CN101741790B - Spline function theory-based method for realizing FQPSK modulating waveform - Google Patents

Abstract

The invention provides a spline function theory-based method for realizing a FQPSK modulating waveform. The method uses the Bezier curve to design the FQPSK modulating waveform in a way of simplifying the FQPSK waveform, optimizing the simplified waveform by the Bezier curve and adjusting the control points of the Bezier curve forming the FQPSK waveform to smoothen joints of the waveform; and the invention also provides two methods for optimizing the waveform: a method which first uses the Bezier curve to design the FQPSK curve that is approximately constantly enveloped and have smooth waveform joints and the uses the non-linear optimization program to adjust the control points of the Bezier curve under a condition of enveloping fluctuation limitation so as to maximize the minimum euclidean distance of the FQPSK signal, and another method which uses the DE algorithm to add limitation conditions and optimization objectives to the cost function in a mode of a cost factor to optimize the control points. The method of the invention has the advantage that: for the FQPSK signal formed by the optimized waveform, the enveloping fluctuation is smaller, the minimum euclidean distance is bigger and the power spectrum efficiency is higher.

Description

Implementation method based on the FQPSK modulation waveform of theory of spline function

Technical field

The present invention relates to a kind of method for designing of baseband waveform; Exactly; Relate to a kind of implementation method that is used for the deep space communication system, belong to the technical field of the physical layer signal design in the wireless communication system based on the quadrature phase keying FQPSK modulation waveform of the conspicuous system of the expense of theory of spline function.

Background technology

In the deep space communication system, the power limited problem is more serious more and urgent than other communication systems.In order to make full use of power resource, system adopts nonlinear high power amplifier, and amplifier is operated in cut-off state.This just requires baseband signal to have less envelope fluctuating, to improve power efficiency.Can cause the diffusion of the power spectral density of signal owing to be operated in the high power amplifier of cut-off state, so require the efficient of power spectrum signal high more good more.FQPSK can be regarded as grid coding TCM modulation, and its error rate under the white noise channel is somewhat dependent upon the minimum Eustachian distance of signal, requires minimum Eustachian distance to be the bigger the better.

At present, all also do not propose a kind of method for designing of the FQPSK of being exclusively used in signal both at home and abroad, introduce general FQPSK modulator approach and its several kinds of improvement versions here earlier.

Method 1:K.Feher etc. are at United States Patent (USP) 4,567, and the coherent signal processor that proposes in 602 is common FQPSK signal generator.This device mainly constitutes (referring to shown in Figure 1) by intersymbol interference and jitter elimination IJF encoder and cross correlation.

Method 2:M.K.Simon and T.-Y.Yan (publish in: " TMO Progress Report " at " Performance Evaluation and Interpretation of Unfiltered Feher-Patented Quadrature-Phase-Shift Keying (FQPSK) "; May 15,1999) in the another kind of way of realization of the FQPSK that proposes: the Trellis-coded modulation form.This device mainly constitutes (referring to shown in Figure 2) by two encoder for convolution codess and a signal mapper.The bit stream of left side input is mapped to 16 waveforms (referring to the general type of these 16 waveforms shown in Figure 3) from figure.The mathematic(al) representation of 16 waveforms of the FQPSK of general type is following:

s ₀(t)=A，?

s ₈(t)＝-s ₀(t)；

$s_1\left(t\right)=\left\{\begin{array}{cc}A,& -\frac{T_s}{2}\&le;t\&le;0\\ 1-(1-A){\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\frac{\mathrm{\&pi;t}}{T_s},& 0\&le;t\&le;\frac{T_s}{2}\end{array}\right.;$ s ₉(t)＝-s ₁(t)；

$s_2\left(t\right)=\left\{\begin{array}{cc}1-(1-A){\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\frac{\mathrm{\&pi;t}}{T_s},& -\frac{T_s}{2}\&le;t\&le;0\\ A,& 0\&le;t\&le;\frac{T_s}{2}\end{array}\right.;$ s ₁₀(t)＝-s ₂(t)；

$s_3\left(t\right)=1-(1-A){\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\frac{\mathrm{\&pi;t}}{T_s},$ $-\frac{T_s}{2}\&le;t\&le;\frac{T_s}{2};$ s ₁₁(t)＝-s ₃(t)；

$s_4\left(t\right)=A{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\frac{\mathrm{\&pi;t}}{T_s},$ $-\frac{T_s}{2}\&le;t\&le;\frac{T_s}{2};$ s ₁₂(t)＝-s ₄(t)；

$s_5\left(t\right)=\left\{\begin{array}{cc}A{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\frac{\mathrm{\&pi;t}}{T_s},& -\frac{T_s}{2}\&le;t\&le;0\\ {\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\frac{\mathrm{\&pi;t}}{T_s},& 0\&le;t\&le;\frac{T_s}{2}\end{array}\right.;$ s ₁₃(t)＝-s ₅(t)；

$s_6\left(t\right)=\left\{\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\frac{\mathrm{\&pi;t}}{T_s},& -\frac{T_s}{2}\&le;t\&le;0\\ \mathrm{<figure-callout\; id="2"\; label="A\; sin"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">A</figure-callout>}{\sin }^{}{}^2\frac{\mathrm{\&pi;t}}{T_s},& 0\&le;t\&le;\frac{T_s}{2}\end{array}\right.;$ s ₁₄(t)＝-s ₆(t)；

$s_7\left(t\right)={\mathrm{<figure-callout\; id="2"\; label="Sin"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">Sin</figure-callout>}}^2\frac{\mathrm{\&pi;\; t}}{T_s},$ $-\frac{T_s}{2}\&le;t\&le;\frac{T_s}{2};$ s ₁₅(t)=-s ₇(t); In the formula, T _sBe the length of single waveform, A gets

Method 3:Zhidong Xie; " (A Novel Waveform for FQPSK Modulation) " that Gengxin Zhang and Hongpeng Zhu propose (publishes in: ICCS; 2008); This method is on the basis of method 2, the waveform of signal mapper output in the method 2 to be made amendment, and makes signal have the characteristics of permanent envelope.

