CN103391053A - Linearization predistortion method based on Volterra series - Google Patents
Linearization predistortion method based on Volterra series Download PDFInfo
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- CN103391053A CN103391053A CN2012101411628A CN201210141162A CN103391053A CN 103391053 A CN103391053 A CN 103391053A CN 2012101411628 A CN2012101411628 A CN 2012101411628A CN 201210141162 A CN201210141162 A CN 201210141162A CN 103391053 A CN103391053 A CN 103391053A
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Abstract
The invention provides a linearization predistortion method based on Volterra series, belongs to the technical field of linear modulation and particularly relates to a linearization predistortion method based on Volterra series for simplifying a relational expression between input signals and output signals of a Volterra predistortion device in an ordinary form. The invention aims at providing the linearization predistortion method based on Volterra series easily applied to the power amplifying modeling or the predistortion device design. The linearization predistortion method has the characteristic that the relational expression between input signals and output signals of the Volterra predistortion device in the ordinary form is shown as the accompanying drawing.
Description
Technical field:
The invention belongs to the linearity modulation technique field, relate in particular to a kind of input of the Volterra predistorter of general type, pre-distortion method of the linearisation based on Volterra progression of the relational expression between output signal simplified.
Background technology:
Along with the development of digital communication technology and the maturation of 3G technology, it is more and more precious that band resource seems.Therefore with regard to requiring, the utilance of frequency band is increased, this has the good linearity with regard to an urgent demand power amplifier.In mobile communication system, there is within the specific limits signal to cover in order to guarantee mobile communication system, before signal is launched by radio-frequency front-end and antenna system, usually with power amplifier, carry out signal and amplify.The linearity of power amplifier directly affects the fine or not degree of emission and acknowledge(ment) signal, and therefore adopting digital pre-distortion technology is in order well to solve linearity problems, can to improve power amplification efficiency simultaneously, thereby meets the demand of 3G development.
General radio-frequency power amplifier all can produce the spectral re-growth effect, and these phenomenons are all due to the non-linear generation of power amplifier, so we must carry out linearization process to power amplifier and namely improve the linearity of power amplifier.This just requires us to adopt some linearization techniques to realize.Can well solve signal in the demand channel to the interference of other adjacent channel for linearization technique itself.In the base station construction of 3G, the cost of power amplifier accounts for more than 1/3 of total cost, if so power amplifier solved the linearity and efficiency, this brings a large amount of subduing for undoubtedly the cost of base station.
Mainly contain both at home and abroad at present: the linearization technique of the radio-frequency power amplifiers such as feed forward approach, back-off, feedback transmitter, predistortion.Wherein the advantage of feed-forward technique is, stable performance, can be good at improving the linearisation index of power amplifier, and cost is high, device property can not be compensated over time, the shortcomings such as design comparison complexity of loop but its also exists simultaneously; Power back has return back to the linear work district to operating voltage from 1dB, therefore it has the linearity preferably, but also sacrificed the efficiency of power amplifier simultaneously, make dc power very large, so just cause the problem of power amplifier heat radiation, and heat radiation is the Research Challenges of power amplifier, therefore this technology is replaced gradually by other linearization techniques.And negative-feedback technology requirement input signal and feedback signal are the signals of synchronization, and system itself has delay, and putting from this is to be difficult to realize.Why pre-distortion technology can be widely used in current power amplifier, that its advantage is is simple in structure, need not consider its stability problem, while can be processed multi-carrier signal, cost is lower, is the higher a kind of power amplifier linearization technology of present cost performance.
The input of the Volterra predistorter of general type, the relational expression between output signal are only applicable to the situation of low order small nonlinearity and in broadband system the memory radio-frequency (RF) power amplification being arranged, low order small nonlinearity model is difficult to accurately describe its characteristic or contrary characteristic.Therefore, it is very difficult directly the volterra progression of general type being applied to the designs of power amplifier modeling or predistorter, must simplify improvement.
Summary of the invention:
The object of the present invention is to provide a kind of pre-distortion method of the linearisation based on Volterra progression that is easy for power amplifier modeling or predistorter design.
