CN110109061B - Frequency spectrum zero setting signal design method based on template matching - Google Patents

Abstract

The invention discloses a frequency spectrum zero setting signal design method based on template matching, belongs to the field of radar signal processing, and particularly relates to a radar fast time domain signal design method which is suitable for multi-system frequency spectrum coexistence under radar anti-interference or frequency spectrum resource shortage in a narrow-band interference environment. Aiming at the problem of template matching and fitting, the method has higher descending speed and convergence speed, better fitting effect with the template and better optimization effect, and in addition, compared with other template algorithms, the algorithm used by the method has lower calculation complexity and improves the algorithm efficiency.

Description

Frequency spectrum zero setting signal design method based on template matching

Technical Field

The invention belongs to the field of radar signal processing, and particularly relates to a radar fast time domain signal design method which is suitable for multi-system frequency spectrum coexistence under the condition of radar anti-interference or frequency spectrum resource shortage in a narrow-band interference environment.

Background

Due to the limited electromagnetic spectrum resources and the rapid development of electromagnetic space applications, the spectrum resources are increasingly tense, and the problem of spectrum compatibility is increasingly prominent. The frequency spectrums of radar in modern battlefield environment and wireless applications such as timely wireless communication, remote sensing and navigation are overlapped and interleaved. The frequency spectrum overlapping causes mutual interference among applications, and simultaneously, the radar detection performance is seriously influenced, so that the problem of frequency spectrum compatibility between the radar and the applications is very important to solve, and the requirement of a radar system on the frequency spectrum utilization effectiveness of a transmitted waveform is increased day by day. The power spectrum information can be obtained through electromagnetic environment sensing, and further the influence of mutual interference and hostile interference of radar signals and civil signals is prevented through design of waveforms.

Dynamic spectrum estimation information is obtained through an electromagnetic environment sensing process, and a phase sequence of a phase coding waveform is designed in an auxiliary mode, so that power spectral density distribution of the waveform is adjusted, and the method is an effective method for solving the problem of frequency spectrum compatibility. In order to meet the practical application, the radar emission signal generally needs to satisfy some constraints. Specifically, to fully utilize the transmit power of the radar transmitter, the designed signal satisfies an energy constraint and a peak-to-average ratio (PAR) constraint. Assuming that the waveform to be designed has a very low power spectral density over some frequency band at the normalized frequency, the spectrum of the designed waveform is brought close to the desired template by minimizing the covariance of the spectrum of the designed signal and the designed template. Documents "p.ge, g.cui, s.m.karbasi, l.kong, and j.yang," a template fixing for coherent unidentive uniform sequence design, "Signal Processing, vol.128, pp.360-368, nov.2016" use the principle of iterative decrement of tolerance to make the power spectrum of the design waveform and the autocorrelation function gradually iteratively approximate to a template in the algorithm, thereby realizing the requirements of spectrum compatibility and target detection performance. However, this approach has limited optimization performance, and employs a constant modulus constraint, not a PAR constraint.

Disclosure of Invention

Aiming at the problem of spectrum coexistence in a narrow-band interference environment, the invention provides a method for designing a spectrum nulling signal based on template matching by considering PAR constraint and energy and minimizing covariance of a spectrum of a design signal and a design template on the assumption of target narrow-band interference resistance, such as other communication systems. Firstly, establishing a template according to a frequency spectrum environment, and deducing a target function; then, an optimization problem is constructed, and finally the optimization problem is solved.

The technical scheme of the invention is as follows: a frequency spectrum zero setting signal design method based on template matching comprises the following steps:

step 1, establishing a problem model;

consider the transmit waveform s ═ s (1), s (2), …, s (n)] ^T Is a fast time signal of dimension Nx 1 ^T Representing a transpose; the pass band and stop band of the frequency spectrum are defined as omega respectively _pass And Ω _stop And satisfy omega _pass ∪ Ω _stop 0,1, …, N-1 }; s (n) an nth code word representing a phase encoded waveform, the discrete Fourier transform of the signal s being y, f _i The ith lattice point which is the normalized frequency; assuming that the desired energy spectral density template p (i) is

