Joint estimation of timing offset and frequency offset for non-orthogonal multicarrier signals

Abstract

This invention discloses a joint estimation method for timing deviation and frequency offset of non-orthogonal multicarrier signals, relating to the field of information and communication technology. The method includes determining an observation window, performing correlation operations on the sampling points of the received signal within the observation window, and obtaining the result of the correlation operation; sliding the observation window and obtaining a timing deviation estimate based on the position of the peak value in the correlation operation result; obtaining multiple sampling points at the positions of the timing deviation estimate, and performing frequency offset estimation on these multiple sampling points to obtain the frequency offset estimate. This invention solves the problem in existing technologies where the non-orthogonal characteristics of the signals in non-orthogonal multicarrier transmission technology lead to inter-symbol interference and inter-subcarrier interference, resulting in a more complex autocovariance matrix of the received signal and making the design of timing deviation and carrier frequency offset estimation algorithms at the receiving end difficult. The proposed algorithm can adapt to different compression factors of non-orthogonal multicarrier signals in multipath channels and achieves better estimation performance.

Description

Technical Field

[0001] This invention relates to the field of information and communication technology, and in particular to a joint estimation method for timing deviation and frequency deviation of non-orthogonal multicarrier signals. Background Technology

[0002] Non-orthogonal multicarrier transmission technology reduces the occupied signal bandwidth by decreasing the spacing between subcarriers. Compared with traditional orthogonal frequency division multiplexing (OFDM) signals, the non-orthogonal nature of the signals in non-orthogonal multicarrier transmission technology leads to inter-symbol interference and inter-subcarrier interference, making the autocovariance matrix of the received signal more complex and posing certain difficulties for the design of timing offset estimation and carrier frequency offset estimation algorithms at the receiver. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a joint estimation method for timing deviation and frequency offset of non-orthogonal multi-carrier signals. This method solves the problem that the non-orthogonal characteristics of the signals in non-orthogonal multi-carrier transmission technology lead to inter-symbol interference and inter-subcarrier interference, which makes the autocovariance matrix of the received signal more complex and makes it difficult to design timing deviation estimation and carrier frequency offset estimation algorithms at the receiving end.

[0004] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0005] In a first aspect, the present invention provides a joint estimation method for timing deviation and frequency offset of non-orthogonal multicarrier signals, the method comprising:

[0006] Define the observation window, perform correlation calculations on the sampling points of the received signal within the observation window, and obtain the results of the correlation calculations;

[0007] Slide the observation window and obtain the estimated timing deviation value based on the position of the peak in the results of the relevant calculations;

[0008] Multiple sampling points are used to obtain the location of the timing deviation estimate, and frequency deviation is estimated for the multiple sampling points to obtain the frequency deviation estimate value;

[0009] The related operations include first performing conjugate operations, then multiplying the corresponding values ​​and summing them up.

[0010] In conjunction with the first aspect, it further includes initializing the receive buffer and acquiring the received signal before determining the observation window, and storing the sampling points of the received signal in the receive buffer.

[0011] In conjunction with the first aspect, further, acquiring the received signal includes:

[0012] The received signal is passed sequentially through a low-noise amplifier, a downconverter, and an analog-to-digital converter.

[0013] In conjunction with the first aspect, it further includes setting the observation window to the length of the loop prefix when determining the observation window, wherein the sliding distance of the observation window is one sampling point.

[0014] In conjunction with the first aspect, further, the frequency offset estimation of the multiple sampling points includes using a likelihood function to estimate the frequency offset of the multiple sampling points, wherein the expression of the likelihood function is:

[0015]

[0016] In the formula, n represents the sampling point number, ε represents the normalized carrier frequency offset, and e j2πε Represents complex exponentiation. This represents the nth sample point of the received signal. Represents the (n+N)th digit of the received signal. b The result after the conjugate operation of each sample point, N b N represents the number of samples for a symbol. CP Re represents the length of the cyclic prefix, Re{} represents the mathematical operation of taking the real part, and Λ(ε) represents the likelihood function of the normalized carrier frequency offset.

[0017] In conjunction with the first aspect, further, obtaining the frequency offset estimate includes obtaining the frequency offset estimate when the likelihood function reaches its maximum value, and the expression for the frequency offset estimate is:

[0018]

[0019]

[0020]

[0021] In the formula, C represents the frequency offset estimate. Im C represents the imaginary part of the result of the operation. Re The real part of the result is represented by , and Im{} represents the mathematical operation of taking the imaginary part.

