CN110324041B - Channel mismatch estimation method for broadband cross sampling system - Google Patents
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Abstract
The invention belongs to the technical field of broadband signal sampling, and relates to a channel mismatch estimation method of a broadband cross sampling system. Carrying out bias mismatch estimation on noise data acquired by a broadband cross sampling system, obtaining an amplitude value and a phase value of each channel at each test frequency point by adopting a sine fitting estimation method, selecting a reference channel to obtain a gain discrete function and a phase difference discrete function of each channel at each test frequency point, and carrying out frequency range expansion on the obtained gain discrete function and phase difference discrete function of each test frequency point to obtain gain mismatch frequency response and phase mismatch frequency response of each channel; the estimation precision of the channel mismatch is improved by removing the influence of the offset mismatch; data acquisition and processing are only needed to be carried out on the concerned frequency band, and gain mismatch and phase mismatch of the frequency band which is not concerned are obtained by carrying out frequency range expansion on a gain discrete function and a phase difference discrete function of each test frequency point, so that the workload of data acquisition and processing in the channel mismatch estimation process is reduced.
Description
Technical Field
The invention belongs to the technical field of broadband signal sampling, and relates to a channel mismatch estimation method of a broadband cross sampling system.
Background
The high-speed high-resolution sampling system is a key component of instruments and equipment such as a broadband digital receiver, a communication system, an oscilloscope and the like. The contradiction between high sampling rate and high resolution has constrained the development of Analog-to-Digital converters (ADCs). Cross-sampling (TIADC) techniques can effectively solve this problem. An ideal structure of an M-channel cross-sampling system is shown in fig. 1. A plurality of ADCs with lower sampling rates alternately acquire signals under the same clock frequency and different clock phases, and then the sampling sequences of the sub-ADCs are combined to serve as system output to improve the sampling rate.
While cross-sampling techniques can multiply the sampling rate of a system, channel mismatches are introduced into the system at the same time. Channel mismatches include primarily bias mismatches, gain mismatches, and phase mismatches. Channel mismatches can severely degrade the dynamic performance of the cross-sampling system and must be corrected. Cross-sampling channel mismatch correction consists essentially of two steps: 1. channel mismatch estimation, and channel mismatch compensation.
Accurate channel mismatch estimation is a key condition for implementing cross-sampling channel mismatch compensation. The existing cross sampling channel mismatch estimation algorithms are mainly divided into two types, namely forward estimation and backward estimation: the forward estimation algorithm has higher precision and stability, but if the system environment changes, the calibration signal needs to be input again to calculate the channel mismatch; the backward estimation algorithm can directly reconstruct the original signal without a pre-input calibration signal. Although the backward estimation algorithm can estimate the change of channel mismatch in real time, the complexity is high, the precision is low, or certain special requirements are made on the form of an input signal. In practical applications, in order to ensure the estimation accuracy, a forward estimation method is generally adopted. In the case of a large bandwidth, the offset mismatch can be regarded as a fixed value that does not vary with frequency, and the gain mismatch and the phase mismatch vary with frequency and cannot be regarded as fixed values. An estimation Method of gain mismatch and phase mismatch in a cross sampling System is given in a reference (j.li, j.pan and y.zhang, "Automatic Calibration Method of Channel Mismatches for Wideband TI-ADC System", electronics,2019,8 (56), pp.1-13), but an estimation Method of offset mismatch is not described, and data does not remove the influence of offset mismatch before gain mismatch and phase mismatch estimation, so that the estimation accuracy of Channel mismatch is reduced; the frequency of the test frequency point in the article needs to cover the whole first Nyquist domain, and the workload of data acquisition and processing is increased. In order to make the dynamic performance of the cross sampling system after correction close to the performance of its sub-channels, accurate estimation is performed on the mismatch of the three channels within the frequency band of interest.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a channel mismatch estimation method of a broadband cross sampling system.
The technical scheme of the invention is as follows: a channel mismatch estimation method of a broadband cross sampling system is disclosed, which comprises the following steps that aiming at an M-channel broadband cross sampling system, M is more than or equal to 2, bias mismatch, gain mismatch and phase mismatch are estimated:
where N =1,2, \ 8230, N, N is the length of the discrete sequence, N is large enough (N.gtoreq.32000) to reduce accidental errors; m =0,1, \ 8230, M-1,M is the number of channels; by ADC 0 Offset of 0 For reference, the bias mismatch of each channel is obtained:
o m ＝offset m -offset 0 ；
and step 5, performing frequency range expansion on the gain discrete function and the phase difference discrete function of each test frequency point obtained in the step 4, obtaining gain mismatch frequency response and phase mismatch frequency response of each channel of the cross sampling system according to the conjugate symmetry of real signal frequency response, and realizing accurate estimation of channel mismatch of the broadband cross sampling system.
