A carrier frequency offset estimation method based on Newton orthogonal matching pursuit

Abstract

The application 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 specific steps of the application comprise the following steps: CFO is split into two parts of off-grid deviation and grid frequency, and then an observation signal is modeled as a parameter weighted compressed sensing problem; a Newton orthogonal matching pursuit algorithm is used to respectively iteratively optimize the estimation of the off-grid deviation and the grid frequency of CFO, so that a CFO candidate frequency set is obtained; preamble information of a target user is used to obtain a required CFO estimation result from the candidate set. The application can meet the actual system complexity requirement, significantly improve the precision of CFO estimation, and has good robustness.

Description

Technical Field

[0001] This invention belongs to the field of frequency offset estimation technology, and specifically relates to a carrier frequency offset estimation method. Background Technology

[0002] With the continuous development of passive IoT technology, its application in the field of wireless communication is becoming increasingly widespread. This type of technology utilizes radio frequency (RF) signals, light energy, and heat energy in the environment to enable devices to power themselves autonomously. However, during data transmission, low-cost, low-power IoT terminals often face carrier frequency offset issues due to imperfect crystal oscillator characteristics, which affects data decoding and system performance.

[0003] In traditional communication systems, phase-locked loops (PLLs) are widely used for carrier frequency offset (CFO) estimation due to their high accuracy. However, the complex implementation of PLLs is often unacceptable for passive IoT systems. Traditional passive IoT RFID systems, due to their lower transmission rates and shorter transmission times, are relatively less affected by CFO and typically use Fast Fourier Transform (FFT) for CFO estimation. However, with the development of emerging passive IoT communication systems, their transmission times and rates have increased significantly, making it difficult to meet the high accuracy requirements by relying solely on FFT methods. Summary of the Invention

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

[0005] In passive IoT frequency division multiple access (FDMA) systems, users share the system's bandwidth resources. To fully utilize the bandwidth, the frequency spacing between different transmitters is very small; however, due to the high carrier fundamental frequency, the absolute frequency offset of the receiver's local oscillator is large. To ensure that the target signal is not filtered out, in practical designs, the bandwidth of the receiving filter and down-conversion filter is usually increased, leading to the introduction of out-of-band user uncertainty interference into the intermediate frequency (IF) signal. Based on this, the IF signal after down-conversion at the receiver can be expressed as:

[0006]

[0007] Where K is the total number of users; α i For transmitter i activity; h i η is the channel between transmitter i and receiver; i For transmitter i, the baseband symbol; F iIn an ideal, frequency-off-bias-free scenario, the reference frequency of user i's RF signal after down-conversion by a specific target receiver is ΔF, where ΔF is the frequency offset between the receiver and the target transmitter; T S is the oversampling time interval of the ADC during intermediate frequency signal analog-to-digital conversion; m is the sampling point number; w is the additive white Gaussian noise introduced during signal transmission, and w~CN(w; 0,σ) 2 I)).

[0008] The carrier frequency offset estimation method provided by this invention includes a Newtonized Orthogonal Matching Pursuit (NOMP) algorithm (hereinafter referred to as the Newton method) for carrier frequency offset estimation in multi-user passive IoT systems. The specific steps are shown below. It should be noted that, since the algorithm involves an iterative process, the superscript t of each variable in the relevant formulas represents the number of iterations.

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

[0010] Observing the frequency offset estimation problem form 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 onto the oversampled DFT frequency grid A, and define the grid frequencies corresponding to the non-zero elements of the frequency grid coefficient x as the candidate grid frequency set of CFO; correspondingly, we define the frequency interval between the real CFO and its nearby grid frequencies as the off-grid deviation of CFO. After obtaining the two frequency estimates, the candidate frequency set of CFO can be obtained by summing them. Then, using the preamble sequence known to both the transmitter and receiver, the CFO estimate can be screened. 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 the CFO; f i This indicates the frequency of the oversampled DFT grid.

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

[0014]

[0015] In the formula, the ⊙ operator represents the Hadmar product of vectors. Equation (2) is the parameter-weighted compressed sensing form. After estimating the off-network bias Δf, the influence of the phase weight can be removed, and it can be rewritten as the standard compressed sensing problem form.

[0016] Step (2) uses Newton's method to optimize the estimation of the off-grid deviation Δf part of CFO;

[0017] According to equation (3), the joint likelihood function of the DFT grid coefficient x and the 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] Where, x I The frequency grid coefficients x form a subvector composed of the estimated active elements; A I It is x I The submatrix formed by the corresponding columns in the oversampled DFT grid A;

[0020] Point estimation of the input activity coefficient Substituting into equation (4), the above equation can be approximated as:

[0021]

[0022] Therefore, the estimate of Δf is updated using Newton's method; the goal is to obtain the maximum likelihood estimate of Δf. * ,Right now:

[0023]

[0024] Before using Newton's method, consider 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) uses an OMP-type algorithm to estimate the activity coefficient x of the DFT frequency grid A. IThen return to step (2) for iterative optimization until the convergence condition is met, and obtain the candidate frequency set of CFO; specifically including:

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

[0031]

[0032] Step (3.2), jump to step (2), and set x I (t) Substituting into equation (7), 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 a new matrix A composed of the active columns of matrix A using a projection method. I Above, that is:

[0034]

[0035] in, Representing matrix A I The false reversal;

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

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

[0038] When y (t+1) ⊙e(-Δf (t) The iteration stops when the energy projected onto each column of A is less than the threshold.