Wherein: ζ represents the expected amplitude of the stop band, and in order to make the ESD of the signal close to the expected ESD template, an objective function is defined as

Wherein,

representing a frequency f _i A time Fourier transform vector, w (i) ≧ 0, i ═ 0, …, N-1 is the weight to the ith frequency bin, and α is the matching scale factor of expected ESD and design ESD energy; | · | represents modulo;

furthermore, the transmit signal s satisfies an energy constraint and a peak-to-average ratio (PAR) constraint, i.e.

s ^H s＝N

Gamma represents the amplitude constraint on the waveform and therefore the optimization problem of the constraint

Step 2: solving the problem by adopting a sequence iteration four-time optimization algorithm;

step 2.1:

let α be the ratio of the design ESD and the expected ESD energy, then α is converted to α ═ s ^H Cs; wherein C isIs a hermitian matrix; build a satisfaction

Her-rice matrix y(s), her

h(α,s)＝s ^H Υ(s)s

Due to the fact that

Y(s) is thus a semi-positive definite matrix, with no non-negative characteristic values;

equivalence translates into the following optimization problem:

step 2.2:

in the form of sequence iteration

Is converted into

Wherein s is ^(t) Expressing the optimized variable obtained by the t iteration, wherein I represents a unit array; will be provided with

Is further converted into

The solution to the problem is

s ^(t+1) ＝Q(s ^(t) )

Wherein Q (·) represents solving

A function of the problem solution;

and step 3: an acceleration algorithm;

accelerating by adopting an EM algorithm during each iteration;

first solve for s _a ＝Q(s ^(t) )，s _b ＝Q(s _a ) (ii) a Then solving for r ═ s _a -s ^(t) ，u＝s _b -s _a -r，α＝-||r||/||u||，s ^(t+1) ＝Q(s ^(t) -2αr+α ² u)，s _a Represents when s ^(t) When it is an initial value

Solution of the problem, s _b Represents when s _a When it is an initial value

Solution of the problem, r denotes the two previous and subsequent iterations s _a And s ^(t) U represents the difference between two successive iteration differences r; when s is ^(t+1)H [λI-Υ(s ^(t) )]s ^(t) ＜s ^(t)H [λI-Υ(s ^(t) )]s ^(t) Let α be (α -1)/2, s ^(t+1) ＝Q(s ^(t) -2αr+α ² u), when α is-1, exit iteration,

representing a real part; when | | | s ^(t+1) -s ^(t) When | | < epsilon or a preset iteration number or preset iteration time is reached, exiting the iteration, wherein epsilon is a preset threshold value; at this time s ^(t+1) The spectrum nulling signal optimized for the present invention.

Compared with the prior art, the invention has the following advantages:

aiming at the problem of template matching and fitting, the method has higher descending speed and convergence speed, better fitting effect with the template and better optimization effect, and in addition, compared with other template algorithms, the algorithm used by the method has lower calculation complexity and improves the algorithm efficiency.

Drawings

FIG. 1 is a flow chart of a sequence iteration four-time optimization algorithm;

FIG. 2 is a graph comparing the variation of the average power spectrum of the stop band with the iteration number obtained by the optimization of the algorithm and the template matching (TFA) algorithm

FIG. 3 is a power spectrum diagram of the sequence obtained by the algorithm of the present invention and the TFA algorithm under different PAR constraints.

Detailed Description

The specific implementation steps of the invention are described as follows:

step 1, establishing a problem model;

Consider the transmit waveform s ═ s (1), s (2), …, s (n)] ^T Is a fast time signal of Nx 1 dimension, and the passband and stopband of the frequency spectrum are defined as omega respectively _pass And Ω _stop And satisfy Ω _pass ∪Ω _stop 0,1, …, N-1. The Discrete Fourier Transform (DFT) of the signal s is

Wherein,

(·) ^T 、(·) ^H respectively representing transpose and conjugate transpose, f _i Is the ith lattice point of the normalized frequency. Assume a desired Energy Spectral Density (ESD) template p (i) is

To approximate the ESD of a signal to a desired ESD template, an objective function is defined as

Where w (i) ≧ 0, i ═ 0, …, and N-1 are the weights for the ith frequency bin, and α is the matching scale factor for the expected ESD and design ESD energies. | · | represents modulo.