Specifically, the step 4 includes the following steps:
step 401, according to the K data files obtained in step 3, subtracting o obtained in step 1 from each channel data in each data file m To eliminate the effect of bias mismatch;
step 402, obtaining the amplitude value and phase value of each channel at each test frequency point by using a sine fitting estimation method:
any single frequency sine wave expression can be written as:
x(t)＝Acos(2πf 0 t+φ)；
wherein f is 0 For sine wave frequencies, A is the amplitude and φ is the phase. From the properties of the trigonometric function the following form can be obtained:
x(t)＝A 0 cos(2πf 0 t)+B 0 sin(2πf 0 t)；
wherein
Let the sampling period of the ADC be T 1 According to N sampling points x [1 ]],x[2],…,x[N]A can be obtained by solving the minimum of the following formula by least squares 0 And B 0 ：
The ADC at f can then be estimated from the N samples 0 Amplitude a and phase ofφ。
Step 403, estimating the amplitude and phase of the data collected by each channel on each frequency point by using the method in step 402, so as to obtain the frequency f of the M channels of the broadband cross sampling system k Amplitude value A of m (f k ) And phase value phi m (f k ) Wherein M =0,1, \8230;, M-1,k =1,2, \8230;, K.
Step 404, selecting a reference channel to obtain a gain discrete function and a phase difference discrete function of each channel at each test frequency point: ADC with reference channel 0 Amplitude value A of 0 (f k ) And phase value phi 0 (f k ) For reference, the frequency f of each channel can be obtained k Gain dispersion function of (1):
g m (f k )＝A m (f k )/A 0 (f k )
and a phase difference dispersion function:
τ m (f k )＝φ 0 (f k )-φ m (f k )+f k /f S ·2π·m。
specifically, the step 5 includes the following steps:
step 501, performing frequency range expansion on the gain discrete function and the phase difference discrete function of each test frequency point obtained in step 404: the working frequency band of the broadband cross sampling system is f L ,f H ]Then [0, f L ) And (f) H ,f S /2]To disregard the frequency bands, each channel is in the frequency band 0, f L ) May be respectively represented by g m (f 1 ) And τ m (f 1 ) Instead, frequency band (f) H ,f S /2]May be respectively represented by g m (f K ) And τ m (f K ) Instead, a gain discrete function and a phase difference discrete function are obtained, wherein the frequency range corresponds to the complete first nyquist domain.
Step 502, obtaining a gain mismatch frequency response and a phase mismatch frequency response of each channel of the broadband cross sampling system according to the conjugate symmetry of the real signal frequency response, and realizing accurate estimation of the channel mismatch of the broadband cross sampling system: according to the conjugate symmetry of the real signal frequency response, the result in step 501 can obtain the mismatch frequency response of each channel of the broadband cross sampling system:
wherein
And then gain mismatch frequency response and phase mismatch frequency response of each acquisition channel are obtained, and accurate estimation of the broadband cross sampling system channel mismatch is realized.
The invention has the beneficial effects that: the method comprises the steps of performing offset mismatch estimation on noise data acquired by a broadband cross sampling system, obtaining an amplitude value and a phase value of each channel at each test frequency point by adopting an estimation method based on sine fitting, selecting a reference channel to obtain a gain discrete function and a phase difference discrete function of each channel at each test frequency point, and finally performing frequency range expansion on the obtained gain discrete function and phase difference discrete function of each test frequency point to obtain gain mismatch frequency response and phase mismatch frequency response of each channel; the influence of bias mismatch is removed before the gain mismatch and phase mismatch estimation is carried out on the data, so that the estimation precision of channel mismatch is improved; data acquisition and processing are only needed to be carried out on the concerned frequency band, and the gain mismatch and the phase mismatch of the unconcerned frequency band are obtained by carrying out frequency range extension on the gain discrete function and the phase difference discrete function of each test frequency point, so that the workload of data acquisition and processing in the channel mismatch estimation process is reduced.