[0022] Secondly, the present invention provides a joint estimation apparatus for timing deviation and frequency deviation of non-orthogonal multicarrier signals, comprising:

[0023] The window determination module is used to determine the observation window, perform correlation calculations on the sampling points of the received signals in the observation window, and obtain the results of the correlation calculations.

[0024] The sliding window module is used to slide the observation window and obtain the timing deviation estimate based on the position of the peak in the results of relevant calculations.

[0025] The frequency offset estimation module is used to obtain multiple sampling points at the estimated position of the timing offset, perform frequency offset estimation on the multiple sampling points, and obtain the frequency offset estimate value.

[0026] The related operations include first performing conjugate operations, then multiplying the corresponding values ​​and summing them up.

[0027] Thirdly, the present invention provides a joint estimation device for timing deviation and frequency deviation of non-orthogonal multicarrier signals, including a processor and a storage medium;

[0028] The storage medium is used to store instructions;

[0029] The processor is configured to operate according to the instructions to perform the steps of a joint estimation method for timing deviation and frequency offset of a non-orthogonal multicarrier signal as described in any of the first aspects.

[0030] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a joint estimation method for timing deviation and frequency deviation of a non-orthogonal multicarrier signal as described in any of the first aspects.

[0031] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0032] This invention discloses a joint estimation method for timing deviation and frequency offset of non-orthogonal multicarrier signals, relating to the field of information and communication technology. The method includes: determining an observation window; performing correlation operations on sampling points of the received signal within the observation window to obtain the correlation result; sliding the observation window and obtaining a timing deviation estimate based on the position of the peak value in the correlation result; obtaining multiple sampling points at the positions of the timing deviation estimate; and performing frequency offset estimation on the multiple sampling points to obtain the frequency offset estimate. The algorithm proposed in this invention can adapt to different compression factors of non-orthogonal multicarrier signals in multipath channels, avoids inter-symbol interference and inter-subcarrier interference caused by the non-orthogonal characteristics of the non-orthogonal multicarrier transmission technology signal itself, and achieves good estimation performance. Attached Figure Description

[0033] Figure 1 This is a flowchart of the steps of a joint estimation method for timing deviation and frequency offset of a non-orthogonal multicarrier signal provided in Embodiment 1 of the present invention;

[0034] Figure 2 This is a schematic diagram of the method for finding the peak position by performing correlation calculations in a joint estimation method for timing deviation and frequency deviation of a non-orthogonal multicarrier signal provided in Embodiment 1 of the present invention.

[0035] Figure 3 This is a schematic diagram showing the change of the likelihood function value of timing deviation estimation under different trial values ​​in a joint estimation method for timing deviation and frequency deviation of non-orthogonal multicarrier signals provided in Embodiment 1 of the present invention.

[0036] Figure 4 This is a schematic diagram illustrating how the timing deviation estimation performance changes with the signal-to-noise ratio in a joint estimation method for timing deviation and frequency deviation of a non-orthogonal multicarrier signal provided in Embodiment 1 of the present invention.

[0037] Figure 5 This is a schematic diagram illustrating the frequency offset estimation performance as the signal-to-noise ratio changes in a joint estimation method for timing deviation and frequency offset of a non-orthogonal multicarrier signal provided in Embodiment 1 of the present invention.

[0038] Figure 6 This is a schematic diagram illustrating the impact of residual timing deviation and residual carrier frequency deviation on bit error rate in a joint estimation method for timing deviation and frequency deviation of a non-orthogonal multicarrier signal provided in Embodiment 1 of the present invention. Detailed Implementation

[0039] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0040] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0041] Example 1:

[0042] Reference Figure 1 This invention provides a method for jointly estimating the timing deviation and frequency offset of a non-orthogonal multicarrier signal, comprising:

[0043] Define the observation window, perform correlation calculations on the sampling points of the received signal within the observation window, and obtain the results of the correlation calculations;

[0044] Slide the observation window and obtain the estimated timing deviation value based on the position of the peak in the results of the relevant calculations;

[0045] Multiple sampling points are used to obtain the location of the timing deviation estimate, and frequency deviation is estimated for the multiple sampling points to obtain the frequency deviation estimate value;

[0046] The related operations include first performing conjugate operations, then multiplying the corresponding values ​​and summing them up.

[0047] Specifically, the steps include the following:

[0048] Step 1: Initialize the receive buffer;

[0049] Initializing the receive buffer, parameter settings, and variables is to ensure that the wireless signal receiver can function properly.

