Carrier frequency offset estimation method based on Newton orthogonal matching pursuit

Abstract

The invention belongs to the technical field of carrier frequency offset estimation, and particularly relates to a carrier frequency offset estimation method based on Newton orthogonal matching pursuit. The method comprises the following specific steps of: splitting CFO into two parts of frequencies, namely off-grid deviation and grid point frequency, and further modeling an observation signal as a parameter weighted compressed sensing problem; using a Newton orthogonal matching pursuit algorithm to iteratively optimize the off-grid deviation of the CFO and the estimation of the grid point frequency, and obtaining a CFO candidate frequency set; and obtaining a required CFO estimation result from the candidate set by using the lead code information of the target user. According to the method, the complexity requirement of an actual system is met, meanwhile, the precision of CFO estimation is remarkably improved, and good robustness is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of frequency offset estimation, and in particular relates to a carrier frequency offset estimation method. Background Art

[0002] With the continuous development of passive IoT technology, its application in the field of wireless communication has become more and more extensive. This type of technology uses radio frequency (RF) signals, light energy and thermal energy in the environment to realize autonomous power supply of devices. However, during data transmission, low-cost and low-power IoT terminals often face the problem of carrier frequency deviation due to unsatisfactory crystal oscillator characteristics, which will affect data decoding and system performance.

[0003] In traditional communication systems, phase-locked loop solutions are widely used to handle carrier frequency offset (CFO) estimation problems due to their high precision. However, for passive IoT systems, the complex implementation of phase-locked loops is often unacceptable. Traditional passive IoT RFID systems are relatively less susceptible to CFO due to their lower transmission rates and shorter transmission times, and usually use fast Fourier transform (FFT) for CFO estimation. However, with the development of emerging passive IoT communication systems, their transmission time and transmission rate have increased significantly, and relying solely on FFT methods can no longer meet the high-precision requirements. Summary of the invention

[0004] The purpose of the present invention is to provide a low-complexity, high-precision, and highly robust carrier frequency offset estimation algorithm for an Internet of Things terminal, so as to solve the problem of carrier frequency offset estimation in a passive Internet of Things frequency division multiple access (FDMA) system and improve the communication reliability of the system.

[0005] In the passive IoT frequency division multiple access (FDMA) system, users share the bandwidth resources of the system. In order to make full use of the frequency band resources, the frequency interval between different transmitters is very small; and because the carrier base frequency is very high, the absolute frequency deviation of the receiver local oscillator is very large. In order to ensure that the target signal is not filtered out, in actual design, the bandwidth of the receiving filter and the down-conversion filter is usually increased, resulting in the intermediate frequency signal being mixed with the uncertain interference of out-of-band users. Based on this, the intermediate frequency signal after down-conversion at the receiving end can be expressed as:

[0006]

[0007] Among them, K is the total number of users; α i is the activity of transmitter i; h i is the channel between transmitter i and receiver; η i is the baseband code element of transmitter i; F iis the reference frequency of the RF signal of user i after down-conversion by a specific target receiver under the ideal condition of no frequency deviation, ΔF is the frequency offset between the receiver and the target transmitter; T S is the oversampling time interval of ADC during analog-to-digital conversion of intermediate frequency signal; m is the serial number of sampling point; w is the additive Gaussian white noise introduced in the process of signal transmission, and w~CN(w;0,σ 2 I)).

[0008] The carrier frequency offset estimation method provided by the present invention designs a Newtonized Orthogonal Matching Pursuit (NOMP) algorithm (Newton method for short) for carrier frequency offset estimation of a multi-user passive Internet of Things system, and the specific steps are as follows. It should be pointed out that since the algorithm involves an iterative process, the superscript t of each variable in the formula involved represents the number of iterations.

[0009] Step (1), splitting the carrier frequency offset (CFO) into two frequencies: off-grid deviation and grid frequency, and then modeling the observed signal as a parameter-weighted compressed sensing problem;

[0010] Observe the form of the frequency offset estimation problem in equation (1). When the carrier frequency offset ΔF is greater than the reference frequency interval F1-F2, the solution to the problem is generally not unique, and the signal form needs to be further modified. Specifically, we map the signal to the oversampled DFT frequency grid A, and define the grid frequency corresponding to the non-zero elements of the frequency grid coefficient x as the candidate grid frequency set of the CFO; and correspondingly, define the frequency interval between the true CFO and the grid frequency near it as the off-grid deviation of the CFO. After obtaining the two-part frequency estimate, the candidate frequency set of the CFO can be obtained by adding them. Then, using the preamble code sequence known to both the transceiver and the transmitter, the estimate of the CFO can be screened out. Based on this idea, the present invention further modifies the signal form (1) to obtain:

[0011]

[0012] Where Δf represents the off-grid deviation of CFO; f i Represents the frequency of the oversampled DFT grid.

