CN109217843A - A kind of asymmetric FIR distortion compensation filter design method of satellite launch channel dual domain - Google Patents
A kind of asymmetric FIR distortion compensation filter design method of satellite launch channel dual domain Download PDFInfo
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- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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- H03H2017/0081—Theoretical filter design of FIR filters
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Abstract
The invention discloses a kind of spaceborne asymmetric FIR distortion compensation filter design methods of dual domain: 1, extracting the amplitude and group delay characteristic of launch channel；2, according to the amplitude of system and group delay index request, the filter target amplitude group delay for needing to be designed is calculated；3, using FIR amplitude distortion compensating filter target amplitude proposed by the present invention, the amplitude distortion compensating filter coefficient for meeting step 2 amplitude characteristic is calculated by lagrange's method of multipliers.4, according to the target group delay of the asymmetric FIR group delay distortion compensating filter of proposition, the group delay distortion compensating filter coefficient for meeting the group delay characteristic of step 1 extraction is iterated to calculate out by lagrange's method of multipliers.5, distortion compensation filter coefficient carries out convolution, obtains the asymmetric FIR distortion compensation filter of dual domain.The present invention is solved in the case where occupying fewer resource and guaranteeing navigation downlink signal continuity and real-time, and the non-linear distortion of navigation launch channel can be compensated using method of the invention, promotes navigation downlink signal quality in real time.
Description
Technical field
The present invention relates to a kind of asymmetric FIR distortion compensation filter design methods of satellite launch channel dual domain, belong to and lead
Boat technical field.
Background technique
With the construction of Beidou satellite navigation system, No. three satellite navigation systems of Beidou propose signal quality higher
It is required that.Navigation downlink signal to real-time, continuity, high reliablity requirement under, and in order to occupy less spaceborne money
In the case where source, need to recompense to the non-linear distortion in Beidou navigation satellite launch channel using distortion compensation filter
To improve navigation downlink signal quality.
Traditional distortion compensation filter is divided into memoryless distortion compensating filter and has memory distortion compensating filter.Nothing
Memory distortion compensating filter mainly utilizes offline or on-line study look-up table, carries out distortion compensation to input signal.And
There is memory distortion compensating filter mainly to utilize the learning structure of closed loop, adjusts distortion compensation parameter constantly to reach distortion compensation
Effect.Since navigation downlink signal is to real-time and the demanding feature of continuity, above two conventional distortion compensation
Filter design method is not appropriate for navigation satellite.
In the limited situation of spaceborne resource, in order to meet navigation downlink signal requirement, can using FIR filter this
Kind structure, but in presently disclosed design method, FIR filter is mainly used to be filtered signal, phase characteristic is
Linearly, nonlinear phase can not be compensated, is designed high pass or low-pass filter, there is no for entire channel
Distortion is designed to distortion compensation filter, carries out relevant design particular without the group delay specifically for channel.
Summary of the invention
Technology of the invention solves the problems, such as: overcome the deficiencies in the prior art, proposes a kind of satellite launch channel dual domain
Asymmetric FIR distortion compensation filter design method can navigate in the case where occupying less spaceborne resource, and meeting
Under conditions of downlink signal real-time, continuity, reliability, the distortion of navigation downlink signal is effectively compensated for, is improved under navigation
Row signal quality.
