CN117713960A - Channel calibration and equalization method for broadband zero intermediate frequency receiving array - Google Patents
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Abstract
The invention discloses a channel calibration and equalization method of a broadband zero intermediate frequency receiving array, which comprises the following steps: acquiring a baseband digital complex signal of each receiving channel of the digital array; acquiring a baseband digital complex single-frequency signal; obtaining the frequency spectrum value of the single-frequency signal per se of each channel and the frequency spectrum value of the corresponding mirror image signal; calculating a first compensation value and a second compensation value of IQ imbalance frequency response of each channel; estimating first FIR equalizer coefficients and second FIR equalizer coefficients of the IQ imbalance; acquiring an IQ imbalance compensated complex signal; calculating inter-channel frequency response compensation values of other channels relative to the reference channel by taking the first receiving channel as a reference; estimating a third FIR equalizer coefficient between the channels; when the array receives a target signal, compensating the baseband digital complex signal received by the array; the invention has the advantages that: and estimating and compensating various errors of the broadband zero intermediate frequency receiving channel, and realizing calibration and equalization of the broadband zero intermediate frequency receiving digital array channel.
Description
Technical Field
The invention relates to the technical field of electronic information, in particular to a channel calibration and equalization method of a broadband zero intermediate frequency receiving array.
Background
With the continuous progress of digital signal processing technology and continuous improvement of corresponding processing capability, the broadband digital array has gradually replaced analog array antennas due to the characteristics of wide coverage frequency band, multiple scanning beams, high design flexibility and the like, and is widely applied to the technical fields of electronic information such as communication, countermeasure, radar and the like. Compared with a super-heterodyne intermediate frequency sampling receiving array, the broadband digital array constructed by multichannel zero intermediate frequency receiving has the characteristics of low cost, low power consumption, high integration and the like, and is a main research direction of the current broadband digital array.
In practical engineering, due to the limitation of the current device technology level, the channel error of the broadband zero intermediate frequency receiving array mainly consists of an inter-channel frequency response error and in-phase (I) and quadrature (Q) branch imbalance errors in the channel. The inter-channel frequency response error mainly comes from analog devices (antennas, pre-selection band-pass filters, low noise amplifiers, etc.) before the inter-channel analog quadrature mixing, while the IQ imbalance error mainly depends on the non-orthogonality of the in-phase local oscillator and the quadrature local oscillator of the analog quadrature mixing, and the frequency response inconsistency between the in-phase branch and the quadrature branch after the analog quadrature mixing. Compared with the inter-channel frequency response error, the IQ imbalance error in the channel has more serious influence on the beam synthesis performance of the digital array, so that after the zero intermediate frequency receiving array is subjected to beam synthesis, not only the frequency domain mirror image component is present, but also the space domain mirror image component is generated. The presence of these mirror components will greatly impact the overall performance of the receiving array.
Currently, many researches are made on IQ imbalance estimation and compensation methods of a wideband single-channel zero intermediate frequency receiver, for example, a zero intermediate frequency receiving array IQ imbalance beam level compensation method disclosed in chinese patent publication No. CN116684239a, but a calibration and equalization method in which an inter-channel frequency response error and an intra-channel IQ imbalance error exist in a wideband zero intermediate frequency receiving array at the same time is discussed. If the broadband array only has the inter-channel frequency response error, the broadband signal is used as a calibration source, and the inter-channel frequency response error can be estimated easily by collecting broadband signal samples (calibration signal samples) of each channel, and the error can be compensated. However, in the wideband zero intermediate frequency receiving array, if the wideband signal is still used as the calibration source, because of IQ imbalance errors in the channels, the signal samples collected by each channel include both the samples of the wideband signal and the image signal samples thereof, which will cause distortion of the calibration signal samples and cannot accurately estimate the frequency response errors of each channel of the array.
In order to estimate and compensate various errors of the broadband zero intermediate frequency receiving channel, and simplify the complexity of the design of the correction source in the broadband digital array, it is necessary to find a method for estimating and compensating the frequency response errors of the broadband receiving channel, simplifying the complexity of the design of the correction source, adapting to the situation that the correction source cannot generate a modulation signal, facilitating the engineering realization of the multi-point frequency signal joint processing method, and solving the problems of calibration and equalization of the broadband zero intermediate frequency receiving digital array channel.
Disclosure of Invention
The invention aims to solve the technical problem that the prior art cannot estimate and compensate various errors of a broadband zero intermediate frequency receiving channel, so that the calibration and equalization of the broadband zero intermediate frequency receiving digital array channel cannot be realized.
