WO2022257046A1 - 载波频率、初始相位、相位噪声的估计方法和相关设备 - Google Patents

载波频率、初始相位、相位噪声的估计方法和相关设备 Download PDF

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WO2022257046A1
WO2022257046A1 PCT/CN2021/099179 CN2021099179W WO2022257046A1 WO 2022257046 A1 WO2022257046 A1 WO 2022257046A1 CN 2021099179 W CN2021099179 W CN 2021099179W WO 2022257046 A1 WO2022257046 A1 WO 2022257046A1
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moment
carrier
covariance matrix
phase
nth
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PCT/CN2021/099179
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English (en)
French (fr)
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王倩
全智
毕宿志
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深圳大学
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Priority to PCT/CN2021/099179 priority Critical patent/WO2022257046A1/zh
Priority to CN202180005311.5A priority patent/CN114514525B/zh
Publication of WO2022257046A1 publication Critical patent/WO2022257046A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/10—Noise analysis or noise optimisation

Definitions

  • the present application relates to the technical field of communications, and in particular to a method for estimating carrier frequency, initial phase, and phase noise, and related equipment.
  • Carrier frequency and phase estimation is a classic and important problem in communications, biomedical engineering, radar/sonar applications, and other signal processing domains such as grid power quality monitoring. All of these applications can be used for algorithm design and performance analysis with the help of a signal model of a single sinusoidal carrier.
  • AWGN additive Gaussian noise
  • ML maximum likelihood estimation theory
  • a well-known solution is a frequency-domain method based on Fourier transform, that is, a one-dimensional search to find the peak of the periodogram, but this scheme is computationally complex and computationally intensive.
  • Embodiments of the present application provide a method for estimating carrier frequency and initial carrier phase and related equipment, which can reduce the amount of calculation for estimating carrier frequency and/or initial carrier phase.
  • the embodiment of the present application provides a method for estimating the carrier frequency and/or the initial phase of the carrier, including: obtaining the amplitude and phase of k+1 received signals, and the k+1 received signals are in continuous k+1 signals received at k+1 moments, the k is an integer greater than or equal to zero; the first covariance matrix ⁇ ⁇ is determined according to the magnitude of the k+1 received signals, wherein, by the The first vector ⁇ composed of additive observation phase noise corresponding to k+1 received signals obeys the following Gaussian distribution: ⁇ N(0, ⁇ ⁇ ); the second vector ⁇ r and the second covariance matrix ⁇ r determine the first The carrier frequency and/or the initial phase of the carrier at time k, wherein the second vector ⁇ r is a vector composed of the phases of the k+1 received signals, and the second covariance matrix ⁇ r is the first The sum of a covariance matrix ⁇ ⁇ and a third covariance matrix ⁇ ⁇ , the third vector
  • the first covariance matrix ⁇ ⁇ is the covariance matrix corresponding to the Gaussian distribution that the first vector ⁇ obeys, and the first vector ⁇ is a vector composed of additive observation phase noise corresponding to k+1 received signals , the additive observation phase noise is equivalent to additive Gaussian noise, the first covariance matrix ⁇ ⁇ is only related to the amplitude of the received signal; the second covariance matrix ⁇ r is the first covariance matrix ⁇ ⁇ and the third covariance matrix The sum of ⁇ ⁇ ; the third covariance matrix ⁇ ⁇ is the covariance matrix corresponding to the Gaussian distribution of the third vector ⁇ which is composed of the first carrier phase noise of the random walk corresponding to k+1 received signals, and the third covariance matrix
  • the variance matrix ⁇ ⁇ is known; therefore, after obtaining the amplitude and phase of the k+1 received signals, the first covariance matrix ⁇ ⁇ can be determined according to the amplitudes of the k+1 received
  • k N-1
  • the N is a positive integer
  • the carrier frequency at the N-1 moment is determined by the following formula:
  • the method further includes: acquiring the amplitude and phase of the received signal corresponding to the Nth moment, where the received signal corresponding to the Nth moment is the signal received at the Nth moment;
  • the carrier frequency at time N is determined by the following formula:
  • a (N-1) (N T ⁇ r -1 ⁇ r) (N-1)
  • B (N-1) (1 T ⁇ r -1 1) (N-1)
  • C (N -1) (1 T ⁇ r -1 N) (N-1)
  • D (N-1) (1 T ⁇ r -1 ⁇ r) (N-1)
  • E (N-1) ( N T ⁇ r -1 N) (N-1) ;
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ r(N) represents the phase of the received signal corresponding to the Nth moment
  • N 0 represents the SSB power spectral density of white noise
  • A represents the amplitude of the transmitted signal
  • Indicates the magnitude of the received signal corresponding to the Nth moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector, 1 [1,1,...,1] T
  • ⁇ r(1) represents the phase of the received signal corresponding to the first moment
  • represents the amplitude of the received signal corresponding to the first moment
  • k N-1
  • the N is a positive integer
  • the initial phase of the carrier at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector
  • 1 [1,1,...,1] T .
  • the method further includes: acquiring the amplitude and phase of the received signal corresponding to the Nth moment, where the received signal corresponding to the Nth moment is the signal received at the Nth moment;
  • the initial phase of the carrier at time N is determined by the following formula:
  • a (N-1) (N T ⁇ r -1 ⁇ r) (N-1)
  • B (N-1) (1 T ⁇ r -1 1) (N-1)
  • C (N -1) (1 T ⁇ r -1 N) (N-1)
  • D (N-1) (1 T ⁇ r -1 ⁇ r) (N-1)
  • E (N-1) ( N T ⁇ r -1 N) (N-1) ;
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ r(N) represents the phase of the received signal corresponding to the Nth moment
  • N 0 represents the SSB power spectral density of white noise
  • A represents the amplitude of the transmitted signal
  • Indicates the magnitude of the received signal corresponding to the Nth moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector, 1 [1,1,...,1] T
  • ⁇ r(1) represents the phase of the received signal corresponding to the first moment
  • represents the amplitude of the received signal corresponding to the first moment
  • the method further includes: according to the second covariance matrix ⁇ r , the third covariance matrix ⁇ ⁇ , the second vector ⁇ r, the The carrier frequency and the initial carrier phase at the kth moment determine the second carrier phase noise at the kth moment.
  • k N-1
  • the second carrier phase noise at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • ⁇ ⁇ represents the third covariance matrix at the N-1th moment
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector
  • N [0,1,...,N-1] T
  • 1 [1,1,...,1] T .
  • the second carrier phase noise at the Nth moment is determined by the following formula:
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ ⁇ (N) represents the third covariance matrix at the Nth moment
  • ⁇ r (N) represents the second covariance matrix at the Nth moment
  • ⁇ r (N) represents the Nth moment
  • the second vector of , N (N) [0,1,...,N-1,N] T
  • 1 (N) [1,1,...,1] T
  • represents the magnitude of the received signal corresponding to
  • the embodiment of the present application provides a carrier frequency and/or carrier initial phase estimation device, including: an acquisition unit, configured to acquire the amplitude and phase of k+1 received signals, and the k+1 received signals
  • the signals are k+1 signals respectively received at consecutive k+1 moments, and the k is an integer greater than or equal to zero;
  • the determining unit is configured to determine the first protocol according to the amplitudes of the k+1 received signals Variance matrix ⁇ ⁇ , wherein the first vector ⁇ formed by the additive observation phase noise corresponding to the k+1 received signals obeys the following Gaussian distribution: ⁇ N(0, ⁇ ⁇ ); and according to the second vector ⁇ r and the second covariance matrix ⁇ r determine the carrier frequency and/or the initial phase of the carrier at the kth moment, wherein the second vector ⁇ r is a vector formed by the phases of the k+1 received signals, and the The second covariance matrix ⁇ r is the sum of the first covariance matrix ⁇ ⁇ and the third
  • k N-1, where N is a positive integer, and the carrier frequency at the N-1th moment is determined by the following formula:
  • the acquiring unit is further configured to: acquire the amplitude and phase of the received signal corresponding to the Nth moment, where the received signal corresponding to the Nth moment is the signal received at the Nth moment;
  • the carrier frequency at the Nth moment is determined by the following formula:
  • a (N-1) (N T ⁇ r -1 ⁇ r) (N-1)
  • B (N-1) (1 T ⁇ r -1 1) (N-1)
  • C (N -1) (1 T ⁇ r -1 N) (N-1)
  • D (N-1) (1 T ⁇ r -1 ⁇ r) (N-1)
  • E (N-1) ( N T ⁇ r -1 N) (N-1) ;
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ r(N) represents the phase of the received signal corresponding to the Nth moment
  • N 0 represents the SSB power spectral density of white noise
  • A represents the amplitude of the transmitted signal
  • Indicates the magnitude of the received signal corresponding to the Nth moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector, 1 [1,1,...,1] T
  • ⁇ r(1) represents the phase of the received signal corresponding to the first moment
  • represents the amplitude of the received signal corresponding to the first moment
  • k N-1
  • the N is a positive integer
  • the initial phase of the carrier at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector
  • 1 [1,1,...,1] T .
  • the acquiring unit is further configured to: acquire the amplitude and phase of the received signal corresponding to the Nth moment, where the received signal corresponding to the Nth moment is the signal received at the Nth moment;
  • the carrier initial phase at the Nth moment is determined by the following formula:
  • a (N-1) (N T ⁇ r -1 ⁇ r) (N-1)
  • B (N-1) (1 T ⁇ r -1 1) (N-1)
  • C (N -1) (1 T ⁇ r -1 N) (N-1)
  • D (N-1) (1 T ⁇ r -1 ⁇ r) (N-1)
  • E (N-1) ( N T ⁇ r -1 N) (N-1) ;
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ r(N) represents the phase of the received signal corresponding to the Nth moment
  • N 0 represents the SSB power spectral density of white noise
  • A represents the amplitude of the transmitted signal
  • Indicates the magnitude of the received signal corresponding to the Nth moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector, 1 [1,1,...,1] T
  • ⁇ r(1) represents the phase of the received signal corresponding to the first moment
  • represents the amplitude of the received signal corresponding to the first moment
  • the determining unit is further configured to: according to the second covariance matrix ⁇ r , the third covariance matrix ⁇ ⁇ , the second vector ⁇ r, the kth The carrier frequency at the moment and the initial phase of the carrier at the kth moment determine the second carrier phase noise at the kth moment.
  • k N-1
  • the second carrier phase noise at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • ⁇ ⁇ represents the third covariance matrix at the N-1th moment
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector
  • N [0,1,...,N-1] T
  • 1 [1,1,...,1] T .
  • the second carrier phase noise at the Nth moment is determined by the following formula:
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ ⁇ (N) represents the third covariance matrix at the Nth moment
  • ⁇ r (N) represents the second covariance matrix at the Nth moment
  • ⁇ r (N) represents the Nth moment
  • the second vector of , N (N) [0,1,...,N-1,N] T
  • 1 (N) [1,1,...,1] T
  • represents the magnitude of the received signal corresponding to
  • the third aspect of the embodiment of the present application provides an electronic device, including a processor, a memory, a communication interface, and one or more programs, the one or more programs are stored in the memory, and configured by the processor For execution, the above program includes instructions for executing the steps in the method according to any one of the above first aspects.
  • the fourth aspect of the embodiment of the present application provides a chip, which is characterized in that it includes: a processor, configured to call and run a computer program from the memory, so that the device installed with the above-mentioned chip executes any one of the above-mentioned first aspects. the above method.
  • a fifth aspect of the embodiment of the present application provides a computer-readable storage medium, which stores a computer program for electronic data exchange, wherein the computer program causes a computer to execute the method described in any one of the above-mentioned first aspects.
  • a sixth aspect of the embodiments of the present application provides a computer program product, which enables a computer to execute the method described in any one of the above first aspects.
  • FIG. 1 is a schematic flowchart of a carrier frequency and/or carrier initial phase estimation method provided by an embodiment of the present application
  • Fig. 2 is a schematic diagram of a geometric vector provided by the embodiment of the present application.
