CN112835075B

CN112835075B - Method and device for tracking orthogonal frequency division multiplexing carrier phase and electronic equipment

Info

Publication number: CN112835075B
Application number: CN201911198870.3A
Authority: CN
Inventors: 达人; 于大飞; 任斌; 李刚; 郑占旗; 张振宇; 孙韶辉
Original assignee: Datang Mobile Communications Equipment Co Ltd
Current assignee: Datang Mobile Communications Equipment Co Ltd
Priority date: 2019-11-25
Filing date: 2019-11-25
Publication date: 2024-04-02
Anticipated expiration: 2039-11-25
Also published as: CN112835075A

Abstract

The embodiment of the invention discloses a method, a device and electronic equipment for tracking an orthogonal frequency division multiplexing carrier phase, wherein the method comprises the following steps: acquiring a state vector predicted value of an Orthogonal Frequency Division Multiplexing (OFDM) carrier phase and a scalar measurement value of the OFDM carrier phase at each moment; based on the state vector predicted value of the OFDM carrier phase and the scalar measured value of the OFDM carrier phase at each moment, the state vector estimated value of the OFDM carrier phase is obtained, the OFDM carrier phase is tracked, and the carrier phase in a 5G NR/4G LTE FDD/TDD system can be tracked in real time.

Description

Method and device for tracking orthogonal frequency division multiplexing carrier phase and electronic equipment

Technical Field

The present invention relates to the field of communications technologies, and in particular, to a method and an apparatus for tracking an orthogonal frequency division multiplexing carrier phase, and an electronic device.

Background

GNSS (Global Navigation Satellite System ) carrier phase positioning technology is a well-known high-precision positioning technology. In GNSS carrier phase positioning, a GNSS receiver precisely determines the position of the GNSS receiver by measuring carrier phase measurements obtained from GNSS satellite signals. The main drawback of GNSS positioning is the inability to operate in environments where the terminal does not receive GNSS satellite signals.

Whether carrier phase positioning of GNSS signals or carrier phase positioning based on signals of the wireless communication system itself, one of the keys is that the receiver must be able to track and lock the carrier signal from the transmitter in real time to obtain carrier phase measurements. In recent years, more researches on carrier phase tracking of GNSS have been carried out, and the technology has been mature, wherein the tracking method of carrier signals of GNSS based on EKF (Extended Kalman Filter ) is one of the common methods, but the researches on carrier phase tracking of signals of a wireless communication system are few; and GNSS is a wireless communication system based on a CDMA (Code Division Multiple Access ) system, but a 3GPP (3 rd Generation Partnership Project, third Generation partnership project) 5G (5 th Generation, fifth Generation mobile communication technology) NR (New Radio) system is a wireless communication system based on an OFDM (Orthogonal Frequency Division Multiplexing ) system, which mainly includes a 5G (5 th Generation, fifth Generation mobile communication technology) NR system and a 4G (4 th Generation, fourth Generation mobile communication technology) LTE (Long Term Evolution ) FDD (Frequency Division Duplexing, frequency division duplex)/TDD (Time Division Dual, time division duplex) system. While carrier signal tracking methods of GNSS are not necessarily suitable for OFDM systems.

Thus, it is currently not possible to track carrier phases in an OFDM system in real time.

Disclosure of Invention

Because the conventional method cannot realize real-time tracking of the OFDM carrier phase, the embodiment of the invention provides a method, a device and electronic equipment for tracking the OFDM carrier phase.

In a first aspect, an embodiment of the present invention provides a method for tracking an orthogonal frequency division multiplexing carrier phase, including:

acquiring a state vector predicted value of an Orthogonal Frequency Division Multiplexing (OFDM) carrier phase and a scalar measurement value of the OFDM carrier phase at each moment;

based on the state vector predicted value of the OFDM carrier phase and the scalar measured value of the OFDM carrier phase at each moment, the state vector estimated value of the OFDM carrier phase is obtained, and the OFDM carrier phase is tracked.

In a second aspect, an embodiment of the present invention further provides a tracking apparatus for an ofdm carrier phase, including:

the value acquisition module is used for acquiring a state vector predicted value of the Orthogonal Frequency Division Multiplexing (OFDM) carrier phase and a scalar measured value of the OFDM carrier phase at each moment;

and the tracking module is used for acquiring a state vector estimated value of the OFDM carrier phase based on the state vector predicted value of the OFDM carrier phase at each moment and the scalar measured value of the OFDM carrier phase and tracking the OFDM carrier phase.

