CN113726453B - Method for calibrating broadband antenna array in time domain - Google Patents
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Abstract
The invention discloses a method for calibrating a broadband antenna array in the time domain, which comprises the steps of calibrating the antenna array in the time domain, determining the time delay range according to the number of antennas, applying a simultaneous disturbance random estimation (SPSA) algorithm, and respectively using P in And P k Difference between P and P in Ratio of sum 1-R k As a loss function, the target time delay is obtained by optimization, the algorithm can be directly applied to the calibration of the broadband antenna array, and the problems of excessive measurement times and low efficiency existing in the traditional phase calibration in the frequency domain are greatly reduced. The method for realizing synchronous receiving of each unit of the antenna array by utilizing random disturbance and iterative calibration time delay in the time domain makes up the blank of realizing the calibration of the broadband antenna array in the time domain, solves the problem of excessive measurement times in the current frequency domain calibration method of the antenna array, and greatly improves the efficiency of calibrating the broadband antenna array.
Description
Technical Field
The invention relates to a method for calibrating a broadband antenna array in a time domain, belonging to the fields of microwave engineering and automatic control.
Background
The aperture array has wide application prospect and advantage in the fields of microwave engineering and technology. A high signal-to-noise ratio can be obtained even without any mechanical operation, while directional disturbance can be suppressed and multi-beam scanning can be achieved. However, accurate pointing of the phased array antenna beam requires accurate control of the phase and amplitude of each element, requiring a large number of array antennas to maximize array performance. Thus, achieving phase calibration of an array antenna is of great significance for aperture array applications. Most of the existing calibration methods are to perform phase calibration in the frequency domain. The number of measurements required for these methods can be very large. The time domain phase calibration method provided by the scheme can effectively reduce the measurement times in the calibration process. The present approach uses a simultaneous disturbance random estimation (Simultaneous Perturbation Stochastic Approximation, SPSA) algorithm during calibration, which is an efficient way to achieve multi-parameter optimization. In the implementation process of the algorithm, the gradient problem of the general optimization algorithm is solved. The scheme realizes the calibration of the broadband antenna array in the time domain by applying the algorithm.
Disclosure of Invention
The invention aims to: the invention provides a method for calibrating a broadband antenna array in the time domain, which is used for assuming that a source signal is a short pulse working in the time domain. The invention uses the simultaneous disturbance random estimation (SPSA) optimization algorithm to respectively use P in And P k Difference between P and P in Ratio of sum 1-R k As a loss function, the target time delay is obtained by optimization, the algorithm can be directly applied to the calibration of the broadband antenna array, and the problems of excessive measurement times and low efficiency existing in the traditional phase calibration in the frequency domain are greatly reduced.
The technical scheme is as follows: a method for calibrating a broadband antenna array in a time domain comprises the steps of calibrating the antenna array in the time domain, determining a time delay range according to the number of antennas, and optimizing by using a simultaneous disturbance random estimation (SPSA) algorithm so as to obtain corresponding time delays of all the antennas; in the algorithm, P is respectively used in And P k Difference between P and P in Ratio of sum 1-R k As a function of loss. The method specifically comprises the following steps:
step 1, determining a range of time t and an input source signal s (t);
step 2, determining the time delay of each antenna according to the number of antennas, that is, when the number of antennas is N, the instantaneous time delay vector of each antenna can be expressed as T in And the maximum delay range of each channel is [ -0.01XN, 0.01XN]；
Step 3, determining an instantaneous delay vector T in And the estimated delay vector T k Where the number of iterations k=0;
step 4, receiving the source signal transmitted in the far field of the array through an actual antenna array system, and outputting an instantaneous signal S by the receiving system in Measuring instantaneous signal power P in ；
Step 5, inputting source signals in the virtual receiving system constructed in the algorithm to generate a predicted delay vector T k Representing the estimated time delay of each antenna, outputting an estimated signal S synthesized according to the estimated time delay k Measuring the estimated signal power P k ；
Step 6, respectively using P in And P k Difference between P and P in Ratio of sum 1-R k As a loss function, where R k Is S in And S is equal to k Is a correlation coefficient of (2); optimizing time delay by using a simultaneous disturbance random estimation algorithm, and obtaining an estimated signal S conforming to convergence conditions through k iterations k At this time, the corresponding estimated delay vector T k Can be used to calibrate the instantaneous delay vector T in 。
Further, in the step 6, P is in And P k Difference between P and P in The specific steps of optimizing the time delay by using the simultaneous disturbance random estimation algorithm are as the loss function:
s1, with P in And P k Difference between P and P in Ratio ofAs a loss function, a parameter ap is determined k ,cp k The method comprises the steps of carrying out a first treatment on the surface of the Wherein P is in For instantaneous signal power, P k To estimate the signal power;
s2, whenIn the time-course of which the first and second contact surfaces,
T k+1 ＝T k -ap k gp k (2)
k＝k+1 (3)
wherein gp is k Is a gradient vector generated by the perturbation; and (V) k Is an M-dimensional vector, where M is the number of antenna elements in the array, its elements are +1, -1, and the bernoulli distribution with probability of 0.5 is met;
s3, judgingIf true, record T at this time k The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to the step S2.