The technical solution of the invention is as follows: a kind of asymmetric FIR distortion compensation filter of satellite launch channel dual domain is set
Meter method, this method include the following steps:
(1), the actual amplitude characteristic of satellite launch channel is extracted | Horigin(ω) | with group delay characteristic grporigin(ω)；
(2), the amplitude characteristic according to required by satellite launch channel | Hcons(ω) | and group delay characteristic grpcons(ω) and
The actual amplitude characteristic of satellite launch channel | Horigin(ω) | with group delay characteristic grporigin(ω), calculates separately amplitude distortion
The target amplitude frequency response of compensating filter | Hobj(ω) | and the target group delay-frequency of group delay distortion compensating filter is rung
Answer grpobj(ω)；
(3), the coefficient h of amplitude distortion compensating filter is designed1(n), it is allowed to meet its frequency response and corresponding frequency point
Fluctuation is no more than the first pre-determined threshold χ, and the smallest condition of order between target amplitude frequency response；
(4), the coefficient h of group delay distortion compensating filter is designed2(n), it is allowed to meet group delay distortion compensating filter
Frequency response square and corresponding frequency point target group delay frequency response square difference be no more than the second pre-determined threshold, and group
The frequency response of delay distortion compensating filter with and corresponding frequency point target group delay frequency response difference square the smallest item
Part；
(5), by amplitude distortion compensating filter h1(n) with group delay distortion compensating filter h2(n) convolution, obtain amplitude,
The anti-distortion filter h (n) of group delay dual domain:
The value range of the first pre-determined threshold χ in the step (2) are as follows: 0dB~0.5dB；
The value range of the second pre-determined threshold c in the step (3) are as follows: 0ns~1ns；
The coefficient h of step (2) amplitude filter1(n) it is solved using lagrange's method of multipliers, specific step is such as
Under:
(2.1), the maximum value n of n is arranged according to system resource situation by the order n for initializing amplitude filtermaxAnd minimum
Value nmin；
(2.2), according to amplitude filter order n, target amplitude frequency response | Hobj(ω) |, be arranged according to channel width
Filter coefficient h is calculated with lagrange's method of multipliers in filter frequencies value range1(n), h is calculated1(n) frequency is rung
Answer Hdesign(ω)；
(2.3), judgeIt is whether true, if set up, then follow the steps (2.4)；Such as
Fruit is invalid, thens follow the steps (2.5)；
(2.4), the order n of amplitude filter is updated to n-1, remaining condition remains unchanged, and continues to execute step (2.2)
~step (2.3), until n >=nminUntil；Export the coefficient of current amplitude filter and the order n of filter；
(2.5), the order n of amplitude filter is updated to n+1, remaining condition remains unchanged, and continues to execute step (2.2)
~step (2.3), until n≤nmaxUntil；Export the coefficient of current amplitude filter and the order n of filter.
The step (3) solves the coefficient of group delay filter using lagrange's method of multipliers, specific steps are as follows:
(3.1), it is responded according to group delay target frequency, defines Fourier's basic matrix Θ when group delay optimization optimization calculates
Wherein, ω (1)~ω (m) indicates the target frequency response of the 1 to m-th frequency point；M=BW/RBW, BW indicate letter
Road bandwidth, RBW indicate resolution ratio, and unit is Hz；
(3.2), the number of iterations i is initialized, the order n of group delay filter is designed2, it is allowed to be equal to amplitude filter
Order；
(3.3), group delay distortion compensating filter coefficient h is designed2(n), it is allowed to meetItem
Part；Θh2Indicate the Fourier's basic matrix Θ and group delay distortion compensating filter coefficient h of group delay optimization2(n) dot product fortune is carried out
It calculates, obtains group delay distortion compensating filter h2(n) frequency response；
(3.4), target group delay is updated using following formula:
Wherein,For the distortion compensation filter h of current iteration2(n) group delay,For target group delay；
(3.5), judgeVariance whether be less than preset third door
Limit, is the coefficient and its order n for then exporting current group delay filter2, otherwise, the number of iterations i is added 1, updates the number of iterations
I re-execute the steps (3.3)~(3.5)；
The value range of preset third thresholding is: 0~1ns.
Compared with the prior art, the invention has the advantages that:
(1), the present invention can be in the case where meeting system to distortion compensation filter amplitudes requirement, to navigation downlink letter
Number amplitude compensate, effectively reduce the order of FIR amplitude distortion compensating filter, reduce and disappear to hardware resource
Consumption.
(2), the invention proposes under the constraint of minimum 2 norm conditions by iteration update target unit shock response,
It is sparse in domain space to seek it, effectively improves FIR group delay distortion compensating filter compensation precision, it can be in real time
The group delay distortion of navigation downlink signal is effectively compensated for, navigation signal capability and performance is greatly improved.
(3), the present invention devises in Fu specifically for the distortion compensation filter design algorithm of asymmetric FIR group delay
Phyllopodium matrix, the frequency domain base can more really reflect the phase change of objective function to be asked, and be conducive to final asymmetric group delay
The solution of filter enables optimization process more rapid convergence.
Detailed description of the invention
Fig. 1 is a kind of spaceborne asymmetric FIR distortion compensation filter design method flow chart of dual domain of the present invention.
Fig. 2 is the asymmetric FIR amplitude distortion compensating filter design flow diagram of the embodiment of the present invention.