[0013] Let x i =α i h i η i is the frequency grid coefficient. I can write the problem in the form of y = Ax⊙e(Δf) + w, that is:

[0014]

[0015] In the formula, the ⊙ operator represents the Hadamard product of the vector. Formula (2) is the parameter weighted compressed sensing form. After estimating the off-grid deviation Δf, the influence of the phase weight can be removed and rewritten as the standard compressed sensing problem form.

[0016] Step (2), optimizing the estimation of the off-grid deviation Δf of the CFO using Newton's method;

[0017] According to formula (3), the joint likelihood function of DFT grid coefficient x and off-grid deviation Δf can be obtained:

[0018] P(y|x,Δf)=CN(y;Ax⊙e(Δf),σ 2 I))=CN(y;A I x I ⊙e(Δf),σ 2 I)), (4)

[0019] Among them, x I A refers to the subvector of the estimated active elements of the frequency grid coefficient x; I is x I The submatrix consisting of the corresponding columns in the oversampled DFT grid A;

[0020] The input activity coefficient point estimate Substituting into formula (4), the above formula can be approximated as:

[0021]

[0022] Therefore, the Newton method is used to update the estimate of Δf; the goal is to obtain the maximum likelihood estimate Δf * ,Right now:

[0023]

[0024] Before using Newton's method, Δf and x I initialization;

[0025] In Newton's method, the estimate of Δf is updated using the following formula:

[0026] in:

[0027]

[0028] χ=-j2πTs[0,1,...,N-1] T

[0029] Step (3), use the OMP algorithm to estimate the active coefficients x of the DFT frequency grid A I, and then return to step (2) to perform iterative optimization until the convergence condition is met to obtain the candidate frequency set of CFO; specifically, it includes:

[0030] Step (3.1) uses the column vectors a of the oversampled DFT grid A i and the residual part y of the observation vector (t) Do the inner product and find the location of the maximum value, which is the new active frequency, and then update the active frequency set, that is:

[0031]

[0032] Step (3.2), jump to step (2), and replace x I (t) Substituting into equation (7), we can get Δf (t-1) Updated to Δf (t) ;

[0033] Step (3.3), using Δf (t) , update x again I (t) Specifically, the observation vector is projected onto the new matrix A composed of the active columns of the A matrix using the projection method. I On, that is:

[0034]

[0035] in, Represents the matrix A I of pseudo-rebellion;

[0036] Step (3.4) updates the residual part of the observation vector and determines whether to stop the iteration of the algorithm; the method for updating the residual part of the observation signal is:

[0037] y (t+1) =yA I x I ⊙e(Δf (t) ); (10)

[0038] When (t+1) ⊙e(-Δf (t) ) The iteration is stopped when the energy of the projection on each column of A is less than the threshold;

[0039] Among them, the setting of the threshold τ is only related to the noise variance and the false alarm probability of the algorithm to achieve constant false alarm probability detection. Its specific value and derivation are as follows:

[0040] The Rao Test statistic calculation formula for binary hypothesis testing problems is:

[0041]

[0042] where θ = [Re{x},Im{x}] T , θ0=[0,0] T ;

[0043] Therefore, we can get the Rao test statistic for a specific problem, which is used to determine the binary hypothesis test problem: whether there are undetected frequency components in the residual part of the signal. The specific expression of the Rao test statistic obtained by calculation is:

[0044]

[0045] The Rao test statistic follows the standard chi-square distribution under the null hypothesis and is closely related to the false alarm probability. The specific expression is:

[0046]

[0047] So, the threshold:

[0048] Step (4), after obtaining the candidate frequency set, select the frequencies in the candidate frequency set in turn, adjust the mixing frequency of the receiver, and replace the broadband filter with a narrowband filter to decode the received signal; by determining which candidate frequency is adjusted to decode the correct target transmitter preamble code, determine the candidate frequency as the estimated value of CFO.

