CN106054140A - Design method of continuous phase modulation waveform with spectral constraints - Google Patents

Abstract

The present invention provides a design method of a continuous phase modulation waveform of which the frequency spectrum has the characteristics that a stop band can be set in a frequency band at will, and the out-of-band energy can be restrained effectively. The waveform possessing the characteristics enables an electromagnetic spectrum to be utilized effectively and a power utilization rate to be increased, and is importantly applied to a radar and communication system. The method uses a discrete version to express the continuous phase waveform approximatively, optimizes a phase sequence, and generates the continuous phase modulation waveform by interpolation. The optimized waveform designed by the method has the characteristics of good in-band stop band, out-of-band inhibition and constant modulus which are called constant modulus spectral constraint characteristics for short.

Description

A kind of method for designing of the Continuous Phase Modulation waveform with spectrum constraint

Technical field

The invention belongs to radar waveform design field.Particularly to Continuous Phase Modulation Waveform Design.

Background technology

In the case of modern electromagnetic spectrum is the most crowded, need interference, the expansion reducing between different electromagnetic equipment System bandwidth, therefore the demand of the spectrum utilization effectiveness of transmitted waveform is increased by radar system day by day.Spectrum utilization effectiveness Have in requiring the band of transmitted waveform frequency spectrum outside appointment stopband and band and there is good rejection characteristic, frequency spectrum is met above-mentioned condition It is referred to as the waveform meeting spectrum constraint, referred to as spectrum constraint waveform.It addition, the energy efficiency of radar system is believed by launching permanent mould Number realize, so make transmitter always work in peak power.

Owing to coding signal is owing to having more design freedom, improve performance and motility, at present to base band from Dissipate coding signal and done widely studied, the coded sequence that in the existing satisfied band of many algorithms design, stopband requires.But, instantaneous phase Position change causes the extension with the spectral sidelobes of sin (x)/x envelope, it is impossible to the energy outside enough strict rejection bands.Therefore exist On the basis of coding signal, its instantaneous phase that slows down changes, and obtains Continuous Phase Modulation waveform and can meet above-mentioned permanent mode spectrum about Beam request.Researchs more existing to continuous phase waveform, document " Highly bandlimited radar signals, Proceedings of 2002IEEE Radar Conference, pp.220-226,2002. " and document " A spectrally clean transmitting system for solid-state phased-array radars,proceedings of 2004IEEE Radar Conference, pp.140-144.2004 " propose Gauss sinc function come discrete as kernel function Coding signal carries out convolution, designs band-limited signal, but the signal designed can not meet constant modulus property.At document " CPM-based Radar waveforms for efficiently bandlimiting a transmitted spectrum, Proceedings of 2009 IEEE Radar Conference, pp.1-6,2009 " in, propose phase contrast convolution kernel letter After number, the method for integration obtains continuous phase signal.But the method perform complex, and do not consider band in stopband is arbitrarily set about Bundle.

Summary of the invention

The technical problem to be solved has been to provide a kind of continuous phase waveform design method, and its frequency spectrum has Stopband and the characteristic of effective rejection band outer energy can be set in frequency band.

The present invention solves that above-mentioned technical problem be employed technical scheme comprise that, wide bandwidth when proposition is more than waveform by length Long-pending sequence carrys out approximate representation spectrum constraint waveform.On this basis, propose the method for designing to this sequence, then obtained by interpolation To having the continuous phase modulated signal that strict frequency band limits in certain limit frequency spectrum；Comprise the following steps:

Step 1: by virtual sampling, obtain phase modulated signal s (n) having N number of sampled point；

Step 2: s (n) is carried out L times of over-sampling, it is thus achieved that by modulated signal x (n) having NL sampled point；

Step 3: employing formula:X (n) is carried out frequency spectrum optimization；

Wherein R is the matrix of NL × NL dimension, and the element on the m row n row of matrix Central China is R_mn:

(f_k1,f_k2) represent a stopband, N_sRepresent the number of stopband, ω_kExpression kth (k=1 ..., N_s) individual stopband correspondence Weights, f_k2Represent the termination frequency of kth stopband, f_k1Represent the initial frequency of kth stopband；