[0050] Step 2: Receive signal;

[0051] After the receiver is initialized, it needs to acquire the received signal. Then, the acquired received signal is passed through a low-noise amplifier, a downconverter, and an analog-to-digital converter in sequence. The sampling points of the received signal are stored in the receiver's buffer for further processing.

[0052] Step 3: Define the observation window;

[0053] In wireless communication systems, since the length of the cyclic prefix (CP) and the number of samples per symbol are set before the data is transmitted, the receiver needs to set both observation windows to the length of the cyclic prefix and set the distance between the two observation windows to the number of samples per symbol.

[0054] Step 4: Perform correlation calculations on the sampling points of the received signal in the observation window and obtain the results of the correlation calculations;

[0055] like Figure 2 As shown, the sampling points of the received signal in the observation window are taken out and correlation operations are performed. The specific method of correlation operation is to first perform conjugate operation, then multiply the corresponding points, and finally sum them up.

[0056] Step 5: Store the results of the relevant calculations;

[0057] The relevant calculation results obtained in step 4 are stored in the buffer of the receiving end for subsequent comparison.

[0058] Step 6: Slide the observation window;

[0059] Once the previous correlation calculation result is completed and stored in the receiver's buffer, the observation window needs to be slid. The observation window slides a distance equal to one sampling point. Sliding the observation window is for performing correlation calculations and finding the position where the correlation peak is the largest.

[0060] Step 7: Obtain the estimated timing deviation value based on the position of the peak value in the results of the relevant calculations;

[0061] For all the relevant calculation results obtained in step 5, the positions of the peaks are identified. Since the cyclic prefix itself has strong correlation, correlation peaks will appear after the correlation calculations. In this embodiment, two correlation peaks will appear, and the positions of these two peaks correspond to the positions of the timing deviation estimates. Therefore, the estimated timing deviation is determined based on the positions of the peaks.

[0062] Step 8: Obtain multiple sampling points at the location of the timing deviation estimate, perform frequency deviation estimation on the multiple sampling points, and obtain the frequency deviation estimate value;

[0063] After obtaining the timing bias estimate, two sampling points corresponding to the two relevant peaks can be extracted for frequency bias estimation. Using the likelihood function to estimate the frequency bias of these multiple sampling points, the expression for the likelihood function can be obtained as follows:

[0064]

[0065] In the formula, n represents the sampling point number, ε represents the normalized carrier frequency offset, and e j2πε Represents complex exponentiation. This represents the nth sample point of the received signal. Represents the (n+N)th digit of the received signal. b The result after the conjugate operation of each sample point, N b N represents the number of samples for a symbol. CP Re represents the length of the cyclic prefix, Re{} represents the mathematical operation of taking the real part, and Λ(ε) represents the likelihood function of the normalized carrier frequency offset.

[0066] When the likelihood function reaches its maximum value, the normalized frequency offset estimate is obtained. The expression for the normalized frequency offset estimate is as follows:

[0067]

[0068]

[0069]

[0070] In the formula, C represents the frequency offset estimate. Im C represents the imaginary part of the result of the operation. Re The real part of the result is represented by , and Im{} represents the mathematical operation of taking the imaginary part.

[0071] Step 9: Output the results.

[0072] After the timing deviation estimation and frequency deviation estimation steps are completed, the estimated timing deviation value and the estimated frequency deviation value are output.

[0073] This embodiment verifies the performance of the proposed timing deviation estimation algorithm and frequency deviation estimation algorithm by using computer Monte Carlo simulation.

[0074] In the simulation diagram Figure 3 In the figure, the horizontal axis represents Trial value △ for STO (Symbol Timing Offset) estimation (sample), which means the situation when the timing offset value △ takes different values ​​during the experiment. Figure 3 The vertical axis represents the Value of Likelihood Function, which means the magnitude of the likelihood function value when the trial value Δ takes different values. Figure 3 Peak Location △ ML The peak position corresponding to the time-biased estimate is represented by Δ. ML .exist Figure 3 In this context, the SEFDM signal has a frequency domain compression factor of 0.5, a signal-to-noise ratio of 10 dB, a subcarrier number of M = 64, and a cyclic prefix length of N. c =16, the number of multipath channels is L=3, the amplitude of each sub-path follows a Rayleigh random distribution, and the total energy of the multipath taps is normalized. The normalized frequency offset is set to 0.1, and the oversampling factor of the received signal is 1. Figure 3 The simulation investigated the variation of the proposed likelihood function under different timing deviation trial values. When the likelihood function reaches its maximum value, the corresponding sample point location is the estimated value of the maximum likelihood timing deviation. Figure 3 The best estimate △ can be seen from this. ML =46, from which we can obtain the initial sample value of a SEFDM symbol. For trial value locations where the peak is far away, the peak of the proposed likelihood function is still obvious; however, when At this time, the values ​​of the likelihood functions do not differ much. The reason is that when the frequency domain compression factor of the SEFDM signal is 0.5, the SEFDM subcarriers are not orthogonal and have relatively serious interference.