Furthermore, the transmit signal s satisfies an energy constraint and a peak-to-average ratio (PAR) constraint, i.e.

s ^H s＝N

Optimization problem of the constraints thus

Step 2: solving the problem by adopting a sequence iteration four-time optimization algorithm;

step 2.1:

let α be the ratio of the design ESD and the desired ESD energy:

wherein,

is a hermitian matrix. Then h (. alpha., s) can be changed to

Wherein,

D _i i-0, …, N-1, y(s) are all hermite matrices. Then

Due to the fact that

Thus γ(s) is a semi-positive definite matrix with no non-negative eigenvalues.

The method can equivalently convert into the following optimization problems:

wherein

Step 2.2:

in the form of sequence iteration

Is converted into

Wherein s is ^(t) Representing an optimized variable obtained by the t iteration;

can be further converted into

The solution to the problem is

s ^(t+1) ＝Q(s ^(t) )

Wherein Q (-) represents the solution s ^(t+1) As a function of (c). In particular, the method of manufacturing a semiconductor device,

wherein s is ^(t+1) (n) representing the optimised variable s from the t +1 th iterationThe nth element.

arg (a) denotes the angle of vector a. v. of ^(t) Can be expressed as

v ^(t) ＝(λI _N -Υ(s ^(t) ))s ^(t)

Let us assume v ^(t) (1)≥v ^(t) (2)≥…≥v ^(t) (N)，v ^(t) The number of elements other than 0 in (1) is z. When z is gamma ² When the content is less than or equal to N,

when z is gamma ² When the content is more than or equal to N,

|s ^(t+1) (n)|＝min{δ|v ^(t) (n)|,γ}

wherein,

δ can be solved by a dichotomy.

Step 2.3:

further, let

Accelerating by adopting an EM algorithm in each iteration, specifically, firstly solving s _a ＝Q(s ^(t) )，s _b ＝Q(s _a ) (ii) a Then solving for r ═ s _a -s ^(t) ，u＝s _b -s _a -r，α＝-||r||/||u||，s ^(t+1) ＝Q(s ^(t) -2αr+α ² u); when in use

Let α be (α -1)/2, s ^(t+1) ＝Q(s ^(t) -2αr+α ² u), when α is-1, the iteration exits. When s is ^{(t +1)} And when the iteration condition is met, exiting the iteration.

The effects of the present invention can be further illustrated by the following simulations:

simulation scene: setting the code length N of fast time waveform as 200, the initial sequence selects random phase code sequence and normalized frequency spectrum stop band as [0.1,0.2 ]]∪[0.7,0.8]Let the stop band level ζ equal to-150 dB, when | | | s ^(t+1) -s ^(t) ||≤10 ^-9 The iteration is exited.

Simulation content:

simulation 1: aiming at the same spectrum coexistence problem, the same convergence condition is set, and the optimization efficiency of the algorithm and the TFA algorithm adopted by the invention is compared. Fig. 2 illustrates a variation curve of the average power spectrum of the stop band optimized by the algorithm of the present invention and other template matching algorithms along with the number of iterations, from which it can be seen that the algorithm of the present invention represents an obvious advantage in optimizing the level, specifically, the algorithm of the present invention can achieve-147.2 dB for 142 iterations of stop band average power spectrum when PAR is 1, and achieve-149.7 dB for 47 iterations of stop band average power spectrum when PAR is 4; and the TFA algorithm reaches-43.41 dB in stopband average power spectrum at PAR 1 for 3000 iterations. Therefore, by means of the algorithm, the invention can realize the energy zero setting of the specific frequency band of the power spectrum, and is beneficial to the coexistence of the frequency spectrum under the complex electromagnetic environment.

Simulation 2: in order to analyze the robustness of the method, based on the simulation parameters, the power spectrum fitting performance of the algorithm and the TFA algorithm under different PAR constraints is compared.

