A channel equalization method based on frequency sampling method

Abstract

The application provides a channel equalization method based on a frequency sampling method, which comprises the following steps: obtaining a frequency domain quotient by taking a frequency response of a channel to be equalized and a reference channel; obtaining a frequency of an ideal equalization filter through a band-pass filter and a frequency domain entropy; performing an IFFT transformation on the ideal equalization filter; and performing several iterations according to channel performance to obtain an ideal equalization filter coefficient. Based on the ideal equalization filter coefficient, an actual equalization filter is constructed through a FIR filter model to complete equalization of the channel to be equalized. The method avoids inverse operation of a matrix of a conventional frequency domain least square method, reduces complexity of the algorithm, and can be realized in real time in engineering. Meanwhile, the method further improves equalization accuracy by using a band-pass filter and an iteration mode.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of radar signal processing, in particular to a channel equalization method based on frequency sampling method. BACKGROUND

[0002] Software radio technology, through the combination of software and hardware, provides a multi-mode, multi-band, multi-functional, effective and economic wireless network configuration scheme. It can not only be applied to the field of communication, but also has more applications in the field related to radio engineering, such as radar, navigation, broadcast television, etc. The hardware part usually contains multiple radio frequency channels, and each radio frequency channel contains power amplifiers, mixers, filters, A / D converters and other analog devices. Due to its own nature, analog devices will have inconsistencies in different temperature, humidity and other environments, resulting in amplitude and phase inconsistencies between channels.

[0003] In order to correct the error caused by channel mismatch, the mismatch of each channel can be compensated by inserting an equalization filter in the channel. The solution of the equalization filter is divided into time domain algorithm and frequency domain algorithm. The time domain algorithm includes Wiener filter method, LMS method and RLS adaptive algorithm. The time domain adaptive filter algorithm avoids matrix inversion and reduces the complexity of the algorithm, but also has the problem of insufficient precision. The frequency domain algorithm includes frequency domain least square fitting method and frequency sampling method (also known as Fourier transform method). The frequency domain least square method overcomes the problem of insufficient precision and has high precision, but the calculation workload is large and is not conducive to engineering implementation. The frequency sampling method is more susceptible to out-of-band noise and signal signal-to-noise ratio, and its performance is not as good as the frequency domain least square method, but it avoids matrix inversion and has smaller calculation amount, so it is more suitable for engineering implementation. SUMMARY

[0004] The purpose of the present application is to provide a channel equalization method based on frequency sampling method, to improve the equalization performance, reduce the calculation amount and facilitate engineering implementation.

[0005] To achieve the above purpose, the present application provides a channel equalization method based on frequency sampling method, which comprises:

[0006] Step 1, obtaining the sampling signals of multiple channels, transforming the sampling signals of multiple channels to the frequency domain by FFT to obtain the frequency domain signals of multiple channels; setting one channel as a reference channel, and taking the frequency of the reference channel as the ideal frequency domain, and the other channels as equalization channels; for each equalization channel, calculating the frequency domain quotient;

[0007] Step 2, designing a band-pass filter, obtaining an ideal equalization filter frequency of the to-be-equalized channel according to the band-pass filter and the frequency domain quotient, sampling the ideal equalization filter frequency to obtain an ideal equalization filter frequency sample value, and determining a transmission function of the ideal equalization filter according to the ideal equalization filter frequency sample value;

[0008] Step 3, iterating according to the channel performance, so that the amplitude mismatch and the phase mismatch of the equalized signal meet the threshold value requirement, and obtaining a transmission function of the ideal equalization filter meeting the design requirement;

[0009] Step 4, performing IFFT transformation on the transmission function of the ideal equalization filter to obtain an ideal equalization filter coefficient corresponding to the to-be-equalized channel;

[0010] Step 5, constructing an actual equalization filter through a FIR filter model based on the obtained ideal equalization filter coefficient of each to-be-equalized channel, and completing equalization of the to-be-equalized channel.