[0075] In the simulation diagram Figure 4 In the diagram, the horizontal axis SNR (Signal-to-Noise Ratio) represents the signal-to-noise ratio. Figure 4The ordinate RMSE (Root Mean Square Error) of STO (Symbol Timing Offset) estimation (sample) represents the root mean square error of the timing offset estimation, and the magnitude of the timing offset is measured by the number of offset sampling points. Quad-Phase Shift Keying (QPSK) is used as the constellation point set. The frequency domain compression factors of SEFDM are set to ρ = 0.5, 0.7, and 0.9, respectively. When the frequency domain compression factor is ρ = 1.0, the SEFDM signal degenerates into an OFDM signal. The number of subcarriers is M = 64 and 128, and the length of the cyclic prefix is ​​N. cp =16. The signal-to-noise ratio (SNR) varies from 2dB to 24dB. Figure 4 The performance of the proposed SEFDM timing error estimation algorithm varies with signal-to-noise ratio (SNR). Simulations show that the estimation variance of the proposed algorithm gradually decreases as the SNR increases. Throughout the entire SNR range, the performance of the proposed SEFDM timing error estimation method approaches that of OFDM. Furthermore, even when the SEFDM frequency domain compression factor is reduced to 0.5 and severe interference exists between subcarriers, the proposed algorithm still achieves good timing error estimation performance. For SEFDM signals, the mutual interference between subcarriers becomes more severe with increasing number of non-orthogonal subcarriers, resulting in better timing error estimation performance at M=64 than at M=128.

[0076] In the simulation diagram Figure 5 In the diagram, the horizontal axis SNR (Signal-to-Noise Ratio) represents the signal-to-noise ratio. Figure 5 The ordinate MSE (Mean Square Error) of Normalized CFO (Carrier Frequency Offset) means the mean square error of the normalized frequency offset estimation. Figure 5 The results show that as the signal-to-noise ratio increases, the frequency offset estimation variance of the proposed algorithm gradually decreases, and it can adapt to different SEFDM frequency domain compression factors. When the number of subcarriers is 64, the proposed frequency offset estimation performance is better than that when the number of subcarriers is 128. This is because the higher the number of subcarriers, the lower the ratio of the cyclic prefix to the data length.

[0077] In the simulation diagram Figure 6 In the diagram, the horizontal axis SNR (Signal-to-Noise Ratio) represents the signal-to-noise ratio. Figure 6The vertical axis BER (Bit Error Rate) affected by Residual CFO (Carrier Frequency Offset) means the impact of different residual frequency offsets on the bit error rate. Figure 6 The simulation primarily investigated the impact of residual timing error and residual carrier frequency offset on the bit error rate (BER) of SEFDM signal transmission. During the simulation, the proposed timing error estimation algorithm was first used to estimate and correct the timing error of the received signal. Then, the frequency offset was estimated and corrected. Next, demodulation was performed based on the minimum mean square error criterion to obtain the bits, which were then compared with the transmitted bits to statistically determine the BER.

[0078] In summary, this invention discloses a joint estimation method for timing deviation and frequency offset of non-orthogonal multicarrier signals. Specifically, for non-orthogonal multicarrier (SEFDM) transmission systems, methods for estimating timing deviation and carrier frequency offset are designed. In the implementation process, correlation operations are performed on the sampling points of the received signal, and the correlation characteristics of the cyclic prefix itself are used to complete timing deviation estimation, and frequency offset estimation is then performed based on this. Simulation results show that in multipath channels, the proposed algorithm can adapt to different compression factors of non-orthogonal multicarrier signals and achieves good estimation performance.

[0079] Example 2:

[0080] This invention provides a joint estimation device for timing deviation and frequency deviation of non-orthogonal multicarrier signals, comprising:

[0081] The window determination module is used to determine the observation window, perform correlation calculations on the sampling points of the received signals in the observation window, and obtain the results of the correlation calculations.

[0082] The sliding window module is used to slide the observation window and obtain the timing deviation estimate based on the position of the peak in the results of relevant calculations.

[0083] The frequency offset estimation module is used to obtain multiple sampling points at the estimated position of the timing offset, perform frequency offset estimation on the multiple sampling points, and obtain the frequency offset estimate value.

