A fast wireless time-frequency synchronization pseudo code capture method based on Goertzel

Abstract

The application relates to a Goertzel-based fast wireless time-frequency synchronization pseudo-code capture method and relates to the technical field of communication. The method comprises the following steps: acquiring a received signal; setting a first frequency index, calculating the total amplitude of frequency points contained in the first frequency index through a Goertzel algorithm, and selecting the frequency with the highest amplitude value as an estimated first carrier frequency; setting a second frequency index based on the first carrier frequency, calculating the total amplitude of frequency points contained in the second frequency index through the Goertzel algorithm, and selecting the frequency with the highest amplitude value as an estimated second carrier frequency; performing time-frequency synchronization on the received signal based on the second carrier frequency, performing correlation calculation on the signal subjected to time-frequency synchronization and a locally generated pseudo-code signal, and performing capture decision based on the correlation calculation result; and when capture is successful, acquiring a captured signal based on the signal subjected to time-frequency synchronization and the pseudo-code signal. Through the double-layer time-frequency synchronization method based on the Goertzel algorithm, the efficiency and accuracy of pseudo-code capture are significantly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of communication technology, in particular to a fast wireless time-frequency synchronization pseudo-code acquisition method based on Goertzel. BACKGROUND

[0002] The communication system is widely used in space, ocean and other systems, and is an important factor in determining the reaction speed. In particular, in the space satellite communication system, the receiver must quickly acquire the initial frequency and time offset of the satellite signal. This is because the satellite moves at high speed, and the signal will be affected by significant Doppler frequency shift, usually in the range of several kilohertz. Therefore, the receiver needs to search for the signal in a large frequency and time range to successfully capture the synchronization signal. Signal acquisition is the first step in the baseband signal processing of the receiving end of the wireless time synchronization system, and the pros and cons of its acquisition performance directly affect the tracking speed and the accuracy of pseudo-range solution, and thus determine the overall accuracy of the system time synchronization.

[0003] In traditional wireless communication, pseudo-code acquisition refers to the process of achieving synchronization by detecting and identifying the synchronization header code word in the received signal. This process usually includes filtering of the signal, extracting the synchronization signal, identifying the code word using correlation detection or energy detection method, and performing code synchronization through phase-locked loop (PLL) or digital phase-locked loop (DPLL) to ensure that the received signal matches the locally generated signal, thereby achieving accurate signal demodulation and information extraction. However, most of the existing technology only performs small-range time-frequency synchronization through FFT, and cannot synchronize in a large frequency offset environment. If FFT synchronization is performed on a large range of spectrum, it will result in high computational complexity, making the receiver load heavy. SUMMARY

[0004] The technical problem to be solved by the present application is:

[0005] In order to avoid the shortcomings of the prior art, the present application provides a fast wireless time-frequency synchronization pseudo-code acquisition method based on Goertzel, which aims to realize low-complexity large-range frequency offset signal time-frequency synchronization in a low-orbit satellite mobile communication system while maintaining high synchronization accuracy. It is a multi-faceted optimization problem and is suitable for most satellite communication time-frequency synchronization systems.

[0006] In order to solve the above technical problems, the technical scheme adopted by the present application is:

[0007] A fast wireless time-frequency synchronization pseudo-code acquisition method based on Goertzel, characterized by comprising:

[0008] Acquire the received signal, and sequentially perform preprocessing, orthogonal I / Q separation, and down-conversion to baseband signal on the received signal;

[0009] A first frequency index is set, the total amplitude of the frequency points contained in the first frequency index is calculated by the Goertzel algorithm, and the frequency with the highest amplitude value is selected as the estimated first carrier frequency;

[0010] A second frequency index is set based on the first carrier frequency, the total amplitude of the frequency points contained in the second frequency index is calculated by the Goertzel algorithm, and the frequency with the highest amplitude value is selected as the estimated second carrier frequency;

[0011] The received signal is time-frequency synchronized based on the second carrier frequency, the signal after time-frequency synchronization is correlated with the locally generated pseudo-code signal, and the capture decision is made based on the correlation calculation result;

[0012] When the capture is successful, the signal after the capture is obtained based on the signal after time-frequency synchronization and the pseudo-code signal.