Method 4:K.Feher etc. are at United States Patent (USP) 4; The filter that the FQPSK signal is handled that proposes in 339,724, this method has reduced the secondary lobe of power spectrum signal significantly; And, kept the original nothing of signal to shake and do not have the advantage of intersymbol interference to a great extent.

More than several kinds improve versions and have his own strong points, be the method that the FQPSK waveform is optimized but do not have a kind of.And these methods are not all taken all factors into consideration the problems such as envelope fluctuating, power spectral density and minimum Eustachian distance that face in the deep space communication.

Because of the design essence of modulation waveform is exactly the curve design, and to select to approach the curve fitting technique that performance is good and the curve derivative is controlled according to the characteristic of waveform.The present invention selects bezier curve to carry out Waveform Design.Briefly introduce a kind of bezier curve method below.This method is the weighted sum that bezier curve is expressed as one group of control point.The control point is the point on the two dimensional surface.Weights are all multiply by at each control point, find the solution then these products add up with.Here use symbol P ₀, P ₁..., P _nAnd B _{N, 0}, B _{N, 1}..., B _{N, n}The weights of representing control point and corresponding control point respectively, and will have the bezier curve at n+1 control point to be called n rank bezier curve.Then the weighted sum expression formula of bezier curve is:

0≤t≤1; Its end product depends on form parameter t.1 P (t) on the corresponding two dimensional surface of each t value, so, the corresponding whole piece bezier curve in 0≤t≤1.Because the control point is pre-determined, so weights must change along with t.So just weight table is shown as function B usually _{N, i}(t) form.

You have selected the weights of Bernstein polynomial form France engineer Betsy, and it defines as follows:

$B_{n,i}\left(t\right)=\left(\begin{array}{c}n\\ i\end{array}\right)t^i{(1-t)}^{n-i},$ $\left(\begin{array}{c}n\\ i\end{array}\right)=\frac{n!}{i!(n-i)!},$ 0≤t≤1; Such weighted value satisfies some character that the present invention utilizes.(in curve calculation, 0 ⁰Value get 1.)

At last, bezier curve is expressed as:

0≤t≤1; A bit on the whole piece bezier curve that each t value wherein is all corresponding.

Introduce the several useful characteristic that bezier curve is correlated with for the present invention below again:

1, two of curve end points are respectively P ₀And P _n, promptly $P\left(0\right)=\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{P}_i{B}_{n,i}\left(0\right)=P_0{B}_{n,0}\left(0\right)={\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_0$

With $P\left(1\right)=\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{P}_i{B}_{n,i}\left(1\right)=P_n{B}_{n,n}\left(1\right)=P_n.$

2. the derivative at endpoint curve place.Here directly provide the first derivative of curve:

Wherein, Δ P _i=P _I+1-P _iThen the derivative of end points is: P ' (0)=n Δ P ₀And P ' (1)=n Δ P _N-1This attributes is used to adjust the control point, makes the waveform junction satisfy smooth condition.

3. curve is carried out rising the rank operation, promptly on the basis that does not change original curve, increase the number at the control point of curve.Suppose that old control point is P ₀, P ₁..., P _n, the new control point that rises behind the rank is Q ₀, Q ₁..., Q _N+1, it is following to rise the rank process: Q ₀=P ₀Q _i=a _iP _I-1+ (1-a _i) P _i, a wherein _i=i/ (n+1), i=1,2 ..., n; Q _N+1=P _nThe order that rises rank is the scope of curve being adjusted in order to enlarge.

4. the bezier curve of nonparametric form.Explicit bezier curve expression formula is s=f (t).Suppose control point P _iAbscissa be positioned at

Consider bezier curve weighted sum characteristic:

So can construct explicit bezier curve:

Wherein, P _iBe control point P _iOrdinate.That is to say that the abscissa at control point is 0 when evenly distributing between 1, bezier curve just has the form of s=f (t), wherein, and 0≤t≤1.

