CN112311394A - Method for accurately calibrating relative delay of array channels - Google Patents

Method for accurately calibrating relative delay of array channels Download PDF

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CN112311394A
CN112311394A CN202011234304.6A CN202011234304A CN112311394A CN 112311394 A CN112311394 A CN 112311394A CN 202011234304 A CN202011234304 A CN 202011234304A CN 112311394 A CN112311394 A CN 112311394A
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戴卫华
王彬
李天昀
吴微
胡泽明
张光伟
于沛东
郭悦
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Information Engineering University of PLA Strategic Support Force
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Abstract

The invention provides a method for accurately calibrating relative delay of array channels. The method comprises the following steps: transmitting calibration signals from a far field to receiving ends of all channels of the array in a preset direction, and simultaneously acquiring signals of all channels by adopting AD (analog-to-digital) synchronous acquisition; selecting one channel signal as a reference signal, and then respectively carrying out delay filtering on other channel signals except the reference signal by adopting an FIR delay filter group obtained by cutting off a group of ideal delay filters to obtain a delay signal set of other channels except the channel where the reference signal is located; and carrying out correlation operation on the reference signal and the delay signal sets of other channels, determining initial relative delay by searching a correlation peak, and removing propagation delay of each channel from the initial relative delay to obtain the calibrated relative delay between the channels. The invention can overcome the limitation of AD sampling rate to the calibration delay precision of the correlation method and improve the calibration precision of the relative delay of the array channel.

Description

Method for accurately calibrating relative delay of array channels
Technical Field
The invention relates to the technical field of array signal processing, in particular to an accurate calibration method for relative delay of array channels.
Background
In the field of array signal processing, it is often necessary to calibrate the relative delay or carrier phase difference between each array element channel. The accurate calibration of the relative delay or the carrier phase difference of the channels is a precondition for applying most array beam forming methods and signal direction of arrival estimation methods. Such as Conventional Beamforming (CBF), Minimum Variance Distortionless Response (MVDR), and MUltiple SIgnal classification (MUSIC), etc., without exception, it is not necessary to precisely calibrate the channel relative delay or carrier phase difference. For a line spectrum or narrow-band signal scene, the relative delay calibration of the array channel can be directly simplified into the calibration of the channel carrier phase difference; but for a broadband signal scenario, the carrier phase difference calibration cannot replace the channel relative delay calibration. Compared with the channel carrier phase difference calibration, the channel relative delay calibration is more basic and universal.
The correlation method is the main method for calibrating the relative delay of array channels, especially for broadband signals. The correlation method (Zhanguan. broadband multichannel phase delay measurement and correction technology research [ D ]. electronic science and technology university. 2015) is generally carried out in a digital domain, namely, calibration signals of all channels received by an array are collected firstly, then time domain correlation is carried out on the collected digital signals of all channels, and relative delay of the channels is determined by searching correlation peaks. When the relative delay of the channel is calibrated by adopting the correlation method, the sampling frequency determines the calibration precision of the relative delay of the channel. The higher the sampling frequency, the higher the channel relative delay calibration accuracy. However, many ADs can only operate below the maximum sampling rate, limited by the hardware level. Taking two AD chips of AD9361 and ADRV9009 as examples, the maximum sampling rates are 61.44MHz and 245.760MHz respectively.
However, if the correlation is performed directly with the channel signal sampled by AD, the channel relative delay calibration accuracy is equal to the sampling interval, i.e., the inverse of the sampling frequency. The calibration accuracy may be too high to meet subsequent array signal processing requirements. For example, taking a 1GHz carrier radio signal as an example, the half wavelength is about 0.15 m. If the linear array is adopted for beam forming and direction finding, the distance between adjacent array elements cannot exceed 0.15m, and the signal propagation delay difference does not exceed +/-0.5 ns. If the beam forming and direction finding algorithm is successfully applied, the relative delay calibration accuracy of the channel needs to be at least higher than one order of magnitude, namely better than 0.05 ns. The sampling frequency corresponding to the 0.05ns delay calibration accuracy is as high as 20GHz, which is obviously not achieved by most AD chips.
Disclosure of Invention
In order to overcome the limitation of AD sampling frequency on the calibration delay precision of a correlation method, the invention provides an array channel relative delay precision calibration method.