[0013] Further technical solutions of the application: the preprocessing includes band-pass filtering and discretization.

[0014] Further technical solutions of the application: the formula of the orthogonal I / Q separation is:

[0015] In-phase component: I[n] = Re(S[n])

[0016] Quadrature component: Q[n] = Im(S[n])

[0017] Wherein, s[n] is the received signal after preprocessing, I(t) represents the in-phase component signal, and represents the in-phase component at time t; Q(t) is the quadrature component signal, and represents the quadrature component at time t.

[0018] Further technical solutions of the application: the down-converted to baseband signal includes:

[0019] According to the working carrier frequency f of the wireless communication system c , a local carrier signal is generated:

[0020]

[0021] Wherein, A is the amplitude coefficient;

[0022] The C1 and C2 signals generated by the local carrier are used to shift the received signal s[n] from the middle and high frequency band to the low frequency band to obtain the baseband signal:

[0023] I base [n] = I[n] * C[n] + Q[n] * S[n]

[0024] Q base [n] = Q[n] * C[n] - I[n] * S[n]

[0025] The baseband signal of the received signal is as follows:

[0026] S base [n]=I base [n]+jQ base [n]。

[0027] The further technical solution of the application is that the first frequency index is set, including:

[0028] A group of frequency groups with an interval of 500Hz are set to perform coarse frequency offset estimation:

[0029] f target =[1000,1500,2000,2500,3000,3500,4000,4500,5000]

[0030] According to the characteristics of the received signal and the expected Doppler shift range, it is assumed that the frequency point to be estimated is f i ∈f target and the signal length N, the corresponding first frequency index k is estimated:

[0031]

[0032] The further technical solution of the application is that the total amplitude of the frequency points contained in the first frequency index is calculated by the Goertzel algorithm, including:

[0033] Initialize temporary variables y[-1]=0 and y[-2]=0, and perform iterative calculation and update state variables for each sample n:

[0034] In-phase variable:

[0035] Quadrature variable:

[0036] After N iterations, all input samples are processed, and the power X[k] of the k frequency point to be estimated is calculated as:

[0037] In-phase result:

[0038] Quadrature result:

[0039] At the same time, the amplitudes of each path are calculated as:

[0040] Amplitude of in-phase signal:

[0041] Amplitude of quadrature signal:

[0042] Total amplitude:

[0043]

[0044] The further technical solution of the present application is that the second frequency index is set based on the first carrier frequency, comprising:

[0045] The fine frequency offset estimation is performed on the first carrier frequency f est , and the frequency resolution of fine synchronization is set as 50 Hz, the fine search range is f est ±250 Hz, and a fine target frequency list is generated:

[0046] f fine_target ={f est -250,f est -200,...,f est +200,f est +250}

[0047] For each fine target frequency f fine_target [i], the corresponding frequency index k is calculated:

[0048]

[0049] The further technical solution of the present application is that the acquisition decision is made based on the correlation calculation result, comprising:

[0050] The maximum value of the correlation function is determined, and the maximum value correlation function is compared with a set acquisition threshold value: if the maximum value correlation function is greater than the acquisition threshold value, it is determined that the acquisition is successful, and the acquired frequency f final and phase information are recorded; if it is less than the acquisition threshold value, it is considered that the acquisition fails.

[0051] The further technical solution of the present application is that the signal acquired by the time-frequency synchronization and the pseudo-code signal is used to obtain the signal of acquisition completion, comprising:

[0052] The time-frequency synchronized signal is multiplied by the pseudo-code signal P local [n-m max ], and the signal of acquisition completion is obtained, wherein m max is the maximum value of the correlation function corresponding to the delay.

[0053] A computer system, characterized by comprising: one or more processors, a computer readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors realize the above-mentioned method.

[0054] The present application has the beneficial effects of:

[0055] The Goertzel-based fast wireless time-frequency synchronization pseudo-code acquisition method provided by the application has the following advantages compared with the prior art.