For achieving the above object, the present invention adopts following technical scheme, and characteristics of the present invention are, with the input of the Volterra predistorter of general type, the relational expression between output signal:
Be reduced to simplified style one after removal DC terms and even item:
Do following simplification for simplified style one, the l rank core in simplified style one is designated as h
l(i
1, i
2..., i
l), l=1 wherein, 3 ..., 2d+1.Setting threshold λ ∈ 1,2 ..., M}.When l=1, h
1(i
1)=h
1(i
1).When l 〉=3,
T ∈ 1,2 ..., l}, if max{|i
s-i
t| 〉=λ, make h
l(i
1, i
2..., i
l)=0; Otherwise h
l(i
1, i
2..., i
l)=h
l(i
1, i
2..., i
l).Described λ value requires to choose according to accuracy.
The present invention simplifies the input of the Volterra predistorter of general type, the relational expression between output signal; thereby make described relational expression be easy for power amplifier modeling or predistorter design; make difficulty and the complexity decrease of power amplifier modeling or predistorter design, improve design efficiency.
Description of drawings:
Fig. 1 is the decomposing schematic representation that the memory nonlinear system is arranged;
Fig. 2 is for adopting the pre-distortion system block diagram of indirect learning structure.
Embodiment:
The present invention is with the input of the Volterra predistorter of general type, the relational expression between output signal:
Be reduced to simplified style one after removal DC terms and even item:
Do following simplification for simplified style one, the l rank core in simplified style one is designated as h
l(i
1, i
2..., i
l), l=1 wherein, 3 ..., 2d+1.Setting threshold λ ∈ 1,2 ..., M}.When l=1, h
1(i
1)=h
1(i
1).When l 〉=3,
T ∈ 1,2 ..., l}, if max{|i
s-i
t| 〉=λ, make h
l(i
1, i
2..., i
l)=0; Otherwise h
l(i
1, i
2..., i
l)=h
l(i
1, i
2..., i
l).Described λ value requires to choose according to accuracy.
The Volterra series theory is to analyze a kind of effective mathematical tool of non linear system.For linear time invariant system, its zero state response equals the convolution of unit impact response h (t) and input signal x (t):
The Volterra series model is a kind of functional series model, and it is promoted the relation of above-mentioned form, and being used for describing has the memory nonlinear system.
By the decomposition theorem of nonlinear dynamic system as can be known, the nonlinear dynamic system that continuous functional F () characterizes, when the finite energy of its input signal, always can be decomposed into the cascade of linear with memory system and a memoryless nonlinear system, as shown in Figure 1.Linear subsystem is designated as respectively F
L1(), F
L2() ..., F
LN(), the output of every sub-systems is followed successively by w
1(t), w
2(t) ..., w
N(t), memoryless nonlinear system is designated as F
NL(), the output of whole system can be expressed as
y(t)＝F
NL[w
1(t)，w
2(t)，…，w
N(t)]
For predistortion linearized system, the design of predistorter is very important.Volterra progression can approach arbitrarily degree accurately with the memory nonlinear system that has that meets certain condition, and it not only can be used for the modeling of radio-frequency power amplifier, and can be used for the structure predistorter.The input of the Volterra predistorter of general type, the relation between output signal are suc as formula shown in (1-1).
In (1-1) formula, the quantity of Volterra nuclear parameter is
As seen in the Volterra series model, the quantity of parameter becomes power function relationship with memory span, and model order exponentially functional relation.Be subjected to the restriction of computation complexity, be only applicable to the situation of low order small nonlinearity without the Volterra model of any simplification.And in broadband system the memory radio-frequency (RF) power amplification being arranged, low order small nonlinearity model is difficult to accurately describe its characteristic or contrary characteristic.Therefore, it is very difficult directly the volterra progression of general type being applied to the designs of power amplifier modeling or predistorter, must simplify improvement.