The invention solves the technical problems by the following technical means: a channel calibration and equalization method for a broadband zero intermediate frequency receiving array comprises the following steps:
step 1: acquiring a baseband digital complex signal of each receiving channel of the digital array;
step 2: acquiring a baseband digital complex single-frequency signal of a p-th frequency point received by an m-th array element;
step 3: calculating discrete time Fourier transform of each baseband digital complex single-frequency signal in each channel to obtain a frequency spectrum value of the single-frequency signal of each channel and a frequency spectrum value of a corresponding mirror image signal;
step 4: calculating a first compensation value and a second compensation value of IQ imbalance frequency response of each channel;
step 5: estimating first FIR equalizer coefficients and second FIR equalizer coefficients of the IQ imbalance;
step 6: compensating the baseband digital complex single-frequency signals of all frequency points in each channel to obtain complex signals after IQ imbalance compensation;
step 7: calculating inter-channel frequency response compensation values of other channels relative to the reference channel by taking the first receiving channel as a reference according to the complex signal after IQ imbalance compensation;
step 8: estimating a third FIR equalizer coefficient between channels according to the inter-channel frequency response compensation value;
step 9: when the array receives a target signal, the baseband digital complex signal received by the array is compensated by utilizing the FIR equalizer coefficients of IQ imbalance, and the complex signal after IQ imbalance error compensation and channel frequency response error compensation is obtained.
Further, the step 1 includes:
the mth array element of the digital array receives the target signal as
x m (t)＝A(t-τ m )cos[(Ω c +Ω d )(t-τ m )+φ(t-τ m )]
Wherein phi (t) is the instantaneous phase of the signal at time t, omega c For the carrier analog angular frequency of the received signal, A (t) is the instantaneous amplitude at time t of the signal, Ω d For analog angular frequency offset of signal τ m Is the spatial delay difference;
baseband digital complex signal s of mth receiving channel m (n) there are
Wherein the symbols areRepresents a linear convolution, ++>T s For A/D sampling frequency, n is the nth sampling point, symbol e is natural constant, +.> For signal u m (n) complex conjugate signals, denoted by complex conjugate operations, λ 1,m (n) and lambda 2,m (n) are respectively
g 1,m (n) and g 2,m (n) are respectively
Wherein, and->Respectively is a real low-pass filter->Anddiscrete sample sequence of>Is->Relative to->Delta (n) is a discrete unit impulse sequence, epsilon m Is made up of in-phase local oscillator->And orthogonal local oscillation->Amplitude error, θ, due to amplitude difference between m Is made up of in-phase local oscillator->And orthogonal local oscillation->Phase error due to phase difference between them, h L,m (n) is an equivalent low-pass filter impulse response sequence corresponding to the mth radio frequency front end,/and (b)>Is h L,m Complex conjugate of (n).
Still further, the step 2 includes:
when the digital array is calibrated, each channel receives baseband digital complex single-frequency signals of P frequency points in the working bandwidth B, and the corresponding baseband frequencies are f respectively 1 ,f 2 ,…,f P And has a ratio of-B/2.ltoreq.f 1 <f 2 <…<f P B/2, the frequency points are equally spaced in the working bandwidth B, and P baseband frequencies f 1 ,f 2 ,…,f P None equal zero, where m=1, 2,3, …, M, p=1, 2, …, P;
the base band digital complex single frequency signal of the p-th frequency point received by the m-th array element is
Wherein,φ 0 for initial phase, A 0 Is the amplitude, omega of the single-frequency signal p ＝2πf p T s Not equal to 0 is the digital angular frequency of the single frequency signal, lambda 1,m (ω p ) And lambda (lambda) 2,m (-ω p ) Respectively lambda 1,m (n) and lambda 2,m (n) discrete time Fourier transform, i.e
Still further, the step 3 includes:
collecting calibration signals of M channels, wherein each channel comprises P baseband digital complex single-frequency signals s m,p (N) the number of sampling points of the single signal is N (more than or equal to 1), and each baseband digital complex single frequency signal s in each channel is calculated m,p (n) discrete time Fourier transform to obtain single frequency signals of each channelOwn spectral value S m,p (ω p ) And corresponding spectral value S of the image signal m,p (-ω p ) Respectively expressed as
Where n=1, 2, …, N.
Still further, the step 4 includes:
step 4-1: according to the frequency spectrum value S of the channel single-frequency signal m,p (ω p ) And corresponding spectral value S of the image signal m,p (-ω p ) Estimating frequency point omega p Amplitude error ρ of IQ imbalance p And phase error eta p I.e.
Step 4-2: according to frequency point omega p Amplitude error ρ of IQ imbalance p And phase error eta p Wherein p=1, 2, …, P, construct a first estimate of the IQ imbalance error frequency responseAnd a second estimate +.>I.e.
Step 4-3: from the first estimation value of IQ imbalance error frequency responseAnd a second estimate +.>Constructing a first compensation value W of IQ imbalance frequency response 1,m (ω p ) And a second compensation value W 2,m (ω p ) I.e.