More than these character all be used to design wavy curve, the first method that the present invention carries out design and optimization to bezier curve also needs the approximate algorithm of a bezier curve.Here briefly introduce a kind of curve fitting algorithm that Junyeong Yang and Hyeran Byun propose at " Curve Fitting Algorithm Using Iterative Error Minimization for Sketch Beautification ", and this algorithm is expanded.This algorithm purpose is to use bezier curve that an existing curve is farthest approached.Suppose to use the second order bezier curve that a target curve is approached, the control point is P ₀, P ₁And P ₂, the curve representation formula is: P (t)=P ₀B _2,0(t)+P ₁B _2,1(t)+P ₂B _2,2(t); And the regulation two ends two end points in control point and aim curve overlap, then curve P (t) is just by P ₁Confirm, and at t _iConstantly: $P({\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1,t_i)={\hat{P}}_0{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{2,0}}\left(t_i\right)+P_1{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{2,1}}\left(t_i\right)+{\hat{P}}_2{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="H2009102426101E00011.png,H2009102426101E00012.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{2,2}}\left(t_i\right);$ If aim curve is at t _iSampled value constantly does

, total number of sample points is k, and the error function between definition bezier curve and the aim curve is:

The target function that defines this iterative algorithm again is:

This target function is asked the first derivative of Δ P, and find the solution the value that this first derivative equals 0 o'clock Δ P, use P ₁+ Δ P replaces original P ₁, calculate P then ₁Upgrade the error function between back bezier curve and the aim curve.If the error function than before upgrading is big, then to abandon this time upgrading, and think that curve has been approached to greatest extent, algorithm stops; If the error function than before upgrading is little, then keep this time upgrading, get into next iteration, promptly calculate by the P after upgrading ₁The first derivative of the target function of confirming equals the value of 0 o'clock Δ P.

In this algorithm; The number at the control point of bezier curve is set; This has just limited bezier curve approaching some curve; That introduces bezier curve here rises rank operations, if bezier curve and the error between the aim curve of certain exponent number of promptly having accomplished above-mentioned iterative algorithm just carried out rising rank to bezier curve and operated greater than certain threshold value; Use above-mentioned iterative algorithm that aim curve is approached then, the error function between bezier curve and aim curve is less than this threshold value.

Briefly introduce the differential evolution DE algorithm that uses in second kind of optimization method of the present invention at last.The DE algorithm is a kind of optimized Algorithm, be characterized in can a plurality of optimization aim and the restrictive condition form with work factor being joined in total cost function, and these optimization aim and restrictive condition depends on a plurality of parameters.The present invention reaches envelope fluctuating, power spectrum efficiency and the minimum Eustachian distance of optimizing the FQPSK signal through adjusting a plurality of bezier curves control point.The DE algorithm is fit to the optimization problem of this multi-parameter, many optimization aim.

Suppose the performance that a system has W needs to optimize: g _mM=1,2 ..., W, these performances are determined by D parameter: x _jJ=1,2 ..., D; The optimization of system can be regarded as through adjustment D dimension parameter vector: x=(x ₁, x ₂..., x _D) and make performance g ₁, g ₂..., g _wBe optimized.These performances are rewritten into the minimum problem form: min h _m(x), be used to represent h _mMinimizing (x) will make performance g _mObtain optimization.All these h _m(x) be combined into a cost function: Weight w wherein _mBe used for defining the importance of Different Optimization target.

The DE algorithm is a kind of optimized Algorithm that biotic population is evolved of simulating, and a plurality of individualities are arranged in the population, and individual parameter needs to optimize, and whole population pursues generation with cost function to the trend that minimizes the direction convergence and evolves, and obtains more excellent cost function at last.

The DE algorithm is when carrying out, and each generation is all used Z parameter vector, and promptly the population size is Z:x _{I, G}I=1,2 ..., Z; In the formula, G representes the residing algebraically of population, and each parameter vector in the per generation population is called individuality.Parameter vector is evolved in the interative computation of algorithm, and promptly cost function is optimized.Z remains unchanged in the algorithm implementation.The parameter of individuality size random initializtion in the population.The core concept of DE algorithm is to produce the method for test parameters vector.The DE algorithm is through obtaining new parameter vector with the weighted value of the parameter vector difference of two individuals and the parameter vector addition of the 3rd individuals.If the cost function value of the parameter vector that this is new is less than the cost function value of predetermined parameters vector, then this new argument vector replaces this predetermined parameters vector.

In addition, also want optimum individual x in the mark population of per generation _{Best, G}, with the minimization process of track algorithm.The method that the DE algorithm that the present invention uses produces new test parameters vector u is: at first produce an interim parameter vector:

In the formula, r ₁And r ₂Be integer from picked at random between [1, W], r ₁And r ₂Unequal mutually, and unequal with i, λ and F are predefined adjustable constants.After interim parameter vector generates, according to setting principle from some element substitution x of picked at random wherein _{I, G}In corresponding element, so just constituted new trial vector u.If the cost function of u is less than x _{I, G}Cost function, then u replaces x _{I, G}If the cost function of u is less than x _{Best, G}Cost function, then u replaces x _{Best, G}When the algorithm implementation, each the individual renewal process in the per generation colony can independently be carried out, and that is to say that algorithm has good parallel computation characteristic.

Summary of the invention

In view of this; The purpose of this invention is to provide a kind of implementation method that is used for the deep space communication system based on the FQPSK modulation waveform of theory of spline function; This method can address the deficiencies of the prior art preferably, and the baseband modulation waveform signal that make to generate has the characteristics of accurate permanent envelope, higher-wattage spectrum efficiency and bigger minimum Eustachian distance.