Drawings
Fig. 1 is an ideal structure diagram of an M-channel cross sampling system according to the channel mismatch estimation method of a broadband cross sampling system of the present invention;
fig. 2 is a schematic diagram of an acquisition recording system in an embodiment of a channel mismatch estimation method for a broadband cross sampling system according to the present invention;
FIG. 3 is a flow chart of an embodiment of a method for estimating channel mismatch in a broadband cross sampling system according to the present invention;
fig. 4 shows the channel mismatch frequency response of each channel estimated in the embodiment of the channel mismatch estimation method for the broadband cross sampling system of the present invention, where (a) is the gain mismatch frequency response, and (b) is the phase mismatch frequency response.
Detailed Description
The invention is further described with reference to the following drawings and specific embodiments.
Channel mismatch can seriously reduce the dynamic performance of a cross sampling system, and accurate channel mismatch estimation is a key condition for realizing cross sampling channel mismatch compensation. The invention aims at a broadband cross sampling system to estimate bias mismatch, gain mismatch and phase mismatch. Firstly, a cross sampling system collects and records noise and estimates the bias mismatch of each channel; secondly, selecting test frequency points at equal frequency intervals in the concerned frequency band; then, the cross sampling system sets a signal generator according to the selected test frequency points, and collects and records data of each test frequency point to obtain data files of all the test frequency points; sequentially reading the data file of each test frequency point, obtaining the amplitude value and the phase value of each channel at each test frequency point by using a sine fitting estimation method, selecting a reference channel, and obtaining a gain discrete function and a phase difference discrete function of each channel at each test frequency point; and finally, performing frequency range expansion on the obtained gain discrete function and phase difference discrete function of each test frequency point, and obtaining gain mismatch frequency response and phase mismatch frequency response of each channel of the cross sampling system according to the conjugate symmetry of real signal frequency response, thereby realizing accurate estimation of the channel mismatch of the broadband cross sampling system.
For better illustration and understanding of the present invention, a four-channel wideband interleaved sampling system is exemplified herein. Fig. 2 is a schematic diagram of the composition of the broadband cross-sampling system of the present invention. In the two ADC chips of the system, 4 sub-ADCs with the sampling rate of 2.6GS/s are subjected to cross sampling to obtain a cross sampling system with the sampling rate of 10.4 GS/s. The system mainly comprises: the system comprises a collecting board, a clock board, an interface expansion board, a back board, a receiving board and a storage server. Two FPGA (Field Programmable Gate Array) acquisition cards in the form of FMC (Field Programmable Gate Array) are integrated on the acquisition board. The test signal is connected to a power divider, divided into two paths and respectively transmitted to two ADC chips of the acquisition board. A signal generator (SMJ 100A) provides a 100MHz reference clock for the system. The Reference clock is connected with the clock board, and the generated sampling clock and SYSREF (System Reference) clock are used for driving the acquisition board to acquire data. The backplane is mainly used for power supply and interconnection of the circuit boards. The sampling data is transmitted to an interface expansion board through a Gigabit high-speed serial bus (MGT), an optical Transceiver on the interface expansion board converts an electric signal into an optical signal, and the optical signal is transmitted to a receiving board of a storage server through an optical fiber. The receiving board transmits data to the memory of the storage server through a PCIE (Peripheral Component Interconnect Express) interface. The data is ultimately stored in the disk array of the server. The storage server runs acquisition and recording software, and the main functions of the software are to set a signal generator (E8257D) and control data recording according to the selected test frequency point. The broadband cross-sampling channel mismatch estimation algorithm also runs on the storage server.
For the wideband cross-sampling system shown in fig. 2, the flow of the implementation of the present invention is shown in fig. 3.
The bias mismatch during the analysis can be considered as a fixed value that does not vary with frequency. The signal generator closes the output and the system collects the noise. Setting the noise signal as x (t), closing the output of the signal generator, sampling by each channel of the cross sampling system to obtain the discrete time sequence x m (n), then the offset for each channel is:
wherein N =1,2, \8230;, N, N =32000 is the length of the discrete sequence; m =0,1, \8230:, M-1,m =4 is the number of channels. By ADC 0 Offset of 0 For reference purposesThe bias mismatch of each channel can be obtained:
o m ＝offset m -offset 0 。
operating band of acquisition system f L ,f H ]＝[100MHz,5000MHz]And K is taken as
Then K =491 testing frequency points are selected in the concerned frequency band at equal frequency intervals, and the frequency points to be collected are 100MHz, 110MHz, 120MHz, ·, 4990MHz and 5000MHz.
