CN112305496B - Passive direction finding channel phase correction method - Google Patents

Passive direction finding channel phase correction method Download PDF

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CN112305496B
CN112305496B CN202011156033.7A CN202011156033A CN112305496B CN 112305496 B CN112305496 B CN 112305496B CN 202011156033 A CN202011156033 A CN 202011156033A CN 112305496 B CN112305496 B CN 112305496B
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蒋伊琳
张玉欣
赵忠凯
郭立民
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Harbin Engineering University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
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Abstract

The invention discloses a passive direction finding channel phase correction method, which utilizes a DNN network to extract the phase characteristics of a signal received by a receiver, converts the correction problem into a DNN network characteristic extraction problem, finds out the mapping of the phase difference of a channel output signal and the original phase difference of an antenna signal, and corrects the phase error of the channel. The method comprises the steps of establishing a phase error model for received signals, taking the product of antenna signals and a channel frequency response function as input, and correcting sparse points of the initial phase difference of the antenna signals from 0 to 180 degrees so as to achieve full-phase correction. Compared with the traditional method, the method has better flexibility, and the stability of the network can be better explained by showing the phase of the corrected signal in a standard deviation mode, so that a better correction effect is brought.

Description

Passive direction finding channel phase correction method
Technical Field
The invention relates to a passive direction finding channel phase correction method, in particular to a passive direction finding channel phase correction method based on DNN, and belongs to the field of radar signal processing.
Background
Channel amplitude phase non-uniformity can severely degrade the performance of a series of array signal processing algorithms. Channel mismatch can degrade DOA estimation performance, and thus the performance of the beamforming algorithm is also severely degraded. The channel mismatch causes the sharpness of the MUSIC angle estimation spectral peak to be reduced, the spectral peak has deviation, and when the channel mismatch degree is serious, two signals with similar angles cannot be distinguished, so that the angle estimation precision is greatly reduced. The channel amplitude and phase inconsistency is different between channels in a concrete form that frequency response functions of different channels are different, and when the channels are relatively correct, correction methods of the channel amplitude and phase inconsistency of the broadband signals and the narrow-band signals are different.
The early channel correction method has the disadvantages of complex operation, strict requirement on equipment for channel correction and poor applicability. A major breakthrough of channel correction is to establish a channel amplitude and phase error model, convert the channel correction problem into the estimation and compensation problem of channel errors, and greatly reduce the difficulty degree of channel active correction and robust algorithm research. The existing literature proposes that under the condition that the accurate azimuth information of the auxiliary signal source is not clear, the minimum mean square error criterion is adopted to fit the actual channel error so as to realize channel correction, the proposed error correction method can correct any array form, and can correct the array with position error, amplitude error and phase error at the same time, thereby solving a plurality of correction problems in practice.
In recent years, with continuous research and study in the field of deep learning, great success has been achieved in the fields of voice recognition, image recognition, and natural language. Deep learning can be applied to the phase correction technique to replace the original active correction and passive correction techniques.
Disclosure of Invention
Aiming at the prior art, the technical problem to be solved by the invention is to provide a passive direction finding channel phase correction method based on a deep neural network, solve the problems of insufficient precision, poor effect, insufficient flexibility and the like of the existing method for correcting a channel by designing an equalization filter, establish channel mismatch model data, correct sparse phase point data of a received signal on a frequency band, and achieve full-phase correction.
In order to solve the above technical problem, the method for correcting the phase of the passive direction finding channel of the present invention comprises the following steps:
step 1: an improved sine wave dynamic model is adopted as a mismatch model of a channel, and the sine wave dynamic model specifically comprises the following steps:
Figure BDA0002742766660000021
where H (ω) is the amplitude frequency response of the channel, the subscript i denotes the frequency response of the ith channel, a0iIs an amplitude constant, a1iAs peak of amplitude fluctuation, b0iIs the slope of the phase, b1iIs the peak of the phase fluctuation. K1iAnd K2iRespectively representing the number of periods of the amplitude and phase fluctuation over the whole bandwidth B,
Figure BDA0002742766660000022
and
Figure BDA0002742766660000023
indicating the starting phase of the fluctuation;
step 2: a network training set is constructed, the antenna signal selects a single carrier frequency sinusoidal signal s (t), and the double channels meet the following conditions:
s1(t)＝sin(2πfi1+θi2)
s2(t)＝sin(2πfi1)