In order to achieve the above object; The invention provides a kind of implementation method that is used for the deep space communication system based on the quadrature phase keying FQPSK modulation waveform of the conspicuous system of the expense of theory of spline function; It is characterized in that: said method is to use bezier curve to design the FQPSK modulation waveform: earlier the FQPSK waveform is simplified; With bezier curve the waveform after simplifying is optimized again; Then the bezier curve control point that constitutes the FQPSK waveform is adjusted, made the waveform junction satisfy smooth or fairing; This method comprises following operating procedure:

(1) according to the characteristics of 16 waveforms of general type FQPSK and the correlation between each waveform, it is identical and waveform that need not design is reduced to following three waveforms with optimization objects: the 4th waveform s in 16 waveforms of this FQPSK to delete wherein shape ₃(t), the 5th waveform s ₄(t) and the 8th waveform s ₇(t) the part of positive axis separately, and rebuild out 16 whole waveforms with these three sections waveforms;

(2) waveform after the bezier curve of the explicit form of use is simplified above-mentioned steps is optimized, and makes new FQPSK signal have less envelope fluctuating, higher-wattage spectrum efficiency and bigger minimum Eustachian distance; The method of said optimized waveform has two kinds, and all is that a longitudinal axis amplitude to the bezier curve control point is optimized; Wherein, first kind of optimization method comprises following operating procedure:

(21) use the waveform after the iterative approach algorithm is simplified step (1) to approach, with the FQPSK wavy curve of the bezier curve form that obtains approximate permanent envelope form to the corresponding waveform of the FQPSK of permanent envelope form signal;

(22) control point of the FQPSK wavy curve of the bezier curve form that obtains is finely tuned, make the waveform junction smooth, simultaneously the power spectrum efficiency of this FQPSK waveform signal is made constraint; The envelope that calculates this waveform then rises and falls, if less than setting threshold, then finishes this step, carries out subsequent operation; Otherwise, all bezier curves are not destroyed bezier curve display format rise rank operations, return then and carry out the operations of bezier curve iterative approach algorithms to removing two all control points beyond the end control points in the execution in step (21);

(23) rise and fall less than setting threshold and waveform junction under the smooth condition satisfying envelope; Nonlinear optimization program with satisfying common Optimization Model is optimized the bezier curve control point except that end points, so that the waveform after optimizing satisfies the minimum Eustachian distance maximum of the smooth and FQPSK signal in waveform junction;

Second kind of optimization method is to use differential evolution DE algorithm to come the optimal control point, and it comprises following concrete operations step:

(2a) confirm sum, population size and the population evolutionary generation of the individual parameter in the population; Wherein the sum of individual parameter is a sum of removing the bezier curve control point at beginning control point in the waveform that will optimize;

(2b) according to optimised waveform, all individualities in the random initializtion first generation population suitably;

(2c) with envelope fluctuating, power spectrum efficiency, minimum Eustachian distance and junction waveform smooth degree respectively with the form weighted sum of work factor as the total cost function of DE algorithm, carry out DE algorithm, optimal control point with this total cost function again;

(3) under the prerequisite of envelope fluctuating less than setting threshold; Finely tune at the bezier curve control point that optimization obtains to above-mentioned steps; So that the smooth of high-order satisfied in the waveform junction as far as possible, promptly its first derivative is continuous, and further retrains the power spectrum efficiency of FQPSK signal; If adjusted envelope rises and falls less than setting threshold, then carry out this step (3) again, continue adjustment; When envelope rises and falls greater than setting threshold, abandon this time adjustment, finish this step.

The present invention is a kind of implementation method based on the FQPSK modulation waveform of theory of spline function that is used for the deep space communication system; It with the advantage that traditional follow-on FQPSK method is compared is: take all factors into consideration envelope fluctuating, power spectrum efficiency and the minimum Eustachian distance factor of signal, and they are carried out global optimization.

The technological innovation part of the inventive method is: used bezier curve design waveform.Bezier curve has and realizes simple, the controlled characteristics of derivative as a kind of SPL, and the control point is more, the scope of curvilinear motion is just big more, and these characteristics all help using optimized Algorithm that three big performances of FQPSK signal are optimized.And in second kind of optimization method, used the DE algorithm, through with the work factor weighted sum of envelope fluctuating, power efficiency, smooth condition and minimum Eustachian distance as last cost function, can adjust the weight of each work factor as required.In addition, because the inherent characteristic of DE algorithm is particularly suitable for parallel computation.In a word, the present invention can design the FQPSK modulation waveform that the envelope fluctuating is less, power efficiency is higher and minimum Eustachian distance is bigger, has good popularization and application prospect.

Description of drawings

Fig. 1 is the FQPSK signal generator schematic diagram of existing general type.

Fig. 2 is the Trellis-coded modulation schematic diagram of FQPSK signal.

Fig. 3 is 16 waveform sketch mapes of signal mapper output in the Trellis-coded modulation.

Fig. 4 is the operating process block diagram of the implementation method of FQPSK modulation waveform of the present invention.

Fig. 5 is a bezier curve approximate algorithm flow diagram.

Fig. 6 is to use the sketch map of the optimised waveform of the inventive method.

Fig. 7 is to use the comparison diagram of power spectrum of power spectral density and the general type FQPSK signal of the FQPSK signal that first kind of optimization method of the present invention realize.

Fig. 8 is to use the comparison diagram of power spectrum of power spectral density and the general type FQPSK signal of the FQPSK signal that second kind of optimization method of the present invention realize.

FQPSK signal and the bit error rate performance comparison diagram of general type FQPSK signal under awgn channel that Fig. 9 is to use two kinds of optimization methods of the present invention to realize.

Embodiment

For making the object of the invention, technical scheme and advantage clearer, the present invention is made further detailed description below in conjunction with accompanying drawing.

