CN112083227B - A FPA-based I/Q Imbalance Phase Error Compensation Method - Google Patents

A FPA-based I/Q Imbalance Phase Error Compensation Method Download PDF

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CN112083227B
CN112083227B CN202010877152.5A CN202010877152A CN112083227B CN 112083227 B CN112083227 B CN 112083227B CN 202010877152 A CN202010877152 A CN 202010877152A CN 112083227 B CN112083227 B CN 112083227B
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phase error
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fpa
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CN112083227A (en
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孟婕
曾浩
郭连平
叶芃
赵禹
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University of Electronic Science and Technology of China
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Abstract

本发明公开了一种基于FPA的I/Q失衡相位误差补偿方法，先通过输入连续的单音扫频信号获取待补偿的I/Q失衡相位误差θ(ω)，再基于失衡相位误差θ(ω)，利用FPA设计I/Q失衡相位补偿模块，将I/Q失衡相位补偿模块设计等效为一个非线性优化问题，再用FPA计算该非线性优化问题的解，求得补偿模块的最优参数，最后利用设计的I/Q失衡相位补偿模块进行I/Q相位误差补偿。

Figure 202010877152

The invention discloses an I/Q unbalanced phase error compensation method based on FPA. First, the I/Q unbalanced phase error θ(ω) to be compensated is obtained by inputting a continuous single-tone frequency sweep signal, and then based on the unbalanced phase error θ( ω), use the FPA to design the I/Q unbalanced phase compensation module, the design of the I/Q unbalanced phase compensation module is equivalent to a nonlinear optimization problem, and then use the FPA to calculate the solution of the nonlinear optimization problem, and obtain the maximum compensation module. Finally, the designed I/Q imbalance phase compensation module is used to compensate the I/Q phase error.

Figure 202010877152

Description

I/Q unbalance phase error compensation method based on FPA
Technical Field
The invention belongs to the technical field of error correction, and particularly relates to an I/Q unbalance phase error compensation method based on an FPA (field programmable Gate array).
Background
The choice of front-end architecture greatly affects receiver integratability and flexibility, with zero-if architectures being favored over the past decade for their advantages of ease of monolithic integration, simplicity of construction, and low cost and power consumption. However, this architecture employs in-phase and quadrature (I/Q) mixing, which is particularly sensitive to I/Q imbalance. Ideally, the I and Q signals should have an exact 90 ° phase difference and equal amplitude. However, in practical situations, errors in the used devices, circuit design, and PCB layout, and differences in the frequency responses of the I-path and Q-path low-pass filters all cause amplitude and phase mismatch I/Q imbalance of the I-path and Q-path signals, which results in incomplete attenuation of the image signal and increases the error rate of baseband signal processing. The effects of I/Q imbalance become more pronounced with the use of higher order modulated waveforms or large bandwidth multichannel signals, which must be improved using additional analog or digital signal processing methods.
The phase unbalance of I/Q unbalance is a key problem, and compared with amplitude errors, the calculation and compensation difficulty of the phase errors is higher; the Flower Pollination Algorithm (FPA) is a natural heuristic that simulates the principle of natural pollination to represent the solution to the problem as pollen of the flower and the process of iterating new solutions as the pollination process between flowers. In recent years, FPA receives wide attention due to the effectiveness of solving practical problems, and compared with a traditional optimization algorithm based on gradient, the FPA is not easy to fall into local optimization and can better find an approximate optimal solution closer to global optimization. By setting proper individual number and iteration number, the solution obtained by FPA can well solve the problem of I/Q unbalance phase error compensation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an I/Q unbalance phase error compensation method based on an FPA (field programmable gate array), wherein a compensation module of the I/Q unbalance phase error is designed to be equivalent to a nonlinear optimization problem, the nonlinear optimization problem is calculated by the FPA, the optimal parameters of the compensation module are obtained, and then phase compensation is completed.