[0011] Further, the step 1 comprises:

[0012] Step 11, designing a wideband calibration linear frequency modulation signal, inputting the wideband calibration linear frequency modulation signal into each channel, and obtaining a sampling signal of the multi-channel:

[0013] ;

[0014] ;

[0015] ;

[0016] wherein, is the wideband calibration linear frequency modulation signal, is a signal form represented by an Euler formula, B is a signal bandwidth, T is a signal pulse width, and k is a relative size or proportion of the signal bandwidth and the pulse width, is an equalization system sampling rate;

[0017] inputting the wideband calibration linear frequency modulation signal into the reference channel, collecting the reference channel to obtain a collection signal of the reference channel ; wherein n is a quantization value of a sampling time;

[0018] inputting the wideband calibration linear frequency modulation signal into the to-be-equalized channel, collecting the to-be-equalized channel to obtain a collection signal of the to-be-equalized channel ; wherein, is the sampling signal of the i th to-be-equalized channel, is a serial number of the to-be-equalized channel, and N is a total number of to-be-equalized channels;

[0019] Step 12, windowing the sample signal of the channel to be equalized, cutting the signal part, and obtaining a windowed signal:

[0020] ;

[0021] wherein, is the windowed signal; is a time domain window;

[0022] Step 13, performing FFT transform on the windowed signal of the channel to be equalized, and obtaining a frequency domain signal of the channel to be equalized , wherein ω is frequency;

[0023] Step 14, based on the frequency signal of the channel to be equalized , and given the frequency signal of the reference channel , calculating the frequency domain quotient of each channel to be equalized:

[0024] ;

[0025] ;

[0026] wherein, is the frequency domain quotient of the i th channel to be equalized; H ref (ω) is the frequency signal of the all-pass filter; L is the order of the all-pass filter, is the time domain form of the all-pass filter represented by the Euler formula.

[0027] Further, the step 2 comprises:

[0028] Step 21, designing a band-pass filter:

[0029] According to the bandwidth of the channel, the sampling rate and the carrier signal frequency, a band-pass filter is constructed by a direct type FIR filter ;

[0030] Step 22, passing the frequency domain quotient through the band-pass filter, and obtaining an ideal equalization filter frequency:

[0031] ;

[0032] wherein, H m (ω) is the ideal equalization filter frequency; m is the channel serial number of the ideal equalization filter, ;

[0033] Step 23, sampling the ideal equalization filter frequency, and obtaining M frequency sampling values of the ideal equalization filter :

[0034] ;

[0035] wherein, is the serial number of the discrete frequency sampling point, M is the total number of sampling points;

[0036] Step 24, according to the ideal equalization filter frequency sampling value, the transfer function of the ideal equalization filter is determined:

[0037] According to the sampling theorem, the transfer function of the ideal equalization filter is:

[0038] ;

[0039] wherein, is the unit sampling sequence obtained by performing IDFT on , and the IDFT is inverse discrete Fourier transform; Z is a complex number domain representation of discrete Fourier transform, wherein ; is the rotation factor of the IDFT.

[0040] Further, the step 3 is iterated according to the channel performance, specifically:

[0041] ;

[0042] wherein, represents the performance of the channel, is the frequency response sampling of the ideal equalization filter of the i-th channel; is the frequency response sampling of the ideal equalization filter of the reference channel; is the amplitude mismatch; is the phase mismatch.

[0043] Further, the step 3 includes:

[0044] According to the design requirements, the constraint condition of iterating the predetermined channel performance is performed, so that the amplitude mismatch and the phase mismatch of the equalized signal meet the threshold value requirements, the threshold value includes the amplitude mismatch threshold and the phase mismatch threshold, and a designed ideal equalization filter is obtained; the specific constraint condition is:

[0045] The absolute value of the difference between the amplitude mismatch average value and 1 is less than 0.1;

[0046] The absolute value of the difference between the amplitude mismatch variance and 0 is less than 0.1;

[0047] The absolute value of the difference between the phase mismatch average value and 0 is less than 0.1°;

[0048] The absolute value of the difference between the phase mismatch variance and 0 is less than 0.1°.

