] [3]Schmidl T M,Cox D C.Robust frequency and timing synchronizationfor OFDM[J].

[0071] IEEE transactions on communications,1997,45(12):1613-1621。

Claims

1. An anti-interference Wi-Fi synchronization method, characterized in that: The specific steps are as follows: The first step is to define the synchronization sequence specified by the Wi-Fi protocol as s, where s is the FFT transform of the first sixty-four sampling points of the L-STF sequence, and the length is N = 64; there are values ​​on 12 subcarriers of the s sequence, and the amplitude of the other 52 subcarriers is 0. Let the coordinate set corresponding to the subcarriers with subcarrier amplitude 0 be T1, and the coordinate set corresponding to the subcarriers with signals be T2. Hypothesis test: H0 means that the receiver does not receive the target signal, and H1 means that the receiver receives the target signal. The received signal is defined as y(n), which is expressed as follows: H0∶y(n)=z(n)#(1) H1:y(n)=s(n)+z(n)#(2) Where z(n) is additive complex Gaussian white noise, satisfying the distribution is the noise variance; let the number of receiving antennas be M r ,definition: Indicates M r A complex matrix with N rows and N columns, Indicates M r Line M r A complex matrix of columns, Indicates M r dimensional column vector; The design statistic θ(k) is as follows: θ(k)=r(k) H Q(k) -1 r(k) #(6) If there is no target signal in the received signal, that is, y(n) = z(n); For r(k) H Q(k) -1 r(k), it is known that r(k) and Q(k) are independent of each other. Define R(k) to satisfy: make but And there exists a unitary matrix U(k) such that: but make get: because For the numerator of θ(k), we have: For the denominator The following lemma is known: For the matrix Its elements obey the standard complex Gaussian distribution of independent and identical distribution, that is, Define h n is the nth column of H, H n Delete h from matrix H n The sub-matrix after , then is: For the matrix H whose elements obey the distribution specified above, we have: According to the above lemma, for have: make Then we have: From formula (12) in the lemma, we can see that Where L is the number of elements in set T1, L = 52, M r =4; So, for the estimator θ(k), we have: Substitute L = 52, M into formula (15) r =4 to get: It obeys the F distribution with degrees of freedom (8, 98). In order to facilitate the threshold judgment, consider Right now It follows an F distribution with (8.98) degrees of freedom; When the estimated Less than the threshold R 2 , receiving H0, it is considered that the receiver has not received the target signal, and the false alarm probability is given as Threshold R 2 satisfy: The estimator follows a specific F distribution and sets the false alarm probability According to the quantile table of F distribution, we can get R 2 The value of Since the CFAR detection algorithm is performed in the frequency domain, when y(n) = z(n), the estimated have: In the second step, according to the random variable obeying the F distribution modeled by the received signal in the first step, constant false alarm probability detection is implemented to synchronize the received signal; Symbols used in this paper: Bold uppercase letters are matrices, bold lowercase letters are column vectors; I is the unit matrix; (·) T , (·) * and(·) H are transpose, conjugate, and conjugate transpose respectively; (·) -1 Indicates the inverse, represents pseudo-inverse; diag(A) represents the column vector consisting of the diagonal elements of A, diag(a) represents the diagonal matrix with the elements in a as diagonal elements, vec(·) represents column vectorization; ‖·‖2 represents the Euclidean norm, ‖·‖ F represents the Frobenius norm; E{·} represents expectation; FFT(a) represents fast Fourier transform of vector a; IFFT(a) represents inverse fast Fourier transform of vector a.

2. The anti-interference Wi-Fi synchronization method according to claim 1, characterized in that: In the first step, the quantile table of the F distribution is shown in Table 1 below: Table 1 Quantile table of F distribution with degrees of freedom (8.98) 。 3. The interference-resistant Wi-Fi synchronization method according to claim 2, characterized in that: In the second step, the received signal is synchronized through constant false alarm probability detection. The specific process is as follows: (1) According to the set false alarm probability The corresponding detection threshold R is obtained by using the F distribution quantile table shown in Table 1 2 ; (2) Calculate the estimated quantity of received signal modeling according to the first step (3) Compare the estimated value with the threshold. If the estimated value is less than the threshold, calculate the estimated value corresponding to the next sampling point. (4) Repeat steps (2) to (3). When the estimated value is greater than the threshold, it indicates that the target signal is detected. The sampling position at this time is output, and the synchronization process is completed.

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