In a third aspect, an embodiment of the present invention further provides an electronic device, including:

at least one processor; and

at least one memory communicatively coupled to the processor, wherein:

the memory stores program instructions executable by the processor, the processor invoking the program instructions capable of performing the method of:

In a fourth aspect, embodiments of the present invention also propose a non-transitory computer-readable storage medium storing a computer program, the computer program causing the computer to carry out the method of:

As can be seen from the above technical solutions, in the embodiments of the present invention, the state vector predicted value of the OFDM carrier phase and the scalar measurement value of the OFDM carrier phase at each time are calculated, so as to obtain the state vector estimated value of the OFDM carrier phase, track the OFDM carrier phase, and can track the carrier phase in the 5G NR/4G LTE FDD/TDD system in real time.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions of the prior art, the drawings that are necessary for the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention and that other drawings can be obtained from these drawings without inventive effort for a person skilled in the art.

Fig. 1 is a flowchart of a method for tracking an ofdm carrier phase according to an embodiment of the present invention;

fig. 2 is a schematic flow chart of an EKF receiver with carrier phase tracking in an open loop structure according to an embodiment of the present invention;

fig. 3 is a schematic flow chart of an EKF receiver for carrier phase tracking with a closed loop structure according to an embodiment of the present invention;

Fig. 4 is a schematic diagram of a CPRS-OFDM symbol and a CPRS RE of an OFDM system according to an embodiment of the present invention;

fig. 5 is a schematic structural diagram of a tracking device for an ofdm carrier phase according to an embodiment of the present invention;

fig. 6 is a logic block diagram of an electronic device according to an embodiment of the present invention.

Detailed Description

The following describes the embodiments of the present invention further with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.

Fig. 1 shows a flow chart of a tracking method of an ofdm carrier phase according to the present embodiment, including:

s101, acquiring a state vector predicted value of the OFDM carrier phase and a scalar measurement value of the OFDM carrier phase at each moment.

Wherein the parameters characterizing carrier phase include parameters of two dimensions, a state vector and a scalar.

Wherein the state vector x is: x= [ x ] _t ,x _f ,x _o ] ^T Wherein: x is x _t To correspond to f _c Time shift of carrier phase (at carrier frequency f _c Is the unit of the period); x is x _f Is carrier frequency offset (in Hz); x is x _o Is the carrier frequency offset rate of change (in Hz/s).

Wherein, the scalar y of the carrier phase is the radian value of the phase; for example, a signal at a certain moment is expressed as: s=a×e ^j0.5π Wherein: a is the signal amplitude, then the scalar y=0.5pi of the carrier phase.

The state vector predicted value is a predicted value of the state vector of the OFDM carrier phase obtained through calculation.

The state vector estimation value is the calculated estimation value of the state vector of the OFDM carrier phase.

The scalar measurement is a scalar measurement of the calculated OFDM carrier phase.

The scalar predicted value is a scalar predicted value of the calculated OFDM carrier phase.

The scalar measurement value of the OFDM carrier phase is a value of the OFDM carrier phase calculated according to specific parameters in an OFDM symbol.

The predicted value of the OFDM carrier phase state vector is the value of the OFDM carrier phase state vector predicted according to an EKF time updating algorithm.

The EKF time updating algorithm is used for updating the predicted value of the OFDM carrier phase state vector at the current moment according to the estimated value of the OFDM carrier phase state vector at the previous moment.

S102, based on the state vector predicted value of the OFDM carrier phase at each moment and the scalar measurement value of the OFDM carrier phase, obtaining the state vector estimated value of the OFDM carrier phase, and tracking the OFDM carrier phase.

To track the OFDM carrier phase, it is necessary to acquire a state vector predicted value of the OFDM carrier phase at each time and a scalar measurement value of the OFDM carrier phase, and then obtain a state vector estimated value of the corresponding OFDM carrier phase based on the state vector predicted value of the OFDM carrier phase at the corresponding time and the scalar measurement value of the OFDM carrier phase at the corresponding time to track the OFDM carrier phase at the corresponding time.