Step 4: use cyclic iterative method that phase place is optimized；

Step 4.1: the phase place through modulated signal x (n) of frequency spectrum optimization obtaining step 3 initializes；

Step 4.2: calculate auxiliary variable α, α=Bx (n), wherein B=U (I-Σ) U^*, R is carried out Eigenvalues Decomposition, i.e. R =U Σ U^*, wherein Σ be after R is decomposed eigenvalue constitute matrix, U is the characteristic vector after being decomposed by R；

Step 4.3: use formula x (n)_new=exp (j arg (α)) calculates modulated signal x (n) made new advances_new；

Step 4.4: if | | x (n)_new-x(n)||₂< ε, ε are the threshold values set according to practical situation, | | | |₂Represent to 2 norms of amount, then stop iteration, optimal solution x (n)_opt=x (n)_new；Otherwise make x (n)=x (n)_new, repeat step 4.2-4.4, Until meeting condition；

Step 5: step 4 is obtained x (n) and carries out difference, obtain final continuous modulation signal x (n).

The present invention can have the good transmitted waveform suppressed to have in design effectively band to specify outside stopband band.From Fig. 1 and The contrast of Fig. 2 is it can be seen that when over-sampling rate L increases, in the band optimizing waveform obtained, stopband is the lowest, and Out-of-band rejection is imitated Fruit is the best, i.e. spectrum binding feature is the best.

Accompanying drawing explanation

Fig. 1 is to optimize the waveform frequency spectrum figure obtained；

Fig. 2 be obtain optimize the waveform frequency spectrum figure obtained after waveform interpolation.

Detailed description of the invention

The present invention mainly uses the method for Computer Simulation to verify, institute is in steps, conclusion is all at MATLAB-R2010a Upper checking confirms

If the Timed automata of waveform is 400, first it is optimized with the waveform of over-sampling, if the multiple of over-sampling is L, point Do not make L=1,1.5,2,3.Being optimized with cyclic iterative method, iterations is 200 times.It is embodied as step as follows:

Step 1 initiation parameter；

Under normal circumstances, the number of chips of coding signal is equal with the Timed automata of time-domain signal, is designated as N.Then length For the phase modulated signal s of N, its each chip is expressed as follows:

Wherein φ (n) (0≤φ (n) < 2 π) is the phase place of the n-th subpulse of signal, wherein n=1 ..., N.φ represents The vector that φ (n) forms, i.e. φ=[φ (1) ..., φ (N)]^T.Without loss of generality, use normalized frequency, by signal band Wide be designated as 1, then s (n) place frequency band is designated as [-1/2,1/2].

Step 2 over-sampling；

In order to provide smoother phase place to change in time interval given in time domain, need to increase sample rate.Assume Sample rate is increased to original L times, L sub-chip will be divided into by each chip.

The waveform phase after over-sampling is made to be expressed as

Corresponding waveform is designated as

The value rationally selecting L is closely related with the performance of method and efficiency.When L selects less, it is impossible to enough effectively expressions Continuous print phase place；When L selects bigger, increase the amount of calculation of waveform design method.We will pass through different L's in emulation part Value is observed simulation result and is provided suitable L-value.

Step 3 constructs object function；

After over-sampling, signal spectrum scope is [-L/2, L/2], needs the preferable frequency in consideration [-L/2, L/2] frequency range Spectral property.

Frequency outside band needs all suppression, and the frequency outside band can be designated as

Ω_O=(-L/2 ,-1/2) ∪ (1/2, L/2)

The stop-band frequency specified in band is

Wherein (f_k1,f_k2) represent a stopband, N_sRepresent the number of stopband.It is thus desirable to the spectral range of suppression is written as Ω =Ω_O∪Ω_I。

Definition NL × NL ties up matrix R, and wherein the element on the m row n row of R matrix is

It is said that in general, R is the matrix that a rank defect lacks, i.e. rank (R) < NL.R is carried out Eigenvalues Decomposition, i.e. R=U Σ U^*, wherein Σ be R eigenvalue constitute matrix.Definition matrix B, B=U (I-Σ) U^*。

For making the interfering energy in stopband Ω minimum, design cost function:

S.t. | x (n) |=1, n=1,2 ..., NL

Step 4 cyclic iterative method calculates optimum angle；

4.1, l=0, random initializtion perseverance mould vector, to over-sampling phase placeInitialize, as rightNL phase place Independent random is distributed.