wherein, fi1For the frequency of the signal, a training set signal frequency range and a signal frequency point, theta, are selectedi2Setting the initial phase of another channel to be 0 for the initial phase of the antenna signal, then thetai2Taking 0-180 degrees and taking every 10 degrees for thinning the initial phase difference of the two signals; and (3) performing fast Fourier transform on S (t) to obtain a frequency domain expression S (omega), and multiplying the frequency domain expression S (omega) by H (omega) to introduce a phase error into an original signal to obtain:
G(ω)＝S(ω)H(ω)
and step 3: constructing DNN branches, and defining layers and parameters of DNN;
and 4, step 4: training the model by using a training set, evaluating the model by using a verification set, and adjusting the model parameters to obtain a neural network model;
and 5: and carrying out correction test on the trained model by using the test set, and outputting an initial phase difference estimation result of the antenna signal.
The invention also includes:
1. in step 3, the DNN includes an input layer, an output layer, and three hidden layers, where the output of each layer is defined as:
al＝σ(zl)＝σ(Wlal-1+bl)
σ (-) is an activation function, assuming layer l-1 has m neurons and layer l has n neurons, the linear coefficients W of layer l form an n × m matrix WlThe bias b of the l-th layer constitutes an n x 1 vector blThe output a of layer l-1 constitutes an m x 1 vector al-1The linear output z of the l-th layer before being activated constitutes an n x 1 vector zlThe output a of the l-th layer constitutes an n x 1 vector alI.e. the output of the l-th layer.
2. And 5, the initial phase difference estimation result of the antenna signal meets the following requirements:
Figure BDA0002742766660000031
wherein y represents the true value and y' represents the predicted value.
The invention has the beneficial effects that: the present invention will replace the conventional filter equalization method with a DNN network. The channel mismatch models with various different parameters are used, and data of the mismatch models are trained, so that compared with the traditional method, the method has better flexibility, and the stability of the network can be better explained by showing the phase of the corrected signal in a standard deviation mode, thereby bringing better correction effect.
Drawings
FIG. 1 is a block diagram of the overall system architecture of the present invention;
FIG. 2 is an experimental flow chart of the present invention;
FIG. 3 is a graph of the gradient of the minimum mean square error of the present invention as a function of training steps;
FIG. 4 is a graph of the results of 20 rounds of prediction and standard deviation calculations for 100 test sets according to the present invention.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
The invention provides a channel correction method based on a deep learning DNN network, which utilizes the DNN network to extract the phase characteristics of signals received by a receiver, converts the correction problem into the DNN network characteristic extraction problem, finds out the mapping between the phase difference of channel output signals and the original phase difference of antenna signals, and corrects the phase error of the channel. The method comprises the steps of establishing a phase error model for received signals, taking the product of antenna signals and a channel frequency response function as input, and correcting sparse points of the initial phase difference of the antenna signals from 0 to 180 degrees so as to achieve full-phase correction. The invention does not specially research the DNN network, but modifies the structure and parameters of the mature neural network to make it suitable for training the signal received by the receiver.
The technical scheme of the invention is a DNN-based channel correction method, which comprises the following steps:
the method comprises the following steps: here a sinusoidal dynamics model is used for the channel as a mismatch model for this channel. The sine wave dynamic model describes the channel frequency characteristics by directly utilizing the frequency response of the channel. Assuming that the frequency response of the channel is expressed as:
H(ω)＝|H(ω)|exp(jθ(ω)) (1)
in the formula, ω is an angular frequency. H (omega) is the amplitude-frequency response of the channel, theta (omega) is the phase-frequency response of the channel, and the two responses are respectively expanded by Fourier series, aiConstant coefficients of a Fourier series expansion, c1Is the i-th harmonic component of the fourier series expansion.
Figure BDA0002742766660000041
Figure BDA0002742766660000042
This is a sinusoidal wave model that spreads the amplitude-frequency response and the phase-frequency response of the channel into the sum of a plurality of sinusoidal waves. In addition to the constant terms, the first term, the second term,. n.th term are respectively called primary distortion, secondary distortion and … n-th distortion, and the higher the distortion times, the more severe the fluctuation and the more severe the channel distortion. If the higher order terms of the Fourier series are omitted, then:
|H(ω)|＝a0+a1cos(c1ω) (4)
θ(ω)＝-b0ω+b1sin(c2ω) (5)
thus, the frequency response of an ideal channel can be expressed as:
H0(ω)＝a0exp(-jb0ω) (6)
the above equation illustrates that the amplitude-frequency characteristic of an ideal channel is constant over the signal bandwidth, a0Represents the amplitude, b0The phases are all constant. The phase frequency characteristic is linear with frequency over the signal bandwidth. The frequency response of the mismatched channel can be expressed as:
H(ω)＝[a0+a1cos(c1ω)]exp[-jb0ω+jb1sin(c2ω)] (7)
the first-order sine wave motion model is very convenient for analyzing the influence of single-channel frequency-dependent amplitude and phase errors on radar performance, but the mismatch between broadband multiple channels is too simple to simulate. And the multi-order sine fluctuation is expressed as the sum of a plurality of sine fluctuations, and although the model is accurate, the method is complex for theory and simulation. Therefore, a compromise is to modify the model slightly as follows