In order to achieve the above object, the present invention provides an I/Q imbalance phase error compensation method based on FPA, comprising the following steps:
(1) acquiring an I/Q imbalance phase error to be compensated by inputting a single-tone frequency sweeping signal;
(1.1) carrying out equal-interval frequency sweeping on the bandwidth to be tested by using a signal generator, so that single-tone frequency sweeping signals with N frequency values are output at equal intervals within the frequency range of the bandwidth to be tested and are sequentially input to an I/Q receiver;
(1.2) the monophonic frequency sweep signal ri(t) has phase error in the two paths with I/Q, respectively
Figure BDA0002652940480000021
Local oscillator signal cos (ω)LOt) and
Figure BDA0002652940480000022
multiplication of ω whereinLOIs the local oscillator signal frequency;
then, obtaining an unbalanced I/Q test signal after low-pass filtering processing;
xI(t)＝cos(ωit)
xQ(t)＝sin(ωit+θ(ωi))
where i is 1,2, … N, θ (ω)i) Representing frequency omegaiThe phase error is detected, and the phase error is detected,
Figure BDA0002652940480000023
φ(ωi) Representing a frequency dependent phase error;
(1.3) sampling the unbalanced I/Q test signal by an ADC to obtain an unbalanced I/Q test signal x after samplingI(n) and xQ(n)；
Then inputting the test signal into a frequency domain conversion processor, performing discrete Fourier transform to complete the conversion of the I/Q test signal from a time domain to a frequency domain, wherein the converted frequency domain I/Q test signal is as follows:
Figure BDA0002652940480000024
Figure BDA0002652940480000025
(1.4) testing the frequency domain I/Q test signal XI(ω)、XQ(ω) inputting to the imbalance phase estimator to estimate the imbalance phase error;
Figure BDA0002652940480000026
(1.5) continuously processing the N single tone frequency sweep signals according to the method of the steps (1.2) - (1.4) to obtain an imbalance phase error theta (omega), wherein omega is [ omega ], [ omega ]1,ω2,…,ωN]T；
(2) Designing an I/Q unbalance phase compensation module by using an FPA (field programmable gate array) based on the unbalance phase error theta (omega);
(2.1) building an I/Q unbalance phase compensation module, which specifically comprises a delay module, an FD compensation module and an all-pass filter;
(2.2) designing the total phase-frequency response function phi of the I/Q unbalance phase compensation modulec(ω,R)；
φc(ω,R)＝-δd·ω+φAPF(ω,R)
Wherein R is [ delta ]d,M,ψ]，δdFor fractional delay of FD compensation module, M ═ Mn]T＝[M1,M2,…,MN/2]T，MnIs the amplitude of the nth second-order junction pole of the all-pass filter, [ psi ═ phi [ [ phi ]n]T＝[ψ1,ψ2,…,ψN/2]T，ψnThe phase angle of the nth second-order junction pole of the all-pass filter; phi is aAPF(ω, R) is the phase frequency response function of the all-pass filter;
(2.3) defining an error matrix E;
E＝[e(ω,R)]T＝[e(ω1,R),e(ω2,R),…,e(ωi,R),…,e(ωN,R)]T
wherein e (ω)i,R)＝φc(ωi,R)-θ(ωi)；
(2.4) defining a cost function J (R);
Figure BDA0002652940480000031
(2.5) optimizing J (R) by using a flower pollination algorithm FPA to minimize J (R) and satisfy Mn＜1,n＝1,2,…,N/2；
(3) Compensating the I/Q phase error by utilizing an I/Q unbalance phase compensation module;
testing the unbalanced I/Q signal x after samplingI(n) and xQ(n) input to the I/Q imbalance phase compensation module to output a compensated I/Q signal xIC[n]、xQC[n]。
The invention aims to realize the following steps:
the invention relates to an I/Q unbalance phase error compensation method based on an FPA (field programmable gate array), which comprises the steps of firstly obtaining an I/Q unbalance phase error theta (omega) to be compensated through inputting a continuous single tone frequency sweep signal, then designing an I/Q unbalance phase compensation module by utilizing the FPA based on the unbalance phase error theta (omega), equivalently designing the I/Q unbalance phase compensation module into a nonlinear optimization problem, then calculating the solution of the nonlinear optimization problem by utilizing the FPA to obtain the optimal parameter of the compensation module, and finally compensating the I/Q phase error by utilizing the designed I/Q unbalance phase compensation module.
Meanwhile, the I/Q unbalance phase error compensation method based on the FPA also has the following beneficial effects:
(1) the method comprises the steps of obtaining the I/Q unbalance phase error to be compensated by inputting a single-tone frequency sweeping signal, and equating the phase error in the whole bandwidth to be tested to the phase error of each frequency sweeping frequency point by utilizing the principle that the phase error in a small bandwidth of a frequency sweeping interval can be approximated to be a constant, so that the novel method for testing the I/Q unbalance phase error is provided.
