CN101545929A - Phase detection method based on only amplitude detection - Google Patents
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Abstract
The invention discloses a kind of phase detection methods based on only amplitude detection, this method comprises: selecting any reference signal s0 (t), and assign any initial value to reception signal s (t) to be reconstructed; Calculate the gradient of price function phi; It calculates the Polak-Ribere conjugate gradient of price function phi: calculating the optimum stepsize λ changed along conjugated gradient direction; Judge that the error criterion met needed for whether φ is less than utilizes if being less than
The desired signal restored is calculated, is then log out circulation; Otherwise, if more than or be equal to, then continue iteration. Utilize the present invention, realize the phase detection of only amplitude detection, solve the problems, such as that the phase retrieval method in the fields such as X-ray crystallography, optics and astronomical images processing needs prior information, and lay a good foundation for no phase-detection imaging theory, so as to substantially reduce microwave, Terahertz and the hardware cost of optical imaging system.
Description
Technical Field
The invention relates to the technical fields of signal and image processing, microwave measurement, microwave or THZ imaging and the like, in particular to a phase detection method for detecting the phase of a received signal only by measuring the amplitude of the signal, so as to greatly reduce the complexity of a receiver system, reduce the hardware cost of the receiver and improve the phase measurement precision.
Background
The phase measurement of signals is developed rapidly almost with the development of military radio electronics and communication broadcasting industries, and particularly, the development of phased array radar technology requires a large amount of measurement to components such as an electric control phase shifter of an antenna array element. At present, the phase measurement of signals is widely applied, such as near-field measurement of antennas, microwave imaging, THZ imaging, production and development of microwave devices and the like.
Many methods for phase measurement have been developed, such as phase comparison, phase detection, zero-crossing time, and variable-frequency phase measurement. The methods can effectively measure the phase of the signal when the frequency is lower, but in a microwave frequency band, particularly when the frequency is more than 10GHz, the phase measurement is inaccurate or even can not be directly measured due to the influence of factors such as probe positioning deviation, inherent noise and temperature drift caused by a receiver phase demodulation circuit in the measurement process. This phenomenon is particularly prominent in millimeter wave/submillimeter wave and terahertz frequency bands, and phase measurement can greatly increase hardware cost.
Therefore, reducing the cost of receiver systems, whether in military or civilian applications, is currently an important goal pursued by designers.
The most common method used in current phase detection is quadrature demodulation, which is shown in schematic block diagram form in fig. 1. Fig. 1 is a schematic diagram of a quadrature demodulator for detecting signal phase in the prior art, in which 0 ° and 90 ° power dividers, mixers, and low-pass filters are required, which not only cause signal loss and nonlinear distortion, but also are expensive.
Quadrature demodulators in the microwave band are mainly limited by the following parameters:
(1) center frequency: determining the working frequency of the system;
(2) bandwidth: the bandwidth of a typical quadrature demodulator hardly reaches 10% of the center frequency;
(3) maximum input power: determining the power of the maximum input signal;
(4) local oscillation power: determining the maximum power of a local oscillation signal;
(5) frequency conversion loss, insertion loss: will cause attenuation of the received signal;
(6)1dB compression point, third order intermodulation: non-linear distortion of the received signal may result;
(7) the signal of the I/Q channel is unbalanced.
If the phase of the received signal can be detected only from the amplitude of the measured signal, the complexity of the receiver system can be greatly reduced, the hardware cost can be reduced, and the competitiveness of the product can be improved.
Phase reconstruction methods have been developed in the fields of X-ray crystallography, optics, and astronomical image processing to reconstruct the amplitude and phase of a signal from the amplitude of the fourier transform of the resulting signal. Its implementation requires the use of a priori information of the support domain of the recovered signal and its fourier (or inverse fourier) transform domain. However, in the general microwave measurement, only the amplitude of the signal can be obtained, and no prior information of the fourier (or inverse fourier) transform domain exists, so that the application of the phase recovery methods in the field of microwave measurement is limited.