Figure BDA0002742766660000043
The index i denotes the frequency response of the ith channel, a0iIs an amplitude constant, a1iAs peak of amplitude fluctuation, b0iIs the slope of the phase, b1iIs the peak of the phase fluctuation. K1iAnd K2iRepresenting the number of cycles that the amplitude and phase, respectively, fluctuate over the bandwidth B.
Figure BDA0002742766660000044
And
Figure BDA0002742766660000045
indicating the starting phase of the fluctuation.
Step two: the training set of the network is explained with reference to fig. 1. The channel model selects the sine wave dynamic model described above, the frequency response of the channel is H (ω) given by equation (8), and the antenna signal selects a simple single carrier frequency sine signal s (t), considering two channels as follows:
s1(t)＝sin(2πfi1+θi2) (9)
s2(t)＝sin(2πfi1) (10)
fi1for the frequency of the signal, the frequency band of the training set is selected to be 0-200 MHz, and each 1MHz is selected and used as the signal frequency of the training set, thetai2For the initial phase of the antenna signal, the initial phase of the other channel is set to 0, so θ can be considered asi2For the initial phase difference of the two signals, thinning is performed by taking 0 to 180 ° every 10 °. And (3) performing fast Fourier transform on S (t) to obtain a frequency domain expression S (omega), and multiplying the frequency domain expression S (omega) by H (omega) to introduce the phase error into the original signal.
G(ω)＝S(ω)H(ω) (11)
Step three: constructing DNN branches, defining layers and parameters of DNN
DNN is defined as five layers including an input layer, an output layer and three hidden layers, wherein sigma (-) is an activation function, and the output of the l-th layer is defined as
al＝σ(zl)＝σ(Wlal-1+bl) (12)
Assuming that layer l-1 has m neurons and layer l has n neurons, the linear coefficients W of layer l form an n × m matrix WlThe bias b of the l-th layer constitutes an n × 1 vector blThe output a of the l-1 layer constitutes an m x 1 vector al-1The linear output z of the l-th layer before being activated constitutes an n x 1 vector zlThe output a of the l-th layer constitutes an n x 1 vector alI.e. the output of the l-th layer.
The activation functions are all ReLU functions, and compared with sigmoid functions and tanh functions, the method can overcome the problem of gradient disappearance, accelerate training speed and activate sparsity of the functions. The ReLU activation function is as follows:
Figure BDA0002742766660000051
step four: and training the model by using a training set, evaluating the model by using a verification set, and continuously adjusting the model parameters so as to obtain the optimal neural network model. The loss function adopts a quadratic loss function, the formula is shown as formula (14), y represents a true value, and y' represents a predicted value. The training batch size is set to 512, the test batch size is 256, and training is 750 steps.
Figure BDA0002742766660000052
The initial value of the learning rate is 0.001, and an exponential decay automatic learning rate adjusting mode is adopted. Calculating the signal plus channel data through a DNN network, and outputting the original phase difference of the antenna signals; and after multiple times of iterative training, adjusting the weight of each neuron of the DNN model through the error of the estimation result, and storing the training model.
Step five: and carrying out correction test on the trained model by using the test set, and outputting an initial phase difference estimation result of the antenna signal. The test set signal selects two channels, f, as shown in equations (9) (10)i1Then from 5 to 140MHz, θ, once every 5MHzi2The test is performed with every 1 deg. pick from 0 to 180 deg.. And finally, taking random data of 100 test sets as a round of test, and solving the standard deviation of the output phase difference to obtain a result.
Figure BDA0002742766660000061
(15) For the formula of the standard deviation, the same formula (14) y represents the real value, and y' represents the predicted value.
The performance of the network is further verified in simulation with fig. 2:
1. an experimental scene is as follows: the experiment adopts python language to build a network, and the model is trained based on tensierflow. The simulation platform uses pycharm software for performance verification. The training set G (M) is that the signal frequency is set from 0 to 200M, the frequency point setting of one point is selected every 1M, the phase is set from 0 to 180 degrees, the phase difference setting of one point is selected every 10 degrees, each sample is repeated 10 times, and 38000 groups of training data are obtained in total. After the deep neural network is used for training, variables such as network weight deviation are stored, and a test set is used for testing. The test set G (M) is that the signal frequency is set from 5M to 140M, the frequency point of one point is selected every 15M, the phase is set from 0 to 180 degrees, the phase difference of one point is selected every 1 degree, each sample is repeated for 10 times, 18100 groups of test data are totally obtained, finally, the random data of 100 test sets are used as one test, and the standard deviation is obtained for the output phase difference, so that the result is obtained.
2. Analysis of Experimental content
From fig. 3, it can be seen that the minimum mean square error varies with the number of training steps, and it can be seen that the minimum mean square error of the final training is close to 0, and the minimum mean square error of the test is close to 20; fig. 4 shows that random data of 100 test sets are used as a test round, standard deviations are calculated on phase differences output by the test round, 20 test rounds are total, and the results of the final standard deviations are all between 4 and 6, which indicates that the final phase difference correction results are all between 3 degrees and 5 degrees, and indicates that the effect is good.