(2) The I/Q phase unbalance compensation module based on the all-pass filter and the fractional delay filter is designed, and a new thought for compensating I/Q phase unbalance is provided for innovatively converting the design problem of the I/Q phase unbalance compensation module into a constrained nonlinear optimization problem in order to ensure the stability of the all-pass filter realized by adopting an IIR filter structure.
(3) Compared with the traditional optimization algorithm based on gradient, the FPA is not easy to fall into local optimization and can better find an approximate optimal solution closer to global optimization, thereby better completing the compensation work of I/Q (input/output) unbalance phase.
Drawings
FIG. 1 is a flow chart of an FPA-based I/Q imbalance phase error compensation method of the present invention;
FIG. 2 is a schematic diagram of I/Q imbalance phase error;
FIG. 3 is a block diagram of an I/Q imbalance phase compensation module;
fig. 4 is a flow chart of FPA optimization.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a flow chart of the I/Q imbalance phase error compensation method based on FPA according to the present invention.
In this embodiment, as shown in fig. 1, the method for compensating an I/Q imbalance phase error based on FPA of the present invention mainly includes three stages S1-S3:
s1, acquiring an I/Q imbalance phase error to be compensated by inputting a single tone frequency sweep signal;
assuming that there is no amplitude imbalance error in the path, the I/Q imbalance model is shown in the dashed box of fig. 2. OmegaLO＝2πfLOIn order to be the angular frequency of the local oscillator signal,
Figure BDA0002652940480000051
the phase difference between two local oscillation signals is irrelevant to the frequency. And the frequency-dependent phase error is partly caused by the frequency response differences introduced by the different components between the I/Q paths, denoted as (ω). The low pass filter LPF is used to remove high frequency components and the analog-to-digital converter ADC is used to sample the I/Q signal. Without loss of generality, the total phase error between the I/Q channels is all equivalent to the Q channel, denoted as
Figure BDA0002652940480000052
Where ω is the baseband signal angular frequency.
In order to correctly compensate the phase error, the I/Q phase imbalance error to be compensated needs to be accurately measured, and the embodiment estimates the I/Q phase imbalance error by using a single-tone test signal, and the specific process is as follows:
s1.1, performing equal-interval frequency sweeping on a bandwidth to be tested by using a signal generator, so that single-tone frequency sweeping signals with N frequency values are output at equal intervals within the frequency range of the bandwidth to be tested and are sequentially input to an I/Q receiver;
in this embodiment, the N single tone frequency sweep signals cover the entire test bandwidth, i.e., the entire test bandwidth is divided into N equal narrow frequency bands, where the phase error parameter in each frequency band can be considered as a constant. Therefore, the phase error in the whole test bandwidth can be equivalent to the phase error of the N frequency points.
S1.2, tone frequency sweep signal ri(t) has phase error in the two paths with I/Q, respectively
Figure BDA0002652940480000053
Local oscillator signal cos (ω)LOt) and
Figure BDA0002652940480000054
multiplication of ω whereinLOIs the local oscillator signal frequency;
then, obtaining an unbalanced I/Q test signal after low-pass filtering processing;
xI(t)＝cos(ωit)
xQ(t)＝sin(ωit+θ(ωi))
where i is 1,2, … N, θ (ω)i) Representing frequency omegaiThe phase error is detected, and the phase error is detected,
Figure BDA0002652940480000055
φ(ωi) A phase error portion, which represents a frequency dependence, is caused by differences in the frequency response of different components between the I/Q paths;
s1.3, sampling the unbalanced I/Q test signal by an ADC (analog to digital converter) to obtain an unbalanced I/Q test signal x after samplingI(n) and xQ(n)；
Then inputting the test signal into a frequency domain conversion processor, performing discrete Fourier transform to complete the conversion of the I/Q test signal from a time domain to a frequency domain, wherein the converted frequency domain I/Q test signal is as follows:
Figure BDA0002652940480000056
Figure BDA0002652940480000061
s1.4, testing the frequency domain I/Q test signal XI(ω)、XQ(omega) is input to an imbalance phase estimator to obtain an imbalance phase estimation result;
Figure BDA0002652940480000062
so as to estimate the unbalanced phase error;
Figure BDA0002652940480000063
s1.5, continuously processing the N monophonic frequency sweep signals according to the method of steps S1.2-S1.4 to obtain an imbalance phase error θ (ω), where ω is [ ω ═ ω1,ω2,…,ωN]T；
S2, designing an I/Q unbalance phase compensation module by using an FPA (field programmable gate array) based on the unbalance phase error theta (omega);
s2.1, building an I/Q unbalance phase compensation module, as shown in fig. 3, specifically comprising a Fractional Delay (FD) compensation module, an all-pass filter and a delay module. Since the FD compensation filter introduces a delay associated with the order of the FD filter on the channel to be compensated, the delay module adds the delay value to the other channel to keep the delay consistent.