Fig. 3 is the asymmetric FIR group delay distortion compensating filter design flow diagram of the embodiment of the present invention.
Specific embodiment
Embodiment of the present invention is described in further detail below.
The invention proposes a kind of satellite launch channel magnitude, group delay dual domain distortion compensation filter design method, energy
It is excellent in the case where guaranteeing to navigate downlink signal continuity, real-time, stability enough in the case where spaceborne resource-constrained processed
Corresponding FIR distortion compensation filter is dissolved, the amplitude domain distortion that can preferably compensate navigation launch channel is lost with group delay
Very, guarantee navigation downlink signal quality.
As shown in Figure 1, this method includes the following steps:
(1), the actual amplitude characteristic of satellite launch channel is extracted | Horigin(ω) | with group delay characteristic grporigin(ω)；
It can use vector signal Network Analyzer, by inputting single carrier swept-frequency signal to launch channel, and receive hair
The single carrier for penetrating channel output output, extracts the amplitude characteristic of launch channel | Horigin(ω) | with group delay characteristic grporigin
(ω)；Transmitted bandwidth required for the range of frequency sweep is set as is BW (unit Hz), and frequency sweep resolution ratio is that (unit is RBW
Hz), it is traditionally arranged to be 1KHz.
(2), the amplitude characteristic according to required by satellite launch channel | Hcons(ω) | and group delay characteristic grpcons(ω) and
The actual amplitude characteristic of satellite launch channel | Horigin(ω) | with group delay characteristic grporigin(ω), calculates separately amplitude distortion
The target amplitude frequency response of compensating filter | Hobj(ω) | and the target group delay-frequency of group delay distortion compensating filter is rung
Answer grpobj(ω)；
|Hobj(ω) |=| Hcons(ω)|-|Horigin(ω)| (1)
grpobj(ω)=grpcons(ω)-grporigin(ω) (2)
Ideally, | Hcons(ω)|、grpcons(ω) is constant, indicates ideal amplitude characteristic and group delay characteristic
Fluctuation is 0, under actual conditions, | Hcons(ω)|、grpcons(ω) is the amplitude and phase amount changed according to frequency.For example,
System index requires amplitude | Hcons(ω) | flatness 0.5dB, group delay grpcons(ω) fluctuation < 1ns.|Hcons(ω) | be
One curve with frequency fluctuation, fluctuation range maximum 0.5dB, grpcons(ω) is a curve with frequency fluctuation, fluctuation
Range maximum 1ns.
Specific design cycle as shown in Fig. 2, amplitude filter coefficient h1(n) it is solved using lagrange's method of multipliers,
Specific steps are as follows:
(2.1), the order n for initializing amplitude filter, is set as 50 under normal circumstances, is arranged according to system resource situation
The maximum value n of nmaxWith minimum value nmin, wherein nmaxAnd nminSelection it is related to system resource, need according in system allow
The resource used is configured；
(2.2), according to amplitude filter order n, target amplitude frequency response | Hobj(ω) |, channel width setting filtering
Filter coefficient h is calculated with lagrange's method of multipliers in device frequency value range1(n), h is calculated1(n) frequency response
Hdesign(ω)；
For example, bandwidth range is 10MHz~20MHz, sample frequency 100MHz, then, 2 π of bandwidth range */sampling frequency
Rate.
(2.3), judgeIt is whether true, if set up, then follow the steps (2.4)；Such as
Fruit is invalid, thens follow the steps (2.5)；Wherein, n is FIR distortion compensation filter order, | Hdesign(ω) | it is h1(n) width
Degree, χ are the amount of the amplitude fluctuation for the system requirements being arranged in step 2, are known quantity.
(2.4), the order n of amplitude filter is updated to n-1, remaining condition remains unchanged, and continues to execute step (2.2)
~step (2.3), until n >=nminUntil；Export the coefficient of current amplitude filter and the order n of filter；
(2.5), the order n of amplitude filter is updated to n+1, remaining condition remains unchanged, and continues to execute step (2.2)
~step (2.3), until n≤nmaxUntil；Export the coefficient of current amplitude filter and the order n of filter.
(2), the coefficient h of amplitude distortion compensating filter is designed1(n), it is allowed to meet its frequency response and corresponding frequency point
Fluctuation is no more than the first pre-determined threshold χ, and the smallest condition of order between target amplitude frequency response, it may be assumed that
min filter order n
The value range of first pre-determined threshold χ are as follows: 0dB~0.5dB.