Still further, the step 5 includes:
step 5-1: order D of a given FIR equalizer 1 Obtaining the first FIR equalizer coefficient w of IQ imbalance by solving the following optimization problem 1,m (n), i.e
Wherein P is>D 1 ；
Step 5-2: order D of a given FIR equalizer 2 Obtaining the second FIR equalizer coefficient w of IQ imbalance by solving the following optimization problem 2,m (n), i.e
Wherein P is>D 2 。
Still further, the step 6 includes:
first FIR equalizer coefficient w using IQ imbalance 1,m (n) and second FIR equalizer coefficients w 2,m (n) for baseband digital complex single frequency signal s of all frequency points in each channel m,p (n) compensating to obtain IQ imbalance compensated complex signalDenoted as->
Still further, the step 7 includes:
based on IQ imbalance compensated complex signalsCalculating inter-channel frequency response compensation values G of other channels relative to the reference channel by taking the first receiving channel as a reference m (ω p ) Expressed as
Still further, the step 8 includes:
order D of a given inter-channel FIR equalizer 3 According to the inter-channel frequency response compensation value G m (ω p ) P=1, 2, …, P, the third FIR equalizer coefficient c between the channels is estimated by solving an optimization problem m (n) third FIR equalizer coefficient c between channels m (n) optimization problem satisfied is
Wherein P is>D 3 。
Still further, the step 9 includes:
step 9-1: first FIR equalizer coefficient w using IQ imbalance 1,m (n) and second FIR equalizer coefficients w 2,m (n) receiving a baseband digital complex signal from the arrayCompensating to obtain complex signal after IQ imbalance error compensation>I.e.
Step 9-2: using third FIR equalizer coefficients c between channels m (n) complex signals after IQ imbalance error compensationCorrection is carried out to obtain complex signals after channel frequency response error compensation>I.e.
The invention has the advantages that:
(1) The invention obtains the first FIR equalizer coefficient and the second FIR equalizer coefficient of IQ imbalance and the third FIR equalizer coefficient between channels respectively through a series of calculations, then compensates the baseband digital complex signal received by the array by utilizing each FIR equalizer coefficient of IQ imbalance to obtain the complex signal after IQ imbalance error compensation and channel frequency response error compensation, thereby realizing estimation and compensation of various errors of the broadband zero intermediate frequency receiving channel and realizing calibration and equalization of the broadband zero intermediate frequency receiving digital array channel.
(2) The invention does not need to send complex broadband calibration signals, not only can use the point frequency signals as a correction source and simplify the design complexity of the correction source, but also can calibrate and correct the frequency response inconsistency between channels and IQ imbalance errors in the channels respectively, thereby reducing the implementation complexity of the correction device and facilitating engineering implementation.
(3) The invention does not need to store the reference signal sent by the correction source in advance, has simple principle and small operation amount and saves the storage space. The IQ imbalance error estimated by the invention is not an absolute error in a channel, but after IQ imbalance error compensation, the image component caused by IQ imbalance can be effectively restrained, and the overall image rejection ratio of the array is improved.
(4) The invention can calibrate and correct the frequency response error between channels and IQ imbalance error in channels, thereby improving the correction performance and facilitating engineering realization. The method related by the whole scheme is not limited by the array structure, and is applicable to both planar digital arrays and conformal digital arrays.
Drawings
Fig. 1 is a flowchart of a channel calibration and equalization method for a wideband zero intermediate frequency receiving array according to an embodiment of the present invention;
fig. 2 is a block diagram of IQ imbalance error and inter-channel frequency response compensation in a channel calibration and equalization method for a wideband zero intermediate frequency receiving array according to an embodiment of the present invention;
fig. 3 is a schematic diagram of channel frequency response corresponding to a target signal in a channel calibration and equalization method of a wideband zero intermediate frequency receiving array according to an embodiment of the present invention; fig. 3 (a) is a schematic diagram of channel amplitude-frequency response corresponding to the target signal; FIG. 3 (b) is a schematic diagram of the channel phase-frequency response corresponding to the target signal;
fig. 4 is a schematic diagram of channel frequency response corresponding to a mirror signal in a channel calibration and equalization method of a wideband zero intermediate frequency receiving array according to an embodiment of the present invention; FIG. 4 (a) is a schematic diagram of channel amplitude-frequency response corresponding to the image signal; FIG. 4 (b) is a schematic diagram of the channel phase-frequency response corresponding to the image signal;
fig. 5 shows a method for calibrating and equalizing channels of a wideband zero intermediate frequency receiving array according to an embodiment of the present invention 1,m (ω p ) Amplitude-frequency response schematic of the FIR fitting and estimation of (2);
fig. 6 shows a method for calibrating and equalizing channels of a wideband zero intermediate frequency receiving array according to an embodiment of the present invention 1,m (ω p ) A schematic of the phase-frequency response of the FIR fitting and the estimation of (2);