In this embodiment, the FD compensation module of the Q channel is implemented by an FD filter, and the order of D (D is an even number) will bring D/2 delay to the Q channel, so in order to make the I/Q channel delay consistent, the delay module is used to delay the I channel by D/2.
S2.2, the implementation structure of the all-pass filter adopts a cascade structure of an Infinite Impulse Response (IIR) filter, can be expressed in a form of multiplication of a plurality of second-order nodes, and the expression in a z domain is shown as the following formula
Figure BDA0002652940480000064
Wherein N is an even number and is the order of the all-pass filter,
Figure BDA0002652940480000065
is the pole of the nth second-order junction, and has amplitude and phase angle of MnAnd psinThe phase frequency response of the all-pass filter can be expressed as:
Figure BDA0002652940480000066
assuming fractional delay delta of FD compensation moduledThus, the total phase-frequency response of the phase compensation module can be expressed as:
φc(ω,R)＝-δd·ω+φAPF(ω,R)
wherein R is [ delta ]d,M,ψ]，M＝[Mn]T＝[M1,M2,…,MN/2]T，MnIs the amplitude of the nth second-order junction pole of the all-pass filter, [ psi ═ phi [ [ phi ]n]T＝[ψ1,ψ2,…,ψN/2]T，ψnThe phase angle of the nth second-order junction pole of the all-pass filter; phi is aAPF(ω, R) is the phase frequency response function of the all-pass filter;
s2.3, in order to compensate for the previously obtained theta (omega), phic(ω, R) should be equal to θ (ω), thus defining an error matrix E;
E＝[e(ω,R)]T＝[e(ω1,R),e(ω2,R),…,e(ωi,R),…,e(ωN,R)]T
wherein e (ω)i,R)＝φc(ωi,R)-θ(ωi)；
S2.4, the design of the I/Q unbalance phase compensation module can be equivalent to a nonlinear optimization problem, so that a cost function J (R) is defined;
Figure BDA0002652940480000071
s2.5, in the embodiment, an all-pass filter in the I/Q imbalance phase compensation module is realized by adopting an IIR filter structure, and the stability of the all-pass filter is guaranteed to be crucial, so that constraint is added in a nonlinear optimization problem to guarantee a stability condition, the stability condition is further converted into a least square problem with constraint, and finally J (R) is optimized by using a pollination algorithm FPA to enable J (R) to be minimum and meet Mn< 1, N ═ 1,2, …, N/2; compared with the traditional optimization algorithm based on gradient, the FPA is not easy to fall into local optimum, and an approximate optimal solution closer to global optimum can be better found, so that I/Q imbalance phase compensation is better completed.
As shown in fig. 4, we describe in detail the specific process of FPA optimizing j (r), specifically:
1) and setting the pollen individual number S of the FPA, wherein the maximum iteration number maximum and the conversion probability p are 0.8. Randomly generating an initial population containing S individuals, taking a cost function J (R) as a fitness function and calculating the fitness value of each individual of the initial population;
2) and starting to circularly perform population propagation: during each circulation, sequentially traversing each individual and generating a new individual corresponding to the next generation; wherein, when the t-th cycle is performed, the mth individual is traversed
Figure BDA0002652940480000072
Then, a number r is randomly generatedm,t∈[0,1]Then, a new individual of the next generation is generated according to the following formula
Figure BDA0002652940480000073
Figure BDA0002652940480000081
Wherein ε is [0,1 ]]The random parameters are uniformly distributed on the surface of the substrate,
Figure BDA0002652940480000082
is the current optimal solution and gamma is a scale factor, set to 0.01. The global pollination step length L follows the levy distribution:
Figure BDA0002652940480000083
where Γ (λ) is the standard gamma function, s is the Levy flight step, s is0Is the step minimum, step s can be given by:
Figure BDA0002652940480000084
Figure BDA0002652940480000085
where U and V satisfy a gaussian distribution and the constant λ is set to 1.5.