Further, the ap k ,cp k To ensure gradient vector gp k Does not spread with the increase of the iteration number, and recommends a value ap k Less than 0.01P in Recommended value cp k Less than 0.001P in 。
Further, in the step 6, 1-R is used k As a loss function, the specific steps of optimizing the time delay by using the simultaneous disturbance random estimation algorithm are as follows:
p1, S in And S is equal to k Is a functional correlation coefficient of R k Will L r ＝1-R k As a loss function, the parameter ar is determined k ,cr k ，
Wherein Cov (S in ,S k ) Is S in And S is equal to k Covariance of Var [ S ] in ]Is S in Variance of Var [ S ] k ]Is S k Is a variance of (2);
p2, when L r ＝1-R k When the temperature is more than or equal to 0.01,
T k+1 ＝T k -ar k gr k (6)
k＝k+1 (7)
wherein gr k Representing gradient vectors generated by the perturbation; and (V) k Is an M-dimensional vector, where M is the number of antenna elements in the array, its elements are +1, -1, and the bernoulli distribution with probability of 0.5 is met;
p3, judge L r ＝1-R k <0.01 is established, if so, recording T at the time k The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to the step P2.
Further, the ar k ,cr k The gradient vector gr is to be guaranteed k Does not spread with the increase of the iteration number, and recommends a value cr k ＝0.01，ar k The following are provided:
the beneficial effects are that:
the invention provides a method for calibrating a broadband antenna array in the time domain, which directly uses a short pulse broadband signal in the time domain, applies SPSA algorithm and uses P respectively in And P k Difference between P and P in Ratio of sum 1-R k And simultaneously perturbing each channel as a loss function, and obtaining the corresponding time delay of each antenna through iteration until the convergence condition is met, thereby realizing the calibration of the phased array in the time domain. The traditional antenna array is calibrated in the frequency domain, the method creatively proposes to directly calibrate in the time domain, the condition of excessive measurement and calculation times in the past calibration is improved, the efficiency of realizing the array antenna calibration is greatly improved, and the guarantee is provided for the ultra-wideband phased array antenna, in particular for the application of a large-scale array.
Drawings
FIG. 1 shows an ideal output signal and a source signal received by an actual antenna array system, the receiving system outputting an instantaneous signal S in The number of antennas at this time is 10.
FIG. 2 shows an instantaneous signal and a predicted signal after time domain calibration.
FIG. 3 shows that the loss function is P in And P k Difference between P and P in The number of antennas is compared with the iteration of the algorithmTimes k and T in And T is k Is a standard deviation relation graph of (2).
FIG. 4 shows a loss function of 1-R k The number of antennas and the number of iterations k and T in And T is k Is a standard deviation relation graph of (2).
Fig. 5 is a graph of the number of iterations k versus the rate of convergence of the loss function for two loss function cases.
Fig. 6 is a flowchart of the algorithm of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
in this embodiment, a phased array antenna with the number N of antennas being 1000 is taken as an example, and the instantaneous delay vector of the antenna array is T in The instantaneous signal is S in Measuring to obtain the instantaneous signal power P in . Generating an initial estimated delay vector T 0 Range and T in The same applies.
With P in And P k Difference between P and P in The ratio is used as a loss function, SPSA algorithm is used for optimizing time delay, and k iterations are carried out to obtain an estimated signal S meeting convergence conditions k At this time, the corresponding estimated delay vector T k Can be used for calibrating the time delay vector T in 。
Will S in And S is equal to k The phase relation number of (C) is recorded as R k At 1-R k For loss function, the SPSA algorithm is used for optimizing time delay, and k iterations are carried out to obtain an estimated signal S meeting convergence conditions k At this time, the corresponding estimated delay vector T k Can be used for calibrating the time delay vector T in 。
A method for calibrating a wideband antenna array in the time domain, as shown in fig. 6, comprising the steps of:
step 1, determining a time range t;
-15ns≤t≤15ns (1)
step 2, determining an input source signal s (t), wherein the input source signal s (t) is:
step 3, determining T according to the number N of antennas in the phased array in And T k For example, when the number of antennas n=1000, T in And T k Is defined by the range of (2);
-0.01N≤T in ,T 0 ≤0.01N (3)
T in ＝[T in,1 T in,2 … T in,m … T in,N ] (4)
T k ＝[T k,1 T k,2 … T k,m … T k,N ] (5)
step 4, determining an initial output signal S in And measure its power P in ；
P in ＝E{|S in (t)| 2 } (7)
Step 5, determining the loss function and the parameter ap k ,cp k
ap k ＝0.01 (9)
cp k ＝0.001 (10)
Step 6, whenIn the time-course of which the first and second contact surfaces,
T k+1 ＝T k -ap k gp k (12)
k＝k+1 (13)
wherein, is delta k Is an M-dimensional vector in whichM is the number of antenna elements in the array, the elements of which are +1, or-1, and which conform to a Bernoulli distribution with a probability of 0.5;
step 7, judgingIf true, record T at this time k Otherwise, returning to the step 6.