[0049] Further, the step 3 further comprises:

[0050] Initialize iteration counter C1, the initial value of C1 is 1; set iteration times C2;

[0051] According to the designed ideal equalization filter, perform equalization processing, calculate the amplitude mismatch value and the phase mismatch value of the equalized signal, and compare them with the constraint condition:

[0052] If the variance and mean of the signal amplitude and the variance and mean of the phase are all less than the threshold value, it is indicated that the ideal equalization filter performance meets the requirement; otherwise, C1 is added by 1, and the step 2 is repeated until the design requirement is met or the maximum value of C1 exceeds .

[0053] Further, the step 4 comprises:

[0054] Perform IFFT transformation on the transfer function of the ideal equalization filter to obtain the corresponding ideal equalization filter coefficient:

[0055] ;

[0056] Wherein, is the ideal equalization filter coefficient.

[0057] Compared with the prior art, the present application has the following beneficial effects:

[0058] (1) The present application uses frequency sampling method and IFFT calculation to obtain the filter coefficient of the ideal equalization filter, and the algorithm complexity is very low, which is very easy to realize in engineering;

[0059] (2) The present application uses band-pass filter to intercept frequency and smoothes the sideband signal, reduces the error of frequency sampling method, and improves the design accuracy of the band-pass filter;

[0060] (3) The present application uses equalization effect evaluation method to iterate the ideal equalization filter, and improves the equalization effect. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 is the flow chart of the channel equalization method based on frequency sampling method of the present application;

[0062] Figure 2 is the actual equalization filter structure schematic diagram provided by the present application. DETAILED DESCRIPTION

[0063] In order to make the above objectives, features and advantages of the present application more obvious and comprehensible, the specific embodiments of the present application are described in detail below with reference to the drawings. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the spirit of the present application, so the present application is not limited to the specific embodiments disclosed below.

[0064] Embodiment one:

[0065] The present application provides a channel equalization method based on frequency sampling method, as shown in Figure 1 The method comprises the following steps:

[0066] Step 1, obtaining a multi-channel sampling signal, transforming the multi-channel sampling signal to the frequency domain through FFT to obtain a multi-channel frequency domain response; setting one channel as a reference channel, and taking the frequency domain response of the reference channel as an ideal frequency domain response, and the other channels as equalization channels; for each equalization channel, calculating the frequency domain quotient;

[0067] Step 11, designing a wideband calibration linear frequency modulation signal, inputting the wideband calibration linear frequency modulation signal into each channel to obtain a multi-channel sampling signal:

[0068] ;

[0069] ;

[0070] ;

[0071] wherein, is a wideband calibration linear frequency modulation signal, is a signal form represented by Euler formula; B is the signal bandwidth, which is consistent with the bandwidth of the equalization channel; T is the signal pulse width; k is the relative size or ratio of the signal bandwidth and the pulse width, is the sampling rate of the equalization system;

[0072] inputting the wideband calibration linear frequency modulation signal into the reference channel, collecting the reference channel to obtain the collection signal of the reference channel ; wherein, n is the quantization value of the sampling time;

[0073] inputting the wideband calibration linear frequency modulation signal into the equalization channel, collecting the equalization channel to obtain the sampling signal of the equalization channel ; wherein, is the sampling signal of the i th equalization channel, is the serial number of the equalization channel, and N is the total number of equalization channels;

[0074] Step 12, windowing the sample signal of the channel to be equalized, cutting the signal part, and obtaining a windowed signal:

[0075] ;

[0076] wherein, is the windowed signal; is the sample signal of the channel to be equalized; is the time domain window;

[0077] Step 13, performing FFT transformation on the windowed signal of the channel to be equalized, and obtaining frequency domain data of the channel to be equalized , wherein ω is frequency, and FFT transformation is fast Fourier transformation;

[0078] Step 14, based on the frequency signal of the channel to be equalized , and given the frequency signal of the reference channel , calculating the frequency domain quotient of each channel to be equalized:

[0079] ;

[0080] ;

[0081] wherein, is the frequency domain quotient of the i-th channel to be equalized; H ref (ω) is the frequency signal of the all-pass filter; L is the order of the filter, is the time domain form of the all-pass filter represented by Euler's formula.

