A method for extracting radio frequency fingerprints of broadband signals based on nonlinear features

Abstract

This invention discloses a method for extracting radio frequency fingerprints of broadband signals based on nonlinear features, comprising the following steps: extracting all preamble symbol groups from the received signal frame and performing preprocessing; constructing a matrix using the known preamble signal to obtain the vector value of the nonlinear coefficient mixed with multipath propagation; eliminating multipath effects based on the vector value to obtain a fingerprint value containing only nonlinear features; obtaining the nonlinear feature value of the mixture of nonlinear coefficient and local preamble based on linear convolution rules; and combining the above values ​​containing only nonlinear coefficients with the values ​​of the mixture of nonlinear coefficient and local preamble to provide a reliable transmitter identification method as a nonlinear fingerprint. The radio frequency fingerprint extraction method proposed in this invention is less affected by channel conditions and has high feature dimension scalability, thus providing a technical means for high-precision transmitter identification using radio frequency fingerprinting technology.

Description

Technical Field

[0001] This invention belongs to the field of information security technology and relates to a method for extracting radio frequency fingerprints of broadband signals based on nonlinear features. Background Technology

[0002] Radio frequency power amplifiers (PAs) are an indispensable component of wireless transmitting equipment. Due to their high efficiency, their operating point is always close to the saturation region, which leads to severe nonlinear effects and out-of-band radiation. Nonlinearity is an inherent characteristic of PAs. Due to variations in manufacturing processes, different amplifiers cannot have completely identical characteristics, meaning that no single transmitting device can have exactly the same nonlinear characteristics.

[0003] Nonlinearity is a characteristic inherent to power amplifier (PA) devices, resulting in long-term stability and uniqueness. This characteristic can be used to identify wireless transmitters and authenticate their identities, thereby protecting communication security. Currently, mathematical modeling of PAs is mainly divided into models with and without memory. Memoryless models are relatively simple, but in reality, all power amplifiers exhibit some degree of memory effect. Therefore, models with memory effect can comprehensively describe the characteristics of PAs in actual devices, but memory effect is generally too complex, making accurate parameter estimation difficult. In particular, the multipath channel in wireless communication is convolved with the transmitted signal, and RF fingerprints are also convolved with the transmitted signal to some extent. Removing multipath effects may affect RF fingerprint extraction, thus significantly limiting the accurate extraction of RF fingerprints. Furthermore, channel noise is also an interference factor in RF fingerprints, and accumulation operations can obscure the details of the RF fingerprint.

[0004] Due to environmental noise and multipath effects in wireless transmission channels, received signals can suffer severe distortion, making it extremely difficult to extract weak radio frequency fingerprint signals, especially for broadband signals. Based on currently available literature, no radio frequency fingerprint extraction method has yet been theoretically found that truly resists random noise and multipath effects. Summary of the Invention

[0005] To address the aforementioned issues, this invention seeks a breakthrough in the signal frame structure of wireless communication and proposes a broadband signal RF fingerprint extraction method based on nonlinear features. This method utilizes a series of operations between several symbols in the received frame preamble signal, including LS estimation, calculation of convolutional residual values, removal of the influence of channel multipath effects, and further extraction of the nonlinear RF fingerprint.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for extracting radio frequency fingerprints from broadband signals based on nonlinear features includes the following steps:

[0008] Step 1: The receiving end extracts all the preamble signals from the received signal and performs preprocessing operations on the preamble signals.

[0009] Step 2: Construct a matrix D that conforms to the power amplifier memory effect model based on the known preamble symbol d;

[0010] Step 3: Based on D and the received signal y, use parameter estimation methods to obtain the mixed value F, which includes the power amplifier nonlinear coefficient f and the multipath tap h.

[0011] Step 4: Calculate the ratio of the first term to the second term, the ratio of the second-to-last term to the last term, and the ratio of the sum of odd-numbered terms to the sum of even-numbered terms in F. The calculated values ​​only include the nonlinear coefficients of the power amplifier.

[0012] Step 5: Truncate the preamble signal, calculate the convolution residue of preambles of different lengths after passing through the power amplifier PA and the channel, add the corresponding convolution residue to the preamble group of different lengths and compare them to obtain the RF fingerprint value of the nonlinear coefficient mixed with the preamble d.