To the analysis of amplifier nonlinearity characteristic as can be known, odd item produces odd order harmonics frequency component and the odd order intermodulation frequency component of output signal, and the even item produces DC component, even order harmonics frequency component and even order intermodulation frequency component.Generally, only have odd order intermodulation frequency component to drop in passband, and other distortion component all drop on beyond passband, can easily use the filter filtering.Although comprise the even item in predistorter, have certain effect to improving the linearisation effect,, for the consideration that reduces the model complexity, still rejected the even item in the predistorter.After removing DC terms and even item, (1-1) formula can be written as
If use the Volterra progression with symmetric kernel to construct predistorter, number of parameters will further reduce.The symmetric connotation of Volterra core is as follows.If k rank Volterra core h
k(i
1, i
2..., i
k) meet
h
k(i
1，i
2，…，i
k)＝h
k(i
π(1)，i
π(2)，…，i
π(k)) (1-4)
Claim h
k(i
1, i
2..., i
k) be symmetric kernel.In formula, π () expression 1,2 ..., any one arrangement of k.For example, establish h
3(i
1, i
2, i
3) be three rank symmetric kernels, have
h
3(i
1，i
2，i
3)＝h
3(i
1，i
3，i
2)＝h
3(i
2，i
1，i
3)＝h
3(i
2，i
3，i
1)＝h
3(i
3，i
1，i
2)＝h
3(i
3，i
2，i
1)
Time domain Volterra progression with symmetric kernel meets following uniqueness theorem: if the input/output relation of a non linear system can be described with Volterra progression, and its each rank core is symmetrical, and the Volterra progression of describing this non linear system input/output relation is unique.
Utilize the symmetry of core, can merge the redundancy in Voiterra progression predistorter, number of parameters is significantly reduced.Can be written as after utilizing symmetry to simplify to (1-3) formula
But when the exponent number of system is higher or memory effect when stronger, the quantity of Voiterra core is still huger.When this makes Voiterra progression recall predistorter for the hypermnesia of structure high-order, still can produce larger amount of calculation, so will consider further simplification.
In pertinent literature, often can see a kind of polynomial power amplifier of memory or predistorter model of being known as, its expression formula is as follows:
In formula, k is model order, and M is memory span, a
kiFor multinomial coefficient.It is actually a kind of special case of Volterra series model.In the Volterra series model, if only keep diagonal angle core (diagonal kemel), and, with all non-diagonal angle core zero setting, just obtained the memory multinomial model.The memory multinomial model is too simplified, and with it, designs predistorter, is difficult to accurately describe the contrary characteristic of memory power amplifier.
In Volterra progression, not " coupling " effect between input signal in the same time that the border representing has been examined at non-diagonal angle.Such as, h
3(1,1,3) have represented n-1 constantly and n-3 " coupling " between input signal constantly.If the sampling instant of several input signals of amplifier is at a distance of far away, " coupling " effect therebetween also should be more weak, and the value of the Volterra core of their correspondences can be less so, and is also less to the contribution of output.
For following 2 considerations, we there is no need to keep the very little core of those moulds in the Volterra model.
(1) these output contributions of checking model are very little, and they are carried out identification, will increase larger amount of calculation;
(2), because the word length of computer is limited, the very little core of these moulds is carried out identification inevitably can introduce error.
Therefore they are retained in the accuracy that in fact may not necessarily obviously improve model in model.Consider the corresponding relation that exists between power amplifier model and predistorter, we adopt following algorithm further to simplify the described Volterra predistorter of (1-5) formula.L rank core in (1-5) formula is designated as h
l(i
1, i
2..., i
l), l=1 wherein, 3 ..., 2d+1.Setting threshold λ ∈ 1,2 ..., M}.When l=1, h
1(i
1)=h
1(i
1).When l 〉=3,
T ∈ 1,2 ..., l}, if max{|i
s-i
t| 〉=λ, make h
l(i
1, i
2..., i
l)=0; Otherwise h
l(i
1, i
2..., i
l)=h
l(i
1, i
2..., i
l).