[0082] Further explanation, because the FIR filter in engineering will introduce time delay, in order to make the signal through different channels align, the all-pass filter is introduced in the reference channel, so that the delay of different channels is consistent.

[0083] Step 2, designing a band-pass filter; according to the band-pass filter and the frequency domain quotient, obtaining the ideal equalization filter frequency of the channel to be equalized; sampling the ideal equalization filter frequency, and obtaining the sampled ideal equalization filter frequency response; according to the sampled ideal equalization filter frequency response, determining the transfer function of the ideal equalization filter;

[0084] Step 21, designing a band-pass filter;

[0085] According to the bandwidth, sampling rate and carrier signal frequency of the channel, a band-pass filter is constructed by a direct type FIR filter ;

[0086] Step 22, passing the frequency domain quotient through the band-pass filter , and obtaining the ideal equalization filter frequency:

[0087] ;

[0088] Among them, H m (ω) is the frequency of the ideal equalizer filter; H w (ω) represents the bandpass filter; m is the channel number;

[0089] Step 23: Sample the frequency of the ideal equalizer filter. Equally spaced sampling is performed to obtain M frequency sample values ​​for the ideal equalization filter. :

[0090] ;

[0091] in, The discrete frequency sampling point number; M is the total number of sampling points;

[0092] Step 24: Determine the transfer function of the ideal equalizer based on the frequency sampled values ​​of the ideal equalizer.

[0093] According to the sampling theorem, the transfer function of an ideal equalizer filter is:

[0094] ;

[0095] in, To The unit sample sequence obtained by performing the IDFT is used as the transfer function designed for the unit impulse response. IDFT stands for Inverse Discrete Fourier Transform; Z is the complex-domain representation of the Discrete Fourier Transform, where... , is the twiddle factor of IDFT;

[0096] like Figure 2 As shown, the time-domain form of the filter is constructed based on the transfer function of the ideal equalizer filter. In the figure, the signal is input to the reference channel and the channel to be equalized via a power divider. In the channel to be equalized, the signal passes through the frequency signal of the channel to be equalized. Signal received later .Signal The input equalization filter performs equalization filtering on the signal, that is, the signal is time-delayed. (can be simplified to () )) respectively with the corresponding filter coefficients Multiply and sum to obtain the corresponding channel output. In the reference channel, the frequency signal of the channel. and all-pass filter The corresponding channel output is obtained as .

[0097] Step 3, iteration is performed according to the channel performance, so that the amplitude mismatch and phase mismatch of the equalized signal meet the threshold requirement, and a designed ideal equalization filter transfer function is obtained;

[0098] According to the channel performance, iteration is performed, specifically as follows:

[0099] ;

[0100] wherein, represents the performance of the channel, is the frequency sample of the ideal equalization filter of the i-th channel; is the frequency sample of the ideal equalization filter of the reference channel; is the amplitude mismatch, the closer the mean value is to 1 and the closer the variance is to 0, the better the amplitude performance of the channel is; is the phase mismatch, the closer the mean value and the variance are to 0, the better the phase performance of the channel is;

[0101] According to the design requirement, a constraint condition for iteration of the predetermined channel performance is performed, so that the amplitude mismatch and the phase mismatch of the equalized signal meet the threshold requirement, the threshold includes an amplitude mismatch threshold and a phase mismatch threshold, and a designed ideal equalization filter is obtained; the specific constraint condition is as follows:

[0102] The absolute value of the difference between the amplitude mismatch mean value and 1 is less than 0.1;

[0103] The absolute value of the difference between the amplitude mismatch variance and 0 is less than 0.1;

[0104] The absolute value of the difference between the phase mismatch mean value and 0 is less than 0.1°;

[0105] The absolute value of the difference between the phase mismatch variance and 0 is less than 0.1°.