[0013] Furthermore, step 2 specifically includes the following process:

[0014] Let T be the linear convolution length resulting from channel taps and power amplifier memory effects; construct the following matrix and use the least squares (LS) method to find the corresponding T. here Let represent the mixed value of nonlinear coefficients and channel taps. When the number of standard signals d(l) is N, the interval [L,R] is artificially set, and it is assumed that T is within the interval [L,R]. Let M be any value within the interval, M∈[L,R]. Then, the matrix D corresponding to M is... (M) :

[0015]

[0016] d l The vector consisting of d(l) can be represented as:

[0017] d l =[d(l) |d(l)| 2 d(l) … |d(l)| 2K d(l)]

[0018] K represents the nonlinear order.

[0019] Furthermore, step 3 specifically includes the following process:

[0020] Based on D (M) The mixed value of the nonlinear coefficient and the channel tap can be obtained. Then M corresponds to for:

[0021]

[0022] Among them, (D) (M) ) -1 D represents (M) The inverse matrix is ​​obtained by repeating the above steps for values ​​in the interval [L,R].

[0023]

[0024] beg The ratio of the sum of odd-numbered terms to the sum of even-numbered terms of each vector within the vector is denoted as f, resulting in:

[0025] [f L …f M …f R ]

[0026] Calculate the variance of several consecutive f values, select the point where the value changes abruptly, and use this point as the estimated location of T; based on D... (M) Construct the corresponding D (T) Take its LS estimate as

[0027]

[0028] Where f 2k+1,m h represents the nonlinear coefficient of the power amplifier. l L represents the channel tap, and L represents the channel tap length.

[0029] Furthermore, the parameter estimation method in step 3 is the least squares method.

[0030] Furthermore, step 4 specifically includes the following process:

[0031] Based on the results obtained in step 3 We obtain three fingerprints containing only nonlinear coefficients:

[0032]

[0033] end represents a vector The last item, end-1, indicates The second to last item.

[0034] Furthermore, step 5 includes the following sub-steps:

[0035] Step 5-1, find the convolution residues of different lengths of leader symbols: Based on point T, truncate the D obtained in step 3. (T) The last T rows of the matrix are then compared with the resulting matrix. Multiplication yields the corresponding convolutional residue I;

[0036] Step 5-2, calculate the sum of the preamble signal and I, expressed as:

[0037]

[0038] Where P i This indicates the end point of the truncated leader symbol, which is also the length of the truncated leader symbol. P represents i The sum of the received symbols, where d(i) is the local preamble, can be obtained by truncating preambles of different lengths and summing them:

[0039] S = [S P0 ,...,S Pi ,....,S Pn ]

[0040] Take any two elements S from S Pi S Pj The calculated hybrid nonlinear radio frequency fingerprint is as follows:

[0041]

[0042] The values ​​obtained in the above manner, which contain only nonlinear coefficients and the values ​​that combine nonlinear coefficients with the local preamble symbol d, are combined as nonlinear radio frequency fingerprints.

[0043] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0044] Compared with existing methods, the nonlinear radio frequency fingerprint extracted in this invention is less affected by the channel, has scalable feature dimensions, and is more accurate. Therefore, radio frequency fingerprinting technology can be used for high-precision transmitter identification. This method is applicable to communication systems with preamble frame structures composed of multiple different symbols, and is particularly suitable for broadband communication systems. Attached Figure Description

[0045] Figure 1 This is an overall flowchart of the present invention;

[0046] Figure 2 This is a schematic diagram of signal frame capture;

[0047] Figure 3 This is a diagram of the IEEE 802.11 OFDM preamble frame structure in an embodiment of the present invention;

[0048] Figure 4 The classic constellation diagram of the IEEE 802.11 nonlinear radio frequency fingerprint is extracted. Detailed Implementation

[0049] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0050] The following description uses the IEEE 802.11 communication system as an example to further illustrate the method implemented in this example. The present invention provides a nonlinear-based radio frequency fingerprint extraction method, the process of which is as follows: Figure 1 As shown, firstly, all preamble symbol groups are extracted from the received signal frame and preprocessed; a matrix is ​​constructed using the known preamble signal to obtain the vector value of the nonlinear coefficient and multipath mixture; the multipath effect is eliminated based on the vector value to obtain a fingerprint value containing only nonlinear features; the nonlinear feature value of the nonlinear coefficient and local preamble is obtained based on the linear convolution rule; combining the above values ​​containing only nonlinear coefficients with the values ​​of the nonlinear coefficient and local preamble mixture can provide a reliable transmitter identification method as a nonlinear fingerprint. Specifically, the present invention includes the following steps:

[0051] 1. Preamble signal acquisition and preprocessing

[0052] The frame structure of the OFDM preamble in the IEEE 802.11 communication system is as follows: Figure 3 As shown in the diagram. In this frame structure, the preamble is divided into two groups: short preambles and long preambles, each occupying 8µs. The short preamble group consists of 10 short preambles t1, t2, ..., t10, each consisting of 12 subcarriers; the long preamble group consists of two long preambles T1 and T2 and a cyclic prefix G12. In the receiver, a... Figure 2 The frame capture method shown captures the OFDM preamble frame from the received signal, and then performs preprocessing operations on the received signal to extract the OFDM preamble symbol.

[0053] 2. Determine the linear convolution length due to multipath propagation and power amplifier memory effects.

[0054] According to the technical requirements of the present invention, the transmitted signal is affected by the power amplifier memory effect and multipath propagation, resulting in a linear convolution tail of length T at the receiving end.

[0055] For 802.11 OFDM signals, at a sampling rate of 20MHz, the OFDM preamble frame length is 320, with the short and long preambles each occupying 160.

[0056] The local signal reaches the receiver after passing through the PA and undergoing multipath transmission. Using the memory polynomial model of the PA, the process of obtaining y(·) from the standard signal d after passing through the PA and multipath can be expressed as:

[0057]

[0058] Where h(·) represents the channel tap, n represents additive noise, and y(·) represents the received signal. Where f 2k+1,m d represents the nonlinear coefficient, K represents the nonlinear order, and M represents the number of memory layers in the PA. d(·) represents the standard signal, and L... h Indicates the channel tap length.

[0059] Representing it in matrix form is as follows:

[0060]

[0061] It is an L r ×(K+1)(M+L h ) matrix, L r L represents the length of the received signal. r =N+M+L h -1, where N represents the length of the local standard signal. It is a (K+1)(M+L) h A )×(K+1)(M+1) matrix. (M) It is composed of nonlinear coefficient f 2k+1,m The resulting vector, where n is additive noise. Assume... F can then be represented as:

[0062]

[0063] T represents the multipath length L h And the sum of the number of layers M of the power amplifier memory effect. Where L h Typically, the value is around 50, and M is less than 5. Therefore, based on experience, the range [L,R] of T is set within [5,55]. After setting the interval, iterate through each integer value within the interval, and for each integer value j, construct the corresponding D that conforms to the PA memory effect model structure. (j) Matrix D is constructed based on the known leading symbol d, and its construction process has been described in the invention description.

[0064] The corresponding algorithm for each j is obtained based on the LS algorithm.

[0065]

[0066] (·) +This represents the generalized inverse operation of a matrix, where D... (j) and They have the same structure. Find... Let f be the ratio of the sum of odd-numbered terms to the sum of even-numbered terms in each vector. We can obtain...

[0067] [f L …f j …f R ]

[0068] Calculate the variance of several consecutive f values, extract the point where the value changes abruptly, and use this point as the estimated location of T. 3. Calculate the fingerprint value containing only nonlinear coefficients based on the obtained T value.

[0069] Take the mixed nonlinear coefficients corresponding to T and the LS estimate of the multipath. pass The following three RF fingerprints containing only nonlinearity can be obtained:

[0070]

[0071] in Represents the sum of odd-numbered terms. Let f1 represent the sum of an even number of terms. The three fingerprints are denoted as f1, f2, and f3.

[0072] 4. Calculate the convolutional residues corresponding to different lengths of leading symbols and calculate the fingerprint values ​​of mixed nonlinearity.

[0073] Extract D as described in 3 (T) The last T rows will be used to obtain the matrix and... Multiplying yields the corresponding convolutional residue I. The sum of preamble signals of different lengths and their corresponding convolutional residues can be expressed as:

[0074]

[0075] Where P i The terminator represents the end point of the truncated preamble, which is also the length of the truncated preamble. d(i) is the local preamble, and y(t) is the corresponding preamble at the receiving end.