  • FIG. 3 is a schematic flowchart of a method for estimating carrier phase noise provided by an embodiment of the present application
  • FIG. 4 is a schematic flowchart of a method for iteratively estimating carrier frequency and carrier initial phase provided by an embodiment of the present application
  • FIG. 5 is a schematic flowchart of a method for iteratively estimating carrier phase noise provided by an embodiment of the present application
  • FIG. 6 is a simulation performance diagram of an estimation of carrier frequency and carrier initial phase provided by an embodiment of the present application.
  • FIG. 7 is a simulation performance diagram of an estimation of carrier phase noise provided by an embodiment of the present application.
  • FIG. 8 is a simulation performance diagram of another carrier phase noise estimation provided by an embodiment of the present application.
  • FIG. 9 is a schematic structural diagram of a device for estimating carrier frequency and/or carrier initial phase provided by an embodiment of the present application.
  • FIG. 10 is a schematic structural diagram of an electronic device provided by an embodiment of the present application.
  • phase noise is one of the major drawbacks of modern communication, radar, spectroscopy, and metrology systems.
  • Oscillator phase noise is one of the major drawbacks of modern communication, radar, spectroscopy, and metrology systems.
  • ultra-high-speed communication is now developing to higher frequency bands.
  • the higher the carrier frequency used the greater the carrier phase noise encountered and the more serious the system loss.
  • redundant phase noise can cause time-varying offsets, spurious sidelobes, impulse response broadening, and low-frequency phase modulation of the radar signal, severely degrading radar detection and tracking performance . Therefore, phase noise is an unavoidable factor that must be considered in parameter estimation and performance analysis in practical applications.
  • phase noise is often time-varying.
  • most algorithms are designed based on the assumption of quasi-static phase, without considering the time-varying characteristics of carrier phase, which leads to a significant drop in estimation performance. Therefore, for the carrier frequency and phase estimation problem under time-varying phase noise, there is no systematic method to realize the joint estimation of frequency and phase, and there is no exact method to estimate the phase noise in this case.
  • Oscillator phase noise is one of the major contributors to the performance of modern communications, radar, spectroscopy, and metrology systems.
  • the discrete Wiener phase noise model is generally applicable to carrier phase noise in these physical applications, including frequently used semiconductor laser oscillators and radio frequency oscillators. Therefore, this application will solve the problem of how to jointly estimate the angle parameter of a single sinusoidal signal under the joint action of AWGN and Wiener carrier phase noise.
  • the angle parameter specifically includes three parts: carrier frequency, carrier phase and phase noise.
  • We will design a joint time-domain estimation method of unknown carrier frequency and initial carrier phase based on ML algorithm, and a time-domain estimation method of phase noise based on maximum a posteriori probability (MAP) algorithm at the same time.
  • MAP maximum a posteriori probability
  • FIG. 1 is a schematic flowchart of a method for estimating carrier frequency and/or carrier initial phase provided by an embodiment of the present application. The method is applied to electronic equipment, and the method includes but is not limited to the following steps:
  • Step 101 Obtain the amplitude and phase of k+1 received signals, the k+1 received signals are k+1 signals respectively received at consecutive k+1 times, and the k is greater than or equal to zero integer.
  • the 0th moment corresponds to the first received signal
  • the first moment corresponds to the second received signal
  • the second moment corresponds to the third received signal signal, and so on.
  • Step 102 Determine the first covariance matrix ⁇ ⁇ according to the amplitudes of the k+1 received signals, wherein the first vector ⁇ formed by the additive observation phase noise corresponding to the k+1 received signals obeys the following Gaussian Distribution: ⁇ N(0, ⁇ ⁇ ).
  • Step 103 Determine the carrier frequency and/or initial carrier phase at the kth moment according to the second vector ⁇ r and the second covariance matrix ⁇ r, wherein the second vector ⁇ r is the k+1 received signals
  • the vector formed by the phase of the second covariance matrix ⁇ r is the sum of the first covariance matrix ⁇ ⁇ and the third covariance matrix ⁇ ⁇ , and the random walk corresponding to the k+1 received signals
  • the third vector ⁇ formed by the first carrier phase noise obeys the following Gaussian distribution: ⁇ N(0, ⁇ ⁇ ).
  • the first covariance matrix ⁇ ⁇ is the covariance matrix corresponding to the Gaussian distribution that the first vector ⁇ obeys, and the first vector ⁇ is a vector composed of additive observation phase noise corresponding to k+1 received signals , the additive observation phase noise is equivalent to additive Gaussian noise, the first covariance matrix ⁇ ⁇ is only related to the amplitude of the received signal; the second covariance matrix ⁇ r is the first covariance matrix ⁇ ⁇ and the third covariance matrix The sum of ⁇ ⁇ ; the third covariance matrix ⁇ ⁇ is the covariance matrix corresponding to the Gaussian distribution of the third vector ⁇ which is composed of the first carrier phase noise of the random walk corresponding to k+1 received signals, and the third covariance matrix
  • the variance matrix ⁇ ⁇ is known; therefore, after obtaining the amplitude and phase of the k+1 received signals, the first covariance matrix ⁇ ⁇ can be determined according to the amplitudes of the k+1 received
  • k N-1, where N is a positive integer, and the carrier frequency at the N-1th moment is determined by the following formula:
  • formula (1) can be obtained by:
  • the received signal can be rewritten into the polar coordinate form of amplitude-phase, as shown in formula (3):
  • T represents the transposition of the vector.
  • ⁇ and ⁇ are independent of each other, and ⁇ N(0, ⁇ ⁇ ), ⁇ N(0, ⁇ ⁇ ), where the third covariance matrix ⁇ ⁇ and the second covariance matrix ⁇ ⁇ are:
  • the derivation of the optimal estimation algorithm is mainly based on expression (4) and a theoretical fact: using the ML/MAP estimation of the received signal phase ⁇ r(k) that integrates the received amplitude information into the additive observation phase noise is equivalent to using the received ML/MAP estimation of the signal
  • k N-1
  • the N is a positive integer
  • the initial phase of the carrier at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector
  • 1 [1,1,...,1] T .
  • the present application can obtain the formula (8) by analyzing the formula (7).
  • the method further includes: according to the second covariance matrix ⁇ r , the third covariance matrix ⁇ ⁇ , the second vector ⁇ r, the The carrier frequency and the initial carrier phase at the kth moment determine the second carrier phase noise at the kth moment.
  • k N-1
  • the second carrier phase noise at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • ⁇ ⁇ represents the third covariance matrix at the N-1th moment
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector
  • N [0,1,...,N-1] T
  • 1 [1,1,...,1] T .
  • the present application can obtain the formula (9) by analyzing the formula (7).
  • the estimated values of the carrier frequency, the initial carrier phase, and the second carrier phase noise can be iteratively calculated as the number of samples N increases.
  • the present application exemplarily presents a simple iterative implementation solution.
  • the present application only needs to store the corresponding A (N-1) , B (N-1 ) , C (N-1) , D (N-1) and E (N-1) , when the received signal corresponding to the Nth moment is obtained at the Nth moment, only through the stored A (N-1) , B (N-1) , C (N-1) , D (N-1) and E (N-1) calculate A (N) , B (N) , C (N) , D (N) and E (N) , the carrier frequency or the initial phase of the carrier at the Nth moment can be quickly calculated.
  • the method further includes: acquiring the amplitude and phase of the received signal corresponding to the Nth moment, where the received signal corresponding to the Nth moment is the signal received at the Nth moment;
  • the carrier frequency at time N is determined by the following formula:
  • a (N) , B (N) , C (N) , D (N) and E (N) in formula (14) are related to A (N-1) , B (N-1) , C (N -1) , D (N-1) and E (N-1) Iterative relationship is shown in formula (15):
  • the superscript (N) represents the Nth moment
  • the superscript (N-1) represents the N-1th moment
  • the superscript (1) represents the first moment
  • ⁇ r(N) represents the phase of the received signal corresponding to the Nth moment
  • N 0 represents the SSB power spectral density of white noise
  • A represents the amplitude of the transmitted signal
  • Indicates the amplitude of the received signal corresponding to the Nth moment
  • ⁇ r(1) indicates the phase of the received signal corresponding to the first moment
  • indicates the amplitude of the received signal corresponding to the first moment
  • ⁇ (k) ⁇ is a variance of Gaussian random variable sequence of .
  • this iterative process makes full use of the newly received samples ⁇
  • , ⁇ r(N) ⁇ at time k N to achieve real-time performance.
  • the above iterative estimation process is also applicable to the case of no carrier phase noise, namely
  • the method further includes: acquiring the amplitude and phase of the received signal corresponding to the Nth moment, where the received signal corresponding to the Nth moment is the signal received at the Nth moment;
  • the initial phase of the carrier at time N is determined by the following formula:
  • the second carrier phase noise at the Nth moment is determined by the following formula:
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ ⁇ (N) represents the third covariance matrix at the Nth moment
  • ⁇ r (N) represents the second covariance matrix at the Nth moment
  • ⁇ r (N) represents the Nth moment
  • the second vector of , N (N) [0,1,...,N-1,N] T
  • 1 (N) [1,1,...,1] T
  • represents the magnitude of the received signal corresponding to
  • ( ⁇ r -1 ) (N) when calculating the second carrier phase noise, ( ⁇ r -1 ) (N) can be obtained recursively from ( ⁇ r -1 ) (N-1) , which avoids complex matrix inversion operations, thereby reducing the amount of calculation.
  • the matrix with superscript (N) represents the N+1-dimensional matrix corresponding to the Nth moment
  • the matrix with the superscript (N-1) represents the N-dimensional matrix at the N-1st moment
  • a vector with a superscript (N) indicates an N+1-dimensional vector corresponding to the Nth moment
  • a vector with a superscript (N-1) indicates an N-dimensional vector at the N-1th moment.
  • FIG. 3 is a schematic flowchart of a method for estimating carrier phase noise provided by an embodiment of the present application.
  • the method is applied to electronic equipment, and is specifically applied to an ML/MAP estimator.
  • ML/MAP The specific implementation of the MAP estimator includes but is not limited to the following steps:
  • Step 302 extracting the amplitude
  • FIG. 4 is a schematic flow chart of a method for iteratively estimating carrier frequency and carrier initial phase provided by an embodiment of the present application. This method is applied to electronic equipment, specifically to ML/MAP estimators, ML/MAP estimation The processor adopts iterative processing, including but not limited to the following steps:
  • Step 402 extract the amplitude and phase information ⁇
  • Step 403 using formula (16) to calculate A (1) , B (1) , C (1) , D (1) and E (1) ;
  • Step 404 obtain the received signal r(k), and extract the amplitude
  • and phase ⁇ r(k) of the received signal, k 2, 3, ...;
  • Step 405 obtaining stored A (k-1) , B (k-1) , C (k-1) , D (k-1) and E (k-1) ;
  • Step 406 using formula (15) to calculate A (k) , B (k) , C (k) , D (k) and E (k) ;
  • Step 407 using formula (14) to calculate the carrier frequency at the kth moment;
  • Step 408 Calculate the initial phase of the carrier at the kth moment by using formula (17).
  • FIG. 5 is a schematic flow chart of an iterative estimation method for carrier phase noise provided by an embodiment of the present application.
  • the method is applied to electronic equipment, and is specifically applied to ML/MAP estimators. Processing, including but not limited to the following steps:
  • Step 502 extract the amplitude and phase information ⁇
  • Step 504 at time k-1, use formula (19) to calculate ⁇ r -1 ;
  • Step 505 obtaining the estimated value of the carrier frequency and the estimated value of the initial phase of the carrier at time k;
  • Step 506 using formula (18) to calculate the estimated value of carrier phase noise at time k.
  • IMSE inverse mean square error
  • MSE mean square error
  • N 16
  • Figure 7 considers case
  • Figure 8 considers the case; it can be seen that at low phase noise Under , at about 0dB SNR, the estimator (9), that is, the MSE performance of formula (9) can reach BCRLB; Under the condition, acceptable estimation accuracy can only be achieved when the signal-to-noise ratio is about 5dB, that is, the IMSE has a deviation of about 1dB from the inverse BCRLB.