[0106] It should be noted that the amplitude mismatch and phase mismatch threshold values can be designed according to actual needs.

[0107] Initialize the iteration counter C1, and the initial value of C1 is 1; set the iteration number C2;

[0108] According to the designed ideal equalization filter, equalization processing is performed, the amplitude mismatch value and the phase mismatch value of the equalized signal are calculated, and they are compared with the constraint condition: if the variance, mean value of the signal amplitude and the variance and mean value of the phase are all less than the threshold value, it is considered that the equalization filter performance meets the requirement, otherwise C1 is increased by 1, and step 2 is repeated until the design requirement is met or the maximum value of C1 exceeds .

[0109] Step 4, IFFT transform is made to the transmission function of the ideal equalization filter to obtain the ideal equalization filter coefficients of the to-be-equalized channel:

[0110] ;

[0111] wherein, is the ideal equalization filter coefficient; IDFT() is inverse discrete Fourier transform, and IFFT transform is inverse fast Fourier transform.

[0112] Step 5, the ideal equalization filter coefficients of each to-be-equalized channel obtained are used to construct an actual equalization filter through a FIR filter model to complete equalization of the to-be-equalized channel.

[0113] Further explanation, in the embodiment, firstly, due to the characteristics of the left-right asymmetry of the analog channel, the carrier signal is used to obtain the frequency domain quotient of the to-be-equalized channel and the reference signal, so that the performance of the equalization is further improved. Then, the frequency response of the ideal equalization filter is intercepted by using a band-pass filter, the sideband signal is smoothed, the error of the frequency sampling method is reduced, and the design precision of the filter is improved. Finally, the equalization filter coefficients are obtained by using the IFFT method, the matrix inversion and the approximate algorithm are avoided, the complexity of the equalization filter solution is reduced, and the engineering implementation is facilitated.

[0114] For those skilled in the art, various corresponding changes and modifications can be given according to the above technical solutions and concepts, and all these changes and modifications should be included in the protection scope of the claims of the present application.

Claims

1. A channel equalization method based on frequency sampling, characterized in that, The method includes: Step 1: Acquire multi-channel sampling signals, transform the multi-channel sampling signals to the frequency domain using FFT to obtain multi-channel frequency domain signals; set one channel as the reference channel, and use the frequency of the reference channel as the ideal frequency domain, and the other channels as channels to be equalized; for each channel to be equalized, calculate the frequency domain quotient. Step 2: Design a bandpass filter. Based on the bandpass filter and the frequency domain quotient, obtain the ideal equalization filter frequency of the channel to be equalized. Sample the ideal equalization filter frequency to obtain the ideal equalization filter frequency sample value. Based on the ideal equalization filter frequency sample value, determine the transfer function of the ideal equalization filter. Step 3: Iterate according to the channel performance to make the amplitude mismatch and phase mismatch of the equalized signal meet the threshold requirements, and obtain the ideal equalization filter transfer function that meets the design requirements; Step 4: Perform IFFT transform on the transfer function of the ideal equalizer to obtain the coefficients of the ideal equalizer for the channel to be equalized. Step 5: Based on the obtained ideal equalization filter coefficients of each channel to be equalized, construct the actual equalization filter through the FIR filter model to complete the equalization of the channels to be equalized.