Then will be
Figure BDA0002652940480000086
Substituting into fitness function to calculate its fitness value
Figure BDA0002652940480000087
3) After each circulation is finished, the fitness values of S new individuals generated by the circulation are compared, and the new individual with the minimum fitness value is selected as the optimal individual generated by the circulation
Figure BDA0002652940480000088
4) Comparing the optimal individuals generated by the circulation
Figure BDA0002652940480000089
And the last timeCyclically generated optimal individuals
Figure BDA00026529404800000810
The magnitude of the corresponding fitness value if
Figure BDA00026529404800000811
Then use
Figure BDA00026529404800000812
Is replaced by
Figure BDA00026529404800000813
And is used as the current optimal solution; otherwise, the optimal individuals generated by the last cycle are kept
Figure BDA00026529404800000814
Unchanged and used as the optimal individual generated by the current cycle;
5) judging whether the current cycle time t reaches the maximum iteration number maximum, if not, continuing the cycle; if so, selecting the optimal solution recorded after the maximum cycles
Figure BDA00026529404800000815
As the final optimal solution.
S3, I/Q phase error compensation is carried out by utilizing an I/Q unbalance phase compensation module;
testing the unbalanced I/Q signal x after samplingI(n) and xQ(n) input to the I/Q imbalance phase compensation module to output a compensated I/Q signal xIC[n]、xQC[n]。
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (3)

1.一种基于FPA的I/Q失衡相位误差补偿方法，其特征在于，包括以下步骤：1. an I/Q unbalanced phase error compensation method based on FPA, is characterized in that, comprises the following steps: (1)、通过输入单音扫频信号获取待补偿的I/Q失衡相位误差；(1) Obtain the I/Q imbalance phase error to be compensated by inputting a single-tone frequency sweep signal; (1.1)、利用信号发生器对待测试带宽进行等间隔扫频，使待测试带宽频率范围内等间隔的输出N个频率值的单音扫频信号，并依次输入到I/Q接收器；(1.1), use the signal generator to sweep the bandwidth to be tested at equal intervals, so that the single-tone frequency sweep signals of N frequency values are output at equal intervals within the frequency range of the bandwidth to be tested, and input them to the I/Q receiver in turn; (1.2)、将单音扫频信号ri(t)分别与I/Q两路中带有相位误差
Figure FDA0002652940470000014
的本振信号cos(ωLOt)和
Figure FDA0002652940470000015
相乘，其中，ωLO为本振信号频率；(1.2), connect the single-tone frequency sweep signal r i (t) to the I/Q two-way with phase error respectively
Figure FDA0002652940470000014
The local oscillator signal cos(ω LO t) and
Figure FDA0002652940470000015
Multiply, where ω LO is the local oscillator signal frequency; 然后再经过低通滤波处理后，得到失衡的I/Q测试信号；Then, after low-pass filtering, an unbalanced I/Q test signal is obtained; xI(t)＝cos(ωit)x I (t)=cos(ω i t) xQ(t)＝sin(ωit+θ(ωi))x Q (t)=sin(ω i t+θ(ω i )) 其中，i＝1,2,…N，θ(ωi)表示频率ωi处相位误差，
Figure FDA0002652940470000016
Among them, i=1,2,...N, θ(ω i ) represents the phase error at the frequency ω i ,
Figure FDA0002652940470000016
 (1.3)、将失衡的I/Q测试信号通过ADC采样，得到采样后失衡的I/Q测试信号xI(n)和xQ(n)；(1.3), sample the unbalanced I/Q test signal through the ADC to obtain the unbalanced I/Q test signals x I (n) and x Q (n) after sampling; 然后将其输入至频域转换处理器，并进行离散傅里叶变换，完成I/Q测试信号从时域到频域的转换，转换后的频域I/Q测试信号为：Then it is input to the frequency domain conversion processor, and the discrete Fourier transform is performed to complete the conversion of the I/Q test signal from the time domain to the frequency domain. The converted frequency domain I/Q test signal is:
Figure FDA0002652940470000011
Figure FDA0002652940470000011
Figure FDA0002652940470000012
Figure FDA0002652940470000012
 (1.4)、将频域I/Q测试信号XI(ω)、XQ(ω)输入至失衡相位估计器，估算出失衡相位误差；(1.4), input the frequency domain I/Q test signals X I (ω) and X Q (ω) to the unbalanced phase estimator to estimate the unbalanced phase error;
Figure FDA0002652940470000013
Figure FDA0002652940470000013
 (1.5)、按照步骤(1.2)-(1.4)的方法对N个单音扫频信号进行连续处理后，得到失衡相位误差θ(ω)，ω＝[ω1,ω2,…,ωN]T；(1.5), after continuous processing of N single-tone frequency sweep signals according to the method of steps (1.2)-(1.4), the unbalanced phase error θ(ω) is obtained, ω=[ω 1 ,ω 2 ,...,ω N ] T ; (2)、基于失衡相位误差θ(ω)，利用FPA算法设计I/Q失衡相位补偿模块；(2), based on the unbalanced phase error θ(ω), use the FPA algorithm to design the I/Q unbalanced phase compensation module; (2.1)、搭建I/Q失衡相位补偿模块，具体包括延时模块、FD补偿模块和全通滤波器；(2.1), build an I/Q imbalance phase compensation module, including a delay module, an FD compensation module and an all-pass filter; (2.2)、设计I/Q失衡相位补偿模块的总相频响应函数φc(ω,R)；(2.2), design the total phase-frequency response function φ c (ω, R) of the I/Q imbalance phase compensation module; φc(ω,R)＝-δd·ω+φAPF(ω,R)φ c (ω,R)＝-δ d ·ω+φ APF (ω,R) 其中，R＝[δd,M,ψ]，δd为FD补偿模块的分数延时，M＝[Mn]T＝[M1,M2,…,MN/2]T，Mn为全通滤波器的第n个二阶结极点的幅值，ψ＝[ψn]T＝[ψ1,ψ2,…,ψN/2]T，ψn为全通滤波器的第n个二阶结极点的相角；φAPF(ω,R)为全通滤波器的相频响应函数；Among them, R=[δ d ,M,ψ],δ d is the fractional delay of the FD compensation module, M=[M n ] T =[M 1 ,M 2 ,...,M N/2 ] T ,M n is the amplitude of the nth second-order junction pole of the all-pass filter, ψ=[ψ n ] T =[ψ 1 ,ψ 2 ,…,ψ N/2 ] T , ψ n is the second-order node of the all-pass filter The phase angle of n second-order junction poles; φ APF (ω, R) is the phase-frequency response function of the all-pass filter; (2.3)、定义误差矩阵E；(2.3), define the error matrix E; E＝[e(ω,R)]T＝[e(ω1,R),e(ω2,R),…,e(ωi,R),…,e(ωN,R)]T E=[e(ω,R)] T =[e(ω 1 ,R),e(ω 2 ,R),…,e(ω i ,R),…,e(ω N ,R)] T 其中，e(ωi,R)＝φc(ωi,R)-θ(ωi)；Among them, e(ω i ,R)=φ c (ω i ,R)-θ(ω i ); (2.4)、定义代价函数J(R)；(2.4), define the cost function J(R);
Figure FDA0002652940470000021
Figure FDA0002652940470000021
 (2.5)、利用花授粉算法FPA对J(R)进行优化，使J(R)最小，且满足Mn＜1,n＝1,2,…,N/2；(2.5), using the flower pollination algorithm FPA to optimize J(R) to minimize J(R) and satisfy M n <1, n=1,2,...,N/2; (3)、利用I/Q失衡相位补偿模块进行I/Q相位误差补偿；(3), use the I/Q imbalance phase compensation module to perform I/Q phase error compensation; 将采样后失衡的I/Q测试信号xI(n)和xQ(n)输入至I/Q失衡相位补偿模块，从而输出补偿后的I/Q信号xIC[n]、xQC[n]。Input the sampled unbalanced I/Q test signals x I (n) and x Q (n) to the I/Q unbalance phase compensation module, thereby outputting the compensated I/Q signals x IC [n], x QC [n ]. 2.根据权利要求1所述的基于FPA的I/ Q失衡相位误差补偿方法，其特征在于，所述全通滤波器的相频响应表示为：2. The FPA-based I/Q imbalance phase error compensation method according to claim 1, wherein the phase-frequency response of the all-pass filter is expressed as:
Figure FDA0002652940470000022
。
Figure FDA0002652940470000022