The present invention is a kind of implementation method of the FQPSK modulation waveform based on theory of spline function; This method is to design the FQPSK modulation waveform with bezier curve: earlier the FQPSK waveform is simplified; With bezier curve the waveform after simplifying is optimized again; Then the bezier curve control point that constitutes the FQPSK waveform is adjusted, made the waveform junction satisfy smooth or fairing.The inventive method is applicable to that remote sensing remote measurement and deep space communication and other adopt the communication system of permanent envelope or accurate constant envelope signal.

Referring to Fig. 4, introduce the operating procedure of the inventive method:

Step 1, according to the characteristics of 16 waveforms of general type FQPSK and the correlation between each waveform, it is identical and waveform that need not design is reduced to following three waveform: s with optimization objects to delete wherein shape ₃(t), s ₄(t) and s ₇(t) positive axis part, and rebuild out 16 whole waveforms with these three sections waveforms; Just simplify the waveform number that will design with bezier curve, reservations needs the target waveform of optimization:

The Trellis-coded modulation mode of FQPSK is as shown in Figure 2, these waveform mapper output 16 kinds of different waveforms (referring to Fig. 3), but the present invention need not design by these 16 waveforms all again.Have following relation between these 16 waveforms because find:

At first, waveform s ₀(t) to waveform s ₇(t) the positive and negative negate of amplitude just obtains waveform s ₈(t) to waveform s ₁₅(t).See s again ₀(t) to s ₃(t): s ₁(t) by s ₀(t) negative semiaxis part and s ₃(t) positive axis is partly formed, s ₂(t) by s ₀(t) positive axis part and s ₃(t) negative semiaxis is partly formed, so s ₁(t) and s ₂(t) be by s ₀(t) and s ₃(t) confirm.In like manner, s ₅(t) and s ₆(t) be by s ₄(t) and s ₇(t) confirm.Because s ₀(t) waveform is more special, and the present invention gets rid of it outside the Waveform Design object, and thinks s ₀(t) remain unchanged.s ₃(t) be even function, and s ₄(t) and s ₇(t) be odd function, so as long as know the positive axis part of these three waveforms, whole 16 waveforms of the waveform mapper of FQPSK output just can be confirmed (because of s one by one ₀(t) known).The present invention uses respectively

With

Expression s ₃(t), s ₄(t) and s ₇(t) positive axis part, and as the objective optimization waveform.

Waveform after the bezier curve of step 2, the explicit form of use is simplified above-mentioned steps is optimized, and makes new FQPSK signal have less envelope fluctuating, higher-wattage spectrum efficiency and bigger minimum Eustachian distance.The concrete implementation method of this step has two kinds, and, all be that a longitudinal axis amplitude to the bezier curve control point is optimized.

At first introduce the implementation method of first kind of waveform optimization below:

(21) use

and

three waveforms after the iterative approach algorithm is simplified step (1) to approach, with the FQPSK wavy curve of the bezier curve form that obtains being similar to permanent envelope form to the corresponding waveform of the FQPSK of permanent envelope form signal.The purpose of this step is that one group of bezier curve control point of approaching the FQPSK waveform of permanent envelope form well will be provided, so that the envelope of the follow-up FQPSK signal that bezier curve constituted after the fine setting operation rises and falls still in allowed band.

CEEFQPSK is as a kind of FQPSK of permanent envelope form, its s ₀(t) FQPSK with general type is identical, and the present invention is through making

With

The corresponding waveform that three waveforms approach CEEFQPSK approaches whole 16 waveforms of CEEFQPSK.Just, calculate the quadratic sum of the difference between these sampled points and weigh degree of closeness between the two through to bezier curve and aim curve sampling.

Referring to Fig. 5, introduce the concrete operations content of approaching aim curve in this step (21):

(211) every target curve initial is turned to a second order bezier curve that contains three control points: the control point at two ends overlaps with the end points of aim curve, and intermediate controlled point is the mid point of these two end points lines; In fact; The position of intermediate controlled point can have influence on iterative approach convergence of algorithm speed; But because of convergence rate very fast; So processing is simplified in the initialization to this intermediate controlled point: the abscissa of this intermediate controlled point is chosen the intermediate value of two end points abscissas, and this also is in order to use explicit bezier curve, to reduce the complexity that the target waveform signal performance calculates.

(212) carry out bezier curve iterative approach algorithm to removing two all control points beyond the end control point; So that the bezier curve of existing exponent number can approach aim curve to greatest extent: each iterative computation goes out the renewal amount Δ P of intermediate controlled point; Reduce if upgrade back bezier curve and aim curve error, then get into next iteration immediately; Do not reduce if upgrade the back error, then abandon upgrading, and the finishing iteration algorithm.

(213) calculate error between these bezier curves and the aim curve, if error greater than defined threshold, then to all bezier curves do not destroy bezier curve explicit form once rise the rank operation after, return execution in step (212); If error, then finishes this step (21) less than setting threshold.

(22) control point of the FQPSK wavy curve of the bezier curve form that obtains is finely tuned, make the waveform junction satisfy smooth condition, simultaneously the power spectrum efficiency of this FQPSK waveform signal is made constraint; The envelope that calculates this waveform then rises and falls, if less than setting threshold, then finishes this step, carries out subsequent operation; Otherwise, all bezier curves are not destroyed bezier curve display format rise rank operations, return then and carry out the operations of bezier curve iterative approach algorithms to removing two all control points beyond the end control points in the execution in step (21).