[0049] In the present invention, a compressed sensing algorithm is introduced to achieve high-precision, low-complexity frequency deviation estimation; in the compressed sensing algorithm, compared with the sparse Bayesian learning algorithm commonly used in spectrum estimation, the orthogonal matching pursuit algorithm has significant advantages in implementation complexity, and is therefore more suitable for low-complexity, low-power passive Internet of Things scenarios.

[0050] The traditional orthogonal matching pursuit algorithm (Orthogonal Matching Pursuit, OMP) is a gridded frequency estimation method, and its final frequency estimation result must be located on the grid point, which limits the estimation accuracy of the OMP algorithm. To this end, the present invention estimates the off-grid deviation through the Newton method, and realizes the off-grid estimation of CFO with high accuracy on the coarse grid. The NOMP algorithm of the present invention replaces the fine grid with a coarse grid, which reduces the complexity of the algorithm on the one hand, and on the other hand, reduces the correlation of the perception matrix, so that the convergence of the algorithm is guaranteed.

[0051] The Newton orthogonal matching pursuit scheme proposed in the present invention significantly improves the accuracy of CFO estimation while meeting the actual system complexity requirements, and has good robustness. Compared with the FFT scheme currently used in passive IoT systems, the frequency offset estimation method based on NOMP can still achieve high-precision estimation of the CFO of IoT terminals in the case of dealing with more interference frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a structural diagram of the passive Internet of Things system processed by the present invention.

[0053] Figure 2 It is a principle block diagram of the present invention.

[0054] Figure 3 This is a comparison chart of the MSE of the CFO estimation error between the algorithm of the present invention and the traditional FFT algorithm under the condition of less interference.

[0055] Figure 4 This is a comparison chart of the MSE of the CFO estimation error between the algorithm of the present invention and the traditional FFT algorithm under the condition of more interference. DETAILED DESCRIPTION

[0056] The present invention will be further described below in conjunction with the accompanying drawings:

[0057] Figure 1 The system model of the present invention is described. The passive Internet of Things communication system in the present invention adopts frequency division multiplexing. Considering the downlink scenario, the baseband signals of transmitters on different base station sides are modulated by on-off keying (OOK) on a high-frequency carrier with a frequency difference of 200kHz. After passing through the transmitting filter, the signal is sent to the Internet of Things terminal. Then, it passes through the receiving filter, and is mixed with the carrier with frequency deviation generated by the local oscillator of the Internet of Things terminal, and the intermediate frequency part of the signal is retained by a low-pass filter. Finally, it is converted into a digital signal through an analog-to-digital converter, and the carrier frequency deviation is estimated using the Newton orthogonal matching pursuit algorithm of the present invention.

[0058] Figure 2 This is a principle block diagram of the present invention, and the specific steps of implementation are:

[0059] Step (1) models the down-converted signal at the receiving end as a parameter-weighted compressed sensing problem. In an actual system, there are at most 12 interference transmitters in the passband, and the received signal within one symbol time can be expressed as:

[0060]

[0061] According to the actual system accuracy requirements, the frequency range of the DFT frequency grid A of the signal mapping is [-2.2MHz, 2.2MHz], and the grid interval is 100kHz, so the number of frequency grid points of A, that is, the number of columns, is 45. In addition, in the actual system, the symbol rate is 90kbps, and the ADC sampling frequency is 4.5MHz, so there are about 50 sampling points in one symbol interval. We select the first 45 sampling points for CFO estimation, so M = 45. In other words, the number of rows of the frequency grid A is 45. Therefore, the specific expression of the parameter weighted compressed sensing form of the intermediate frequency signal is:

[0062]

[0063] Step (2) uses Newton's method to estimate the off-grid deviation part Δf of CFO.

[0064] Step (2.1) Before using Newton's method, I initialization.

[0065] According to the derivation of the loss function, for Δf and x I The initialization method is:

[0066]

[0067]

[0068] where Δf'∈{-50,-40,...,40,50}kHz, {a} sup The operation is to take the elements in vector a that are greater than the given threshold 0.5 to form a new vector.