Disclosure of Invention
Technical problem to be solved
In view of the above, in order to solve the problem that the phase recovery method in the fields of X-ray crystallography, optics, astronomical image processing and the like needs prior information, the invention provides a phase detection method based on only amplitude detection to realize phase detection based on only amplitude detection.
(II) technical scheme
To achieve the above object, the present invention provides a phase detection method based on amplitude-only detection, the method comprising:
selecting an arbitrary reference signal s0(t) and assigning any initial value to the received signal s (t) to be reconstructed;
calculate the gradient of the price function phi:
calculate Polak-Riber conjugate gradient of price function φ:
the optimum step length λ, is calculated four times for the change in the direction of the conjugate gradientPolynomial phi (x + lambdan) ═ a lambda4+bλ3+cλ2+ d λ + e takes a minimum value, n is the conjugation direction;
judging whether phi is less than the error standard to be met, if so, utilizing <math> <mrow> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>n</mi> <mo>=</mo> <mo>-</mo> <mi>N</mi> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>ξ</mi> <mi>n</mi> </msub> <mo>+</mo> <mi>j</mi> <msub> <mi>γ</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mfrac> <mi>kn</mi> <mrow> <mn>2</mn> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </msup> </mrow></math>
Calculating to obtain a signal expected to be recovered, and then exiting the loop; otherwise, if the value is larger than or equal to the threshold value, the iteration is continued.
In the above scheme, the receiving signal s (t) and the reference signal s0(t) satisfies the following relationship:
|s(t)|2-|s0(t)|2＝|s(t)|2+2Re[s(t)·(s0(t))*]。
in the above scheme, the price function phi (f:)x)＝‖D2-|s(t)|2-2Re[s(t)·(Einc)*]‖2Wherein D is2＝|s(t)|2-|s0(t)|2。
In the above schemeWhen calculating the optimal step length lambda changing along the direction of the conjugate gradient, the fourth-order polynomial phi (x + lambda n) is a lambda4+bλ3+cλ2In the + d λ + e range,
e＝φ(x)，
in the above solution, in the step of determining whether the price function phi is smaller than the error criterion to be satisfied, the error criterion is determined according to the actual situation and is usually a minimum value.
(III) advantageous effects
According to the technical scheme, the invention has the following technical effects:
1. the phase detection method based on only amplitude detection provided by the invention recovers the amplitude and the phase of a signal by measuring the amplitude of the signal (namely the sum of the signal to be reconstructed and a known reference signal), realizes the phase detection only by amplitude detection, solves the problem that the phase recovery method in the fields of X-ray crystallography, optics, astronomical image processing and the like needs prior information,
2. the phase detection method based on only amplitude detection provided by the invention realizes the restoration of the amplitude and the phase of the received signal only by measuring the amplitude of the signal, simplifies the complexity of a receiver system and reduces the hardware cost.
3. According to the phase detection method based on only amplitude detection, the required reference signal is any reference signal, and the reference signal with very low frequency can be adopted, so that the design of a signal source is facilitated.
4. The phase detection method based on only amplitude detection provided by the invention has very high processing speed, and does not cause the reduction of phase measurement precision while reducing the complexity of the system.
5. The phase detection method based on only amplitude detection provided by the invention is effective to any frequency receiving signal and can be used for different receiver systems.
Drawings
Fig. 1 is a schematic diagram of a prior art quadrature demodulator for detecting signal phase;
FIG. 2 is a flow chart of a method for phase detection based on amplitude-only detection provided by the present invention;
FIG. 3 is a schematic diagram of the phase detection based on optimization technique only for amplitude detection provided by the present invention;
fig. 4 shows the amplitude and phase of a received signal recovered from the amplitude of a measured signal using the method of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
First, the implementation principle of the present invention is introduced:
let s (t) be the received signal, which is expressed in more detail as s (t) ═ a (t) cos phi (t)]Let the reference signal be s0(t)＝a0(t)cos[φ0(t)]. The invention provides a method for detecting s (t) + s only by detecting s0The envelope or amplitude of (t) (in the case of a frequency domain signal, t is changed to frequency f) allows the received signal s (t) to be recovered.