(3), the coefficient h of group delay distortion compensating filter is designed2(n), it is allowed to meet group delay distortion compensating filter
Frequency response square and corresponding frequency point target group delay frequency response square difference be no more than the second pre-determined threshold, and group
The frequency response of delay distortion compensating filter with and corresponding frequency point target group delay frequency response difference square the smallest item
Part；That is:
In above formula, c is the second pre-determined threshold, is control h2(n) coefficient of amplitude, value range are value range are as follows: <
1ns。
This step solves the coefficient of group delay filter using lagrange's method of multipliers, specific steps are as follows:
(3.1), it is responded according to group delay target frequency, defines Fourier's basic matrix Θ of group delay optimization
In group delay distortion compensating filter design optimization, needs to carry out operation using FFT and IFFT, be when calculating
Based on plural base eixIt carries out, in order to accelerate convergence rate when group delay distortion compensation optimizing, design is special right for this problem
The frequency domain basic matrix answered.Using Euler's formula by eix=cosx+isinx is expressed as Θ, as shown in formula (4), using practical frequency
Shown in the Θ that rate w (i) is derived such as formula (4), left-half is the real part after Euler's formula is decomposed, and right half part is Euler
Imaginary part after formula decomposition.For group delay optimization Fourier's basic matrix, the basic matrix by the real part of Fourier's base with
Imaginary part is separated, and really reflects the phase change of objective function to be asked, conducive to final asymmetric group delay filter
It solves, optimization process can be made faster to restrain.
Wherein, ω (1)~ω (m) indicates the target frequency response of the 1 to m-th frequency point；M=BW/RBW, BW indicate letter
Road bandwidth, RBW indicate resolution ratio, and unit is Hz；It is traditionally arranged to be 1KHz.
(3.2), the number of iterations i is initialized, the order n of group delay filter is designed2, it is allowed to be equal to amplitude filter
Order；
(3.3), group delay distortion compensating filter coefficient h is designed2(n), it is allowed to meetItem
Part；Θh2Indicate the Fourier's basic matrix Θ and group delay distortion compensating filter coefficient h of group delay optimization2(n) dot product fortune is carried out
It calculates, obtains group delay distortion compensating filter h2(n) frequency response；
(3.4), target group delay is updated using following formula:
Wherein,For the distortion compensation filter h of current iteration2(n) group delay,For target group delay；
(3.5), judgeVariance whether be less than preset third door
Limit, is the coefficient and its order n for then exporting current group delay filter2, otherwise, the number of iterations i is added 1, updates the number of iterations
I re-execute the steps (3.3)~(3.5)；The value range of preset third thresholding is: 0~1ns.
(4), by amplitude distortion compensating filter h1(n) with group delay distortion compensating filter h2(n) convolution, obtain amplitude,
The anti-distortion filter h (n) of group delay dual domain:
Fig. 3 is the design cycle example of FIR group delay distortion compensating filter, and wherein the first step is to be listed according to formula (5)
Corresponding target equation, second step are the initial value that filter order n is arranged, and are set as obtaining most in step 2 under normal circumstances
The value of small n, third step are that target equation is solved using lagrange's method of multipliers shown in FIG. 1, and the 4th step is to utilize formula (6)
Carry out the target group delay in newer (5).Then judge whether current value tends to a constant and be either equal to using formula (7)
0, if meet it is above-mentioned tend to constant or the condition equal to 0, being judged as current filter coefficient is optimal solution, and defeated
Filter coefficient out continues to return to solution if not meeting above-mentioned condition, after meeting condition, stops iteration.
This specification, which is not described in detail, partly belongs to common sense well known to those skilled in the art.