  • the present application solves the problem of optimal real-time estimation of a single sinusoidal carrier frequency, carrier initial phase, and carrier phase noise under the influence of time-varying phase noise, and can obtain higher estimation performance at a lower signal-to-noise ratio.
  • the estimators are all expressed as a weighted linear combination of received signal phases, which are easy to implement iteratively in practice.
  • estimators (1) and (8) can reach the Cramereau lower bound (CRLB) as the benchmark for ML estimation accuracy, and estimator (9) can reach Bayesian as the benchmark for MAP estimation accuracy.
  • CRLB Cramereau lower bound
  • BCRLB BCRLB
  • Estimators (1) and (8) are also suitable for non-phase noise (pure AWGN) environments.
  • this application considers the influence of phase noise, and has better estimation performance; the complexity of time domain estimation is low, and the computational complexity of each time is O(1), and the computational complexity after N iterations is O(N).
  • This application is applicable to communication, biomedical engineering, radar/sonar application and other signal processing fields, such as grid power quality monitoring, etc.; the method of this application does not involve complicated algorithms and is convenient for hardware implementation.
  • FIG. 9 is a schematic structural diagram of a carrier frequency and/or carrier initial phase estimation device 900 provided by an embodiment of the present application, which is applied to electronic equipment.
  • the estimation device 900 may include an acquisition unit 901 and a determination unit 902 , where the detailed description of each unit is as follows:
  • the acquisition unit 901 is configured to acquire the amplitude and phase of k+1 received signals, the k+1 received signals are k+1 signals respectively received at consecutive k+1 moments, and the k is greater than or an integer equal to zero;
  • a determining unit 902 configured to determine a first covariance matrix ⁇ ⁇ according to the amplitudes of the k+1 received signals, where the first vector ⁇ formed by the additive observed phase noise corresponding to the k+1 received signals Obey the following Gaussian distribution: ⁇ N(0, ⁇ ⁇ ); and determine the carrier frequency and/or carrier initial phase at the kth moment according to the second vector ⁇ r and the second covariance matrix ⁇ r , wherein the second Vector ⁇ r is a vector formed by the phases of the k+1 received signals, and the second covariance matrix ⁇ r is the sum of the first covariance matrix ⁇ ⁇ and the third covariance matrix ⁇ ⁇ , obtained by The third vector ⁇ formed by the first carrier phase noise of the random walk corresponding to the k+1 received signals obeys the following Gaussian distribution: ⁇ ⁇ N(0, ⁇ ⁇ ).
  • k N-1, where N is a positive integer, and the carrier frequency at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • N [0,1,...,N- 1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • Two vectors, 1 [1,1,...,1] T .
  • the acquiring unit 901 is further configured to: acquire the amplitude and phase of the received signal corresponding to the Nth moment, where the received signal corresponding to the Nth moment is the signal received at the Nth moment;
  • the carrier frequency at the Nth moment is determined by the following formula:
  • a (N-1) (N T ⁇ r -1 ⁇ r) (N-1)
  • B (N-1) (1 T ⁇ r -1 1) (N-1)
  • C (N -1) (1 T ⁇ r -1 N) (N-1)
  • D (N-1) (1 T ⁇ r -1 ⁇ r) (N-1)
  • E (N-1) ( N T ⁇ r -1 N) (N-1) ;
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ r(N) represents the phase of the received signal corresponding to the Nth moment
  • N 0 represents the SSB power spectral density of white noise
  • A represents the amplitude of the transmitted signal
  • Indicates the magnitude of the received signal corresponding to the Nth moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector, 1 [1,1,...,1] T
  • ⁇ r(1) represents the phase of the received signal corresponding to the first moment
  • represents the amplitude of the received signal corresponding to the first moment
  • k N-1
  • the N is a positive integer
  • the initial phase of the carrier at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector
  • 1 [1,1,...,1] T .
  • the acquiring unit 901 is further configured to: acquire the amplitude and phase of the received signal corresponding to the Nth moment, where the received signal corresponding to the Nth moment is the signal received at the Nth moment;
  • the carrier initial phase at the Nth moment is determined by the following formula:
  • a (N-1) (N T ⁇ r -1 ⁇ r) (N-1)
  • B (N-1) (1 T ⁇ r -1 1) (N-1)
  • C (N -1) (1 T ⁇ r -1 N) (N-1)
  • D (N-1) (1 T ⁇ r -1 ⁇ r) (N-1)
  • E (N-1) ( N T ⁇ r -1 N) (N-1) ;
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ r(N) represents the phase of the received signal corresponding to the Nth moment
  • N 0 represents the SSB power spectral density of white noise
  • A represents the amplitude of the transmitted signal
  • Indicates the magnitude of the received signal corresponding to the Nth moment
  • N [0,1,...,N-1] T
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector, 1 [1,1,...,1] T
  • ⁇ r(1) represents the phase of the received signal corresponding to the first moment
  • represents the amplitude of the received signal corresponding to the first moment
  • the determining unit 902 is further configured to: according to the second covariance matrix ⁇ r , the third covariance matrix ⁇ ⁇ , the second vector ⁇ r, the first The carrier frequency at time k and the initial phase of the carrier at the k time determine the second carrier phase noise at the k time.
  • k N-1
  • the second carrier phase noise at the N-1th moment is determined by the following formula:
  • the superscript (N-1) indicates the N-1th moment
  • ⁇ ⁇ represents the third covariance matrix at the N-1th moment
  • ⁇ r represents the second covariance matrix at the N-1th moment
  • ⁇ r represents the The second vector
  • N [0,1,...,N-1] T
  • 1 [1,1,...,1] T .
  • the second carrier phase noise at the Nth moment is determined by the following formula:
  • the superscript (N) represents the Nth time
  • the superscript (N-1) represents the N-1th time
  • the superscript (1) represents the first time
  • ⁇ ⁇ (N) represents the third covariance matrix at the Nth moment
  • ⁇ r (N) represents the second covariance matrix at the Nth moment
  • ⁇ r (N) represents the Nth moment
  • the second vector of , N (N) [0,1,...,N-1,N] T
  • 1 (N) [1,1,...,1] T
  • represents the magnitude of the received signal corresponding to
  • each unit may also refer to corresponding descriptions of the embodiments shown in FIG. 1 to FIG. 8 .
  • the estimating device 900 provided in the embodiment of the present application includes but is not limited to the above unit modules, for example, the estimating device 900 may also include a storage unit 903 , and the storage unit 903 may be used to store program codes and data of the estimating device 900 .
  • the storage unit 903 may be used to store program codes and data of the estimating device 900 .
  • FIG. 10 is a schematic structural diagram of an electronic device 1010 provided by an embodiment of the present application.
  • the electronic device 1010 includes a processor 1011, a memory 1012, and a communication interface 1013. They are connected to each other through the bus 1014 .
  • Memory 1012 includes, but is not limited to, random access memory (random access memory, RAM), read-only memory (read-only memory, ROM), erasable programmable read-only memory (erasable programmable read only memory, EPROM), or Portable read-only memory (compact disc read-only memory, CD-ROM), the memory 1012 is used for related computer programs and data.
  • the communication interface 1013 is used to receive and send data.
  • the processor 1011 may be one or more central processing units (central processing unit, CPU).
  • CPU central processing unit
  • the CPU may be a single-core CPU or a multi-core CPU.
  • the processor 1011 in the electronic device 1010 is used to read the computer program code stored in the above-mentioned memory 1012, and perform the following operations: obtain the amplitude and phase of k+1 received signals, and the k+1 received signals are continuous The k+1 signals received respectively at the k+1 moments of k+1, the k is an integer greater than or equal to zero; the first covariance matrix ⁇ ⁇ is determined according to the amplitude of the k+1 received signals, wherein, by The first vector ⁇ formed by the additive observation phase noise corresponding to the k+1 received signals obeys the following Gaussian distribution: ⁇ N(0, ⁇ ⁇ ); determined according to the second vector ⁇ r and the second covariance matrix ⁇ r The carrier frequency and/or the initial phase of the carrier at the kth moment, wherein the second vector ⁇ r is a vector composed of the phases of the k+1 received signals, and the second covariance matrix ⁇ r is the The sum of the first covariance matrix ⁇ ⁇ and the third
  • each operation may also refer to corresponding descriptions of the embodiments shown in FIG. 1 to FIG. 8 .
  • the beneficial effects brought by the electronic device 1010 described in FIG. 10 reference may be made to the description of the foregoing embodiments, and the description will not be repeated here.
  • the embodiment of the present application also provides a chip, the above-mentioned chip includes at least one processor, memory and interface circuit, the above-mentioned memory, the above-mentioned transceiver and the above-mentioned at least one processor are interconnected by lines, and the above-mentioned at least one memory stores a computer program; the above-mentioned When the computer program is executed by the above-mentioned processor, the method flow shown in Fig. 1 or Fig. 3 to Fig. 5 is realized.
  • the embodiment of the present application also provides a computer-readable storage medium.
  • the above-mentioned computer-readable storage medium stores a computer program. When it is run on an electronic device, the method flow shown in FIG. 1 or FIG. 3 to FIG. 5 is realized. .
  • An embodiment of the present application further provides a computer program product.
  • the computer program product is run on an electronic device, the method flow shown in FIG. 1 or FIG. 3 to FIG. 5 is realized.
  • processors mentioned in the embodiment of the present application may be a central processing unit (Central Processing Unit, CPU), and may also be other general-purpose processors, digital signal processors (Digital Signal Processor, DSP), application-specific integrated circuits ( Application Specific Integrated Circuit, ASIC), off-the-shelf programmable gate array (Field Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.
  • a general-purpose processor may be a microprocessor, or the processor may be any conventional processor, or the like.
  • the memory mentioned in the embodiments of the present application may be a volatile memory or a nonvolatile memory, or may include both volatile and nonvolatile memories.
  • the non-volatile memory can be read-only memory (Read-Only Memory, ROM), programmable read-only memory (Programmable ROM, PROM), erasable programmable read-only memory (Erasable PROM, EPROM), electrically programmable Erase Programmable Read-Only Memory (Electrically EPROM, EEPROM) or Flash.
  • the volatile memory can be Random Access Memory (RAM), which acts as external cache memory.
  • RAM Static Random Access Memory
  • SRAM Static Random Access Memory
  • DRAM Dynamic Random Access Memory
  • Synchronous Dynamic Random Access Memory Synchronous Dynamic Random Access Memory
  • SDRAM double data rate synchronous dynamic random access memory
  • Double Data Rate SDRAM, DDR SDRAM enhanced synchronous dynamic random access memory
  • Enhanced SDRAM, ESDRAM synchronous connection dynamic random access memory
  • Synchlink DRAM, SLDRAM Direct Memory Bus Random Access Memory
  • Direct Rambus RAM Direct Rambus RAM
  • the processor is a general-purpose processor, DSP, ASIC, FPGA or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components
  • the memory storage module
  • sequence numbers of the above-mentioned processes do not mean the order of execution, and the execution order of the processes should be determined by their functions and internal logic, and should not be used in the embodiments of the present application.
  • the implementation process constitutes any limitation.
  • the disclosed systems, devices and methods may be implemented in other ways.
  • the device embodiments described above are only illustrative.
  • the division of the above units is only a logical function division. In actual implementation, there may be other division methods.
  • multiple units or components can be combined or can be Integrate into another system, or some features may be ignored, or not implemented.
  • the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces, and the indirect coupling or communication connection of devices or units may be in electrical, mechanical or other forms.
  • the units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.
  • each functional unit in each embodiment of the present application may be integrated into one processing unit, each unit may exist separately physically, or two or more units may be integrated into one unit.
  • the technical solution of the present application is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including Several instructions are used to make a computer device (which may be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the methods shown in the various embodiments of the present application.
  • the aforementioned storage media include: U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), magnetic disk or optical disc and other media that can store program codes. .
  • the modules in the device of the embodiment of the present application can be combined, divided and deleted according to actual needs.