[0056] Firstly, the application significantly improves the efficiency and accuracy of pseudo-code acquisition through the double-layer time-frequency synchronization method based on the Goertzel algorithm. In the coarse synchronization stage, the Goertzel algorithm is used to quickly estimate the carrier frequency of the signal, effectively resisting dynamic frequency offset and Doppler effect, thereby quickly locking the signal. In the fine synchronization stage, the frequency group with higher resolution is used to estimate the frequency near the result obtained by the coarse frequency offset. This layered synchronization method not only reduces the computational complexity, but also enhances the anti-interference ability of the system in complex channel conditions, ensuring efficient and real-time signal demodulation and synchronization.

[0057] Secondly, the application introduces dynamic frequency offset correction and adaptive noise suppression mechanism. The application introduces dynamic frequency offset correction in the acquisition process, that is, a module for real-time estimation of Doppler shift and noise level according to the parameters of the received signal, dynamically adjusts the frequency compensation and filter parameters. This dynamic adjustment mechanism can adapt to different signal environments, enhance signal quality, improve acquisition probability and system robustness. BRIEF DESCRIPTION OF DRAWINGS

[0058] The accompanying drawings are included to provide a further understanding of the application and are incorporated herein and constitute a part of the application. The same reference numbers in different drawings refer to the same elements throughout the drawings.

[0059] Figure 1 The flowchart of the application.

[0060] Figure 2 The module data flowchart of the application.

[0061] Figure 3 The simulation experiment result graph of the application. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical scheme and advantages of the application clearer, the application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the application and do not limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0063] The application provides a fast wireless time-frequency synchronization pseudo-code capture method based on Goertzel, which first uses a preliminary Goertzel algorithm to perform frequency estimation on the received signal to quickly identify possible pseudo-code frequencies. Then, the received signal is adjusted through dynamic frequency compensation, and then a fine Goertzel algorithm is used for fine frequency synchronization to obtain the spectral information of the signal and determine the optimal frequency. Finally, the correlation calculation with the locally generated pseudo-code signal is performed to realize the capture and synchronization of the pseudo-code, thereby improving the accuracy and efficiency of signal demodulation.

[0064] As shown in Figure 1 , the specific steps are as follows:

[0065] (1) Signal pre-processing:

[0066] (1a) Pre-process the received wireless signal, including band-pass filtering to remove unnecessary frequency components and retain the effective frequency range of the received signal. The passband of the filter should be designed according to the spectral characteristics of the target wireless signal to be received.

[0067] (1b) Sample the received continuous signal, i.e., convert the received signal S(t) to a discrete signal S[n] in the application, as follows:

[0068]

[0069] Where t is the time variable, T s is the sampling period, n is the sample, and the sampling frequency f s satisfies the Nyquist sampling theorem.

[0070] (2) Orthogonal I / Q separation of received signal:

[0071] Separate the pre-processed received signal s[n] into orthogonal components:

[0072] In-phase component: I[n] = Re(S[n])

[0073] Quadrature component: Q[n] = Im(S[n])

[0074] Where I(t) represents the in-phase component signal, and I(t) represents the in-phase component at time t. Q(t) is the quadrature component signal, and Q(t) represents the quadrature component at time t.

[0075] (3) Down-conversion to baseband signal:

[0076] (3a) Local carrier generation: generate a local carrier signal according to the working carrier frequency f c of the wireless communication system:

[0077]

[0078] Wherein, A is the amplitude coefficient, indicating the amplitude of the local carrier signal. By setting the amplitude coefficient A, the strength of the local carrier signal can be enhanced to ensure that the amplitude of the signal is large enough in the subsequent mixing or demodulation process, avoiding the influence of noise.