fig. 7 shows a wideband zero intermediate frequency receiving method according to an embodiment of the present inventionW in channel calibration and equalization method of array 2,m (ω p ) Amplitude-frequency response schematic of the FIR fitting and estimation of (2);
fig. 8 is a schematic diagram of a method for calibrating and equalizing channels of a wideband zero intermediate frequency receiving array according to an embodiment of the present invention 2,m (ω p ) A schematic of the phase-frequency response of the FIR fitting and the estimation of (2);
fig. 9 is a spectrum diagram of a calibration signal before IQ imbalance compensation in a channel calibration and equalization method of a wideband zero intermediate frequency receiving array according to an embodiment of the present invention;
fig. 10 is a spectrum diagram of a calibration signal after IQ imbalance compensation in a channel calibration and equalization method of a wideband zero intermediate frequency receiving array according to an embodiment of the present invention;
FIG. 11 is a schematic diagram of a single simulated inter-channel relative phase-frequency response and amplitude-frequency response in a channel calibration and equalization method for a wideband zero intermediate frequency receiving array according to an embodiment of the present invention; FIG. 11 (a) is a schematic diagram of the inter-channel relative amplitude-frequency response of a single simulation; FIG. 11 (b) is a schematic diagram of the inter-channel relative phase-frequency response of a single simulation;
fig. 12 is a schematic diagram of an estimated value of a relative amplitude-frequency response between channels in a channel calibration and equalization method for a wideband zero intermediate frequency receiving array according to an embodiment of the present invention;
fig. 13 is a schematic diagram of an estimated value of a relative phase-frequency response between channels in a channel calibration and equalization method for a wideband zero intermediate frequency receiving array according to an embodiment of the present invention;
fig. 14 is an array normal beam pattern corresponding to a target and an image signal before channel error compensation, wherein the radio frequency is 8GHz in a channel calibration and equalization method of a broadband zero intermediate frequency receiving array according to an embodiment of the present invention;
fig. 15 is an array normal beam pattern corresponding to a mirror signal after channel error compensation, wherein the radio frequency is 8GHz in a channel calibration and equalization method for a broadband zero intermediate frequency receiving array according to an embodiment of the present invention;
fig. 16 is an array beam pattern corresponding to a target and an image signal after channel error compensation, wherein the radio frequency is 7.9GHz in a channel calibration and equalization method of a broadband zero intermediate frequency receiving array according to an embodiment of the present invention;
fig. 17 is an array beam pattern corresponding to a target and an image signal after channel error compensation, in a channel calibration and equalization method for a broadband zero intermediate frequency receiving array according to an embodiment of the present invention, where the radio frequency is 8.1 GHz.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the invention provides a channel calibration and equalization method for a broadband zero intermediate frequency receiving array, which comprises the following steps:
step 1: the digital array has M (more than or equal to 2) array elements, and the working bandwidth of each array element corresponding to the receiving channel is B. Within the working bandwidth, the target signal received by the array element is subjected to preselection filtering, low noise amplification, in-phase and quadrature mixing, low-pass filtering and A/D acquisition of each channel of the zero intermediate frequency receiving array to obtain baseband digital complex signals of M receiving channelsThe specific process is as follows:
within the working bandwidth B, the m-th array element of the digital array receives the target signal as
x m (t)＝A(t-τ m )cos[(Ω c +Ω d )(t-τ m )+φ(t-τ m )]
Wherein phi (t) is the instantaneous phase of the signal at time t, omega c For the carrier analog angular frequency of the received signal, A (t) is the instantaneous amplitude at time t of the signal, Ω d For analog angular frequency offset of signal τ m Is formed by array element position and signal inputThe space time delay difference determined by the shooting angle;
after preselection filtering, low noise amplification, in-phase and quadrature mixing, low-pass filtering and A/D acquisition of each channel of the zero intermediate frequency receiving array, the baseband digital complex signal s of the mth receiving channel is obtained m (n) there are
Wherein the symbols areRepresents a linear convolution, ++>T s For A/D sampling frequency, n is the nth sampling point, symbol e is natural constant, +.> For signal u m (n) complex conjugate signals, denoted by complex conjugate operations, λ 1,m (n) and lambda 2,m (n) are respectively
g 1,m (n) and g 2,m (n) are respectively
Wherein, and->Respectively is a real low-pass filter->Anddiscrete sample sequence of>Is->Relative to->Delta (n) is a discrete unit impulse sequence, epsilon m Is made up of in-phase local oscillator->And orthogonal local oscillation->Amplitude error, θ, due to amplitude difference between m Is made up of in-phase local oscillator->And orthogonal local oscillation->Phase error due to phase difference between them, h L,m (n) is defined by the mth RF front endIs an equivalent low-pass filter impulse response sequence, < ->Is h L,m Complex conjugate of (n).