. 3.根据权利要求1所述的基于FPA的I/ Q失衡相位误差补偿 方法，其特征在于，所述步骤(2.5)中利用FPA算法对J(R)进行优化的具体过程为：3. the I/Q unbalanced phase error compensation method based on FPA according to claim 1, is characterized in that, in described step (2.5), utilize FPA algorithm to optimize the concrete process that J (R) is: 1)、设置FPA算法的花粉个体数S，最大迭代数Maxiter和转换概率p； 随机产生包含S个个体的初始种群，代价函数J(R)作为适应度函数并计算初始种群每个个体的适应度值；1) Set the number of pollen individuals S, the maximum iteration number Maxiter and the transition probability p of the FPA algorithm; Randomly generate an initial population containing S individuals, the cost function J(R) is used as the fitness function and the fitness of each individual in the initial population is calculated. degree value; 2)、开始循环进行种群繁殖：每一次循环时，依次遍历每个个体并产生下一代对应的新个体；其中，当第t次循环时，遍历到第m个个体
Figure FDA0002652940470000031
时，随机产生一个数rm,t∈[0,1]，然后按照如下公式产生下一代的新个体
Figure FDA0002652940470000032
2) Start the cycle for population reproduction: in each cycle, traverse each individual in turn and generate a new individual corresponding to the next generation; among them, when the t-th cycle is performed, the m-th individual is traversed
Figure FDA0002652940470000031
, randomly generate a number r m,t ∈[0,1], and then generate a new individual of the next generation according to the following formula
Figure FDA0002652940470000032
Figure FDA0002652940470000033
Figure FDA0002652940470000033
 其中，ε为[0,1]上均匀分布的随机参数，
Figure FDA0002652940470000034
是当前最优解，γ是尺度因子，L全局授粉步长，m≠j≠k，m,j,k∈[1,S]；where ε is a random parameter uniformly distributed on [0,1],
Figure FDA0002652940470000034
is the current optimal solution, γ is the scale factor, L global pollination step size, m≠j≠k, m,j,k∈[1,S]; 然后将
Figure FDA0002652940470000035
代入到适应度函数中，计算其适应度值
Figure FDA0002652940470000036
followed by
Figure FDA0002652940470000035
Substitute into the fitness function to calculate its fitness value
Figure FDA0002652940470000036
 3)、每次循环结束后，比较本次循环产生的S个新个体的适应度值，选出适应度值最小的新个体作为本次循环产生的最优个体
Figure FDA0002652940470000037
3) After each cycle is over, compare the fitness values of the S new individuals generated in this cycle, and select the new individual with the smallest fitness value as the optimal individual generated in this cycle.
Figure FDA0002652940470000037
 4)、比较本次循环产生的最优个体
Figure FDA0002652940470000038
与上一次循环产生的最优个体
Figure FDA0002652940470000039
对应的适应度值的大小，若
Figure FDA00026529404700000310
则用
Figure FDA00026529404700000311
替换掉
Figure FDA00026529404700000312
并作为当前最优解；否则，保持上一次循环产生的最优个体
Figure FDA00026529404700000313
不变，并作为本次循环产生的最优个体；4), compare the optimal individuals generated by this cycle
Figure FDA0002652940470000038
and the optimal individual generated by the previous cycle
Figure FDA0002652940470000039
The size of the corresponding fitness value, if
Figure FDA00026529404700000310
then use
Figure FDA00026529404700000311
replace
Figure FDA00026529404700000312
and as the current optimal solution; otherwise, keep the optimal individual generated by the previous cycle
Figure FDA00026529404700000313
remain unchanged, and serve as the optimal individual generated by this cycle; 5)、判断当前循环次数t是否达到最大迭代数Maxiter，如果未达到，则继续循环；如果达到，则选择Maxiter次循环后记录的最优解
Figure FDA00026529404700000314
作为最终最优解。5), determine whether the current number of cycles t reaches the maximum number of iterations Maxiter, if not, continue the cycle; if it does, select the optimal solution recorded after the Maxiter cycle
Figure FDA00026529404700000314
as the final optimal solution.
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