The initial value of the loop variable i in the acquisition and recording process is set to 1. When i is less than or equal to K, the cross sampling system sends a program control instrument Standard Command (SCPI) to the signal generator through the Ethernet, the frequency and the amplitude of the ith point are set, and the frequency is f i = (90 + 10. I) MHz, amplitude is-1 dB of ADC full scale. The signal generator returns a completion flag after completion of the setting. And after the system receives the completion mark, starting to record the acquired data when the output of the signal generator is stable, and naming the data file as i.dat. When a Direct Memory Access (DMA) is completed, the file record data size is 4MB, and the file record is ended. And circulating the variable i = i +1 until i > K, and ending the acquisition and recording process.
And then entering a process of reading a file and estimating the amplitude value and the phase value of each channel at each test frequency point by using a sine fitting estimation method. Let the initial value of the loop variable j be set to 1. When j is less than or equal to K, 32000 point data is read from the number of j.dat files, and then o is subtracted from each channel data m To eliminate bias mismatch.
Any single frequency sine wave expression can be written as:
x(t)＝Acos(2πf 0 t+φ)
wherein f is 0 For sine wave frequencies, A is the amplitude and φ is the phase. From the properties of the trigonometric function the following form can be obtained:
x(t)＝A 0 cos(2πf 0 t)+B 0 sin(2πf 0 t)
wherein
Sampling period of ADC
Record N =32000 sample points x [ 1%],x[2],…,x[N]A can be obtained by solving the minimum of the following formula by least squares 0 And B 0 ：
The ADC at f can then be estimated from the acquired sinusoidal sequence 0 Amplitude a and phase phi. And (4) circulating the variable j = j +1 until j is larger than K, and ending the process of estimating the amplitude value and the phase value of each channel at each test frequency point. Obtaining the frequency f of the 4 channels of a cross-sampled system k Amplitude value A of m (f k ) And phase value phi m (f k ) Wherein m =0,1,2,3, k =1,2, \ 8230;, 491.
By ADC 0 Amplitude discrete function A of 0 (f k ) And phase dispersion function phi 0 (f k ) For reference, the frequency f of each channel can be obtained k Gain dispersion function of (1):
g m (f k )＝A m (f k )/A 0 (f k )
and a phase difference dispersion function:
the obtained gain discrete function and phase difference discrete function are subjected to frequency range expansion, and the working frequency band of the acquisition system is [ f L ,f H ]＝[100MHz,5000MHz]Then [0,100MHz ] and (5000MHz, 5200MHz)]To disregard the frequency band, the gain and phase difference of each channel in the frequency band [0,100MHz ] can be represented by g m (100 MHz) and τ m (100 MHz) instead, frequency bands (5000MHz, 5200MHz)]May be respectively represented by g m (5000 MHz) and τ m (5000 MHz) to obtain a gain discrete function and a phase difference discrete function with a frequency range corresponding to the complete first nyquist domain.
Obtaining the mismatch frequency response of each channel of the system according to the conjugate symmetry of the real signal frequency response:
wherein
Namely, gain mismatch frequency response and phase mismatch frequency response of each acquisition channel are obtained, as shown in fig. 4, and accurate estimation of channel mismatch of the broadband cross sampling system is realized.
The above examples are only preferred embodiments of the present invention, and the use of the present invention is not limited to the examples, and any modifications, equivalent substitutions, improvements, etc. within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A channel mismatch estimation method of a broadband cross sampling system is used for estimating bias mismatch, gain mismatch and phase mismatch aiming at an M-channel broadband cross sampling system, wherein M is more than or equal to 2, and the method is characterized by comprising the following steps:
step 1, a broadband cross sampling system collects and records noise, and estimates the bias mismatch of each channel:
setting the noise signal as x (t), closing the output of the signal generator, sampling by each channel of the broadband cross sampling system to obtain the discrete time sequence x of the noise signal x (t) m (n), then the offset for each channel is:
wherein N =1,2, \8230, N is the length of the discrete sequence, and N is large enough to reduce accidental errors; m =0,1, \8230, M-1, M is the number of channels; with an ADC 0 Offset of 0 For reference, the bias mismatch for each channel is obtained:
o m ＝offset m -offset 0 ；
step 2, selecting K test frequency points at equal frequency intervals in the concerned frequency band: the working frequency band of the broadband cross sampling system is set as f L ,f H ]Wherein f is L ＞0，f H ＜f S /2，f S The sampling rate of a broadband cross sampling system is obtained, and the obtained K test frequency points to be collected are respectively f 1 ＝f L ,f 2 ,f 3 ,…,f K-1 ,f K ＝f H ；
Step 3, the broadband cross sampling system sets the frequency of the signal generator to be f according to the selected test frequency points in sequence 1 ,f 2 ,…,f K After the signal generator is set each time, the broadband cross sampling system respectively collects and records the signals of the K test frequency points on the premise of ensuring the stable output of the signal generator to obtain K data files;
step 4, sequentially reading the data file of each test frequency point, obtaining the amplitude value and the phase value of each channel at each test frequency point by using a sine fitting estimation method, and selecting a reference channel to obtain a gain discrete function and a phase difference discrete function of each channel at each test frequency point;
and step 5, performing frequency range expansion on the gain discrete function and the phase difference discrete function of each test frequency point obtained in the step 4, obtaining gain mismatch frequency response and phase mismatch frequency response of each channel of the cross sampling system according to the conjugate symmetry of real signal frequency response, and realizing accurate estimation of the channel mismatch of the broadband cross sampling system.