Step 2: when the digital array is calibrated, each channel receives baseband digital complex single-frequency signals s with P (more than or equal to 4) frequency points in the working bandwidth B m,p (n) the corresponding baseband frequencies are f 1 ,f 2 ,…,f P And has a ratio of-B/2.ltoreq.f 1 <f 2 <…<f P B/2, the frequency points are equally spaced in the working bandwidth B, and P baseband frequencies f 1 ,f 2 ,…,f P None equal zero, where m=1, 2,3, …, M, p=1, 2, …, P;
the base band digital complex single frequency signal of the p-th frequency point received by the m-th array element is
Wherein,φ 0 for initial phase, A 0 Is the amplitude, omega of the single-frequency signal p ＝2πf p T s Not equal to 0 is the digital angular frequency of the single frequency signal, lambda 1,m (ω p ) And lambda (lambda) 2,m (-ω p ) Respectively lambda 1,m (n) and lambda 2,m (n) discrete time Fourier transform, i.e
Step 3: collecting calibration signals of M (more than or equal to 2) channels, wherein each channel comprises P (more than or equal to 4) baseband digital complex single-frequency signals s m,p (N) the number of sampling points of the single signal is N (more than or equal to 1), and each baseband digital complex single frequency signal s in each channel is calculated m,p (n) discrete time Fourier transform to obtain the frequency of each channel single frequency signalSpectral value S m,p (ω p ) And corresponding spectral value S of the image signal m,p (-ω p ) Respectively expressed as
Where m=1, 2,3, …, M, p=1, 2, …, P, n=1, 2, …, N.
Step 4: according to the frequency spectrum value S of the single-frequency signal per se of each channel m,p (ω p ) And corresponding spectral value S of the image signal m,p (-ω p ) Calculating the first compensation value W of IQ imbalance frequency response of each channel 1,m (ω p ) And a second compensation value W 2,m (ω p ) Wherein m=1, 2,3, …, M, p=1, 2, …, P; the calculation method of the IQ imbalance frequency response compensation value of each channel is the same, and for the mth channel, the specific process is as follows:
step 4-1: according to the frequency spectrum value S of the channel single-frequency signal m,p (ω p ) And corresponding spectral value S of the image signal m,p (-ω p ) Estimating frequency point omega p Amplitude error ρ of IQ imbalance p And phase error eta p I.e.
Step 4-2: according to frequency point omega p Amplitude error ρ of IQ imbalance p And phase error eta p Wherein p=1, 2, …, P, construct a first estimate of the IQ imbalance error frequency responseAnd a second estimate +.>I.e.
Step 4-3: from the first estimation value of IQ imbalance error frequency responseAnd a second estimate +.>Constructing a first compensation value W of IQ imbalance frequency response 1,m (ω p ) And a second compensation value W 2,m (ω p ) I.e.
Step 5: according to IQ imbalance frequency response first compensation value W 1,m (ω p ) And a second compensation value W 2,m (ω p ) P=1, 2, …, P, first FIR equalizer coefficients w of IQ imbalance are estimated, respectively 1,m (n) and second FIR equalizer coefficients w 2,m (n); the specific process is as follows:
step 5-1: order D of a given FIR equalizer 1 Obtaining the first FIR equalizer coefficient w of IQ imbalance by solving the following optimization problem 1,m (n), i.e
Wherein P is>D 1 ；
Step 5-2: order D of a given FIR equalizer 2 Obtaining the second FIR equalizer coefficient w of IQ imbalance by solving the following optimization problem 2,m (n), i.e
Wherein P is>D 2 。
Step 6: first FIR equalizer coefficient w using IQ imbalance 1,m (n) and second FIR equalizer coefficients w 2,m (n) for baseband digital complex single frequency signal s of all frequency points in each channel m,p (n) compensating to obtain IQ imbalance compensated complex signalDenoted as->
Step 7: based on IQ imbalance compensated complex signalsCalculating inter-channel frequency response compensation values G of other channels relative to the reference channel by taking the first receiving channel as a reference m (ω p ) Expressed as
Step 8: order D of a given inter-channel FIR equalizer 3 According to the inter-channel frequency response compensation value G m (ω p ) P=1, 2, …, P, the third FIR equalizer coefficient c between the channels is estimated by solving an optimization problem m (n) third FIR equalizer coefficient c between channels m (n) optimization problem satisfied is
Wherein P is>D 3 。
Step 9: when arrayWhen the column receives the target signal as in step 1, the IQ imbalance is utilized to generate the first FIR equalizer coefficient w 1,m (n), second FIR equalizer coefficient w 2,m (n) third FIR equalizer coefficient c between channels m (n) the baseband digital complex signal received by the opposite array as shown in FIG. 2Sequentially compensating to obtain complex signal +.f after IQ imbalance error compensation and channel frequency response error compensation>The specific process is as follows:
step 9-1: first FIR equalizer coefficient w using IQ imbalance 1,m (n) and second FIR equalizer coefficients w 2,m (n) receiving a baseband digital complex signal from the arrayCompensating to obtain complex signal after IQ imbalance error compensation>I.e.