The invention provides a method for accurately calibrating relative delay of an array channel, which comprises the following steps:
step 1: transmitting calibration signals from a far field to receiving ends of all channels of the array in a preset direction, and simultaneously acquiring signals of all channels by adopting AD (analog-to-digital) synchronous acquisition;
step 2: selecting one channel signal as a reference signal, and then respectively carrying out delay filtering on other channel signals except the reference signal by adopting an FIR delay filter group obtained by cutting off a group of ideal delay filters to obtain a delay signal set of other channels except the channel where the reference signal is located;
and step 3: and carrying out correlation operation on the reference signal and the delay signal sets of other channels, determining initial relative delay by searching a correlation peak, and removing propagation delay of each channel from the initial relative delay to obtain the calibrated relative delay between the channels.
Further, in step 1, a predetermined direction is selected according to the array configuration.
Further, if the array is a linear array, a direction perpendicular to a base line where the array is located is selected as a preset direction.
Further, the FIR delay filter bank in step 2 is:
Figure BDA0002766243110000021
wherein eta is1,η2…,ηKIs a value obtained by equally dividing the (0,1) interval K,
Figure BDA0002766243110000022
k＝1,2,…,K.，nmthe value of an integer part is obtained after the relative delay between the channel signal of the channel m and the reference signal is converted into the sampling interval multiple; m is the number of channels in the array.
Further, channel signal x obtained by filtering through FIR delay filter bankmSet of delayed signals ym,1(n),ym,2(n),…ym,K(n) } is:
Figure BDA0002766243110000031
wherein x ismAnd representing the acquired channel signal of the channel m, and N is the signal length of each channel.
Further, according to the channel signal of the channel m and the reference signal, the sliding correlation in the time domain and the searching of the correlation peak are carried out to obtain nm：
Figure BDA0002766243110000032
Wherein arg { max { r }m(i) Represents the sequence rm(i) The time at which the maximum is located.
Further, step 3 specifically comprises:
step 3.1: and carrying out correlation operation on the reference signal and the delayed signal sets of other channels according to the following formula:
Figure BDA0002766243110000033
wherein R ism(1),Rm(2),…Rm(K) Representing the correlation operation result of the reference signal and the delay signal set of the channel m;
step 3.2: from Rm(1),Rm(2),…Rm(K) Searching correlation peak, determining fractional delay corresponding to the correlation peak as fractional part of relative delay, and recording as etac,m(ii) a Compensating for integer delay part nmAnd removing the propagation delay difference (tau) of each channel signalm-τc) The relative time delay between the channel m and the channel of the reference signal is obtained and is recorded as delta tauc,m：
Figure BDA0002766243110000041
Wherein, taucCalibrating the propagation delay of a signal from a far field to a receiving end of a channel where a reference signal is located; tau ismCalibrating the propagation delay of a signal from a far field to a receiving end of a channel m; f. ofsRepresenting the sampling frequency.
The invention has the beneficial effects that:
according to the method for accurately calibrating the relative delay of the array channel, when the relative delay of the channel is calibrated by adopting a correlation method, the limitation of the AD sampling rate on the calibration delay precision of the correlation method is overcome by accurately delaying and filtering signals of each channel based on a filtering interpolation method, and the calibration precision of the relative delay of the array channel is improved. The calibration method is irrelevant to signal frequency, and can be well applied to both narrow-band signal scenes and broadband signal scenes.
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Fig. 1 is a schematic flow chart of a method for accurately calibrating relative delay of array channels according to an embodiment of the present invention;
fig. 2 is a second flowchart of a method for accurately calibrating relative delay of array channels according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 1, an embodiment of the present invention provides a method for accurately calibrating relative delay of array channels, including:
s101: transmitting calibration signals from a far field to receiving ends of all channels of the array in a preset direction, and simultaneously acquiring signals of all channels by adopting AD (analog-to-digital) synchronous acquisition;
specifically, the purpose of selecting the preset direction is to remove the signal propagation delay when calibrating the relative delay of the channel; the aim of emitting the calibration signal from the far field is to ensure that the receiving end of each channel of the array approximately receives the plane wave. For example, assuming that there are M channels in the array, the propagation delay of the calibration signal from the far field to the receiving end of each channel can be sequentially denoted as τ1,τ2,…,τM(ii) a The signals of each channel can be sequentially denoted as x1(n),x2(n),…,xMN is 0,1, …, N-1, N represents the signal length of each channel.
In practical applications, the predetermined direction can be selected according to the array configuration
Figure BDA0002766243110000051
Theta is the azimuth angle and theta is the azimuth angle,
Figure BDA0002766243110000052
is a pitch angle. For example, if the array is a linear array, a direction perpendicular to a baseline of the array may be selected as a preset direction, and then the calibration signal is transmitted from a far fieldAt this time, the propagation delay of the calibration signals received by the receiving ends of the channels of the linear array can be considered to be equal, and the propagation delay of the signals does not need to be additionally removed when the relative delay of the channels is calibrated.