Let the measurement signal be sm(t)＝s(t)+s0(t)＝A(t)cos[Φ(t)]Then, the following relationship is given:
A(t)＝|a(t)exp[jφ(t)]+a0(t)exp[jφ0(t)]|
Φ(t)＝Angle[a(t)exp[jφ(t)]+a0(t)exp[jφ0(t)]]
where Angle represents the phase of the complex signal. The above equation shows that detecting the envelope of the time domain signal is equivalent to detecting the amplitude of the complex signal corresponding to the signal; detecting the phase of a time domain signal is equivalent to detecting the phase of the signal corresponding to the complex signal. To this end, we discuss below in the complex signal domain, a technique for recovering the amplitude and phase of the received signal s (t) from the amplitude a (t) of the measured signal. The invention will enable signal detection with only amplitude detection.
Due to the fact that the received signal s (t) and the reference signal s0(t) satisfies the following relationship
|s(t)|2-|s0(t)|2＝|s(t)|2+2Re[s(t)·(s0(t))*]
Introduction of D2＝|s(t)|2-|s0(t)|2And defining a price function
φ(x)＝‖D2-|s(t)|2-2Re[s(t)·(Einc)*]‖2
To recover the signal s (t), it is represented as a finite long sequence { x }nFourier transform of }:
wherein s (t)k) Expressed as the signal sample, ξ, at the kth timen，γnAre respectively xnReal and imaginary parts of (c).
By iteratively finding the sequence { x) that minimizes the price function phi (x)nFrom { x } finallynThe amplitude and phase of the signal to be reconstructed can be determined by fourier transformation. The present invention proposes optimization using Polak-Ribiere conjugate gradient method, where the gradient needs to be solved
And an optimum step size λ that varies along the direction of the conjugate gradient.
As shown in fig. 2, fig. 2 is a flowchart of a method for phase detection based on only amplitude detection according to the present invention, where the method includes:
STEP 1: selecting an arbitrary reference signal s0(t) and assigning any initial value to the received signal s (t) to be reconstructed;
STEP 2: calculate the gradient of the price function phi:
STEP 3: calculate Polak-Riber conjugate gradient of price function φ:
STEP 4: calculating an optimum step length λ that varies along the direction of the conjugate gradient, λ being such that a fourth order polynomial phi (x + λ n) is a λ4+bλ3+cλ2+ d λ + e takes a minimum value, n is the conjugation direction;
wherein, <math> <mrow> <mi>a</mi> <mo>=</mo> <munder> <mi>Σ</mi> <mi>k</mi> </munder> <msup> <mrow> <mo>|</mo> <msub> <mi>N</mi> <mi>k</mi> </msub> <mo>|</mo> </mrow> <mn>4</mn> </msup> </mrow></math>
e＝φ(x)
STEP 5: it is determined whether the price function phi is less than the required error criterion (which is a small value, e.g. 1e-5, depending on the actual situation), and if so, it is used <math> <mrow> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>n</mi> <mo>=</mo> <mo>-</mo> <mi>N</mi> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>ξ</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>jγ</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mfrac> <mi>kn</mi> <mrow> <mn>2</mn> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </msup> </mrow></math>
Calculating to obtain a signal expected to be recovered, and then exiting the loop; otherwise, if the value is larger than or equal to the threshold value, the iteration is continued.
Fig. 3 is a schematic diagram of the phase detection based on only amplitude detection of the optimization technique provided by the present invention. It can be seen from fig. 3 that the method provided by the present invention requires only one adder for hardware, which greatly simplifies the complexity of the hardware system and also reduces the hardware cost.
Figure 4 shows the amplitude and phase of a received signal recovered from the amplitude of a measured signal using the method of the invention. It can be seen from fig. 4 that the amplitude and phase (real and imaginary parts) of the received signal recovered by this method fit well with the real values.