Step 9-2: using third FIR equalizer coefficients c between channels m (n) complex signals after IQ imbalance error compensationCorrection is carried out to obtain complex signals after channel frequency response error compensation>I.e.
In the following simulation verification is carried out on the scheme of the invention, in the simulation experiment, the radio frequency of the system operation is 8GHz, the sampling rate of the system is 240MHz, the operation bandwidth B=200MHz, the digital array is a uniform linear array, the array element spacing is 11mm, and the number of array elements is 64.
Scene 1: IQ imbalance error estimation and equalization in a single channel
For a certain channel of the zero intermediate frequency receiving array, the target signal u m (n) corresponding channel frequency response lambda 1,m (omega) As shown in FIG. 3, the mirror signal u m (n) corresponding channel frequency response lambda 2,m (ω) is shown in fig. 4. As can be seen from fig. 3 and 4, the image rejection ratio is approximately between 20dB and 25dB over the entire frequency band.
The array receives single-frequency signals, the signal-to-noise ratio is 20dB, the number of collected samples is 2400, and in the whole working bandwidth, 200 single-frequency signals are received in total, and the frequency points of the signals are uniformly distributed in-100 MHz to 100 MHz. The frequency response compensation value W of IQ imbalance by the method of the invention 1,m (ω p ) And W is 2,m (ω p ) Estimated and used with 16-order FIR equalizer w 1,m (n) and w 2,m (n) compensating value W for frequency response 1,m (ω p ) And W is 2,m (ω p ) Fitting was performed. Frequency response compensation value W of IQ imbalance 1,m (ω p ) Is matched with the FIR equalizer w 1,m (n) fitting the amplitude-frequency response and the phase-frequency response are shown in fig. 5 and 6, respectively. Frequency response compensation value W of IQ imbalance 2,m (ω p ) Is matched with the FIR equalizer w 2,m (n) fitting the amplitude-frequency response and the phase-frequency response are shown in fig. 7 and 8, respectively.
The spectrum diagram of 200 single frequency calibration complex signals before IQ imbalance frequency response compensation is shown in FIG. 9. After the compensation of the FIR equalizer, the spectrograms of 200 single-frequency calibration signals are shown in fig. 10. It can be seen from the figure that the image component due to IQ imbalance in the channel is suppressed after calibration and compensation.
Scene 2: in the two-channel condition, after IQ imbalance compensation, the inter-channel amplitude-phase error estimation
For some two channels of the broadband zero intermediate frequency receiving array, the average value of IQ imbalance frequency response corresponding to the original signal and the image signal of each channel is shown in fig. 3 and fig. 4 in scenario 1. Besides the IQ balance random error, the frequency response random error between the channels exists at each frequency point of the two channels. Within the operating bandwidth, the amplitude imbalance random error maximum is 1dB, and the phase imbalance random error maximum is 5 degrees. The maximum value of the amplitude random error between channels is 1dB, and the maximum value of the phase random error is 10 degrees. In this scenario, the inter-channel relative amplitude-frequency response and phase-frequency response of a single simulation are shown in FIG. 11.
The whole working frequency band is scanned by using 200 single-frequency calibration signals, the signal-to-noise ratio of the single-frequency calibration signals is 20dB, and the estimated value of the relative frequency response between channels is shown in fig. 12 and 13. As can be seen from the figure, the estimated value of the frequency response between channels by the method of the present invention is very similar to the simulation value given in FIG. 11, and the correctness of the method of the present invention is verified.
Scene 3: array beam pattern before and after array channel calibration and equalization
For a wideband zero intermediate frequency receive array, the average IQ imbalance frequency response for each channel primary and image signal is shown in fig. 3 and 4 in scenario 1. Each channel has an inter-channel frequency response random error in addition to an IQ balance random error at each frequency point. Within the operating bandwidth, the amplitude imbalance random error maximum is 1dB, and the phase imbalance random error maximum is 5 degrees. The maximum value of the amplitude random error between channels is 1dB, and the maximum value of the phase random error is 10 degrees.
And in the working bandwidth, the whole working bandwidth is scanned by using 200 single-frequency calibration signals, the signal-to-noise ratio of the single-frequency calibration complex signals is 20dB, the IQ imbalance FIR equalizer order is 16, and the inter-channel FIR equalizer order is 16. After compensating the IQ imbalance frequency response error and inter-channel frequency response error of each channel, the complex signal of each channelAnd respectively carrying out beam weight correction and fractional delay compensation to complete broadband beam synthesis.