[0069] Step (2.2) uses Newton's method to update the estimate of Δf; the goal is to obtain the maximum likelihood estimate Δf * ,Right now:

[0070]

[0071] Therefore, in Newton's method, we use Update the estimate of Δf. Where:

[0072]

[0073] χ=-j2πTs[0,1,...,N-1] T ;

[0074] Step (3) uses an OMP-type algorithm to estimate the active grid frequency coefficients of the DFT frequency grid A.

[0075] Step (3.1) uses the frequency grid A column vector a i and the residual part y of the observation vector (t) Do the inner product and find the location of the maximum value, which is the new active frequency, and then update the active frequency set. That is:

[0076]

[0077] x I (t) =[x I (t-1) ;x m ]

[0078] Step (3.2), jump to step (2.2), and change x I (t) Substituting Δf (t-1) Updated to Δf (t) ;

[0079] Step (3.3) uses Δf (t) , update x again I (t) , we use the projection method to project the observation vector into the new matrix A composed of the active columns of the A matrix I On, that is:

[0080] Step (3.4) updates the residual part of the observation vector and determines whether to stop the iteration of the algorithm. The method for updating the residual part of the observation signal is: (t+1) =yA I x I ⊙e(Δf (t) ).

[0081] When (t+1) ⊙e(-Δf (t) ) The iteration is stopped when the energy of the projections of each column of A is less than the threshold τ. The setting of the threshold and the set false alarm probability P FA (In the specific implementation, P FA Set to 0.01), that is:

[0082]

[0083] In step (4), the CFO estimation result is obtained from the candidate frequency set. The specific method is: the frequencies in the candidate CFO set are used in turn, and the mixing frequency is adjusted until the target preamble code is successfully decoded to obtain the CFO estimation result.

[0084] Figure 3 The MSE of CFO estimation of NOMP algorithm and FFT method with the same number of points is shown under 1000 Monte Carlo simulations with less interference frequency (1). As can be seen from the figure, it is difficult for FFT method to achieve high accuracy due to the limitation of grid point accuracy. The NOMP algorithm proposed in the present invention is significantly better than the former in the entire signal-to-noise ratio range, and can fit to the Cramer-Rao bound in the high signal-to-noise ratio range. This reflects the high-precision characteristics of NOMP algorithm for CFO estimation.

[0085] Figure 4The MSE of CFO estimation of NOMP algorithm and FFT method with the same number of points is shown under 1000 Monte Carlo simulations when there are more interference frequencies (9). It can be seen from the figure that NOMP algorithm can still maintain good CFO estimation performance in the case of more interference transmitters. This shows that NOMP algorithm is very robust to interference.

[0086] In summary, the Newton orthogonal matching pursuit algorithm proposed in the present invention significantly improves the accuracy of CFO estimation while meeting the actual system complexity requirements and has good robustness.

[0087] The above descriptions are only some embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A carrier frequency offset estimation method based on Newton orthogonal matching pursuit. In the passive Internet of Things frequency division multiple access (FDMA) system, the intermediate frequency signal after down-conversion at the receiving end is expressed as: in, K is the total number of users; α i is the activity of transmitter i; h i is the channel between transmitter i and receiver; η i is the baseband code element of transmitter i; F i is the reference frequency of the RF signal of user i after down-conversion by a specific target receiver under the ideal condition of no frequency deviation, ΔF is the frequency offset between the receiver and the target transmitter; T S is the oversampling time interval of ADC during analog-to-digital conversion of intermediate frequency signal; m is the serial number of sampling point; w is the additive Gaussian white noise introduced in the process of signal transmission, and w~CN(w;0,σ 2 I)); It is characterized in that a Newton orthogonal matching pursuit algorithm (NOMP), referred to as Newton's method, is designed for carrier frequency offset estimation of a multi-user passive Internet of Things system, and the specific steps are as follows: Step (1), splitting the carrier frequency offset (CFO) into two frequencies: off-grid deviation and grid frequency, and then modeling the observed signal as a parameter-weighted compressed sensing problem; Step (2), optimizing the estimation of the off-grid deviation Δf of the CFO using Newton's method; Step (3), use the OMP algorithm to estimate the active coefficients x of the DFT frequency grid A I , then return to step (2) and perform iterative optimization until the convergence condition is met to obtain the candidate frequency set of CFO; Step (4), after obtaining the candidate frequency set, select the frequencies in the candidate frequency set in turn, adjust the mixing frequency of the receiver, and replace the broadband filter with a narrowband filter to decode the received signal; by determining which candidate frequency is adjusted to decode the correct target transmitter preamble code, determine the candidate frequency as the estimated value of CFO.