While the present invention has been described in conjunction with specific embodiments, it is evident that many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the foregoing description. Accordingly, it is intended to embrace all such alternatives, modifications and variances which fall within the scope of the appended claims.
Claims (5)
1. A method of phase detection based on amplitude-only detection, the method comprising:
selecting an arbitrary reference signal s0(t) and assigning any initial value to the received signal s (t) to be reconstructed;
calculate the gradient of the price function phi:
calculate Polak-Riber conjugate gradient of price function φ:
calculating an optimum step length λ that varies along the direction of the conjugate gradient, λ being such that a fourth order polynomial phi (x + λ n) is a λ4+bλ3+cλ2+ d λ + e takes a minimum value, n is the conjugation direction;
judging whether phi is less than the error standard to be met, if so, utilizing <math> <mrow> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>n</mi> <mo>=</mo> <mo>-</mo> <mi>N</mi> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>ξ</mi> <mi>n</mi> </msub> <mo>+</mo> <mi>j</mi> <msub> <mi>γ</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mfrac> <mi>kn</mi> <mrow> <mn>2</mn> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </msup> </mrow></math>
Calculating to obtain a signal expected to be recovered, and then exiting the loop; otherwise, if the value is larger than or equal to the threshold value, the iteration is continued.
2. The phase detection method based on amplitude-only detection according to claim 1, wherein the received signal s (t) is related to a reference signal s0(t) satisfies the following relationship:
|s(t)|2-|s0(t)|2＝|s(t)|2+2Re[s(t)·(s0(t))*]。
3. the phase detection method based on amplitude-only detection according to claim 1, wherein the price function Φ (x: (m)), (x)＝‖D2-|s(t)|2-2Re[s(t)·(Einc)*]‖2Wherein D is2＝|s(t)|2-|s0(t)|2。
4. The phase detection method according to claim 1, wherein the optimal step size λ is calculated as a λ when the quadratic polynomial Φ (x + λ n) changes in the direction of the conjugate gradient4+bλ3+cλ2In the + d λ + e range,
e＝φ(x)，
5. the phase detection method based on amplitude-only detection as claimed in claim 1, wherein the step of determining whether the price function Φ is smaller than an error criterion to be satisfied, the error criterion depending on the actual situation being usually a minimum value.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107490729A (en) * | 2017-08-18 | 2017-12-19 | 北京航空航天大学 | A kind of antenna near-field is without Method for Phase Difference Measurement |
| CN107607795A (en) * | 2017-10-23 | 2018-01-19 | 北京经纬恒润科技有限公司 | A kind of measuring method and system of radio-frequency electromagnetic field phase |
| CN108700910A (en) * | 2015-09-28 | 2018-10-23 | 剑桥企业有限公司 | Method and apparatus for executing complex Fourier transform |
| CN114325094A (en) * | 2021-12-29 | 2022-04-12 | 中国科学院上海微系统与信息技术研究所 | Phase information measuring device and method |
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2008
- 2008-03-26 CN CN200810102803A patent/CN101545929A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108700910A (en) * | 2015-09-28 | 2018-10-23 | 剑桥企业有限公司 | Method and apparatus for executing complex Fourier transform |
| CN108700910B (en) * | 2015-09-28 | 2022-03-29 | 剑桥企业有限公司 | Method and apparatus for performing complex Fourier transform |
| CN107490729A (en) * | 2017-08-18 | 2017-12-19 | 北京航空航天大学 | A kind of antenna near-field is without Method for Phase Difference Measurement |
| CN107607795A (en) * | 2017-10-23 | 2018-01-19 | 北京经纬恒润科技有限公司 | A kind of measuring method and system of radio-frequency electromagnetic field phase |
| CN107607795B (en) * | 2017-10-23 | 2019-08-30 | 北京经纬恒润科技有限公司 | A kind of measurement method and system of radio-frequency electromagnetic field phase |
| CN114325094A (en) * | 2021-12-29 | 2022-04-12 | 中国科学院上海微系统与信息技术研究所 | Phase information measuring device and method |
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