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Abstract

本申请提供了一种载波频率、初始相位、相位噪声的估计方法和相关设备，其中方法包括：获取k+1个接收信号的幅度和相位，k+1个接收信号为在连续的k+1个时刻分别接收到的k+1个信号，k为大于或等于零的整数；根据k+1个接收信号的幅度确定第一协方差矩阵；根据第二向量和第二协方差矩阵确定第k时刻的载波频率和/或载波初始相位，第二向量为由k+1个接收信号的相位构成的向量，第二协方差矩阵为第一协方差矩阵与第三协方差矩阵的和。采用本申请，能够降低载波频率和/或载波初始相位的估计的计算量。

Description

载波频率、初始相位、相位噪声的估计方法和相关设备 技术领域
本申请涉及通信技术领域，具体涉及一种载波频率、初始相位、相位噪声的估计方法和相关设备。
背景技术
在通信、生物医学工程、雷达/声纳应用以及其他信号处理领域，如电网功率质量监测等，载波频率和相位估计都是一个经典而重要的问题。所有这些应用都可以借助于单一正弦载波的信号模型进行算法设计和性能分析。基于离散时间信号模型，在仅考虑加性高斯噪声(AWGN)时，多种频率、相位估计算法被提出并得到验证。目前最常用的方法是将频率和相位建模为未知的非随机参数，并应用极大似然(ML)估计理论。一个众所周知的解决方案是基于傅里叶变换的频域方法，即通过一维搜索来找到周期图的峰值，但这种方案的计算复杂度很大，计算量很大。
发明内容
本申请实施例提供了一种载波频率、载波初始相位的估计方法及相关设备，能够降低载波频率和/或载波初始相位的估计的计算量。
第一方面，本申请实施例提供了一种载波频率和/或载波初始相位的估计方法，包括：获取k+1个接收信号的幅度和相位，所述k+1个接收信号为在连续的k+1个时刻分别接收到的k+1个信号，所述k为大于或等于零的整数；根据所述k+1个接收信号的幅度确定第一协方差矩阵∑ ∈，其中，由所述k+1个接收信号对应的加性观测相位噪声构成的第一向量∈服从以下高斯分布：∈～N(0,∑ ∈)；根据第二向量∠r和第二协方差矩阵∑ r确定第k时刻的载波频率和/或载波初始相位，其中，所述第二向量∠r为由所述k+1个接收信号的相位构成的向量，所述第二协方差矩阵∑ r为所述第一协方差矩阵∑ ∈与第三协方差矩阵∑ θ的和，由所述k+1个接收信号对应的随机游走的第一载波相位噪声构成的第三向量θ服从以下高斯分布：θ～N(0,∑ θ)。
在本申请实施例中，第一协方差矩阵∑ ∈是第一向量∈服从的高斯分布对应的协方差矩阵，第一向量∈是k+1个接收信号对应的加性观测相位噪声构成的向量，加性观测相位噪声等效于加性高斯噪声，第一协方差矩阵∑ ∈仅与接收信号的幅度有关；第二协方差矩阵∑ r为第一协方差矩阵∑ ∈与第三协方差矩阵∑ θ的和；第三协方差矩阵∑ θ是由k+1个接收信号对应的随机游走的第一载波相位噪声构成的第三向量θ服从的高斯分布对应的协方差矩阵，第三协方差矩阵∑ θ是已知的；因此，在获取到k+1个接收信号的幅度和相位后，可以根据k+1个接收信号的幅度确定第一协方差矩阵∑ ∈，进而与第三协方差矩阵∑ θ相加得到第二协方差矩阵∑ r，再根据由k+1个接收信号的相位构成的第二向量∠r和第二协方差矩阵∑ r即可确定出第k时刻的载波频率和/或载波初始相位，从而获取到k+1个接收信号的幅度和相位即可估计到载波频率和/或载波初始相位，降低了计算复杂度，也即降低了计算量。
在一种可能的实现方式中，k＝N-1，所述N为正整数，第N-1时刻的载波频率通过以下 公式确定：
Figure PCTCN2021099179-appb-000001
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000002
表示第N-1时刻的载波频率，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述方法还包括：获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；所述第N时刻的载波频率通过以下公式确定：
Figure PCTCN2021099179-appb-000003
其中：
Figure PCTCN2021099179-appb-000004
其中，A (N-1)＝(N T∑ r -1∠r) (N-1)，B (N-1)＝(1 T∑ r -11) (N-1)，C (N-1)＝(1 T∑ r -1N) (N-1)，D (N-1)＝(1 T∑ r -1∠r) (N-1)，E (N-1)＝(N T∑ r -1N) (N-1)；
其中：
Figure PCTCN2021099179-appb-000005
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000006
表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000007
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000008
的高斯随机变量序列。
在一种可能的实现方式中，k＝N-1，所述N为正整数，第N-1时刻的载波初始相位通过以下公式确定：
Figure PCTCN2021099179-appb-000009
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000010
表示第N-1时刻的载波初始相位，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述方法还包括：获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；所述第N时刻的载波初始相位通过以下公式确定：
Figure PCTCN2021099179-appb-000011
其中：
Figure PCTCN2021099179-appb-000012
其中，A (N-1)＝(N T∑ r -1∠r) (N-1)，B (N-1)＝(1 T∑ r -11) (N-1)，C (N-1)＝(1 T∑ r -1N) (N-1)，D (N-1)＝(1 T∑ r -1∠r) (N-1)，E (N-1)＝(N T∑ r -1N) (N-1)；
其中：
Figure PCTCN2021099179-appb-000013
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000014
表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000015
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000016
的高斯随机变量序列。
在一种可能的实现方式中，所述方法还包括：根据所述第二协方差矩阵∑ r、所述第三协方差矩阵∑ θ、所述第二向量∠r、所述第k时刻的载波频率和所述第k时刻的载波初始相位确定所述第k时刻的第二载波相位噪声。
在一种可能的实现方式中，k＝N-1，第N-1时刻的第二载波相位噪声通过以下公式确定：
Figure PCTCN2021099179-appb-000017
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000018
表示第N-1时刻的第二载波相位噪声，
Figure PCTCN2021099179-appb-000019
表示第N-1时刻的载波频率，
Figure PCTCN2021099179-appb-000020
表示第N-1时刻的载波初始相位，∑ θ表示第N-1时刻的第三协方差矩阵，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，N＝[0,1,…,N-1] T，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述第N时刻的第二载波相位噪声通过以下公式确定：
Figure PCTCN2021099179-appb-000021
其中：
Figure PCTCN2021099179-appb-000022
其中：
Figure PCTCN2021099179-appb-000023
其中：
Figure PCTCN2021099179-appb-000024
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000025
表示第N时刻的第二载波相位噪声，
Figure PCTCN2021099179-appb-000026
表示第N时刻的载波频率，
Figure PCTCN2021099179-appb-000027
表示第N时刻的载波初始相位，∑ θ (N)表示第N时刻的第三协方差矩阵，∑ r (N)表示第N时刻的第二协方差矩阵，∠r (N)表示第N时刻的第二向量，N (N)＝[0,1,…,N-1,N] T，1 (N)＝[1,1,…,1] T，∑ r (N-1)表示第N-1时刻的第二协方差矩阵，N (N-1)＝[0,1,…,N-1] T，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(0)|表示第0时刻对应的接收信号的幅度，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000028
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000029
的高斯随机变量序列。
第二方面，本申请实施例提供了一种载波频率和/或载波初始相位的估计装置，包括：获取单元，用于获取k+1个接收信号的幅度和相位，所述k+1个接收信号为在连续的k+1个时刻分别接收到的k+1个信号，所述k为大于或等于零的整数；确定单元，用于根据所述k+1个接收信号的幅度确定第一协方差矩阵∑ ∈，其中，由所述k+1个接收信号对应的加性观测相位噪声构成的第一向量∈服从以下高斯分布：∈～N(0,∑ ∈)；以及根据第二向量∠r和第二协方差矩阵∑ r确定第k时刻的载波频率和/或载波初始相位，其中，所述第二向量∠r为由所述k+1个接收信号的相位构成的向量，所述第二协方差矩阵∑ r为所述第一协方差矩阵∑ ∈与第三协方差矩阵∑ θ的和，由所述k+1个接收信号对应的随机游走的第一载波相位噪声构成的第三向量θ服从以下高斯分布：θ～N(0,∑ θ)。
在一种可能的实现方式中，k＝N-1，所述N为正整数，第N-1时刻的载波频率通过以下公式确定：
Figure PCTCN2021099179-appb-000030
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000031
表示第N-1时刻的载波频率，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述获取单元还用于：获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；所述第N时刻的载波频率通过以下公式确定：
Figure PCTCN2021099179-appb-000032
其中：
Figure PCTCN2021099179-appb-000033
其中，A (N-1)＝(N T∑ r -1∠r) (N-1)，B (N-1)＝(1 T∑ r -11) (N-1)，C (N-1)＝(1 T∑ r -1N) (N-1)，D (N-1)＝(1 T∑ r -1∠r) (N-1)，E (N-1)＝(N T∑ r -1N) (N-1)；
其中：
Figure PCTCN2021099179-appb-000034
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000035
表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000036
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000037
的高斯随机变量序列。
在一种可能的实现方式中，k＝N-1，所述N为正整数，第N-1时刻的载波初始相位通过以下公式确定：
Figure PCTCN2021099179-appb-000038
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000039
表示第N-1时刻的载波初始相位，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述获取单元还用于：获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；所述第N时刻的载波初始相位通过以下公式确定：
Figure PCTCN2021099179-appb-000040
其中：
Figure PCTCN2021099179-appb-000041
其中，A (N-1)＝(N T∑ r -1∠r) (N-1)，B (N-1)＝(1 T∑ r -11) (N-1)，C (N-1)＝(1 T∑ r -1N) (N-1)，D (N-1)＝(1 T∑ r -1∠r) (N-1)，E (N-1)＝(N T∑ r -1N) (N-1)；
其中：
Figure PCTCN2021099179-appb-000042
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000043
表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000044
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000045
的高斯随机变量序列。
在一种可能的实现方式中，所述确定单元还用于：根据所述第二协方差矩阵∑ r、所述第三协方差矩阵∑ θ、所述第二向量∠r、所述第k时刻的载波频率和所述第k时刻的载波初始相位确定所述第k时刻的第二载波相位噪声。
在一种可能的实现方式中，k＝N-1，第N-1时刻的第二载波相位噪声通过以下公式确定：
Figure PCTCN2021099179-appb-000046
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000047
表示第N-1时刻的第二载波相位噪声，
Figure PCTCN2021099179-appb-000048
表 示第N-1时刻的载波频率，
Figure PCTCN2021099179-appb-000049
表示第N-1时刻的载波初始相位，∑ θ表示第N-1时刻的第三协方差矩阵，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，N＝[0,1,…,N-1] T，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述第N时刻的第二载波相位噪声通过以下公式确定：