Specifically, firstly, a scalar predicted value of the OFDM carrier phase at the current time is obtained based on a predicted value of the OFDM carrier phase state vector at the current time, then, an estimated value of the OFDM carrier phase state vector at the current time is obtained based on a scalar measured value of the OFDM carrier phase at the current time and the scalar predicted value of the OFDM carrier phase at the current time, and further, the OFDM carrier phase of the terminal at the current time is obtained, so that tracking of the OFDM carrier phase is realized.

According to the embodiment, the state vector predicted value of the OFDM carrier phase at each moment and the scalar measured value of the OFDM carrier phase are calculated, so that the state vector estimated value of the OFDM carrier phase is obtained, the OFDM carrier phase is tracked, and the carrier phase in the 5G NR/4G LTE FDD/TDD system can be tracked in real time.

Further, S102 specifically includes:

acquiring a scalar predicted value of the OFDM carrier phase at the time k+1 according to the state vector predicted value of the OFDM carrier phase at the time k+1, calculating a difference value between a scalar measured value of the OFDM carrier phase at the time k+1 and the scalar predicted value of the OFDM carrier phase at the time k+1, and updating a state vector estimated value and a covariance matrix estimated value of the OFDM carrier phase at the time k+1 according to an extended Kalman filter EKF measurement updating algorithm;

according to a terminal positioning algorithm, based on a state vector estimation value of an OFDM carrier phase at the time k+1, obtaining the OFDM carrier phase of the terminal at the time k+1 so as to realize tracking of the OFDM carrier phase;

wherein k is a positive integer.

The terminal positioning algorithm obtains the position information of the terminal at each moment by using related algorithms such as a TDOA principle, a carrier phase full period estimation algorithm and the like. The tracking method of the OFDM carrier phase provided in this embodiment is applicable to an open loop structure (fig. 2) and a closed loop structure (fig. 3). The difference between open-loop and closed-loop architectures is that: in an open loop architecture, EKF estimates are used to forward correct for the effects introduced by time and frequency offsets on post-FFT data symbols; whereas in a closed loop architecture, EKF estimates are used to feedback correct for the effects introduced by time and frequency offsets on the pre-FFT incoming data samples.

Specifically, the EKF receiver for OFDM carrier phase tracking performs the following steps: let EKF state vector be x, at initial time kThe estimated state vector and covariance matrix at=0 are respectivelyAnd let OFDM symbol transmitted at a certain k time be +.>With the known CPRS sample sequence +.>The baseband discrete data samples corresponding to the received OFDM symbol are { x } _n N=0, …, N-1), where N is the number of discrete data samples.

As shown in fig. 2, the EKF receiver for OFDM carrier phase tracking based on an open loop structure includes the following steps:

step1: for baseband discrete data samples { x } _n FFT transforming to obtain frequency domain signals corresponding to sub-carriers with known CPRS sample sequence in OFDM symbol

Step2: will beCPRS sample sequence known thereto +.>Performing a correlation calculation to obtain a scalar measurement of its phase +.>

Step3: according to EKF time updating algorithm, using state estimation value based on k timeAnd covariance matrix P (k|k) to predict state vector ++1 at time k+1>And a covariance matrix P (k+ 1|k);

step4: based on the predicted state vectorThe carrier phase is predicted and is marked as +.>

Step5: calculating the difference between the scalar measurement value and the scalar prediction value of the acquired carrier phase at the time k+1, and recording as

Step6: based on EKF measurement update algorithmP (k+ 1|k) and +.>Updating the state vector estimate +.>And covariance matrix P (k+1|k+1);

step7: and repeating Step3 to Step6, calculating scalar measurement values and state vector prediction values of the carrier phase at each moment, and obtaining estimated values of the carrier phase, thereby completing tracking of the carrier phase.

Further, on the basis of the foregoing method embodiment, the obtaining the scalar predicted value of the OFDM carrier phase at the time k+1 according to the state vector predicted value of the OFDM carrier phase at the time k+1, calculating a difference between the scalar measured value of the OFDM carrier phase at the time k+1 and the scalar predicted value of the OFDM carrier phase at the time k+1, and updating the state vector estimated value and the covariance matrix estimated value of the OFDM carrier phase at the time k+1 according to an extended kalman filter EKF measurement update algorithm, further includes:

the baseband discrete data samples at time k+2 are phase rotated based on the state vector estimate of the OFDM carrier phase at time k+1 to correct for the effects of time and frequency offset on the baseband discrete data samples at time k+2.