2. The carrier frequency offset estimation method according to claim 1, characterized in that: The specific process of step (1) is as follows: According to the frequency offset estimation problem in equation (1), when the carrier frequency offset ΔF is greater than the reference frequency interval F1-F2, the solution to the problem is not unique. Therefore, the signal form is modified. Specifically, the signal is mapped to the oversampled DFT frequency grid A, and the grid frequencies corresponding to the non-zero elements of the frequency grid coefficient x are defined as the candidate grid frequency set of the CFO. Correspondingly, the frequency interval between the real CFO and the grid frequency near it is defined as the off-grid deviation of the CFO. After obtaining the two-part frequency estimation, the candidate frequency set of the CFO is obtained by adding them together. Then, the preamble sequence known to both the transmitter and the receiver is used to screen out the CFO estimate. Specifically: Modify the signal form (1) to: Where Δf represents the off-grid deviation of CFO; f i represents the frequency of the oversampled DFT grid; Let x i =α i h i η i is the frequency grid coefficient, so the problem is written in the form of y = Ax⊙e(Δf) + w, that is: Where, the ⊙ operator represents the Hadamard product of the vector; Equation (2) is the parameter weighted compressed sensing form; after estimating the off-grid deviation Δf, the influence of the phase weight can be removed and rewritten as the standard compressed sensing problem form.

3. The carrier frequency offset estimation method according to claim 2, characterized in that: The specific process of step (2) is as follows: According to formula (3), the joint likelihood function of DFT grid coefficient x and off-grid deviation Δf is obtained: P(y|x,Δf)=CN(y;Ax⊙e(Δf),σ 2 I))=CN(y;A I x I ⊙e(Δf),σ 2 I)) , (4) Among them, x I A refers to the subvector of the estimated active elements of the frequency grid coefficient x; I is x I The submatrix consisting of the corresponding columns in the oversampled DFT grid A; The input activity coefficient point estimate Substituting into formula (4), the above formula is approximately: Therefore, the Newton method is used to update the estimate of Δf; the goal is to obtain the maximum likelihood estimate Δf * ,Right now: Before using Newton's method, Δf and x I initialization; In Newton's method, the estimate of Δf is updated using the following formula: in: x=-j2πTs[0,1,...,N-1] T 。 4. The carrier frequency offset estimation method according to claim 3, characterized in that: The specific process of step (3) is as follows: Step (3.1) uses the column vectors a of the oversampled DFT grid A i and the residual part y of the observation vector (t) Do the inner product and find the location of the maximum value, which is the new active frequency, and then update the active frequency set, that is: Step (3.2), jump to step (2), and replace x I (t) Substituting into equation (7), we can get Δf (t-1) Updated to Δf (t) ; Step (3.3), using Δf (t) , update x again I (t) Specifically, the observation vector is projected onto the new matrix A composed of the active columns of the A matrix using the projection method. I On, that is: in, Represents the matrix A I of pseudo-rebellion; Step (3.4) updates the residual part of the observation vector and determines whether to stop the iteration of the algorithm; the method for updating the residual part of the observation signal is: y (t+1) =yA I x I ⊙e(Δf (t) ); (10) When (t+1) ⊙e(-Δf (t) )The iteration is stopped when the energy of the projection on each column of A is less than the threshold.

5. The method for estimating carrier frequency offset according to claim 4, characterized in that: The setting of the threshold is only related to the noise variance and the false alarm probability of the algorithm to achieve constant false alarm probability detection. The specific value is calculated as follows: The Rao test statistic calculation formula for binary hypothesis testing problems is: where θ = [Re{x},Im{x}] T , θ0=[0,0] T ; Therefore, the Rao test statistic for a specific problem is obtained to determine the binary hypothesis test problem: whether there are undetected frequency components in the residual part of the signal; the specific expression of the Rao test statistic obtained by calculation is: The Rao test statistic follows the standard chi-square distribution under the null hypothesis and is closely related to the false alarm probability. The specific expression is: So, the threshold:

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