2. The channel equalization method based on frequency sampling according to claim 1, characterized in that, Step 1 includes: Step 11: Design a broadband calibration linear frequency modulation (LFM) signal, and connect the broadband calibration LFM signal to each channel to obtain multi-channel sampling signals: ； ； ； in, For broadband calibration of linear frequency modulated signals, Let B be the signal form expressed in Euler's formula, T be the signal pulse width, and k be the relative magnitude or ratio of the signal bandwidth to the pulse width. To balance the system sampling rate; A broadband calibration linear frequency modulated signal is input to the reference channel, and the reference channel is sampled to obtain the sampled signal of the reference channel. Where n is the quantization value of the sampling time; A broadband calibration linear frequency modulated signal is input to the channel to be equalized, and the signal is acquired from the channel to be equalized. ;in, Let be the sampled signal of the i-th channel to be equalized. is the sequence number of the channel to be balanced, and N is the total number of channels to be balanced; Step 12: Window the sampled signal of the channel to be equalized, and truncate the signal portion to obtain the windowed signal: ； in, For windowing signals; For time-domain windows; Step 13: Perform FFT transformation on the windowed signal of the channel to be equalized to obtain the frequency domain signal of the channel to be equalized. , where ω is the frequency; Step 14, based on the frequency signal of the channel to be equalized Given the frequency signal of the reference channel Calculate the frequency domain quotient of each channel to be equalized: ； ； in, H is the frequency domain quotient of the i-th channel to be equalized; ref (ω) represents the frequency signal of the all-pass filter; L represents the order of the all-pass filter. This is the time-domain form of an all-pass filter expressed in Euler's formula.

3. The channel equalization method based on frequency sampling according to claim 2, characterized in that, Step 2 includes: Step 21, design a bandpass filter; Based on the channel bandwidth, sampling rate, and carrier signal frequency, a bandpass filter is constructed using a direct-form FIR filter. ; Step 22, frequency domain quotient The ideal equalizer frequency is obtained by using a bandpass filter: ； Among them, H m (ω) represents the frequency of the ideal equalizer filter; m represents the channel number of the ideal equalizer filter. ; Step 23: Sample the frequency of the ideal equalizer filter to obtain M frequency sample values ​​of the ideal equalizer filter. : ； in, The discrete frequency sampling point number. M is the total number of sampling points; Step 24: Determine the transfer function of the ideal equalizer based on the frequency sampled values ​​of the ideal equalizer. According to the sampling theorem, the transfer function of an ideal equalizer filter is: ； in, To The unit sample sequence obtained by performing the IDFT is used as the transfer function designed for the unit impulse response. IDFT stands for Inverse Discrete Fourier Transform; Z is the complex-domain representation of the Discrete Fourier Transform, where... ; is the twiddle factor of IDFT.

4. The channel equalization method based on frequency sampling according to claim 3, characterized in that, Step 3 involves iterating based on channel performance, specifically as follows: ； in, Indicates the performance of the channel. Sample the frequency response of the ideal equalizer filter for the i-th channel; Sample the frequency response of the ideal equalizer filter for the reference channel; This is due to amplitude mismatch. This is due to phase mismatch.

5. The channel equalization method based on frequency sampling according to claim 4, characterized in that, Step 3 includes: According to the design requirements, iterative constraints are applied to the predetermined channel performance to ensure that the amplitude and phase mismatches of the equalized signal meet threshold requirements. These thresholds include amplitude mismatch thresholds and phase mismatch thresholds, resulting in the designed ideal equalization filter. Specific constraints are as follows: The absolute value of the difference between the mean amplitude mismatch and 1 is less than 0.1; The absolute value of the difference between the amplitude deviation and 0 is less than 0.1; The absolute value of the difference between the mean phase mismatch and 0 is less than 0.1°; The absolute value of the difference between the phase loss formula error and 0 is less than 0.1°.

6. The channel equalization method based on frequency sampling according to claim 5, characterized in that: Step 3 also includes: Initialize the iteration counter C1, with an initial value of 1; set the iteration count C2; Equalization is performed using the designed ideal equalizer filter. The amplitude and phase mismatch values ​​of the equalized signal are calculated and compared with the constraints. If the variance, mean, and phase variance and mean of the signal amplitude are all less than the threshold value, it means that the performance of the ideal equalizer filter meets the requirements; otherwise, add 1 to C1 and repeat step 2 until the design requirements are met or the maximum value of C1 exceeds C2-1.

7. The channel equalization method based on frequency sampling according to claim 6, characterized in that: Step 4 includes: Performing an IFFT transform on the transfer function of the ideal equalizer yields the corresponding ideal equalizer coefficients: ； in, These are the coefficients of the ideal equalizer filter.

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