4.2, make l=l+1, calculate auxiliary variable α, α=Bx；

4.3, the x making cost function minimum is calculated_new, x_new=exp (jarg (α))；

4.4, calculate | | x_new-x||₂If, | | x_new-x||₂< ε (ε is a specified value, | | | |₂Represent the 2 of vector Norm), then stop iteration, optimal solution x_opt=x_new；Otherwise make x=x_new, repeating step 4.2-4.4, until meeting condition being Only.

Step 5 interpolation；

It is contemplated that the problem of amount of calculation, L value is limited, and phase place that therefore previous step optimization obtains is it cannot be guaranteed that can With approximate representation continuous phase signal, therefore we carry out M times of interpolation to over-sampling phase place α obtained.The method of interpolation has sample Bar curve method, linear approach etc..

It is an advantage of the invention that and be obtained in that there is stopband and the Continuous Phase Modulation waveform of the outer Energy suppression of band in band, increase Add power utilization, reduce the interference between different electromagnetic equipment.The method is easy, it is easy to accomplish.Present invention can apply to radar The fields such as Continuous Phase Modulation Waveform Design.

The amplitude spectrum optimizing waveform that above-mentioned emulation experiment linear FM signal obtains as initial signal is Fig. 1；

The phase place obtained is carried out interpolation, takes M=10, i.e. its interpolation of counting is 400*10 point.Obtain continuous phase waveform Frequency spectrum be Fig. 2.

Claims (1)

1. there is a method for designing for the Continuous Phase Modulation waveform of spectrum constraint, comprise the following steps:

Step 1: by virtual sampling, obtain phase modulated signal s (n) having N number of sampled point；

Step 2: s (n) is carried out L times of over-sampling, it is thus achieved that by modulated signal x (n) having NL sampled point；

Step 3: employing formula:X (n) is carried out frequency spectrum optimization；

Wherein R is the matrix of NL × NL dimension, and the element on the m row n row of matrix Central China is R_mn:

$\begin{array}{c}{R}_{mn}=\underset{k=1}{\overset{N_s}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_k{\&Integral;}_{f_{k1}}^{f_{k2}}{e}^{j2\mathrm{\&pi;}f(m-n)}df\\ =\underset{k=1}{\overset{N_s}{\&Sigma;}}{\mathrm{\&omega;}}_k\left\{\begin{array}{cc}\frac{e^{j2{\mathrm{\&pi;f}}_{k2}(m-n)}-e^{j2{\mathrm{\&pi;f}}_{k1}(m-n)}}{j2\mathrm{\&pi;}(m-n)},& m\&NotEqual;n\\ f_{k2}-f_{k1},& m=n\end{array}\right.\end{array}$

(f_k1,f_k2) represent a stopband, N_sRepresent the number of stopband, ω_kExpression kth (k=1 ..., N_s) power that individual stopband is corresponding Value, f_k2Represent the termination frequency of kth stopband, f_k1Represent the initial frequency of kth stopband；

Step 4: use cyclic iterative method that phase place is optimized；

Step 4.1: the phase place through modulated signal x (n) of frequency spectrum optimization obtaining step 3 initializes；

Step 4.2: calculate auxiliary variable α, α=Bx (n), wherein B=U (I-Σ) U^*, R is carried out Eigenvalues Decomposition, i.e. R=U Σ U^*, wherein Σ be after R is decomposed eigenvalue constitute matrix, U is the characteristic vector after being decomposed by R；

Step 4.3: use formula x (n)_new=exp (jarg (α)) calculates modulated signal x (n) made new advances_new；

Step 4.4: if | | x (n)_new-x(n)||₂< ε, ε are the threshold values set according to practical situation, | | | |₂Represent vector 2 norms, then stop iteration, optimal solution x (n)_opt=x (n)_new；Otherwise make x (n)=x (n)_new, repeat step 4.2-4.4, until Till meeting condition；

Step 5: step 4 is obtained x (n) and carries out difference, obtain final continuous modulation signal x (n).