[0079] (3b) Use the generated C1 and C2 signals generated by the local carrier to shift the received signal s[n] from the high frequency band to the low frequency band to obtain the baseband signal. The process is as follows:

[0080] I base [n]=I[n]·C[n]+Q[n]·S[n]

[0081] Q base [n]=Q[n]·C[n]-I[n]·S[n]

[0082] At this point, the baseband signal of the received signal can be obtained as follows:

[0083] S base [n]=I base [n]+jQ base [n]

[0084] (4) Coarse frequency offset estimation based on Goertzel algorithm:

[0085] (4a) In the navigation satellite communication environment, the frequency offset is usually 1000Hz to 5000Hz. Therefore, the present application sets a group of frequency groups with an interval of 500Hz to perform coarse frequency offset estimation:

[0086] f target =[1000,1500,2000,2500,3000,3500,4000,4500,5000]

[0087] According to the characteristics of the received signal and the expected Doppler shift range, assume that the frequency point to be estimated is f i ∈f target And the signal length N, then estimate the corresponding frequency index k:

[0088]

[0089] (4b) Use Goertzel algorithm to calculate the total amplitude of the estimated frequency point corresponding to the index k. Initialize temporary variables y[-1]=0, y[-2]=0, for each sample n (from 0 to N-1), the state variables can be calculated iteratively, and the state variables are updated:

[0090] In-phase variable:

[0091] Quadrature variable:

[0092] After N iterations, all input samples are processed, and the power of the k-th frequency point to be estimated X[k] is calculated as:

[0093] In-phase result:

[0094] Quadrature result:

[0095] At the same time, the amplitudes of each path are calculated as:

[0096] Amplitude of in-phase signal:

[0097] Amplitude of quadrature signal:

[0098] Total amplitude:

[0099]

[0100] (4c) So far, for f target all target frequencies, repeat step (4b) to obtain the |X[k]| value of each frequency point, calculate the amplitude of all frequency points to be estimated, and select the frequency with the highest amplitude value as the estimated carrier frequency result:

[0101] f est = f target [k max ]

[0102] where k max is the index that makes |X[k]| maximum.

[0103] (5) Fine frequency offset estimation based on Goertzel algorithm

[0104] (5a) Fine frequency offset estimation is performed around the coarse frequency estimation f est , and the frequency resolution of fine synchronization is set to 50 Hz, and the fine search range is f est ±250 Hz, then the fine target frequency list can be generated as:

[0105] f fine_target = {f est -250, f est -200,..., f est +200, f est +250}

[0106] Then, for each fine target frequency f fine_target [i], calculate its corresponding frequency index k:

[0107]

[0108] (5b) Calculate the amplitude of each frequency point in the fine target frequency ffine_target to be estimated using the Goertzel algorithm. Initialize temporary variables y[-1] = 0, y[-2] = 0, and for each sample n (from 0 to N-1), the iterative calculation can be performed, updating the state variables

[0109] In-phase variable:

[0110] Quadrature variable:

[0111] After N iterations, after processing all input samples, the power X[k] of the kth frequency point to be estimated is calculated as:

[0112] In-phase result:

[0113] Quadrature result:

[0114] At the same time, the amplitudes of each path are calculated as:

[0115] Amplitude of in-phase signal:

[0116] Amplitude of quadrature signal:

[0117] Total amplitude:

[0118]

[0119] (5c) So far, for all target frequencies in f fine_target , repeat step (5b) to obtain the |X[k]| value of each frequency point, calculate the signal amplitude of all estimated frequency points, and select the frequency with the highest amplitude value as the estimated carrier frequency result:

[0120] f final = f fine_target [k fine_max ]

[0121] Where k fine_max is the index that makes |X[k]| maximum.

[0122] (6) Signal frequency offset correction

[0123] Use f final to perform fine synchronization on the signal S[n], and the calculation method is as follows:

[0124]

[0125] Where S′[n] represents the signal after time-frequency synchronization.

[0126] (7) Local pseudocode generator

[0127] A pseudocode sequence b[n] consisting of 0s and 1s, identical to that of the transmitter, is generated locally. After binary phase shift keying modulation, a sequence P consisting of -1s and +1s is obtained. local [n]:

[0128] P local [n] = 2b[n] - 1

[0129] (8) Related calculations

[0130] The time-frequency synchronized signal S′[n] and the local pseudocode signal P local [n], calculate its correlation.