[0039] The threshold τ is set only by 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 formula for calculating the Rao test statistic for binary hypothesis testing problems is as follows:

[0041]

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

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

[0044]

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

[0046]

[0047] Therefore, the threshold is:

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

[0049] In this invention, a compressed sensing algorithm is introduced to achieve high-precision and low-complexity frequency offset estimation. Compared with the sparse Bayesian learning algorithm commonly used for spectrum estimation, the orthogonal matching pursuit algorithm has a significant advantage in terms of implementation complexity, and is therefore more suitable for low-complexity and low-power passive IoT scenarios.

[0050] The traditional Orthogonal Matching Pursuit (OMP) algorithm is a gridded frequency estimation method, and its final frequency estimate must lie on the grid points, which limits the estimation accuracy of the OMP algorithm. To address this, this invention estimates the off-grid deviation using Newton's method, achieving high-precision off-grid estimation of CFO on a coarse grid. The NOMP algorithm of this invention uses a coarse grid instead of a fine grid, which reduces the algorithm's complexity and also reduces the correlation of the sensing matrix, thus ensuring the algorithm's convergence.

[0051] The Newton orthogonal matching pursuit scheme proposed in this invention significantly improves the accuracy of CFO estimation while meeting the complexity requirements of practical systems, and also exhibits good robustness. Compared to the FFT scheme currently used in passive IoT systems, the NOMP-based frequency offset estimation method can still achieve high-precision estimation of the CFO of IoT terminals even when dealing with a large number of interference frequencies. Attached Figure Description

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

[0053] Figure 2 This is a schematic diagram of the principle of the present invention.

[0054] Figure 3 The MSE comparison chart of the CFO estimation error between the algorithm of this invention and the traditional FFT algorithm under conditions of less interference is shown.

[0055] Figure 4 The MSE comparison chart of the CFO estimation error between the algorithm of this invention and the traditional FFT algorithm under conditions of greater interference is shown. Detailed Implementation

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

[0057] Figure 1 The system model of this invention is described. The passive IoT communication system of this invention employs frequency division multiplexing. Considering the downlink scenario, the baseband signals from transmitters on different base stations are modulated using on-off keying (OOK) on high-frequency carriers with a frequency difference of 200kHz. After passing through a transmit filter, the signals are sent to the IoT terminal. Then, after passing through a receive filter, the signals are mixed with a carrier wave containing frequency offset generated by the local oscillator of the IoT terminal, and a low-pass filter is used to retain the intermediate frequency (IF) portion of the signal. Finally, the signals are converted into digital signals by an analog-to-digital converter, and the carrier frequency offset is estimated using the Newton-Orthogonal Matched Pursuit algorithm of this invention.

[0058] Figure 2 The present invention is illustrated in the schematic diagram. The specific implementation steps are as follows:

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

[0060]

[0061] Based on the accuracy requirements of the actual system, the frequency range of the DFT frequency grid A for signal mapping is [-2.2MHz, 2.2MHz], and the grid spacing is 100kHz. Therefore, the number of frequency grid points (columns) in A is 45. Furthermore, in the actual system, the symbol rate is 90kbps, while the ADC sampling frequency is 4.5MHz. Therefore, there are approximately 50 sampling points within one symbol interval. We select the first 45 sampling points for CFO estimation, so M = 45. In other words, the number of rows in 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 Δf of CFO.

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

[0065] Based on the derivation of the loss function, for Δf and x I The initialization method is as follows:

[0066]

[0067]

[0068] Where Δf'∈{-50,-40,...,40,50}kHz, {a} sup The operation refers to taking elements from vector a that are greater than a given threshold of 0.5 to form a new vector.

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

[0070]

[0071] Therefore, in Newton's method, we adopt 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) utilizes the column vectors a of frequency grid A. i and the residual part y of the observation vector (t) Perform the inner product and find the location of the maximum value; this is the new active frequency. 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 set x I (t) Substitute Δf (t-1) Updated to Δf (t) ;

[0079] Step (3.3) utilizes Δf (t) Update x again I (t) We use a projection method to project the observation vectors onto a new matrix A composed of the active columns of matrix A. I Above, that is:

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

[0081] When y (t+1) ⊙e(-Δf (t) The iteration stops when the energy projected in each column of A is less than the threshold τ. The threshold is set in relation to the set false alarm probability P. FA (In the specific implementation, P) FA This is related to setting it 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 as follows: the mixing frequency is adjusted by using the frequencies in the candidate CFO set in turn until the target preamble is successfully decoded and the CFO estimation result is obtained.