Figure PCTCN2021099179-appb-000050
其中：
Figure PCTCN2021099179-appb-000051
其中：
Figure PCTCN2021099179-appb-000052
其中：
Figure PCTCN2021099179-appb-000053
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000054
表示第N时刻的第二载波相位噪声，
Figure PCTCN2021099179-appb-000055
表示第N时刻的载波频率，
Figure PCTCN2021099179-appb-000056
表示第N时刻的载波初始相位，∑ θ (N)表示第N时刻的第三协方差矩阵，∑ r (N)表示第N时刻的第二协方差矩阵，∠r (N)表示第N时刻的第二向量，N (N)＝[0,1,…,N-1,N] T，1 (N)＝[1,1,…,1] T，∑ r (N-1)表示第N-1时刻的第二协方差矩阵，N (N-1)＝[0,1,…,N-1] T，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(0)|表示第0时刻对应的接收信号的幅度，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000057
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000058
的高斯随机变量序列。
本申请实施例第三方面提供了一种电子设备，包括处理器、存储器、通信接口，以及一个或多个程序，上述一个或多个程序被存储在上述存储器中，并且被配置由上述处理器执行，上述程序包括用于执行如上述第一方面中任一项所述的方法中的步骤的指令。
本申请实施例第四方面提供了一种芯片，其特征在于，包括：处理器，用于从存储器中调用并运行计算机程序，使得安装有上述芯片的设备执行如上述第一方面中任一项上述的方法。
本申请实施例第五方面提供了一种计算机可读存储介质，其存储用于电子数据交换的计算机程序，其中，上述计算机程序使得计算机执行如上述第一方面中任一项所述的方法。
本申请实施例第六方面提供了一种计算机程序产品，上述计算机程序产品使得计算机执行如上述第一方面中任一项所述的方法。
本申请的这些方面或其他方面在以下实施例的描述中会更加简明易懂。
附图说明
为了更清楚地说明本申请实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本申请的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1是本申请实施例提供的一种载波频率和/或载波初始相位的估计方法的流程示意图；
图2是本申请实施例提供的一几何向量的示意图；
图3是本申请实施例提供的一种载波相位噪声的估计方法的流程示意图；
图4是本申请实施例提供的一种载波频率和载波初始相位的迭代估计的方法流程示意图；
图5是本申请实施例提供的一种载波相位噪声的迭代估计的方法流程示意图；
图6是本申请实施例提供的一种载波频率和载波初始相位的估计的仿真性能图；
图7是本申请实施例提供的一种载波相位噪声的估计的仿真性能图；
图8是本申请实施例提供的另一种载波相位噪声的估计的仿真性能图；
图9是本申请实施例提供的一种载波频率和/或载波初始相位的估计装置的结构示意图；
图10是本申请实施例提供的一种电子设备的结构示意图。
具体实施方式
为了使本技术领域的人员更好地理解本申请方案，下面将结合本申请实施例中的附图，对本申请实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本申请一部分实施例，而不是全部的实施例。基于本申请中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例，都属于本申请保护的范围。
本申请的说明书和权利要求书及上述附图中的术语“第一”、“第二”等是用于区别不同对象，而不是用于描述特定顺序。此外，术语“包括”和“具有”以及它们任何变形，意图在于覆盖不排他的包含。例如包含了一系列步骤或单元的过程、方法、系统、产品或设备没有限定于已列出的步骤或单元，而是可选地还包括没有列出的步骤或单元，或可选地还包括对于这些过程、方法、产品或设备固有的其他步骤或单元。
在本文中提及“实施例”意味着，结合实施例描述的特定特征、结构或特性可以包含在本申请的至少一个实施例中。在说明书中的各个位置出现该短语并不一定均是指相同的实施例，也不是与其它实施例互斥的独立的或备选的实施例。本领域技术人员显式地和隐式地理解的是，本文所描述的实施例可以与其它实施例相结合。
如前所述，现有方案采用频域估计方法，而现有的频率相位联合估计技术仅考虑脉冲噪声、高斯噪声，并没有考虑振荡器相位噪声的不利影响。本申请采用时域估计方法，将接收信号的相位作为观测数据样本输入估计器，利用极大似然估计理论来估计载波频率和相位。
众所周知，所有的天然和人造振荡器(无论是光学的、电子的、声学的、原子的或任何其他的)表现出相位和频率的不稳定性，统称为相位噪声。振荡器相位噪声是现代通信、雷达、光谱和计量系统的主要缺陷之一。此外，为了获取更高的频谱效率，超高速通信如今正在向更高的频段发展。使用的载波频率越高，所遇到的载波相位噪声就越大，系统损耗就越严重。例如，在实时测距和成像的雷达应用中，冗余相位噪声会引起时变偏移、杂散旁瓣、脉冲响应加宽以及雷达信号的低频相位调制，严重降低了雷达的检测和跟踪性能。因此，相位噪声是在实际应用中进行参数估计和性能分析时必须考虑的一个不可避免的因素。
考虑到无线、光学和雷达应用中实际振荡器的抖动行为，相位噪声通常是时变的。然而，为了简化理论分析，大多数算法都是基于准静态相位的假设设计的，没有考虑载波相位的时变特性，这导致估计性能显著下降。因此，针对时变相位噪声下的载波频率和相位估计问题，还没有系统的方法来实现频率和相位的联合估计，也没有确切的方法来估计这种情况下的相位噪声。
振荡器相位噪声是损害现代通信、雷达、光谱和计量等系统性能的主要因素之一。离散维纳相位噪声模型普遍适用于这些物理应用中的载波相位噪声，其中包括经常使用的半导体激光振荡器和无线射频振荡器。因此，本申请将解决在AWGN和维纳载波相位噪声的共同作用下，如何联合估计单一正弦信号的角度参数的问题。角度参数具体包含载波频率、载波相位和相位噪声三部分。我们将设计基于ML算法的未知载波频率和初始载波相位的联合时域估计方法，以及同时基于最大后验概率(MAP)算法的相位噪声的时域估计方法。并进一步给出具有低复杂度、逐样本迭代处理结构的估计方案，以确保在实际应用中可以实时迭代处理。
请参阅图1，图1是本申请实施例提供的一种载波频率和/或载波初始相位的估计方法的流程示意图，所述方法应用于电子设备，所述方法包括但不限于如下步骤：
步骤101、获取k+1个接收信号的幅度和相位，所述k+1个接收信号为在连续的k+1个时刻分别接收到的k+1个信号，所述k为大于或等于零的整数。
其中，由于k＝0，1，2，3，......；故有第0时刻对应第1个接收信号，第1时刻对应第2个接收信号，第2时刻对应第3个接收信号，以此类推。
步骤102、根据所述k+1个接收信号的幅度确定第一协方差矩阵∑ ∈，其中，由所述k+1个接收信号对应的加性观测相位噪声构成的第一向量∈服从以下高斯分布：∈～N(0,∑ ∈)。
步骤103、根据第二向量∠r和第二协方差矩阵∑ r确定第k时刻的载波频率和/或载波初始相位，其中，所述第二向量∠r为由所述k+1个接收信号的相位构成的向量，所述第二协方差矩阵∑ r为所述第一协方差矩阵∑ ∈与第三协方差矩阵∑ θ的和，由所述k+1个接收信号对 应的随机游走的第一载波相位噪声构成的第三向量θ服从以下高斯分布：θ～N(0,∑ θ)。
在本申请实施例中，第一协方差矩阵∑ ∈是第一向量∈服从的高斯分布对应的协方差矩阵，第一向量∈是k+1个接收信号对应的加性观测相位噪声构成的向量，加性观测相位噪声等效于加性高斯噪声，第一协方差矩阵∑ ∈仅与接收信号的幅度有关；第二协方差矩阵∑ r为第一协方差矩阵∑ ∈与第三协方差矩阵∑ θ的和；第三协方差矩阵∑ θ是由k+1个接收信号对应的随机游走的第一载波相位噪声构成的第三向量θ服从的高斯分布对应的协方差矩阵，第三协方差矩阵∑ θ是已知的；因此，在获取到k+1个接收信号的幅度和相位后，可以根据k+1个接收信号的幅度确定第一协方差矩阵∑ ∈，进而与第三协方差矩阵∑ θ相加得到第二协方差矩阵∑ r，再根据由k+1个接收信号的相位构成的第二向量∠r和第二协方差矩阵∑ r即可确定出第k时刻的载波频率和/或载波初始相位，从而获取到k+1个接收信号的幅度和相位即可估计到载波频率和/或载波初始相位，降低了计算复杂度，也即降低了计算量。
在一种可能的实现方式中，k＝N-1，所述N为正整数，第N-1时刻的载波频率通过以下公式确定：
Figure PCTCN2021099179-appb-000059
在公式(1)中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000060
表示第N-1时刻的载波频率，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
作为一种示例，公式(1)可以通过以下方式得到：
在AWGN和维纳载波相位噪声的共同作用下，在第k时刻的单一正弦的接收信号时域表达式通常如公式(2)所示：
Figure PCTCN2021099179-appb-000061
在公式(2)中，A是已知的发送信号幅度；
Figure PCTCN2021099179-appb-000062
ω是未知的载波频率；
Figure PCTCN2021099179-appb-000063
是未知的载波初始相位；所有的天然和人造振荡器(不论是光学、电子、声学、原子或其他)显示相位和频率的不稳定性统称为相位噪声，即θ(k)，θ(k)是在[-π,π)区间内随机游走的载波相位噪声，服从维纳过程：θ(k)＝θ(k-1)+Δθ(k)，其中，θ(0)＝0，{Δθ(k)}是一个独立、同分布、零均值、方差为
Figure PCTCN2021099179-appb-000064
的实高斯随机变量序列；k为大于或者等于零的整数，例如，k＝0，1，2，3，......；{n(k)}则是一个离散时间、圆对称、零均值、协方差函数为E[n(k)n *(k-l)]＝N 0δ(l)的复高斯随机变量序列。
进一步地，可以将接收信号改写为幅度-相位的极坐标形式，如公式(3)所示：
Figure PCTCN2021099179-appb-000065
在公式(3)中，|r(k)|和∠r(k)分别是接收信号的幅度和相位；∈(k)是等效于AWGN的加性观测相位噪声，已证明在高信噪比下服从均值为0，方差为
Figure PCTCN2021099179-appb-000066
的高斯分布，即
Figure PCTCN2021099179-appb-000067
从图2(接收信号r的几何向量表示)中可以看出，∈(k)就是由AWGN所引起的相位角度的改变。
其中，可以将k＝0至N-1对应时间接收到的信号的相位用矢量形式表示，也即将第0时刻至第N-1时刻对应的接收信号的相位用矢量形式表示，如公式(4)所示：
Figure PCTCN2021099179-appb-000068
在公式(4)中，第二向量∠r＝[∠r(0),∠r(1),…,∠r(N-1)] T，N＝[0,1,…,N-1] T，1＝[1,1,…,1] T，θ＝[θ(0),θ(1),…,θ(N-1)] T，第一向量∈＝[∈(0),∈(1),…,∈(N-1)] T。可以看出，以上向量均是N维列向量，且上标T表示向量的转置。θ和∈互相独立，且θ～N(0,∑ θ)，∈～N(0,∑ ∈)，其中，第三协方差矩阵∑ θ和第二协方差矩阵∑ ∈分别是：
Figure PCTCN2021099179-appb-000069
和
Figure PCTCN2021099179-appb-000070
最优估计算法推导主要是基于表达式(4)和一个理论事实：利用将接收振幅信息融入到加性观测相位噪声的接收信号相位∠r(k)的ML/MAP估计，等价于利用接收信号|r(k)|的ML/MAP估计；该方法可称之为基于相位的时域估计方法。
下面本申请将利用所有观测数据|r(k)|和∠r(k)(k＝0，1，2，3，......，N-1)对ω和
Figure PCTCN2021099179-appb-000071
进行联合ML时域估计，并对θ进行MAP时域估计；其中，相应的估计值可以通过最大化联合概率密度函数
Figure PCTCN2021099179-appb-000072
来获得，如公式(7)所示：
Figure PCTCN2021099179-appb-000073
在公式(7)中，
Figure PCTCN2021099179-appb-000074
和
Figure PCTCN2021099179-appb-000075
分别代表k＝N-1时刻的载波频率和载波初始相位的ML估计值，
Figure PCTCN2021099179-appb-000076
代表在k＝N-1时刻在载波相位噪声的MAP估计值。通过公式(4)可以很容易得出，在给定ω和
Figure PCTCN2021099179-appb-000077
条件下，向量∠r服从联合高斯分布，也即
Figure PCTCN2021099179-appb-000078
其中，协方差矩阵∑ r是∑ θ和∑ ∈的和。本申请通过解析公式(7)即可得出公式(1)。
在一种可能的实现方式中，k＝N-1，所述N为正整数，第N-1时刻的载波初始相位通过以下公式确定：
Figure PCTCN2021099179-appb-000079
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000080
表示第N-1时刻的载波初始相位，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
其中，本申请通过解析公式(7)即可得出公式(8)。
在一种可能的实现方式中，所述方法还包括：根据所述第二协方差矩阵∑ r、所述第三协方差矩阵∑ θ、所述第二向量∠r、所述第k时刻的载波频率和所述第k时刻的载波初始相位确定所述第k时刻的第二载波相位噪声。
在一种可能的实现方式中，k＝N-1，第N-1时刻的第二载波相位噪声通过以下公式确定：
Figure PCTCN2021099179-appb-000081
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000082
表示第N-1时刻的第二载波相位噪声，
Figure PCTCN2021099179-appb-000083
表示第N-1时刻的载波频率，
Figure PCTCN2021099179-appb-000084