[0076] Find the corresponding S by arbitrarily selecting preamble signals of different lengths. Pi By combining any two sums, a hybrid nonlinear radio frequency fingerprint can be obtained:

[0077]

[0078] The values ​​containing nonlinear coefficients obtained through the above method are used as nonlinear radio frequency (RF) fingerprints. The fingerprints obtained above, which combine nonlinear features with the standard signal d, are sequentially denoted as f4, f5, f6, f7, f8, and f9. Combined with f1, f2, and f3, the resulting fingerprint values ​​are displayed on a two-dimensional plane, thus forming an RF fingerprint constellation diagram. The classic RF fingerprint constellation diagram formed using this example is shown below. Figure 4 As shown.

[0079] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A method for extracting radio frequency fingerprints of broadband signals based on nonlinear features, characterized in that, The method comprises the following steps: Step 1, the receiving end extracts all preamble symbols from the received signal and performs a preprocessing operation on the preamble symbols; Step 2, a matrix D conforming to a power amplifier memory effect model is constructed based on a known preamble symbol d; the step specifically comprises the following processes: The linear convolution length caused by channel taps and power amplifier memory effect is denoted as T; the following matrix is constructed Here represents the mixed value of nonlinear coefficient and channel tap, when the number of standard signals d(l) is N, the interval range [L, R] is artificially set, and it is assumed that T is within the interval [L, R], and an arbitrary value M within the interval is assumed, M ∈ [L, R], then the matrix D corresponding to M is (M) : d l is a vector composed of d(l), and is represented by: d l = [d(l) |d(l) 2 d(l) … |d(l) 2K d(l)] K represents a non-linear order; Step 3, a parameter estimation method is used to obtain a mixed value F containing a power amplifier non-linear coefficient f and a multi-path tap h based on D and the receiving end signal y; Step 4, a ratio of a first term to a second term, a ratio of a second last term to a first last term, a ratio of an odd term sum to an even term sum of F are obtained, and the obtained values only contain the non-linear coefficient of the power amplifier; Step 5, the preamble symbols are intercepted, convolution residues of preamble symbols of different lengths after passing through the power amplifier PA and the channel are obtained, and the non-linear coefficient and the radio frequency fingerprint value of the mixed preamble symbol d are obtained by adding and comparing groups of the preamble symbols of different lengths and the corresponding convolution residues.

2. The method of claim 1, wherein the nonlinear feature-based wideband signal RF fingerprinting method is characterized by, The parameter estimation method in step 3 is a least square method LS.

3. The method of claim 1 or 2, wherein, Step 3 specifically comprises the following processes: Based on D (M) , the mixed value of the nonlinear coefficient and the channel tap is obtained M corresponds to is: where (D (M) ) -1 represents the inverse matrix of D (M) , and the above steps are repeated for values in the interval [L, R]. Solve The ratio of the sum of the odd terms to the sum of the even terms in each vector is denoted by f and is found to be: [f L …f M …f R ] Calculate the variance of several consecutive f, intercept the point when the value occurs sharp change, and take the point as the estimated position of T; according to D (M) Construct the corresponding D (T) , take its LS estimate as : where f 2k+1,m represents the nonlinear coefficient of the power amplifier, h l is the channel tap, and L is the channel tap length.

4. The method of claim 1, wherein, Step 4 specifically comprises the following processes: The three fingerprints containing only the nonlinear coefficients are obtained from step 3 The three fingerprints containing only the nonlinear coefficients are obtained from step 3 end represents the last item of the vector end - 1 represents the second last item of the vector.

5. The method of claim 1, wherein, Step 5 comprises the following sub-steps: Step 5-1, finding the convolution residue of different length preambles: according to T points, cut the D matrix in step 3 (T) The last T rows of the matrix, multiply the obtained matrix with The corresponding convolution residue I is obtained; Step 5-2, the sum of the preamble symbols and I is calculated, and is represented as: where P i denotes the end point of the truncated preamble symbol, i.e. the length of the truncated preamble; denotes the sum of P i received end symbols, d(i) is the local preamble symbol, the preambles of different lengths are truncated and summed up to obtain the following values: S = [S P0 ,...,S Pi ,....,S Pn ] arbitrary taking out two elements S in S Pi , S Pj calculating the mixed nonlinear radio frequency fingerprint: The value obtained through the above method and only containing the non-linear coefficient and the value of the mixed non-linear coefficient and the local preamble symbol d are combined as the non-linear radio frequency fingerprint.

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