[0084] The related operations include first performing conjugate operations, then multiplying the corresponding values ​​and summing them up.

[0085] Example 3:

[0086] This invention provides a device for jointly estimating timing deviation and frequency offset of non-orthogonal multicarrier signals, including a processor and a storage medium;

[0087] The storage medium is used to store instructions;

[0088] The processor is configured to operate according to instructions to perform steps according to any of the methods in Embodiment 1.

[0089] Example 4:

[0090] This invention provides a computer-readable storage medium storing a computer program thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of any of the methods in Embodiment 1.

[0091] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0092] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0093] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0094] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0095] The above description is only a preferred 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 technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A joint estimation method for timing deviation and frequency offset of non-orthogonal multicarrier signals, characterized in that, The method includes: Define the observation window, perform correlation calculations on the sampling points of the received signal within the observation window, and obtain the results of the correlation calculations; Slide the observation window and obtain the estimated timing deviation value based on the position of the peak in the results of the relevant calculations; Multiple sampling points are used to obtain the location of the timing deviation estimate, and frequency deviation is estimated for the multiple sampling points to obtain the frequency deviation estimate value; The related operations include first performing conjugate operations, then multiplying corresponding values ​​and summing them up; The frequency offset estimation of the multiple sampling points includes using a likelihood function to estimate the frequency offset of the multiple sampling points, wherein the expression of the likelihood function is: ； In the formula, n represents the sequence number of the sampling point. Indicates the normalized carrier frequency offset. Represents complex exponentiation. This represents the nth sample point of the received signal. Indicates the first received signal The result after the conjugate operation of each sample point Represents the number of samples for a symbol. Indicates the length of the cyclic prefix. Mathematical operations that take the real part. This represents the likelihood function for the normalized carrier frequency offset.

2. The method for jointly estimating timing deviation and frequency offset of non-orthogonal multicarrier signals according to claim 1, characterized in that, It also includes initializing the receive buffer and acquiring the received signal before determining the observation window, and storing the sampling points of the received signal in the receive buffer.

3. The method for jointly estimating timing deviation and frequency offset of non-orthogonal multicarrier signals according to claim 2, characterized in that, The acquisition of the received signal includes: The received signal is passed sequentially through a low-noise amplifier, a downconverter, and an analog-to-digital converter.

4. The method for jointly estimating timing deviation and frequency offset of non-orthogonal multicarrier signals according to claim 1, characterized in that, It also includes setting the observation window to the length of the loop prefix when determining the observation window, wherein the sliding distance of the observation window is one sampling point.

5. The method for jointly estimating timing deviation and frequency offset of non-orthogonal multicarrier signals according to claim 1, characterized in that, The process of obtaining the frequency offset estimate includes obtaining the frequency offset estimate when the likelihood function reaches its maximum value. The expression for the frequency offset estimate is as follows: ； In the formula, This represents the frequency offset estimate. The imaginary part of the result of the operation. This represents the real part of the result of the operation. This represents the mathematical operation of taking the imaginary part.

6. A joint estimation device for timing deviation and frequency deviation of a non-orthogonal multicarrier signal, characterized in that, include: The window determination module is used to determine the observation window, perform correlation calculations on the sampling points of the received signals in the observation window, and obtain the results of the correlation calculations. The sliding window module is used to slide the observation window and obtain the timing deviation estimate based on the position of the peak in the results of relevant calculations. The frequency offset estimation module is used to obtain multiple sampling points at the location of the timing offset estimate, perform frequency offset estimation on the multiple sampling points, and obtain the frequency offset estimate value. The related operations include first performing conjugate operations, then multiplying corresponding values ​​and summing them up; The frequency offset estimation of the multiple sampling points includes using a likelihood function to estimate the frequency offset of the multiple sampling points, wherein the expression of the likelihood function is: ； In the formula, n represents the sequence number of the sampling point. Indicates the normalized carrier frequency offset. Represents complex exponentiation. This represents the nth sample point of the received signal. Indicates the first received signal The result after the conjugate operation of each sample point Represents the number of samples for a symbol. Indicates the length of the cyclic prefix. Mathematical operations that take the real part. This represents the likelihood function for the normalized carrier frequency offset.

7. A joint estimation device for timing deviation and frequency deviation of a non-orthogonal multicarrier signal, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method for jointly estimating timing deviation and frequency offset of a non-orthogonal multicarrier signal according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for jointly estimating timing deviation and frequency offset of non-orthogonal multicarrier signals as described in any one of claims 1 to 5.

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