[0131]

[0132] Where R(m) is the correlation function, and m represents the delay bits. Determine the maximum value of the correlation function and its corresponding delay:

[0133]

[0134] (9) Capture Judgment

[0135] Set a capture threshold T, if R[m max If f > T, then the capture is considered successful, and the capture frequency f is recorded. final With phase information, proceed to step (10).

[0136] If R[m] max If ] < T, it is considered that the capture has failed, return to step (4), and according to the feedback f final Adjust (4a) f i For other nearby frequencies, up to f target None of the frequencies were successfully captured.

[0137] (10) Signal demodulation and synchronization

[0138] By utilizing the correlation between the signal and the pseudocode, that is, the frequency offset corrected signal S′[n] and the synchronized pseudocode signal P local [nm max Multiply to extract useful information:

[0139] S demod [n] = S′[n]·P local [nm max ]

[0140] Among them, S demod[n] is the demodulated signal, representing the product of the received signal and the local pseudo-code signal after corresponding delay adjustment.

[0141] In summary, the present application adopts a double-layer time-frequency synchronization method based on the Goertzel algorithm: first, coarse frequency offset estimation is performed using the Goertzel algorithm to quickly identify the center frequency of the received signal, and then fine frequency offset estimation is performed through the fine Goertzel algorithm to ensure high-precision time-frequency signal synchronization. Through the double-layer synchronization strategy, the speed of pseudo-code acquisition can be significantly improved without losing accuracy, enabling the wireless communication receiver to quickly synchronize the signal with low computational complexity. At the same time, the present application introduces a dynamic frequency offset correction and adaptive noise suppression mechanism: dynamic frequency offset correction is introduced during signal acquisition, and decision information is fed back to the synchronization processing module, and then the Doppler shift and noise level are estimated in real time according to the received signal parameters, and the frequency compensation amount and filter parameters are dynamically adjusted. Unlike common time-frequency synchronization techniques, this dynamic adjustment mechanism can adapt to different signal environments, enhance signal quality, improve acquisition probability and system robustness.

[0142] The effect of the present application will be further described below in combination with simulation experiments.

[0143] 1. Simulation experiment conditions:

[0144] This experiment was conducted on a PC with an Intel Core i7-9700K processor, 16GB DDR4 RAM, and 512GB SSD, running Windows 10 64-bit or Ubuntu 20.04LTS. Python 3.8 and later versions were used, and the NumPy and Matplotlib libraries were used for numerical calculation and result visualization. This environment configuration ensures the smooth progress of the experiment and the accuracy of the results.

[0145] 2. Simulation experiment content and result analysis:

[0146] The main goal of this experiment is to verify the effectiveness of the fast wireless time-frequency synchronization pseudo-code acquisition method based on the Goertzel algorithm. The experimental parameters are set as follows: sampling frequency f s = 10000 Hz, signal duration T = 1 second, total sample number N = 10000. The pseudo-code frequency is set to 2000 Hz, and the signal-to-noise ratio is 10 dB. A random BPSK modulated pseudo-code signal is generated in the experiment, and Gaussian white noise is added to the signal to simulate the actual received signal. The preprocessing steps include signal amplification, filtering, and discretization to ensure good quality of the received signal, preparing for subsequent coarse synchronization and fine synchronization.

[0147] In the first graph of the experimental results, the coarse synchronization capture results of the Goertzel algorithm are shown. The X-axis represents the target frequency range from 1000 Hz to 5000 Hz, and the Y-axis represents the amplitude of the corresponding frequency. The blue bar chart shows the amplitude of each target frequency, and the red dashed line marks the estimated frequency f est . By observing the data in the graph, it can be seen that the amplitude near 3500 Hz is the highest, indicating that the received signal has the maximum energy at this frequency, successfully capturing the main frequency component of the pseudo-code signal.

[0148] In the second graph of the experimental results, the fine synchronization amplitude response is shown. The X-axis represents the fine search frequency range near the coarse synchronization estimated frequency (e.g., ± 250 Hz), and the Y-axis represents the amplitude of the corresponding frequency. The green curve shows the amplitude response in the fine search range, and the red dashed line marks the final estimated frequency f final is 3350 Hz. By observing the data in the graph, the position of the red dashed line indicates the more accurate estimation of the signal frequency after fine search, further confirming the spectral characteristics of the signal. This fine synchronization process effectively improves the accuracy of pseudo-code capture, ensuring the reliability of signal demodulation.