[0084] Figure 3 The figure shows the MSE of CFO estimation using the NOMP algorithm and the FFT method with the same number of points under 1000 Monte Carlo simulations with a small number of interference frequencies (1). As can be seen from the figure, the FFT method struggles to achieve high accuracy due to limitations in grid precision. The NOMP algorithm proposed in this invention significantly outperforms the former across the entire signal-to-noise ratio range, and even reaches the Cramer-Rao boundary in the high signal-to-noise ratio range. This demonstrates the high accuracy of the NOMP algorithm for CFO estimation.

[0085] Figure 4The figure shows the MSE of CFO estimation for the NOMP algorithm and the FFT method with the same number of points under 1000 Monte Carlo simulations with a large number of interference frequencies (9). As can be seen from the figure, the NOMP algorithm maintains good CFO estimation performance even with more interfering transmitters. This demonstrates the strong robustness of the NOMP algorithm against interference.

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

[0087] The above description is only a partial embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A carrier frequency offset estimation method based on Newton's orthogonal matched pursuit, in a passive Internet of Things (IoT) frequency division multiple access (FDMA) system, the intermediate frequency signal after down-conversion at the receiver is represented as: in, K represents the total number of users; α i For transmitter i activity; h i This is the channel between transmitter i and receiver i; η i For transmitter i, the baseband symbol; F i In an ideal, frequency-off-bias-free scenario, the reference frequency of user i's RF signal after down-conversion by a specific target receiver is ΔF, where ΔF is the frequency offset between the receiver and the target transmitter; T S For intermediate frequency signal analog-to-digital conversion, m is the oversampling time interval of the ADC; m is the sampling point number; w is the additive white Gaussian noise introduced during signal transmission, i.e., w ~ CN(w; 0, σ 2 I); characterized by designing a Newton Orthogonal Matching Pursuit Algorithm (NOMP), or simply Newton's method, for carrier frequency offset estimation in a multi-user passive Internet of Things system, the specific steps of which are as follows: Step (1) decomposes the carrier frequency offset (CFO) into two frequency components: off-grid offset and grid frequency, and then models the observed signal as a parameter-weighted compressed sensing problem; Step (2) uses Newton's method to optimize the estimation of the off-grid deviation Δf part of CFO; Step (3) uses the orthogonal matching pursuit algorithm to estimate the active coefficient vector x of the DFT frequency grid A. I Then return to step (2) to perform iterative optimization until the convergence condition is met, and obtain the candidate frequency set of CFO; Step (4): After obtaining the candidate frequency set, select the frequencies in the candidate frequency set in sequence, adjust the mixer frequency of the receiver, replace the broadband filter with a narrowband filter, and decode the received signal; determine which candidate frequency is adjusted to decode the correct target transmitter preamble and 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 form 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 onto 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 CFO. Correspondingly, the frequency interval between the real CFO and its nearby grid frequencies is defined as the off-grid deviation of CFO. After obtaining the two frequency estimates, the candidate frequency set of CFO is obtained by summing them. Then, the CFO estimate is selected using the preamble sequence known to both the transmitter and receiver. Specifically: Equation (1) is modified as follows: Where Δf represents the off-grid deviation of the CFO; f i Indicates the frequency of the oversampled DFT grid; Let x i =α i h i η i Since the frequency grid coefficients are given, equation (2) can be written in the form y = Ax⊙e(Δf) + w, i.e.: In the formula, the ⊙ operator represents the Hadmar product of vectors; Equation (2) is the parameter-weighted compressed sensing form; after estimating the off-network deviation Δf, the influence of phase weight can be removed and it can be 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 equation (3), the joint likelihood function of the DFT grid coefficient x and the 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) Where, x I The frequency grid coefficients x are the active coefficient vector composed of the estimated active elements; A I It is x I The submatrix formed by the corresponding columns in the oversampled DFT grid A; Point estimation of the input activity coefficient Substituting into equation (4), the above equation is approximately: Therefore, the estimate of Δf is updated using Newton's method; the goal is to obtain the maximum likelihood estimate of Δf. * ,Right now: Before using Newton's method, consider Δf and x. I initialization; In Newton's method, the estimate of Δf is updated using the following formula: in:

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) utilizes the column vectors a of the oversampled DFT grid A. i and the residual part y of the observation vector (t) Perform the inner product and find the location of the maximum value, which is the new active frequency. Then update the active frequency set, i.e.: Step (3.2), jump to step (2), and set x I (t) Substituting into equation (7), 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 a new matrix A composed of the active columns of matrix A using a projection method. I Above, that is: in, Representing matrix A I The false reversal; Step (3.4) updates the residual part of the observation vector and determines whether to stop the algorithm iteration; the method for updating the residual part of the observation signal is as follows: y (t+1) =yA I x I ⊙e(Δf (t) ); (10) When y (t+1) ⊙e(-Δf (t) The iteration stops when the energy projected onto each column of A is less than the threshold.

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