表示第N-1时刻的载波初始相位，∑ θ表示第N-1时刻的第三协方差矩阵，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，N＝[0,1,…,N-1] T，1＝[1,1,…,1] T。
其中，本申请通过解析公式(7)即可得出公式(9)。
应理解，通过公式(1)和(8)分别明确给出了载波频率和载波初始相位的联合ML估计值，将其代入(9)中可得到确定的载波相位噪声MAP估计值，也即得到
Figure PCTCN2021099179-appb-000085
此外，在一示例中，对于无载波相位噪声的情况，也即
Figure PCTCN2021099179-appb-000086
∑ r＝∑ ∈，ML估计器，也即公式(1)可简化为公式(10)：
Figure PCTCN2021099179-appb-000087
公式(8)可简化为公式(11)：
Figure PCTCN2021099179-appb-000088
其中，公式(10)和(11)中的|r(k)|和∠r(k)分别为接收信号的幅度和相位。
本申请实施例，载波频率、载波初始相位以及第二载波相位噪声的估计值均可以随着样本数量N的增加迭代计算得到。下面，本申请示例性的给出一个简单的迭代实现方案。
首先，在k＝N-1时刻，令A (N-1)＝(N T∑ r -1∠r) (N-1)，B (N-1)＝(1 T∑ r -11) (N-1)，C (N-1)＝(1 T∑ r -1N) (N-1)，D (N-1)＝(1 T∑ r -1∠r) (N-1)，E (N-1)＝(N T∑ r -1N) (N-1)，则公式(1)简化成公式(12)；其中，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T：
Figure PCTCN2021099179-appb-000089
同理，公式(8)简化成公式(13)：
Figure PCTCN2021099179-appb-000090
如此，随着N的增加，我们可以分别更新A (N-1)，B (N-1)，C (N-1)，D (N-1)和E (N-1)，继而实现估计值
Figure PCTCN2021099179-appb-000091
和
Figure PCTCN2021099179-appb-000092
的迭代计算。也即，在k＝N时刻，A (N)、B (N)、C (N)、D (N)和E (N)可以用A (N-1)、B (N-1)、C (N-1)、D (N-1)和E (N-1)迭代计算得到；将A (N)、B (N)、C (N)、D (N)和E (N)替换A (N-1)、B (N-1)、C (N-1)、D (N-1)和E (N-1)，分别代入公式(12)和公式(13)即可得到第N时刻的载波频率
Figure PCTCN2021099179-appb-000093
和载波初始相位
Figure PCTCN2021099179-appb-000094
因此，本申请当每计算一次载波频率或载波初始相位后，例如在第N-1时刻计算完一次载波频率或载波初始相位，仅需要存储对应的A (N-1)，B (N-1)，C (N-1)，D (N-1)和E (N-1)，在第N时刻获取到第N时刻对应的接收信号时，仅需要通过存储的A (N-1)，B (N-1)，C (N-1)，D (N-1)和E (N-1)计算得到A (N)、B (N)、C (N)、D (N)和E (N)，即可快速 计算得到第N时刻的载波频率或载波初始相位。
在一种可能的实现方式中，所述方法还包括：获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；所述第N时刻的载波频率通过以下公式确定：
Figure PCTCN2021099179-appb-000095
其中，公式(14)中的A (N)、B (N)、C (N)、D (N)和E (N)与A (N-1)、B (N-1)、C (N-1)、D (N-1)和E (N-1)之间的迭代关系如公式(15)所示：
Figure PCTCN2021099179-appb-000096
其中，在k＝1时刻，A (1)、B (1)、C (1)、D (1)和E (1)可以通过公式(16)直接推导得到：
Figure PCTCN2021099179-appb-000097
公式(14)或公式(15)或公式(16)中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000098
表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000099
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000100
的高斯随机变量序列。
应理解，该迭代过程充分利用了k＝N时刻新接收到的样本{|r(N)|，∠r(N)}，实现了实时性。上述迭代估计过程同样适用于无载波相位噪声的情况，即
Figure PCTCN2021099179-appb-000101
在一种可能的实现方式中，所述方法还包括：获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；所述第N时刻的载波初始相位通过以下公式确定：
Figure PCTCN2021099179-appb-000102
同理，在公式(17)中的A (N)、B (N)、C (N)、D (N)和E (N)与 A (N-1）、B (N-1)、C (N-1)、D (N-1)和E (N-1)之间的迭代关系如公式(15)所示；此外，在k＝1时刻，A (1)、B (1)、C (1)、D (1)和E (1)可以通过公式(16)直接推导得到。
应理解，本申请通过上述公式(14)和公式(17)计算得到第N时刻的
Figure PCTCN2021099179-appb-000103
和
Figure PCTCN2021099179-appb-000104
后，可以进一步计算得到第N时刻的第二载波相位噪声的估计值
Figure PCTCN2021099179-appb-000105
在一种可能的实现方式中，所述第N时刻的第二载波相位噪声通过以下公式确定：
Figure PCTCN2021099179-appb-000106
其中，公式(18)中的(∑ r -1) (N)与(∑ r -1) (N-1)的迭代关系如公式(19)所示：
Figure PCTCN2021099179-appb-000107
在公式(19)中，
Figure PCTCN2021099179-appb-000108
其中，在k＝1时刻，(∑ r -1) (1)可通过公式(20)计算得到：
Figure PCTCN2021099179-appb-000109
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000110
表示第N时刻的第二载波相位噪声，
Figure PCTCN2021099179-appb-000111
表示第N时刻的载波频率，
Figure PCTCN2021099179-appb-000112
表示第N时刻的载波初始相位，∑ θ (N)表示第N时刻的第三协方差矩阵，∑ r (N)表示第N时刻的第二协方差矩阵，∠r (N)表示第N时刻的第二向量，N (N)＝[0,1,…,N-1,N] T，1 (N)＝[1,1,…,1] T，∑ r (N-1)表示第N-1时刻的第二协方差矩阵，N (N-1)＝[0,1,…,N-1] T，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(0)|表示第0时刻对应的接收信号的幅度，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000113
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000114
的高斯随机变量序列。
如此，在计算第二载波相位噪声时，(∑ r -1) (N)可由(∑ r -1) (N-1)递归得到，避免了复杂的矩阵求逆运算，从而减少了计算量。
需要说明的是，在本申请中，矩阵有上标(N)表示对应第N时刻的N+1维矩阵，矩阵有上标(N-1)表示第N-1时刻的N维矩阵；同理，向量有上标(N)表示对应第N时刻的N+1维向量，向量有上标(N-1)表示第N-1时刻的N维向量。
请参阅图3，图3是本申请实施例提供的一种载波相位噪声的估计方法的流程示意图，该方法应用于电子设备，具体应用于ML/MAP估计器，在相位噪声环境中，ML/MAP估计器的具体实现包括但不限于如下步骤：
步骤301、获取接收信号r(k)，k＝0，1，2，3，......，N-1；
步骤302、提取接收信号的幅度|r(k)|和相位∠r(k)；
步骤303、已知系统参数A、N 0和
Figure PCTCN2021099179-appb-000115
的条件下，采用公式(1)计算k＝N-1时刻的载波频 率估计值；
步骤304、已知系统参数A、N 0和
Figure PCTCN2021099179-appb-000116
的条件下，采用公式(8)计算k＝N-1时刻的载波初始相位估计值；
步骤305、基于步骤303得到的载波频率估计值和步骤304得到的载波初始相位估计值，采用公式(9)计算得到k＝N-1时刻的载波相位噪声估计值。
请参阅图4，图4是本申请实施例提供的一种载波频率和载波初始相位的迭代估计方法的流程示意图，该方法应用于电子设备，具体应用于ML/MAP估计器，ML/MAP估计器采用迭代处理，包括但不限于如下步骤：
步骤401、获取接收信号r(k)，k＝0，1；
步骤402、提取接收信号的幅度和相位信息{|r(k)|,∠r(k)}；
步骤403、采用公式(16)计算A (1)、B (1)、C (1)、D (1)和E (1)；
步骤404、获取接收信号r(k)，并提取接收信号的幅度|r(k)|和相位∠r(k)，k＝2，3，......；
步骤405、获取存储的A (k-1)、B (k-1)、C (k-1)、D (k-1)和E (k-1)；
步骤406、采用公式(15)计算A (k)、B (k)、C (k)、D (k)和E (k)；
步骤407、采用公式(14)计算第k时刻的载波频率；
步骤408、采用公式(17)计算第k时刻的载波初始相位。
请参阅图5，图5是本申请实施例提供的一种载波相位噪声的迭代估计方法的流程示意图，该方法应用于电子设备，具体应用于ML/MAP估计器，ML/MAP估计器采用迭代处理，包括但不限于如下步骤：
步骤501、获取接收信号r(k)，k＝0，1，2，3，......；
步骤502、提取接收信号的幅度和相位信息{|r(k)|,∠r(k)}；
步骤503、k＝1时刻，采用公式(20)计算∑ r -1；
步骤504、k-1时刻，采用公式(19)计算∑ r -1；
步骤505、获取k时刻的载波频率估计值和载波初始相位估计值；
步骤506、采用公式(18)计算k时刻的载波相位噪声估计值。
示例性的，若给定载波频率0.05和初始相位0.25π，在不同相位噪声环境下，用蒙特卡洛仿真计算ML/MAP估计的逆均方误差(IMSE)，验证估计精度。以载波频率估计为例，即是计算：
Figure PCTCN2021099179-appb-000117
其中，在公式(21)中，q＝10 5以保证仿真精度。
图6为本申请实施例提供一种在不同信噪比下ML估计载波频率和载波初始相位的IMSE和逆克拉美罗下限(inverseCRLB，ICRLB)的仿真性能，其中，图6所示的ML估 计ω和
Figure PCTCN2021099179-appb-000118
的仿真性能中，N＝16；考虑了
Figure PCTCN2021099179-appb-000119
和10 -2rad 2两种情况，可以看出在约0dB信噪比时，估计器(1)和(8)，也即公式(1)和(8)的均方误差(MSE)性能就逼近克拉美罗下限(CRLB)，有效验证了ML时域估计方法的高精度。
图7和图8为本申请实施例提供一种在不同信噪比下MAP估计载波相位噪声{θ(k),k＝1:15}的IMSE和逆贝叶斯-克拉美罗下限(BCRLB)的仿真性能，其中，N＝16，图7考虑了
Figure PCTCN2021099179-appb-000120
的情况，图8考虑了
Figure PCTCN2021099179-appb-000121
的情况；可以看出，在低相位噪声
Figure PCTCN2021099179-appb-000122
下，在约0dB信噪比时，估计器(9)，也即公式(9)的MSE性能就可达到BCRLB；而在
Figure PCTCN2021099179-appb-000123
条件下，在约5dB信噪比时才能达到可接受的估计精度，即IMSE与逆BCRLB有约1dB的偏差。
本申请解决了在时变相位噪声影响下，单一正弦的载波频率和载波初始相位以及载波相位噪声的最优的实时估计问题，可以在较低的信噪比下获得较高的估计性能。估计器都表示为接收信号相位的加权线性组合，在实践中易于迭代实现。
在约0dB信噪比情况下，估计器(1)和(8)可以达到作为ML估计精度基准的克拉美罗下限(CRLB)，估计器(9)可以达到作为MAP估计精度基准的贝叶斯-克拉美罗下限(BCRLB)。估计器(1)和(8)同样适用于非相位噪声(纯AWGN)环境。
本申请与其他现有估计方法相比考虑了相位噪声的影响，具有更好的估计性能；时域估计复杂度低，每一次计算复杂度为O(1)，经过N次迭代的计算复杂度为O(N)。
本申请适用于通信、生物医学工程、雷达/声纳应用以及其他信号处理领域，如电网功率质量监测等；本申请方法不涉及复杂算法，便于硬件实现。
上述详细阐述了本申请实施例的方法，下面提供了本申请实施例的装置。
请参见图9，图9是本申请实施例提供的一种载波频率和/或载波初始相位的估计装置900的结构示意图，应用于电子设备，该估计装置900可以包括获取单元901和确定单元902，其中，各个单元的详细描述如下：
获取单元901，用于获取k+1个接收信号的幅度和相位，所述k+1个接收信号为在连续的k+1个时刻分别接收到的k+1个信号，所述k为大于或等于零的整数；
确定单元902，用于根据所述k+1个接收信号的幅度确定第一协方差矩阵∑ ∈，其中，由所述k+1个接收信号对应的加性观测相位噪声构成的第一向量∈服从以下高斯分布：∈～N(0,∑ ∈)；以及根据第二向量∠r和第二协方差矩阵∑ r确定第k时刻的载波频率和/或载波初始相位，其中，所述第二向量∠r为由所述k+1个接收信号的相位构成的向量，所述第二协方差矩阵∑ r为所述第一协方差矩阵∑ ∈与第三协方差矩阵∑ θ的和，由所述k+1个接收信号对应的随机游走的第一载波相位噪声构成的第三向量θ服从以下高斯分布：θ～N(0,∑ θ)。
在一种可能的实现方式中，k＝N-1，所述N为正整数，第N-1时刻的载波频率通过以下公式确定：
Figure PCTCN2021099179-appb-000124
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000125