Claims (6)
1. a kind of asymmetric FIR distortion compensation filter design method of satellite launch channel dual domain, it is characterised in that including following
Step:
(1), the actual amplitude characteristic of satellite launch channel is extracted | Horigin(ω) | with group delay characteristic grporigin(ω)；
(2), the amplitude characteristic according to required by satellite launch channel | Hcons(ω) | and group delay characteristic grpcons(ω) and satellite
The actual amplitude characteristic of launch channel | Horigin(ω) | with group delay characteristic grporigin(ω) calculates separately amplitude distortion compensation
The target amplitude frequency response of filter | Hobj(ω) | and the target group delay frequency response of group delay distortion compensating filter
grpobj(ω)；
(3), the coefficient h of amplitude distortion compensating filter is designed1(n), it is allowed to the target width for meeting its frequency response with corresponding frequency point
It spends fluctuation between frequency response and is no more than the first pre-determined threshold χ, and the smallest condition of order；
(4), the coefficient h of group delay distortion compensating filter is designed2(n), it is allowed to meet group delay distortion compensating filter frequency sound
Answer square and corresponding frequency point target group delay frequency response square difference be no more than the second pre-determined threshold, and group delay lose
True compensating filter frequency response with and corresponding frequency point target group delay frequency response difference square the smallest condition；
(5), by amplitude distortion compensating filter h1(n) with group delay distortion compensating filter h2(n) convolution, when obtaining amplitude, group
Prolong the anti-distortion filter h (n) of dual domain:
2. the asymmetric FIR distortion compensation filter design method of a kind of satellite launch channel dual domain according to claim 1,
It is characterized in that the value range of the first pre-determined threshold χ in the step (2) are as follows: 0dB~0.5dB.
3. the asymmetric FIR distortion compensation filter design method of a kind of satellite launch channel dual domain according to claim 1,
It is characterized in that the value range of the second pre-determined threshold c in the step (3) are as follows: 0ns~1ns.
4. the asymmetric FIR distortion compensation filter design method of a kind of satellite launch channel dual domain according to claim 1,
It is characterized in that the coefficient h of step (2) amplitude filter1(n) it is solved using lagrange's method of multipliers, specific step is such as
Under:
(2.1), the maximum value n of n is arranged according to system resource situation by the order n for initializing amplitude filtermaxAnd minimum value
nmin；
(2.2), according to amplitude filter order n, target amplitude frequency response | Hobj(ω) |, according to channel width be arranged filter
Filter coefficient h is calculated with lagrange's method of multipliers in device frequency value range1(n), h is calculated1(n) frequency response
Hdesign(ω)；
(2.3), judgeIt is whether true, if set up, then follow the steps (2.4)；If no
It sets up, thens follow the steps (2.5)；
(2.4), the order n of amplitude filter is updated to n-1, remaining condition remains unchanged, and continues to execute step (2.2)~step
Suddenly (2.3), until n >=nminUntil；Export the coefficient of current amplitude filter and the order n of filter；
(2.5), the order n of amplitude filter is updated to n+1, remaining condition remains unchanged, and continues to execute step (2.2)~step
Suddenly (2.3), until n≤nmaxUntil；Export the coefficient of current amplitude filter and the order n of filter.
5. the asymmetric FIR distortion compensation filter design method of a kind of satellite launch channel dual domain according to claim 1,
It is characterized in that the step (3) solves the coefficient of group delay filter using lagrange's method of multipliers, specific steps are as follows:
(3.1), it is responded according to group delay target frequency, defines Fourier's basic matrix Θ when group delay optimization optimization calculates
Wherein, ω (1)~ω (m) indicates the target frequency response of the 1 to m-th frequency point；M=BW/RBW, BW indicate channel strip
Width, RBW indicate resolution ratio, and unit is Hz；
(3.2), the number of iterations i is initialized, the order n of group delay filter is designed2, it is allowed to be equal to the order of amplitude filter；
(3.3), group delay distortion compensating filter coefficient h is designed2(n), it is allowed to meetCondition；
Θh2Indicate the Fourier's basic matrix Θ and group delay distortion compensating filter coefficient h of group delay optimization2(n) dot-product operation is carried out,
Obtain group delay distortion compensating filter h2(n) frequency response；
(3.4), target group delay is updated using following formula:
Wherein, For the distortion compensation filter h of current iteration2(n) group delay,For
Target group delay；
(3.5), judgeVariance whether be less than preset third thresholding,
It is the coefficient and its order n for then exporting current group delay filter2, otherwise, the number of iterations i is added 1, updates the number of iterations i,
It re-execute the steps (3.3)~(3.5).
6. the asymmetric FIR distortion compensation filter design method of a kind of satellite launch channel dual domain according to claim 5,
It is characterized in that the value range of preset third thresholding is: 0~1ns.
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Application publication date: 20190115 |