Claims (3)

1. A passive direction finding channel phase correction method is characterized by comprising the following steps:
step 1: an improved sine wave dynamic model is adopted as a mismatch model of a channel, and the sine wave dynamic model specifically comprises the following steps:
Figure FDA0002742766650000011
where H (ω) is the amplitude frequency response of the channel, the subscript i denotes the frequency response of the ith channel, a0iIs an amplitude constant, a1iAs peak of amplitude fluctuation, b0iIs the slope of the phase, b1iIs the peak value of phase fluctuation; k1iAnd K2iRespectively representing the number of periods of amplitude and phase fluctuation over the whole bandwidth B,
Figure FDA0002742766650000012
and
Figure FDA0002742766650000013
a start phase representing the fluctuation;
step 2: a network training set is constructed, the antenna signal selects a single carrier frequency sinusoidal signal s (t), and the double channels meet the following conditions:
s1(t)＝sin(2πfi1+θi2)
s2(t)＝sin(2πfi1)
wherein f isi1For the frequency of the signal, a training set signal frequency range and a signal frequency point, theta, are selectedi2Setting the initial phase of another channel to be 0 for the initial phase of the antenna signal, then thetai2Taking 0-180 degrees and taking every 10 degrees for thinning the initial phase difference of the two signals; and (3) performing fast Fourier transform on S (t) to obtain a frequency domain expression S (omega), and multiplying the frequency domain expression S (omega) by H (omega) to introduce a phase error into an original signal to obtain:
G(ω)＝S(ω)H(ω)
and step 3: constructing DNN branches, and defining layers and parameters of DNN;
and 4, step 4: training the model by using a training set, evaluating the model by using a verification set, and adjusting model parameters to obtain a neural network model;
and 5: and carrying out correction test on the trained model by using the test set, and outputting an initial phase difference estimation result of the antenna signal.
2. The method of claim 1, wherein the method further comprises: step 3, the DNN includes an input layer, an output layer, and three hidden layers, where the output of each layer is defined as:
al＝σ(zl)＝σ(Wlal-1+bl)
σ (-) is an activation function, assuming layer l-1 has m neurons and layer l has n neurons, the linear coefficients W of layer l form an n × m matrix WlThe bias b of the l-th layer constitutes an n x 1 vector blThe output a of the l-1 layer constitutes an m x 1 vector al-1The linear output z of the l-th layer before being activated constitutes an n x 1 vector zlThe output a of the l-th layer constitutes an n x 1 vector alI.e. the output of the l-th layer.
3. A passive direction finding channel phase correction method according to claim 1 or 2, characterized in that: and 5, the estimation result of the initial phase difference of the antenna signals meets the following requirements:
Figure FDA0002742766650000021
wherein y represents the true value and y' represents the predicted value.
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