Fig. 3 illustrates the power spectral densities of different sequences under different PAR constraints, and it can be seen that all three sequences have power spectral nulls at [0.1,0.2] < 0.7,0.8], where the sequence optimized by the algorithm of the present invention when PAR ═ 4 is closest to the template, and then the sequence optimized by the algorithm of the present invention when PAR ═ 1 is next, and the spectrum fitting effect of TFA is the worst.

In summary, the sequence quartic optimization design method provided by the invention can design the spectrum coexistence sequence aiming at the complex electromagnetic crowding scene, effectively resist the interference of other electromagnetic systems in the space, and enable the designed sequence to have better spectrum compatibility compared with the non-electromagnetic coexistence sequence.

Claims (1)

1. A frequency spectrum zero setting signal design method based on template matching comprises the following steps:

step 1, establishing a problem model;

consider the transmit waveform s ═ s (1), s (2), …, s (n)] ^T Is a fast time signal of dimension Nx 1 ^T Representing a transpose; the pass band and stop band of the frequency spectrum are defined as omega respectively _pass And Ω _stop And satisfy omega _pass ∪Ω _stop 0,1, …, N-1 }; s (n) an nth code word representing a phase encoded waveform, the discrete Fourier transform of the signal s being y, f _i The ith lattice point which is the normalized frequency; assuming that the desired energy spectral density template p (i) is

Wherein: ζ represents the expected amplitude of the stop band, and in order to make the ESD of the signal close to the expected ESD template, an objective function is defined as

Wherein,

representing a frequency f _i A time Fourier transform vector, w (i) ≧ 0, i ═ 0, …, N-1 is the weight to the ith frequency bin, and α is the matching scale factor of expected ESD and design ESD energy; | · | represents modulo;

furthermore, the transmit signal s satisfies an energy constraint and a peak-to-average ratio (PAR) constraint, i.e.

s ^H s＝N

Gamma represents the amplitude constraint on the waveform and therefore the optimization problem of the constraint

Step 2: solving the problem by adopting a sequence iteration four-time optimization algorithm;

step 2.1:

let α be the ratio of the design ESD and the expected ESD energy, then α is converted to α ═ s ^H Cs; wherein C is a hermitian matrix; build a satisfaction

Her-rice matrix y(s), her

h(α,s)＝s ^H Υ(s)s

Due to the fact that

Y(s) is thus a semi-positive definite matrix, with no non-negative characteristic values;

equivalence translates into the following optimization problem:

step 2.2:

in the form of sequence iteration

Is converted into

Wherein s is ^(t) Expressing the optimized variable obtained by the t iteration, wherein I represents a unit array; will be provided with

Is further converted into

The solution to the problem is

s ^(t+1) ＝Q(s ^(t) )

Wherein Q (·) represents solving

A function of the problem solution;

And 3, step 3: an acceleration algorithm;

accelerating by adopting an EM algorithm during each iteration;

first solve for s _a ＝Q(s ^(t) )，s _b ＝Q(s _a ) (ii) a Then solving for r ═ s _a -s ^(t) ，u＝s _b -s _a -r，α＝-||r||/||u||，s ^(t+1) ＝Q(s ^(t) -2αr+α ² u)，s _a Represents when s ^(t) When it is an initial value

Solution of the problem, s _b Represents when s _a When it is an initial value

Solution of the problem, r denotes the two previous and subsequent iterations s _a And s ^(t) U represents the difference between two successive iteration differences r; when s is ^(t+1)H [λI-Υ(s ^(t) )]s ^(t) ＜s ^(t)H [λI-Υ(s ^(t) )]s ^(t) Let α be (α -1)/2, s ^(t+1) ＝Q(s ^(t) -2αr+α ² u), when α is-1, exit iteration,

representing a real part; when | | | s ^(t+1) -s ^(t) | | < epsilon orWhen the preset iteration times or the preset iteration time is reached, the iteration is stopped, and epsilon is a preset threshold value; at this time s ^(t+1) The signal is nulled for an optimized spectrum.

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