For a target rf frequency of 8GHz, the array normal beam pattern for the target and image signal is shown in fig. 14 when channel errors are not compensated. It can be seen from the graph that, compared with the IQ imbalance image rejection level of the single channel, the beam synthesis has no rejection capability on the image component caused by IQ imbalance, and the image rejection ratio after beam synthesis is approximately equal to the average image rejection ratio of the single channel at the center frequency. After channel error compensation, the array normal beam pattern of the target corresponding to the image signal is shown in fig. 15. From the graph, the channel error compensation improves the image rejection ratio from about 23dB before compensation to more than 67 dB. The channel calibration method provided by the invention can further improve the image rejection ratio of the beam synthesis output.
For the target radio frequencies 7.9GHz and 8.1GHz, the beam direction is set to 45 degrees, and after channel error compensation, array beam patterns corresponding to the target and the image signals are shown in fig. 16 and 17 respectively. From the figure, beam synthesis can be performed at the minimum and maximum radio frequency operation frequencies of the system, the channel error compensation increases the frequency domain image rejection ratio from about 23dB before compensation to more than 87dB, and increases the spatial domain image rejection ratio from about 23dB before compensation to more than 67 dB. The channel calibration and equalization method provided by the invention can improve the space domain and frequency domain image rejection ratio of beam synthesis output, and can be used for broadband beam synthesis.
In conclusion, the wideband zero intermediate frequency receiving array channel calibration and equalization method is simple in principle, easy to realize engineering and verified in performance through simulation experiments. The method of the invention does not need to send complex broadband calibration signals, not only can use the point frequency signals as a correction source and simplify the design complexity of the correction source, but also can calibrate and correct the frequency response inconsistency between channels and IQ imbalance errors in the channels respectively, thereby reducing the implementation complexity of the correction device.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. The channel calibration and equalization method for the broadband zero intermediate frequency receiving array is characterized by comprising the following steps of:
step 1: acquiring a baseband digital complex signal of each receiving channel of the digital array;
step 2: acquiring a baseband digital complex single-frequency signal of a p-th frequency point received by an m-th array element;
step 3: calculating discrete time Fourier transform of each baseband digital complex single-frequency signal in each channel to obtain a frequency spectrum value of the single-frequency signal of each channel and a frequency spectrum value of a corresponding mirror image signal;
step 4: calculating a first compensation value and a second compensation value of IQ imbalance frequency response of each channel;
step 5: estimating first FIR equalizer coefficients and second FIR equalizer coefficients of the IQ imbalance;
step 6: compensating the baseband digital complex single-frequency signals of all frequency points in each channel to obtain complex signals after IQ imbalance compensation;
step 7: calculating inter-channel frequency response compensation values of other channels relative to the reference channel by taking the first receiving channel as a reference according to the complex signal after IQ imbalance compensation;
step 8: estimating a third FIR equalizer coefficient between channels according to the inter-channel frequency response compensation value;
step 9: when the array receives a target signal, the baseband digital complex signal received by the array is compensated by utilizing the FIR equalizer coefficients of IQ imbalance, and the complex signal after IQ imbalance error compensation and channel frequency response error compensation is obtained.
2. The method for channel calibration and equalization of a wideband zero intermediate frequency receive array of claim 1, wherein said step 1 comprises:
the mth array element of the digital array receives the target signal as
x m (t)＝A(t-τ m )cos[(Ω c +Ω d )(t-τ m )+φ(t-τ m )]
Wherein phi (t) is the instantaneous phase of the signal at time t, omega c For the carrier analog angular frequency of the received signal, A (t) is the instantaneous amplitude at time t of the signal, Ω d For analog angular frequency offset of signal τ m Is the spatial delay difference;
baseband digital complex signal s of mth receiving channel m (n) there are
Wherein the symbols areRepresents a linear convolution, ++>T s For A/D sampling frequency, n is the nth sampling point, symbol e is natural constant, +.> For signal u m (n) complex conjugate signals, denoted by complex conjugate operations, λ 1,m (n) and lambda 2,m (n) are respectively
g 1,m (n) and g 2,m (n) are respectively
Wherein, and->Respectively is a real low-pass filter->And->Discrete sample sequence of>Is->Relative to->Delta (n) is a discrete unit impulse sequence, epsilon m Is made up of in-phase local oscillator->And orthogonal local oscillation->Amplitude error, θ, due to amplitude difference between m Is made up of in-phase local oscillator->And orthogonal local oscillation->Phase error due to phase difference between them, h L,m (n) is an equivalent low-pass filter impulse response sequence corresponding to the mth radio frequency front end,/and (b)>Is h L,m Complex conjugate of (n).