Step 8, determining a loss function and a parameter ar k ,cr k
L r ＝1-R k (14)
cr k ＝0.01 (16)
Wherein Cov (S in ,S k ) Is S in And S is equal to k Covariance of Var [ S ] in ]Is S in Variance of Var [ S ] k ]Is S k Is a variance of (2);
step 9, when L r ＝1-R k When the temperature is more than or equal to 0.01,
T k+1 ＝T k -ar k gr k (19)
k＝k+1 (20)
wherein, is delta k Is an M-dimensional vector, where M is the number of antenna elements in the array, its elements are +1, or-1, and conforms to a bernoulli distribution with a probability of 0.5;
step 10, judging L r ＝1-R k <0.01 is established, if so, recording T at the time k Otherwise, returning to the step 9.
Claims (5)
1. A method for calibrating a wideband antenna array in the time domain, wherein the method is directly calibrated in the time domain and can be applied to a large-scale array, comprising the steps of:
step 1, determining a range of time t and an input source signal s (t);
step 2, determining the time delay of each antenna according to the number of antennas, that is, when the number of antennas is N, the instantaneous time delay vector of each antenna can be expressed as T in And the maximum delay range of each channel is [ -0.01XN, 0.01XN]；
Step 3, determining an instantaneous delay vector T in And the estimated delay vector T k Where the number of iterations k=0;
step 4, receiving the source signal transmitted in the far field of the array through an actual antenna array system, and outputting an instantaneous signal S by the receiving system in Measuring instantaneous signal power P in ；
Step 5, inputting source signals in the virtual receiving system constructed in the algorithm to generate a predicted delay vector T k Representing the estimated time delay of each antenna, outputting an estimated signal S synthesized according to the estimated time delay k Measuring the estimated signal power P k ；
Step 6, respectively using P in And P k Difference between P and P in Ratio of sum 1-R k As a loss function, where R k Is S in And S is equal to k Is a correlation coefficient of (2); optimizing time delay by using a simultaneous disturbance random estimation algorithm, and obtaining an estimated signal S conforming to convergence conditions through k iterations k At this time, the corresponding estimated delay vector T k Can be used to calibrate the instantaneous delay vector T in 。
2. The method of claim 1, wherein in step 6, P is used for calibrating the wideband antenna array in the time domain in And P k Difference between P and P in The specific steps of optimizing the time delay by using the simultaneous disturbance random estimation algorithm are as the loss function:
s1, with P in And P k Difference between P and P in Ratio ofAs a loss function, a parameter ap is determined k ,cp k The method comprises the steps of carrying out a first treatment on the surface of the Wherein P is in For instantaneous signal power, P k To estimate the signal power;
s2, whenIn the time-course of which the first and second contact surfaces,
T k+1 ＝T k -ap k gp k (2)
k＝k+1 (3)
wherein gp is k Is a gradient vector generated by the perturbation; and (V) k Is an M-dimensional vector, where M is the number of antenna elements in the array, its elements are +1, -1, and the bernoulli distribution with probability of 0.5 is met;
s3, judgingIf yes, recording the T at the moment k The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to the step S2.
3. A method for performing calibration in the time domain for a wideband antenna array as recited in claim 2, wherein said ap k ,cp k The gradient vector gp is ensured to be valued k Does not spread as the iteration number increases, ap k Less than 0.01P in ，cp k Less than 0.001P in 。
4. A method for performing calibration in the time domain for a wideband antenna array as recited in claim 1The method is characterized in that in the step 6, 1-R is used k As a loss function, the specific steps of optimizing the time delay by using the simultaneous disturbance random estimation algorithm are as follows:
p1, S in And S is equal to k Is a functional correlation coefficient of R k Will L r ＝1-R k As a loss function, the parameter ar is determined k ,cr k ，
Wherein Cov (S in ,S k ) Is S in And S is equal to k Covariance of Var [ S ] in ]Is S in Variance of Var [ S ] k ]Is S k Is a variance of (2);
p2, when L r ＝1-R k When the temperature is more than or equal to 0.01,
T k+1 ＝T k -ar k gr k
(6)
k＝k+1 (7)
wherein gr k Representing gradient vectors generated by the perturbation; and (V) k Is an M-dimensional vector, where M is the number of antenna elements in the array, its elements are +1, -1, and the bernoulli distribution with probability of 0.5 is met;
p3, judge L r ＝1-R k <0.01 is established, if yes, recording the T at the moment k The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to the step P2.
5. The method for performing calibration in the time domain for a wideband antenna array as recited in claim 4, wherein the ar k ,cr k Is to ensure gr k Does not spread with the increase of the iteration times, cr k ＝0.01，ar k The following are provided:
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| CN109525530A (en) * | 2017-09-19 | 2019-03-26 | 成都鼎桥通信技术有限公司 | The calibration method of multichannel phase consistency |
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