表示第N-1时刻的载波频率，N＝[0,1,…,N- 1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述获取单元901还用于：获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；所述第N时刻的载波频率通过以下公式确定：
Figure PCTCN2021099179-appb-000126
其中：
Figure PCTCN2021099179-appb-000127
其中，A (N-1)＝(N T∑ r -1∠r) (N-1)，B (N-1)＝(1 T∑ r -11) (N-1)，C (N-1)＝(1 T∑ r -1N) (N-1)，D (N-1)＝(1 T∑ r -1∠r) (N-1)，E (N-1)＝(N T∑ r -1N) (N-1)；
其中：
Figure PCTCN2021099179-appb-000128
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000129
表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000130
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000131
的高斯随机变量序列。
在一种可能的实现方式中，k＝N-1，所述N为正整数，第N-1时刻的载波初始相位通过以下公式确定：
Figure PCTCN2021099179-appb-000132
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000133
表示第N-1时刻的载波初始相位，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述获取单元901还用于：获取第N时刻对应的接收信号的 幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；所述第N时刻的载波初始相位通过以下公式确定：
Figure PCTCN2021099179-appb-000134
其中：
Figure PCTCN2021099179-appb-000135
其中，A (N-1)＝(N T∑ r -1∠r) (N-1)，B (N-1)＝(1 T∑ r -11) (N-1)，C (N-1)＝(1 T∑ r -1N) (N-1)，D (N-1)＝(1 T∑ r -1∠r) (N-1)，E (N-1)＝(N T∑ r -1N) (N-1)；
其中：
Figure PCTCN2021099179-appb-000136
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000137
表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，N＝[0,1,…,N-1] T，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000138
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000139
的高斯随机变量序列。
在一种可能的实现方式中，所述确定单元902还用于：根据所述第二协方差矩阵∑ r、所述第三协方差矩阵∑ θ、所述第二向量∠r、所述第k时刻的载波频率和所述第k时刻的载波初始相位确定所述第k时刻的第二载波相位噪声。
在一种可能的实现方式中，k＝N-1，第N-1时刻的第二载波相位噪声通过以下公式确定：
Figure PCTCN2021099179-appb-000140
其中，上标(N-1)表示第N-1时刻，
Figure PCTCN2021099179-appb-000141
表示第N-1时刻的第二载波相位噪声，
Figure PCTCN2021099179-appb-000142
表示第N-1时刻的载波频率，
Figure PCTCN2021099179-appb-000143
表示第N-1时刻的载波初始相位，∑ θ表示第N-1时刻的第三协方差矩阵，∑ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，N＝[0,1,…,N-1] T，1＝[1,1,…,1] T。
在一种可能的实现方式中，所述第N时刻的第二载波相位噪声通过以下公式确定：
Figure PCTCN2021099179-appb-000144
其中：
Figure PCTCN2021099179-appb-000145
其中：
Figure PCTCN2021099179-appb-000146
其中：
Figure PCTCN2021099179-appb-000147
其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
Figure PCTCN2021099179-appb-000148
表示第N时刻的第二载波相位噪声，
Figure PCTCN2021099179-appb-000149
表示第N时刻的载波频率，
Figure PCTCN2021099179-appb-000150
表示第N时刻的载波初始相位，∑ θ (N)表示第N时刻的第三协方差矩阵，∑ r (N)表示第N时刻的第二协方差矩阵，∠r (N)表示第N时刻的第二向量，N (N)＝[0,1,…,N-1,N] T，1 (N)＝[1,1,…,1] T，∑ r (N-1)表示第N-1时刻的第二协方差矩阵，N (N-1)＝[0,1,…,N-1] T，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(0)|表示第0时刻对应的接收信号的幅度，|r(1)|表示第1时刻对应的接收信号的幅度；
Figure PCTCN2021099179-appb-000151
表示一方差，第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
Figure PCTCN2021099179-appb-000152
的高斯随机变量序列。
需要说明的是，各个单元的实现还可以对应参照图1至图8所示的实施例的相应描述。当然，本申请实施例提供的估计装置900包括但不限于上述单元模块，例如：该估计装置900还可以包括存储单元903，存储单元903可以用于存储该估计装置900的程序代码和数据。图9所描述的估计装置900带来的有益效果可参照前述实施例的描述，此处不在重复描述。
请参见图10，图10是本申请实施例提供的一种电子设备1010的结构示意图，该电子设备1010包括处理器1011、存储器1012和通信接口1013，上述处理器1011、存储器1012和通信接口1013通过总线1014相互连接。
存储器1012包括但不限于是随机存储记忆体(random access memory，RAM)、只读存储器(read-only memory，ROM)、可擦除可编程只读存储器(erasable programmable read only memory，EPROM)、或便携式只读存储器(compact disc read-only memory，CD-ROM)，该存储器1012用于相关计算机程序及数据。通信接口1013用于接收和发送数据。
处理器1011可以是一个或多个中央处理器(central processing unit，CPU)，在处理器1011是一个CPU的情况下，该CPU可以是单核CPU，也可以是多核CPU。
该电子设备1010中的处理器1011用于读取上述存储器1012中存储的计算机程序代码，执行以下操作：获取k+1个接收信号的幅度和相位，所述k+1个接收信号为在连续的k+1个时刻分别接收到的k+1个信号，所述k为大于或等于零的整数；根据所述k+1个接收信号的幅度 确定第一协方差矩阵∑ ∈，其中，由所述k+1个接收信号对应的加性观测相位噪声构成的第一向量∈服从以下高斯分布：∈～N(0,∑ ∈)；根据第二向量∠r和第二协方差矩阵∑ r确定第k时刻的载波频率和/或载波初始相位，其中，所述第二向量∠r为由所述k+1个接收信号的相位构成的向量，所述第二协方差矩阵∑ r为所述第一协方差矩阵∑ ∈与第三协方差矩阵∑ θ的和，由所述k+1个接收信号对应的随机游走的第一载波相位噪声构成的第三向量θ服从以下高斯分布：θ～N(0,∑ θ)。
需要说明的是，各个操作的实现还可以对应参照图1至图8所示的实施例的相应描述。图10所描述的电子设备1010带来的有益效果可参照前述实施例的描述，此处不在重复描述。
本申请实施例还提供一种芯片，上述芯片包括至少一个处理器，存储器和接口电路，上述存储器、上述收发器和上述至少一个处理器通过线路互联，上述至少一个存储器中存储有计算机程序；上述计算机程序被上述处理器执行时，图1或图3至图5所示的方法流程得以实现。
本申请实施例还提供一种计算机可读存储介质，上述计算机可读存储介质中存储有计算机程序，当其在电子设备上运行时，图1或图3至图5所示的方法流程得以实现。
本申请实施例还提供一种计算机程序产品，当上述计算机程序产品在电子设备上运行时，图1或图3至图5所示的方法流程得以实现。
应理解，本申请实施例中提及的处理器可以是中央处理单元(Central Processing Unit，CPU)，还可以是其他通用处理器、数字信号处理器(Digital Signal Processor，DSP)、专用集成电路(Application Specific Integrated Circuit，ASIC)、现成可编程门阵列(Field Programmable Gate Array，FPGA)或者其他可编程逻辑器件、分立门或者晶体管逻辑器件、分立硬件组件等。通用处理器可以是微处理器或者该处理器也可以是任何常规的处理器等。
还应理解，本申请实施例中提及的存储器可以是易失性存储器或非易失性存储器，或可包括易失性和非易失性存储器两者。其中，非易失性存储器可以是只读存储器(Read-Only Memory，ROM)、可编程只读存储器(Programmable ROM，PROM)、可擦除可编程只读存储器(Erasable PROM，EPROM)、电可擦除可编程只读存储器(Electrically EPROM，EEPROM)或闪存。易失性存储器可以是随机存取存储器(Random Access Memory，RAM)，其用作外部高速缓存。通过示例性但不是限制性说明，许多形式的RAM可用，例如静态随机存取存储器(Static RAM，SRAM)、动态随机存取存储器(Dynamic RAM，DRAM)、同步动态随机存取存储器(Synchronous DRAM，SDRAM)、双倍数据速率同步动态随机存取存储器(Double Data Rate SDRAM，DDR SDRAM)、增强型同步动态随机存取存储器(Enhanced SDRAM，ESDRAM)、同步连接动态随机存取存储器(Synchlink DRAM，SLDRAM)和直接内存总线随机存取存储器(Direct Rambus RAM，DR RAM)。
需要说明的是，当处理器为通用处理器、DSP、ASIC、FPGA或者其他可编程逻辑器件、分立门或者晶体管逻辑器件、分立硬件组件时，存储器(存储模块)集成在处理器中。
应注意，本文描述的存储器旨在包括但不限于这些和任意其它适合类型的存储器。
还应理解，本文中涉及的第一、第二、第三、第四以及各种数字编号仅为描述方便进行的区分，并不用来限制本申请的范围。
应理解，本文中术语“和/或”，仅仅是一种描述关联对象的关联关系，表示可以存在三种关系，例如，A和/或B，可以表示：单独存在A，同时存在A和B，单独存在B这三种情况。另外，本文中字符“/”，一般表示前后关联对象是一种“或”的关系。
应理解，在本申请的各种实施例中，上述各过程的序号的大小并不意味着执行顺序的先后，各过程的执行顺序应以其功能和内在逻辑确定，而不应对本申请实施例的实施过程构成任何限定。
本领域普通技术人员可以意识到，结合本文中所公开的实施例描述的各示例的单元及算法步骤，能够以电子硬件、或者计算机软件和电子硬件的结合来实现。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本申请的范围。
所属领域的技术人员可以清楚地了解到，为描述的方便和简洁，上述描述的系统、装置和单元的具体工作过程，可以参考前述方法实施例中的对应过程，在此不再赘述。
在本申请所提供的几个实施例中，应该理解到，所揭露的系统、装置和方法，可以通过其它的方式实现。例如，以上所描述的装置实施例仅仅是示意性的，例如，上述单元的划分，仅仅为一种逻辑功能划分，实际实现时可以有另外的划分方式，例如多个单元或组件可以结合或者可以集成到另一个系统，或一些特征可以忽略，或不执行。另一点，所显示或讨论的相互之间的耦合或直接耦合或通信连接可以是通过一些接口，装置或单元的间接耦合或通信连接，可以是电性，机械或其它的形式。
上述作为分离部件说明的单元可以是或者也可以不是物理上分开的，作为单元显示的部件可以是或者也可以不是物理单元，即可以位于一个地方，或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部单元来实现本实施例方案的目的。
另外，在本申请各个实施例中的各功能单元可以集成在一个处理单元中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个单元中。
上述功能如果以软件功能单元的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读取存储介质中。基于这样的理解，本申请的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的部分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质中，包括若干指令用以使得一台计算机设备(可以是个人计算机，服务器，或者网络设备等)执行本申请各个实施例所示方法的全部或部分步骤。而前述的存储介质包括：U盘、移动硬盘、只读存储器(Read-Only Memory，ROM)、随机存取存储器(Random Access Memory，RAM)、磁碟或者光盘等各种可以存储程序代码的介质。
本申请实施例方法中的步骤可以根据实际需要进行顺序调整、合并和删减。
本申请实施例装置中的模块可以根据实际需要进行合并、划分和删减。
以上所述，以上实施例仅用以说明本申请的技术方案，而非对其限制；尽管参照前述实施例对本申请进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分技术特征进行等同替换；而这些修改或者替换，并不使相应技术方案的本质脱离本申请各实施例技术方案的范围。

Claims (11)

  1. 一种载波频率和/或载波初始相位的估计方法，其特征在于，包括：