3. The method for channel calibration and equalization of a wideband zero intermediate frequency receiving array according to claim 2, wherein said step 2 comprises:
when the digital array is calibrated, each channel receives baseband digital complex single-frequency signals of P frequency points in the working bandwidth B, and the corresponding baseband frequencies are f respectively 1 ,f 2 ,…,f P And has a ratio of-B/2.ltoreq.f 1 <f 2 <…<f P B/2, the frequency points are equally spaced in the working bandwidth B, and P baseband frequencies f 1 ,f 2 ,…,f P None equal zero, where m=1, 2,3, …, M, p=1, 2, …, P;
the base band digital complex single frequency signal of the p-th frequency point received by the m-th array element is
Wherein,φ 0 for initial phase, A 0 Is the amplitude, omega of the single-frequency signal p ＝2πf p T s Not equal to 0 is the digital angular frequency of the single frequency signal, lambda 1,m (ω p ) And lambda (lambda) 2,m (-ω p ) Respectively lambda 1,m (n) and lambda 2,m (n) discrete time Fourier transform, i.e
4. The method for channel calibration and equalization of a wideband zero intermediate frequency receive array of claim 3, wherein said step 3 comprises:
collecting calibration signals of M channels, wherein each channel comprises P baseband digital complex single-frequency signals s m,p (N) the number of sampling points of the single signal is N (more than or equal to 1), and each baseband digital complex single frequency signal s in each channel is calculated m,p (n) discrete time Fourier transform to obtain the spectrum value S of the single-frequency signal per se of each channel m,p (ω p ) And corresponding spectral value S of the image signal m,p (-ω p ) Respectively expressed as
Where n=1, 2, …, N.
5. The method for channel calibration and equalization of a wideband zero intermediate frequency receive array of claim 4, wherein said step 4 comprises:
step 4-1: according to the frequency spectrum value S of the channel single-frequency signal m,p (ω p ) And corresponding spectral value S of the image signal m,p (-ω p ) Estimating frequency point omega p Amplitude error ρ of IQ imbalance p And phase error eta p I.e.
Step 4-2: according to frequency point omega p Amplitude error ρ of IQ imbalance p And phase error eta p Wherein p=1, 2, …, P, construct a first estimate of the IQ imbalance error frequency responseAnd a second estimate +.>I.e.
Step 4-3: from the first estimation value of IQ imbalance error frequency responseAnd a second estimate +.>Constructing a first compensation value W of IQ imbalance frequency response 1,m (ω p ) And a second compensation value W 2,m (ω p ) I.e.
6. The method for channel calibration and equalization of a wideband zero intermediate frequency receive array of claim 5, wherein said step 5 comprises:
step 5-1: order D of a given FIR equalizer 1 Obtaining the first FIR equalizer coefficient w of IQ imbalance by solving the following optimization problem 1,m (n), i.e
Wherein P is>D 1 ；
Step 5-2: order D of a given FIR equalizer 2 Obtaining the second FIR equalizer coefficient w of IQ imbalance by solving the following optimization problem 2,m (n), i.e
Wherein P is>D 2 。
7. The method for channel calibration and equalization of a wideband zero intermediate frequency receive array of claim 6, wherein said step 6 comprises:
first FIR equalizer coefficient w using IQ imbalance 1,m (n) and second FIR equalizer coefficients w 2,m (n) for baseband digital complex single frequency signal s of all frequency points in each channel m,p (n) compensating to obtain IQ imbalance compensated complex signalDenoted as->
8. The method for channel calibration and equalization of a wideband zero intermediate frequency receive array of claim 7, wherein said step 7 comprises:
based on IQ imbalance compensated complex signalsCalculating inter-channel frequency response compensation values G of other channels relative to the reference channel by taking the first receiving channel as a reference m (ω p ) Expressed as
9. The method for channel calibration and equalization of a wideband zero intermediate frequency receive array of claim 8, wherein said step 8 comprises:
order D of a given inter-channel FIR equalizer 3 According to the inter-channel frequency response compensation value G m (ω p ) P=1, 2, …, P, the third FIR equalizer coefficient c between the channels is estimated by solving an optimization problem m (n) third FIR equalizer coefficient c between channels m (n) optimization problem satisfied is
Wherein P is>D 3 。
10. The method for channel calibration and equalization of a wideband zero intermediate frequency receive array of claim 9, wherein said step 9 comprises:
step 9-1: first FIR equalizer coefficient w using IQ imbalance 1,m (n) and second FIR equalizer coefficients w 2,m (n) receiving a baseband digital complex signal from the arrayCompensating to obtain complex signal after IQ imbalance error compensationI.e.
Step 9-2: using third FIR equalizer coefficients c between channels m (n) complex signals after IQ imbalance error compensationCorrection is carried out to obtain complex signals after channel frequency response error compensation>I.e.
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