Referring to Fig. 6, introduce the concrete operation method at fine setting control point among the present invention.Among the figure with s ₀(t) negative semiaxis part

With

With

All being plotted in the same coordinate, is not that expression has such waveform, but for connection situation possible between the waveform is described.

on the left may be?

the right connection; may be right?

left side of the connection.

left side possibly be connected with the right side of

; The right side possibly be connected with the left side of ;

is the same with

shape, is mirror.

on the left may be?

or?

right connections; may be right? or?

left connection.

on the left may be?

or? right connections; may be right?

left connection.

Find that these four waveform end points place identical waveforms of amplitude may interconnect (comprising the waveform that is mirror with these four waveform shapes).So the present invention is through the control point of adjustment

and

; Make that the first derivative on

left and right sides,

and

right side is zero, and make the first derivative in

and left side equate.How explanation adjusts these control points below:

Use ${\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_0^3,{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1^3,...,{\mathrm{<figure-callout\; id="3"\; label="P\; n"\; filenames="H2009102426101E00012.png,H2009102426101E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_n^{},$ ${\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_0^4,{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1^4,...,{\mathrm{<figure-callout\; id="4"\; label="P\; n"\; filenames="H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_n^{}$ With ${\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_0^7,{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1^7,...,{\mathrm{<figure-callout\; id="7"\; label="P\; n"\; filenames="H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_n^{}$ Expression respectively $s_3^{+}\left(t\right),{\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="H2009102426101E00042.png"\; state="\{\{state\}\}">s</figure-callout>}}_4^{+}\left(t\right)$ With

The longitudinal axis amplitude at control point, their corresponding abscissas are identical, all are: 0,

1.The end points of these three bezier curves overlaps with the end points of the FQPSK waveform of general type.

${\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="H2009102426101E00012.png,H2009102426101E00021.png"\; state="\{\{state\}\}">s</figure-callout>}}_3^{+}\left(t\right):$ Adjustment $P_{}^{}$ ${}_1^3$ With $P_{n-1}^3,$ Make ${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1^3={\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="H2009102426101E00012.png,H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_0^3,$ And $P_{n-1}^3={\mathrm{<figure-callout\; id="3"\; label="P\; n"\; filenames="H2009102426101E00012.png,H2009102426101E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_n^{};$

${\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="H2009102426101E00042.png"\; state="\{\{state\}\}">s</figure-callout>}}_4^{+}\left(t\right):$ Adjustment $P_{n-1}^4,$ Make $P_{n-1}^4={\mathrm{<figure-callout\; id="4"\; label="P\; n"\; filenames="H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_n^{};$

${\mathrm{<figure-callout\; id="7"\; label="s"\; filenames="H2009102426101E00042.png"\; state="\{\{state\}\}">s</figure-callout>}}_7^{+}\left(t\right):$ Adjustment $P_{n-1}^7,$ Make $P_{n-1}^7={\mathrm{<figure-callout\; id="7"\; label="P\; n"\; filenames="H2009102426101E00042.png"\; state="\{\{state\}\}">P</figure-callout>}}_n^{};$

Adjustment makes

at last just makes all waveform junctions satisfy smooth condition like this.

After the control point being carried out fine setting, also must calculate new envelope and rise and fall, if the envelope fluctuating value that allows greater than maximum is then returned step (21), continue curve is carried out rising rank and approaches operation, rise and fall to satisfy up to envelope and set requirement.

(23) rise and fall less than setting threshold and waveform junction under the smooth condition satisfying envelope; Nonlinear optimization program with satisfying common Optimization Model is optimized the bezier curve control point except that end points, so that the waveform after optimizing satisfies the minimum Eustachian distance maximum of the smooth and FQPSK signal in waveform junction.

M.K.Simon and T.-Y.Yan have provided the pairing error event of minimum Eustachian distance of general FQPSK in " Performance Evaluation and Interpretation of Unfiltered Feher-Patented Quadrature-Phase-Shift Keying (FQPSK) ".The implementation method of first kind of waveform optimization of the present invention has been used the nonlinear optimization program in the MATLAB software, envelope rise and fall and the smooth condition in waveform junction under, the Euclidean distance of this error event is optimized.

Introduce the implementation method of second kind of waveform optimization below:

(2a) confirm sum, population size and the population evolutionary generation of the individual parameter in the population; Wherein the sum of individual parameter is a sum of removing the bezier curve control point at beginning control point in the waveform that will optimize.For example; If and removes outside the end points control point; Remaining respectively K control point, the number of the individual parameter of population has 3K so.The population size is made as 30K, and evolutionary generation was made as for 800 generations.

(2b) according to optimised waveform, all individualities in the random initializtion first generation population suitably.Because of the span of waveform to be optimized

and

is [0; 1]; And the DE algorithm is an evolution algorithm at random; For computing is oversimplified; All all individual parameters in the population are set; Be that the bezier curve control point is a random initializtion between [1,2].

(2c) carry out the DE algorithm: with envelope fluctuating, power spectrum efficiency, minimum Eustachian distance and junction waveform smooth degree respectively with the form weighted sum of work factor as the total cost function of DE algorithm; Carry out DE algorithm, optimal control point with this total cost function again.