    获取k+1个接收信号的幅度和相位，所述k+1个接收信号为在连续的k+1个时刻分别接收到的k+1个信号，所述k为大于或等于零的整数；
    根据所述k+1个接收信号的幅度确定第一协方差矩阵Σ ε，其中，由所述k+1个接收信号对应的加性观测相位噪声构成的第一向量ε服从以下高斯分布：ε～N(0,Σ ε)；
    根据第二向量∠r和第二协方差矩阵Σ r确定第k时刻的载波频率和/或载波初始相位，其中，所述第二向量∠r为由所述k+1个接收信号的相位构成的向量，所述第二协方差矩阵Σ r为所述第一协方差矩阵Σ ε与第三协方差矩阵Σ θ的和，由所述k+1个接收信号对应的随机游走的第一载波相位噪声构成的第三向量θ服从以下高斯分布：θ～N(0,Σ θ)。
  2. 根据权利要求1所述的方法，其特征在于，k＝N-1，所述N为正整数，第N-1时刻的载波频率通过以下公式确定：
    Figure PCTCN2021099179-appb-100001
    其中，上标(N-1)表示第N-1时刻，
    Figure PCTCN2021099179-appb-100002
    表示第N-1时刻的载波频率，N＝[0,1,…,N-1] T，Σ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
  3. 根据权利要求2所述的方法，其特征在于，所述方法还包括：
    获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；
    所述第N时刻的载波频率通过以下公式确定：
    Figure PCTCN2021099179-appb-100003
    其中：
    Figure PCTCN2021099179-appb-100004
    其中，A (N-1)＝(N TΣ r -1∠r) (N-1)，B (N-1)＝(1 TΣ r -11) (N-1)，C (N-1)＝(1 TΣ r -1N) (N-1)，D (N-1)＝(1 TΣ r -1∠r) (N-1)，E (N-1)＝(N TΣ r -1N) (N-1)；
    其中：
    Figure PCTCN2021099179-appb-100005
    其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
    Figure PCTCN2021099179-appb-100006
    表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，N＝[0,1,…,N-1] T，Σ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
    Figure PCTCN2021099179-appb-100007
    的高斯随机变量序列。
  4. 根据权利要求1所述的方法，其特征在于，k＝N-1，所述N为正整数，第N-1时刻的载波初始相位通过以下公式确定：
    Figure PCTCN2021099179-appb-100008
    其中，上标(N-1)表示第N-1时刻，
    Figure PCTCN2021099179-appb-100009
    表示第N-1时刻的载波初始相位，N＝[0,1,…,N-1] T，Σ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T。
  5. 根据权利要求4所述的方法，其特征在于，所述方法还包括：
    获取第N时刻对应的接收信号的幅度和相位，所述第N时刻对应的接收信号为在第N时刻接收到的信号；
    所述第N时刻的载波初始相位通过以下公式确定：
    Figure PCTCN2021099179-appb-100010
    其中：
    Figure PCTCN2021099179-appb-100011
    其中，A (N-1)＝(N TΣ r -1∠r) (N-1)，B (N-1)＝(1 TΣ r -11) (N-1)，C (N-1)＝(1 TΣ r -1N) (N-1)，D (N-1)＝(1 TΣ r -1∠r) (N-1)，E (N-1)＝(N TΣ r -1N) (N-1)；
    其中：
    Figure PCTCN2021099179-appb-100012
    其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
    Figure PCTCN2021099179-appb-100013
    表示第N时刻的载波频率，∠r(N)表示第N时刻对应的接收信号的相位，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(N)|表示第N时刻对应的接收信号的幅度，N＝[0,1,…,N-1] T，Σ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，1＝[1,1,…,1] T，∠r(1)表示第1时刻对应的接收信号的相位，|r(1)|表示第1时刻对应的接收信号的幅度；第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
    Figure PCTCN2021099179-appb-100014
    的高斯随机变量序列。
  6. 根据权利要求2-5任一项所述的方法，其特征在于，所述方法还包括：
    根据所述第二协方差矩阵Σ r、所述第三协方差矩阵Σ θ、所述第二向量∠r、所述第k时刻的载波频率和所述第k时刻的载波初始相位确定所述第k时刻的第二载波相位噪声。
  7. 根据权利要求6所述的方法，其特征在于，k＝N-1，第N-1时刻的第二载波相位噪声通过以下公式确定：
    Figure PCTCN2021099179-appb-100015
    其中，上标(N-1)表示第N-1时刻，
    Figure PCTCN2021099179-appb-100016
    表示第N-1时刻的第二载波相位噪声，
    Figure PCTCN2021099179-appb-100017
    表示第N-1时刻的载波频率，
    Figure PCTCN2021099179-appb-100018
    表示第N-1时刻的载波初始相位，Σ θ表示第N-1时刻的第三协方差矩阵，Σ r表示第N-1时刻的第二协方差矩阵，∠r表示第N-1时刻的第二向量，N＝[0,1,…,N-1] T，1＝[1,1,…,1] T。
  8. 根据权利要求7所述的方法，其特征在于，所述第N时刻的第二载波相位噪声通过以下公式确定：
    Figure PCTCN2021099179-appb-100019
    其中：
    Figure PCTCN2021099179-appb-100020
    其中：
    Figure PCTCN2021099179-appb-100021
    其中：
    Figure PCTCN2021099179-appb-100022
    其中，上标(N)表示第N时刻，上标(N-1)表示第N-1时刻，上标(1)表示第1时刻，
    Figure PCTCN2021099179-appb-100023
    表示第N时刻的第二载波相位噪声，
    Figure PCTCN2021099179-appb-100024
    表示第N时刻的载波频率，
    Figure PCTCN2021099179-appb-100025
    表示第N时刻的载波初始相位，Σ θ (N)表示第N时刻的第三协方差矩阵，Σ r (N)表示第N时刻的第二协方差矩阵，∠r (N)表示第N时刻的第二向量，N (N)＝[0,1,…,N-1,N] T，1 (N)＝[1,1,…,1] T，Σ r (N-1)表示第N-1时刻的第二协方差矩阵，N (N-1)＝[0,1,…,N-1] T，N 0表示白噪声的单边带功率谱密度，A表示发送信号的幅度，|r(0)|表示第0时刻对应的接收信号的幅度，|r(1)|表示第1时刻对应的接收信号的幅度；第一载波相位噪声θ(k)＝θ(k-1)+Δθ(k)，θ(0)＝0，{Δθ(k)}是一个方差为
    Figure PCTCN2021099179-appb-100026
    的高斯随机变量序列。
  9. 一种载波频率和/或载波初始相位的估计装置，其特征在于，包括：
    获取单元，用于获取k+1个接收信号的幅度和相位，所述k+1个接收信号为在连续的k+1个时刻分别接收到的k+1个信号，所述k为大于或等于零的整数；
    确定单元，用于根据所述k+1个接收信号的幅度确定第一协方差矩阵Σ ε，其中，由所述k+1个接收信号对应的加性观测相位噪声构成的第一向量ε服从以下高斯分布：ε～N(0,Σ ε)；
    以及根据第二向量∠r和第二协方差矩阵Σ r确定第k时刻的载波频率和/或载波初始相位，其中，所述第二向量∠r为由所述k+1个接收信号的相位构成的向量，所述第二协方差矩阵Σ r为所述第一协方差矩阵Σ ε与第三协方差矩阵Σ θ的和，由所述k+1个接收信号对应的随机游走的第一载波相位噪声构成的第三向量θ服从以下高斯分布：θ～N(0,Σ θ)。
  10. 一种电子设备，其特征在于，包括处理器、存储器、通信接口，以及一个或多个程序，所述一个或多个程序被存储在所述存储器中，并且被配置由所述处理器执行，所述程序包括用于执行权利要求1-8任一项所述的方法中的步骤的指令。
  11. 一种计算机可读存储介质，其特征在于，所述计算机可读存储介质存储有计算机程序，所述计算机程序被处理器执行以实现权利要求1-8任一项所述的方法。
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102656824A (zh) * 2009-12-18 2012-09-05 阿尔卡特朗讯 用于相干光系统中非线性损害监视和减轻的载波相位估计器
CN103095615A (zh) * 2011-10-31 2013-05-08 华为技术有限公司 一种相位噪声估计、补偿的方法及装置
WO2014100699A1 (en) * 2012-12-20 2014-06-26 Qualcomm Incorporated Systems and methods to mitigate phase noise
CN111537966A (zh) * 2020-04-28 2020-08-14 东南大学 一种适用于毫米波车载雷达领域的阵列天线误差校正方法
EP3723332A1 (en) * 2019-04-08 2020-10-14 Mitsubishi Electric R&D Centre Europe B.V. Circular pilot sequences for joint channel and phase noise estimation

Family Cites Families (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB0103669D0 (en) * 2001-02-15 2001-03-28 Central Research Lab Ltd A method of estimating the carrier frequency of a phase-modulated signal
US7302016B1 (en) * 2003-08-13 2007-11-27 L-3 Communicaations Corporation Phase estimator with bias correction
US9559417B1 (en) * 2010-10-29 2017-01-31 The Boeing Company Signal processing
US9065555B2 (en) * 2012-09-27 2015-06-23 Intel Mobile Communications GmbH Method of channel estimation and a channel estimator
JP6665562B2 (ja) * 2016-02-05 2020-03-13 沖電気工業株式会社 整相器および整相処理方法
CN106788653B (zh) * 2016-11-25 2020-11-27 西安电子科技大学 一种基于协方差矩阵重构的自适应波束形成方法
CN106646543A (zh) * 2016-12-22 2017-05-10 成都正扬博创电子技术有限公司 基于主从式aukf算法的高动态卫星导航信号载波追踪方法
CN110231638B (zh) * 2019-06-28 2021-06-04 北京邮电大学 一种无线网络下的载波相位定位方法及装置
CN111007557B (zh) * 2019-12-10 2022-05-13 中国矿业大学 自适应运动学模型辅助的gnss载波相位与多普勒融合测速方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102656824A (zh) * 2009-12-18 2012-09-05 阿尔卡特朗讯 用于相干光系统中非线性损害监视和减轻的载波相位估计器
CN103095615A (zh) * 2011-10-31 2013-05-08 华为技术有限公司 一种相位噪声估计、补偿的方法及装置
WO2014100699A1 (en) * 2012-12-20 2014-06-26 Qualcomm Incorporated Systems and methods to mitigate phase noise
EP3723332A1 (en) * 2019-04-08 2020-10-14 Mitsubishi Electric R&D Centre Europe B.V. Circular pilot sequences for joint channel and phase noise estimation
CN111537966A (zh) * 2020-04-28 2020-08-14 东南大学 一种适用于毫米波车载雷达领域的阵列天线误差校正方法

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
HOU YONGHONG: "Research on Key Technology of Digital Television Terrestrial Broadcasting", CHINESE DOCTORAL DISSERTATIONS FULL-TEXT DATABASE, INFORMATION SCIENCES, no. 12, 15 December 2010 (2010-12-15), XP093014510 *

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