This algorithm is in fact to carry out " trading off " between the Volterra of general type predistorter and memory polynomial predistortion distorter.The threshold value λ that chooses is less, and pre-distorter structure is simpler, and accuracy is poorer.If this algorithm is applied to (1-1) formula, when λ=I, predistorter just deteriorates to memory polynomial predistortion distorter.The threshold value λ that chooses is larger, and the nuclear parameter that keeps is more, and the accuracy of predistorter is also higher.When λ=M, all cores all are retained, and predistorter is equal to general Volterra predistorter.
Be summed up, according to following three steps, general type Volterra predistorter simplified successively.(I) remove DC terms and even item, only keep odd item.(2) utilize the symmetry of Volterra core, merge the redundancy in the predistorter model.(3) use shortcut calculation, the number of parameters in predistorter is further reduced.Finally, check input signal by Volterra and constantly adjust, after making it pass through power amplifier, linear output.
To the predistortion linearized system based on working function, implementation is broadly divided into two classes., because the predistorter characteristic is the contrary of amplifier characteristic, therefore can first set up the model of power amplifier, and then solve the predistorter model.When the model of power amplifier was simpler, this method was feasible, but for the memory High Order Nonlinear System is arranged, its inversion model of identification is very difficult.In addition, this method is difficult to realize the self adaptation adjustment of predistorter parameter, and when the amplifier characteristic changed, systematic function can descend rapidly.Another kind method can not set up the model of amplifier, directly obtains the predistorter parameter.The method increases by a bars feedback loop in linearized system,, with feedback signal and the contrast of predistorter output signal, obtain an error signal, in identification process, by the parameter of constantly adjusting predistorter, reduces error signal., when enough hour of error signal, just obtained the parameter of predistorter.The following indirect learning structure that will adopt that Here it is.
Adopt the predistortion linearized system implementation of indirect learning structure as shown in Figure 2.The predistortion process of signal is completed in base band, input signal x (n) after predistorter, forms pre-distorted signals x
p(n).Pre-distorted signals after D/A conversion, modulation and up-conversion, obtains the input signal x of radio-frequency power amplifier
RF(t).Amplifier output signal y
RF(t) the sub-fraction power in is through gain for forming and feed back after the attenuator of 1/G, and wherein G is the expected gain of amplifier.Feedback signal after down-conversion, solution mediation A/D conversion, obtains the input signal u (n) of parameter identification module.The parameter identification module has and the identical structure and parameter of predistorter, and its output signal is designated as u
p(n).u
p(n) and pre-distorted signals x
p(n) compare, obtain error signal e (n).In the course of the work, the parameter by in RLS algorithm adjustment recognition module and predistorter, constantly reduce error signal.In ideal conditions, when error signal e (n), while equalling zero, can obtain y (n)=Gx (n), wherein y (n) is the baseband equivalence signal of amplifier output.
In above-mentioned pre-distortion system, do not need to pick out in advance the model of power amplifier, just can directly obtain the parameter of predistorter.After the Identification of parameter convergence, just feedback loop and parameter identification module temporarily can be disconnected.In the transmitter course of work, the power amplifier characteristic can change.When this variation acquires a certain degree, can lose original matching relationship between predistorter and amplifier.At this moment, feedback loop and parameter identification module can be accessed again, so that the predistorter parameter is carried out adaptive updates.
Claims (1)
1. the linearisation pre-distortion method based on Volterra progression is characterised in that, with the input of the Volterra predistorter of general type, the relational expression between output signal:
Be reduced to simplified style one after removal DC terms and even item:
Do following simplification for simplified style one, the l rank core in simplified style one is designated as h
l(i
1, i
2..., i
l), l=1 wherein, 3 ..., 2d+1.Setting threshold λ ∈ 1,2 ..., M}.When l=1, h
1(i
1)=h
1(i
1).When l 〉=3,
T ∈ 1,2 ..., l}, if max{|i
s-i
t| 〉=λ, make h
l(i
1, i
2..., i
l)=0; Otherwise h
l(i
1, i
2..., i
l)=h
l(i
1, i
2..., i
l).Described λ value requires to choose according to accuracy.
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2012
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Application publication date: 20131113 |