For example, individual corresponding one group of FQPSK waveform in the population, calculating the envelope maximum of the corresponding FQPSK signal of this individuality and the ratio of minimum value is R _f, the work factor that envelope rises and falls is (R _f-1) ²Use fast Fourier transform to carry out power spectrum estimation to one section long signal of FQPSK at random, the ratio that accounts for the gross energy that whole spectrum estimates from the energy of direct current to 0.5 times this band frequency of bit rate is R _pThe work factor of power spectrum is (1-R _p) ²In the network of FQPSK, searching out minimum Eustachian distance is D _Min, the work factor of Euclidean distance is (2-D _Min) ²I individuals x in the population _iParameter x ₁To x _KFor

The bezier curve control point, x _K+1To x _2KFor

The bezier curve control point, x _2K+1To x _3KFor

The bezier curve control point, the auxiliary work factor that then acts on the waveform junction is: (x ₁-A) ²+ (x _K-1) ²+ (x _2K-A) ²+ (x _3K-1) ²+ (x _K+1-x _2K+1) ²Add that at last auxiliary work factor weighted sum obtains total work factor (cost function): H (x)=w ₁(R _f-1) ²+ w ₂(1-R _p) ²+ w ₃(2-D _Min) ²+ w ₄[(x ₁-A) ²+ (x _K-1) ²+ (x _2K-A) ²+ (x _3K-1) ²+ (x _K+1-x _2K+1) ²]; In the formula, w ₁, w ₂, w ₃And w ₄Be the weight of each work factor, A equals

Step 3, the bezier curve that the control point constituted that obtains because of last optimization not necessarily satisfy the smooth condition in junction; Perhaps under envelope rises and falls less than the setting threshold condition; Can make the junction satisfy that more high-order is smooth; So this step is under the prerequisite of envelope fluctuating less than setting threshold; Step 2 is optimized the bezier curve control point obtain finely tune again, make its waveform junction satisfy the smooth of high-order more as far as possible or be referred to as fairing, and further retrain the power spectrum efficiency of FQPSK signal.Just, if adjusted envelope rises and falls less than setting threshold, then execution in step (3) again continues adjustment; And the method for adjustment of this step is identical with the step (22) of first kind of optimization implementation method, repeats no more here.When envelope rises and falls greater than setting threshold, abandon this time adjustment, finish this step.

The applicant has carried out repeatedly implementing test to the inventive method, below the brief description test situation following:

At first provide the longitudinal axis amplitude at the bezier curve control point of

and

that two kinds of methods using optimization of the present invention obtain; Its six corresponding abscissas are respectively: 0, and

1.

Table 1 is the longitudinal axis amplitude that step 2 is used the bezier curve control point that first kind of optimization method obtain:

Table 2 is longitudinal axis amplitudes that step 2 is used the bezier curve control point that second kind of optimization method obtain:

Envelope rises and falls: the FQPSK envelope of general type rises and falls and is 0.0947dB; The envelope of the FQPSK signal that first kind of optimization method of the present invention realized rises and falls and is 0.0106dB; The envelope of the FQPSK signal of second kind of optimization method realization rises and falls and is 0.1063dB.

Power spectral density: the power spectrum of the FQPSK signal that two kinds of optimization methods among the present invention are realized and the power spectrum of general type FQPSK signal compare in Fig. 7 and Fig. 8, and be still higher through the power spectrum efficiency of the FQPSK signal optimized.

The error rate under the awgn channel: the minimum Eustachian distance of three kinds of FQPSK signals is respectively 1.56,1.85 and 1.99.The three is compared in Fig. 9 at the bit error rate performance under the awgn channel, comparatively considerable with the FQPSK signal that two kinds of optimization methods are realized than the performance gain of general type FQPSK.

Claims (6)

1. implementation method of quadrature phase keying FQPSK modulation waveform based on conspicuous system of taking of theory of spline function; It is characterized in that: said method is to use bezier curve to design the FQPSK modulation waveform: earlier the FQPSK waveform is simplified; With bezier curve the waveform after simplifying is optimized again; Then the bezier curve control point that constitutes the FQPSK waveform is adjusted, made the waveform junction satisfy smooth or fairing; This method comprises following operating procedure:

(1) according to the characteristics of 16 waveforms of general type FQPSK and the correlation between each waveform, it is identical and waveform that need not design is reduced to following three waveforms with optimization objects: the 4th waveform s in 16 waveforms of this FQPSK to delete wherein shape ₃(t), the 5th waveform s ₄(t) and the 8th waveform s ₇(t) the part of positive axis separately, and rebuild out 16 whole waveforms with these three sections waveforms;

(2) waveform after the bezier curve of the explicit form of use is simplified above-mentioned steps is optimized, and makes new FQPSK signal have less envelope fluctuating, higher-wattage spectrum efficiency and bigger minimum Eustachian distance; The method of said optimized waveform has two kinds, and all is that a longitudinal axis amplitude to the bezier curve control point is optimized; Wherein, first kind of optimization method comprises following operating procedure:

(21) use the waveform after the iterative approach algorithm is simplified step (1) to approach, with the FQPSK wavy curve of the bezier curve form that obtains approximate permanent envelope form to the corresponding waveform of the FQPSK of permanent envelope form signal;