[0149] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of various equivalent modifications or replacements within the scope of the present application, and these modifications or replacements should be covered within the protection scope of the present application.

Claims

1. A Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method, characterized in that, The method comprises: acquiring a received signal, and sequentially performing pre-processing, orthogonal I / Q separation, and down-conversion to a baseband signal on the received signal; setting a first frequency index, calculating a total amplitude of frequency points contained in the first frequency index by using a Goertzel algorithm, and selecting a frequency with the highest amplitude value as an estimated first carrier frequency; setting a second frequency index based on the first carrier frequency, calculating a total amplitude of frequency points contained in the second frequency index by using the Goertzel algorithm, and selecting a frequency with the highest amplitude value as an estimated second carrier frequency; performing time-frequency synchronization on the received signal based on the second carrier frequency, performing correlation calculation on a signal after time-frequency synchronization and a locally generated pseudo-code signal, and making an acquisition decision based on a correlation calculation result; when acquisition is successful, acquiring a signal after acquisition based on the signal after time-frequency synchronization and the pseudo-code signal.

2. The Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method according to claim 1, characterized in that, The pre-processing comprises band-pass filtering and discretization.

3. The Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method according to claim 1, characterized in that, A formula for the orthogonal I / Q separation is: In-phase component: Quadrature component: wherein is the pre-processed received signal, is the time variable, is the sampling period, is the sampling point.

4. The Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method according to claim 3, characterized in that, The down-conversion to the baseband signal comprises: According to the carrier frequency on which the wireless communication system operates generating a local carrier signal: wherein is the amplitude coefficient, is the sampling frequency; Generated using local carrier and The signal will be received. The baseband signal is obtained by shifting from the mid-to-high frequency band to the low frequency band: A baseband signal of the received signal is as follows: 。 5. The Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method according to claim 4, characterized in that, The setting of the first frequency index comprises: a set of frequency groups with an interval of 500 Hz is set for coarse frequency offset estimation; According to the characteristics of the received signal and the expected Doppler shift range, assuming the frequency point to be estimated is and the signal length N, the corresponding first frequency index is estimated : 。 6. The Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method according to claim 5, characterized in that, The calculation of the total amplitude of the frequency points contained in the first frequency index by using the Goertzel algorithm comprises: Initialize temporary variables , For each sample point n, perform an iterative calculation, updating state variables: In-phase variable: Quadrature variable: After N iterations, all input samples are processed, and the power of the frequency point to be estimated is calculated as follows: P = 1 / N * Σ|X(k)|2 where X(k) is the kth input sample. In-phase result: Orthogonal results: At the same time, the amplitudes of the paths are calculated as follows: amplitude of the in-phase signal: Amplitude of the quadrature signal: Total amplitude: 。 7. The Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method according to claim 6, characterized in that, The setting of the second frequency index based on the first carrier frequency comprises: A fine frequency offset estimation is performed around the first carrier frequency The frequency resolution of the fine synchronization is set to 50 Hz and the fine search range is Hz, a fine target frequency list is generated: For each fine target frequency , its corresponding frequency index is calculated 。 8. The Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method according to claim 7, characterized in that, The acquisition decision based on the correlation calculation result comprises: determining a maximum value of the correlation function, comparing the maximum value of the correlation function with a set capture threshold value: if the maximum value of the correlation function is greater than the capture threshold value, then determining that the capture is successful, and recording the captured frequency and phase information; if less than the capture threshold value, then considering that the capture fails.

9. The Goertzel-based fast wireless time-frequency synchronization pseudo code acquisition method according to claim 8, characterized in that, The acquisition of the signal after acquisition based on the signal after time-frequency synchronization and the pseudo-code signal comprises: Multiplying the time-frequency synchronized signal with the pseudo-code signal to obtain a signal of which acquisition is completed, wherein is a delay corresponding to a maximum value of the correlation function.

10. A computer system, characterized by The method comprises: one or more processors, a computer readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method of claim 1.

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