S102: selecting one channel signal as a reference signal, and then respectively carrying out delay filtering on other channel signals except the reference signal by adopting an FIR delay filter group obtained by cutting off a group of ideal delay filters to obtain a delay signal set of other channels except the channel where the reference signal is located;
specifically, for convenience of description, the channel in which the reference signal is located is denoted as channel c, and correspondingly, the reference signal is denoted as xc. The FIR delay filter bank in the embodiment of the invention is as follows:
Figure BDA0002766243110000053
wherein eta is1,η2…,ηKIs a value obtained by equally dividing the (0,1) interval K,
Figure BDA0002766243110000054
k＝1,2,…,K.，nmthe value of an integer part is obtained after the relative delay between the channel signal of the channel m and the reference signal is converted into the sampling interval multiple; m is the number of channels in the array. Eta1,η2…,ηKAnd the relative delay between the channel signal corresponding to the channel m and the reference signal is converted into a possible value of a fraction part after the sampling interval is multiplied.
Eta. to be noted1,η2…,ηKIs equally divided into equal intervals
Figure BDA0002766243110000055
The length L of the delay filter (2M +1) will directly determine the delay filtering accuracy and will also determine the channel relative delay calibration accuracy. The smaller the equal division interval is, the longer the delay filter length is, the higher the delay filtering precision is, and the higher the relative delay calibration precision of the channel is. For each channel, hm,1(n),hm,2(n),…,hm,KAnd (n) is a FIR delay filter group obtained by cutting through a group of ideal delay filters. When the FIR delay filter length is sufficiently long, the delay of the filter output relative to the filter input will be sufficiently close to the group delay of an ideal delay filter, i.e. the group delay
Figure BDA0002766243110000061
Channel signal x obtained by filtering through FIR (finite Impulse response) delay filter bankmSet of delayed signals ym,1(n),ym,2(n),…ym,K(n) } is:
Figure BDA0002766243110000062
wherein x ismAnd representing the acquired channel signal of the channel m, and N is the signal length of each channel.
N in the abovemAnd performing sliding correlation on the channel signal of the channel m and the reference signal in the time domain and searching a correlation peak to obtain the correlation peak, as shown in the following formula:
Figure BDA0002766243110000063
wherein arg { max { r }m(i) Represents the sequence rm(i) The time at which the maximum is located.
S103: and carrying out correlation operation on the reference signal and the delay signal sets of other channels, determining initial relative delay by searching a correlation peak, and removing propagation delay of each channel from the initial relative delay to obtain the calibrated relative delay between the channels.
Specifically, first, the reference signal and the delayed signal sets of other channels are correlated according to the following formula:
Figure BDA0002766243110000064
wherein R ism(1),Rm(2),…Rm(K) Representing the correlation operation result of the reference signal and the delay signal set of the channel m;
it should be noted that, in the embodiment of the present invention, when each delay signal is correlated with a reference signal, only the waveform of the interval N ∈ [ M, N-M-1] is selected, and the length is (N-2M). The reason is that compared with the input, the waveform of the FIR delay filter is distorted in the interval N epsilon [0, M-1] near the filtering start time and the interval N epsilon (N-M-1, N + L-2] near the filtering end time, and the fidelity of the interval N epsilon [ M, N-M-1] in the middle is extremely high. Waveform distortion is caused by the finite length of the channel signal, and for FIR filtering, as long as the input length is finite, the output is distorted near the start and end times. In order to perform correlation using sufficiently long undistorted waveforms, in channel calibration scenarios where real-time requirements are not high, a long calibration signal can be transmitted and collected such that N > 2M.
Then from Rm(1),Rm(2),…Rm(K) Searching correlation peak, determining fractional delay corresponding to the correlation peak as fractional part of relative delay, and recording as etac,m(ii) a Compensating for integer delay part nmAnd removing the propagation delay difference (tau) of each channel signalm-τc) The relative time delay between the channel m and the channel of the reference signal is obtained and is recorded as delta tauc,m：
Figure BDA0002766243110000071
Wherein, taucCalibrating the propagation delay of a signal from a far field to a receiving end of a channel where a reference signal is located; tau ismCalibrating the propagation delay of a signal from a far field to a receiving end of a channel m; f. ofsRepresenting the sampling frequency.
Example 2
On the basis of the above embodiment 1, in the embodiment of the present invention, the channel signal x of the channel 1 is selected1(n) as a reference signal, for example, the relative delay between channel 2 and channel 1 is precisely calibrated, as shown in FIG. 2, by using the method of the present inventionThe process of (2) is as follows:
s201: and synchronously acquiring array channel signals. This step is the same as S101 in the embodiment, and is not described here again.