(22) control point of the FQPSK wavy curve of the bezier curve form that obtains is finely tuned, make the waveform junction smooth, simultaneously the power spectrum efficiency of this FQPSK waveform signal is made constraint; The envelope that calculates this waveform then rises and falls, if less than setting threshold, then finishes this step, carries out subsequent operation; Otherwise, all bezier curves are not destroyed bezier curve display format rise rank operations, return then and carry out the operations of bezier curve iterative approach algorithms to removing two all control points beyond the end control points in the execution in step (21);

(23) rise and fall less than setting threshold and waveform junction under the smooth condition satisfying envelope; Nonlinear optimization program with satisfying common Optimization Model is optimized the bezier curve control point except that end points, so that the waveform after optimizing satisfies the minimum Eustachian distance maximum of the smooth and FQPSK signal in waveform junction;

Second kind of optimization method is to use differential evolution DE algorithm to come the optimal control point, and it comprises following concrete operations step:

(2a) confirm sum, population size and the population evolutionary generation of the individual parameter in the population; Wherein the sum of individual parameter is a sum of removing the bezier curve control point at beginning control point in the waveform that will optimize;

(2b) according to optimised waveform, all individualities in the random initializtion first generation population suitably;

(2c) with envelope fluctuating, power spectrum efficiency, minimum Eustachian distance and junction waveform smooth degree respectively with the form weighted sum of work factor as the total cost function of DE algorithm, carry out DE algorithm, optimal control point with this total cost function again;

(3) under the prerequisite of envelope fluctuating less than setting threshold; Finely tune at the bezier curve control point that optimization obtains to above-mentioned steps; The smooth of satisfied more higher order so that try one's best in the waveform junction, promptly its first derivative is continuous, and further retrains the power spectrum efficiency of FQPSK signal; If adjusted envelope rises and falls less than setting threshold, then carry out this step (3) again, continue adjustment; When envelope rises and falls greater than setting threshold, abandon this time adjustment, finish this step.

2. method according to claim 1 is characterized in that: said step (21) further comprises following content of operation:

(211) every target curve initial is turned to a second order bezier curve that contains three control points: the control point at two ends overlaps with the end points of wavy curve, and intermediate controlled point is the mid point of these two end points lines; The intermediate value that the abscissa of this intermediate controlled point is chosen two end points abscissas is in order to use explicit bezier curve, thereby reduces the complexity of waveform signal Performance Calculation;

(212) carry out bezier curve iterative approach algorithm to removing two all control points beyond the end control point, so that the bezier curve of existing exponent number can approach aim curve to greatest extent;

(213) calculate error between these bezier curves and the aim curve, if error less than setting threshold, then finishes this step; Otherwise, all bezier curves are not destroyed bezier curve explicit form rise rank operations after, return execution in step (212).

3. method according to claim 1; It is characterized in that: in the said step (22); The concrete operations that the control point of the FQPSK wavy curve of bezier curve form is finely tuned are: interconnective situation occurs between the waveform of representing to these bezier curves and finely tune; After requiring the adjustment control point, make the 4th waveform s in this FQPSK waveform ₃(t) left and right sides of positive axis, the 5th waveform s ₄(t) and the 8th waveform s ₇(t) first derivative on the right side of positive axis all is zero, and makes s ₄(t) and s ₇(t) first derivative in positive axis left side equates, the envelope that calculates the determined FQPSK modulation signal of bezier curve of process fine setting then rises and falls, and its value and setting threshold is compared, with the decision subsequent operation again.

4. method according to claim 1 is characterized in that: in the said step (2b), because of waveform s to be optimized ₃(t), s ₄(t) and s ₇The span of (t) positive axis part is [0,1], and the DE algorithm is evolution algorithm at random, is that computing is oversimplified, and all individual parameters in the population are set, and promptly the bezier curve control point is a random initializtion between [1,2].

5. method according to claim 1 is characterized in that: in the said step (2c), during to each work factor weighted sum, the ratio of the envelope maximum of certain individual corresponding waveform and minimum value is R in the population _f, the work factor that envelope rises and falls is (R _f-1) ²Through power spectrum estimation, the ratio that accounts for gross energy from the energy of direct current to 0.5 times this band frequency of bit rate is R _p, the work factor of power spectrum is (1-R _p) ²Minimum Eustachian distance is D _Min, the work factor of Euclidean distance is (2-D _Min) ²I individuals x in the population _iParameter x ₁To x _KBe s ₃(t) Betsy of positive axis that control point, x _K+1To x _2KBe s ₄(t) Betsy of positive axis that control point, x _2K+1To x _3KBe s ₇(t) Betsy of positive axis that control point, the auxiliary work factor that then acts on the waveform junction is: (x ₁-A) ²+ (x _K-1) ²+ (x _2K-A) ²+ (x _3K-1) ²+ (x _K+1-x _2K+1) ²The cost function that obtains at last is:

H (x)=w ₁(R _f-1) ²+ w ₂(1-R _p) ²+ w ₃(2-D _Min) ²+ w ₄[(x ₁-A) ²+ (x _K-1) ²+ (x _2K-A) ²+ (x _3K-1) ²+ (x _K+1-x _2K+1) ²]; In the formula, w ₁, w ₂, w ₃And w ₄Be the weight of each work factor, A equals

6. method according to claim 1 is characterized in that: said method is applicable to the communication system of permanent envelope of the employing that comprises remote sensing remote measurement and deep space communication or accurate constant envelope signal.

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