2. A method for estimating channel mismatch in a wideband cross-sampling system according to claim 1, wherein: the step 4 comprises the following steps:
step 401, according to the K data files obtained in step 3, subtracting o obtained in step 1 from each channel data in each data file m To eliminate the effect of bias mismatch;
step 402, obtaining the amplitude value and the phase value of each channel at each test frequency point by using a sine fitting estimation method:
any single frequency sine wave expression can be written as:
x(t)＝Acos(2πf 0 t+φ)；
wherein f is 0 Is the sine wave frequency, A is the amplitude, and φ is the phase; from the properties of the trigonometric function the following form can be obtained:
x(t)＝A 0 cos(2πf 0 t)+B 0 sin(2πf 0 t)
wherein
Let the sampling period of the ADC be T 1 According to N sampling points x [1 ]],x[2],…,x[N]Solving the minimum of the following formula by least squares to obtain A 0 And B 0 ：
From these N samples, the ADC at f can then be estimated 0 Amplitude a and phase phi of;
step 403, estimating the amplitude and phase of the data collected by each channel on each frequency point by using the method in step 402, so as to obtain the frequency f of the M channels of the broadband cross sampling system k Amplitude value A of m (f k ) And phase value phi m (f k ) Wherein M =0,1, \8230;, M-1, K =1,2, \8230; K;
step 404, selecting a reference channel to obtain the gain of each channel at each test frequency pointDiscrete function and phase difference discrete function: with reference channel ADC 0 Amplitude value A of 0 (f k ) And phase value phi 0 (f k ) For reference, the frequency f of each channel can be obtained k Gain dispersion function of (1):
g m (f k )＝A m (f k )/A 0 (f k )
and a phase difference dispersion function:
τ m (f k )＝φ 0 (f k )-φ m (f k )+f k /f S ·2π·m。
3. a method for estimating channel mismatch in a wideband cross-sampling system according to claim 1, wherein: the step 5 comprises the following steps:
step 501, performing frequency range expansion on the gain discrete function and the phase difference discrete function of each test frequency point obtained in step 404: the working frequency band of the broadband cross sampling system is f L ,f H ]Then [0, f L ) And (f) H ,f S /2]To disregard the frequency bands, each channel is in the frequency band [0, f L ) May be respectively represented by g m (f 1 ) And τ m (f 1 ) Instead, frequency band (f) H ,f S /2]May be respectively represented by g m (f K ) And τ m (f K ) Replacing, so as to obtain a gain discrete function and a phase difference discrete function of which the frequency range corresponds to the complete first Nyquist domain;
step 502, obtaining gain mismatch frequency response and phase mismatch frequency response of each channel of the broadband cross sampling system according to the conjugate symmetry of real signal frequency response, and realizing accurate estimation of the channel mismatch of the broadband cross sampling system: according to the conjugate symmetry of the real signal frequency response, the result in step 501 can obtain the mismatch frequency response of each channel of the wideband cross sampling system:
wherein
And obtaining gain mismatch frequency response and phase mismatch frequency response of each acquisition channel, and realizing accurate estimation of the channel mismatch of the broadband cross sampling system.
4. A method for estimating channel mismatch in a wideband cross-sampling system according to claim 1, wherein: in step 1, the length N of the discrete sequence is equal to or more than 32000.
5. A method for estimating channel mismatch in a wideband cross-sampling system according to claim 1, wherein: in step 2, in order to obtain an accurate estimation result, the value of K is
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