S202: and delay filtering the channel signals. The FIR delay filter is:
Figure BDA0002766243110000081
wherein the content of the first and second substances,
Figure BDA0002766243110000082
k＝1,2,…,K.，
Figure BDA0002766243110000083
i＝…,-1,0,1,…。
channel signal x of selected channel 11(n) as reference signal, channel 2 as an example, channel signal x2(n) the delayed signal sets obtained by filtering through the FIR delayed filter bank are:
Figure BDA0002766243110000084
s203: the channel signal correlation determines the relative delay. Channel signal x1(n) and channel signal x2(n) performing a correlation operation to determine the relative delay between channel 2 and channel 1, the correlation operation is as follows:
Figure BDA0002766243110000085
then, from R2(1),R2(2),…R2(K) Searching correlation peak, determining fractional delay corresponding to the correlation peak as fractional part of relative delay, and recording as eta1,2(ii) a Compensating for integer delay part n2And removing the propagation delay difference (tau) of each channel signal2-τ1) The relative delay between the channels is obtained and is recorded as delta tau1,2。
Figure BDA0002766243110000091
The relative delay accurate calibration of the pass 2 and the channel 1 is completed. The relative delay calibration procedure for the other channels and channel 1 is similar.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (7)

1. A method for accurately calibrating relative delay of array channels is characterized by comprising the following steps:
step 1: transmitting calibration signals from a far field to receiving ends of all channels of the array in a preset direction, and simultaneously acquiring signals of all channels by adopting AD (analog-to-digital) synchronous acquisition;
step 2: selecting one channel signal as a reference signal, and then respectively carrying out delay filtering on other channel signals except the reference signal by adopting an FIR delay filter group obtained by cutting off a group of ideal delay filters to obtain a delay signal set of other channels except the channel where the reference signal is located;
and step 3: and carrying out correlation operation on the reference signal and the delay signal sets of other channels, determining initial relative delay by searching a correlation peak, and removing propagation delay of each channel from the initial relative delay to obtain the calibrated relative delay between the channels.
2. The method for accurately calibrating relative delay of array channels according to claim 1, wherein in step 1, the predetermined direction is selected according to the array configuration.
3. The method for accurately calibrating the relative delay of the array channel according to claim 2, wherein if the array is a linear array, a direction perpendicular to a base line where the array is located is selected as the preset direction.
4. The method for accurately calibrating relative delay of array channels according to claim 1, wherein the FIR delay filter bank in step 2 is:
Figure FDA0002766243100000011
wherein eta is1,η2…,ηKIs a value obtained by equally dividing the (0,1) interval K,
Figure FDA0002766243100000012
nmthe value of an integer part is obtained after the relative delay between the channel signal of the channel m and the reference signal is converted into the sampling interval multiple; m is the number of channels in the array.
5. The method of claim 4, wherein the channel signal x obtained by filtering with the FIR delay filter bank is used as the channel signal xmSet of delayed signals ym,1(n),ym,2(n),…ym,K(n) } is:
Figure FDA0002766243100000021
wherein x ismAnd representing the acquired channel signal of the channel m, and N is the signal length of each channel.
6. The method for accurately calibrating relative delay of array channels according to claim 4 or 5, wherein n is obtained by performing sliding correlation between the channel signal of channel m and the reference signal in the time domain and searching a correlation peakm：
Figure FDA0002766243100000022
Wherein arg { max { r }m(i) Represents the sequence rm(i) The time at which the maximum is located.
7. The method for accurately calibrating the relative delay of the array channel according to claim 5, wherein the step 3 specifically comprises:
step 3.1: and carrying out correlation operation on the reference signal and the delayed signal sets of other channels according to the following formula:
Figure FDA0002766243100000023
wherein R ism(1),Rm(2),…Rm(K) Representing the correlation operation result of the reference signal and the delay signal set of the channel m;
step 3.2: from Rm(1),Rm(2),…Rm(K) Searching correlation peak, determining fractional delay corresponding to the correlation peak as fractional part of relative delay, and recording as etac,m(ii) a Compensating for integer delay part nmAnd removing the propagation delay difference (tau) of each channel signalm-τc) Obtaining the relative time delay between the channel m and the channel of the reference signal, and recording the relative time delay as delta tauc,m：
Figure FDA0002766243100000031
Wherein, taucCalibrating the propagation delay of a signal from a far field to a receiving end of a channel where a reference signal is located; tau ismCalibrating the propagation delay of a signal from a far field to a receiving end of a channel m; f. ofsRepresenting the sampling frequency.
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