Specifically, as shown in fig. 3, the EKF receiver for OFDM carrier phase tracking based on a closed loop structure includes the following steps:

Step1 to Step 6: step1 to Step 6 of the OFDM carrier phase tracking based on the open loop structure in the embodiment corresponding to fig. 2 are the same;

step7: feedback correction of pre-FFT incoming data samples (baseband discrete data samples { x }, by time and frequency offset using the EKF state vector estimate at time k+1 first at time k+2 _n -a) the influence of the introduction;

step8: and repeating Step1 to Step7, calculating scalar measurement values and state vector prediction values of the carrier phase at each moment, and obtaining estimated values of the carrier phase, thereby completing tracking of the carrier phase. .

Further, on the basis of the above method embodiment, the phase rotation is performed on the baseband discrete data sample at the k+2 time according to the state vector estimated value at the k+1 time to correct the baseband discrete data sample at the k+2 time by the time and frequency offset, which specifically includes:

for baseband discrete data samples x at time k+2 according to the following formula _n (k+2) phase rotation to obtain a new data sample sequence { z }, and _n (k+2)}：

wherein,is made of->Calculated phase rotation +.>j is the unit imaginary number; x is x _n (k+2) is the nth known CPRS sample sequence in the OFDM symbol at time k+2; n is the number of baseband discrete data samples contained in each OFDM symbol; / >The unit of the time offset of the OFDM symbol at the predicted k+2 time is a period, and the size of the time offset is equal to delta t (k+2) f _c Delta t (k+2) is the time offset in seconds between the signal received by the receiver at the beginning of the OFDM symbol at time k+2 and the signal generated by the receiver itself; f (f) _c K is a positive integer for the carrier frequency.

Further, on the basis of the above method embodiment, S101 specifically includes:

performing correlation calculation on a known carrier phase reference signal CPRS sample sequence in an OFDM symbol carried at the moment k and a frequency domain signal of a subcarrier corresponding to the sample sequence at the moment k to obtain a scalar measurement value of an OFDM carrier phase at the moment k, wherein the frequency domain signal of the subcarrier is obtained by performing fast Fourier transform on a baseband discrete data sample received at the moment k;

according to an EKF time updating algorithm, a state vector predicted value and a covariance matrix predicted value of the OFDM carrier phase at the time k+1 are obtained based on the state vector estimated value and the covariance matrix estimated value of the OFDM carrier phase at the time k, and a scalar predicted value of the OFDM carrier phase at the time k+1 is obtained based on the state vector predicted value and a preset EKF measurement matrix of the OFDM carrier phase at the time k+1.

Further, on the basis of the above method embodiment, the performing correlation calculation on the known carrier phase reference signal CPRS sample sequence in the OFDM symbol carried at the k time and the frequency domain signal of the subcarrier corresponding to the sample sequence at the k time to obtain a scalar measurement value of the OFDM carrier phase at the k time specifically includes:

acquiring a frequency domain signal R of a subcarrier corresponding to an ith known CPRS sample sequence in an OFDM symbol carried at k moment _l (k)：

For the frequency domain signal R _l (k) And corresponding known CPRS sample sequence X _l (k) Performing correlation calculation to obtain scalar measurement value y of carrier phase of the first subcarrier of OFDM at k moment _l (k)：

Wherein δf is the normalized frequency deviation; h is a ₀ Attenuation for the first transmission path; n is the number of baseband discrete data samples contained in each OFDM symbol; j is the unit imaginary number; f (f) _c Is the carrier frequency; l is the sequence number of the subcarrier in the known CPRS sample sequence; Δf _SCs Is the subcarrier spacing of an OFDM system; Δt (k) is the time deviation between the signal received by the receiver at the beginning of the OFDM symbol at time k and the signal generated by the receiver itself, in seconds; τ ₀ (k) Time offset generated by Doppler in channel transmission for the OFDM symbol at k time; g _l (k) A wireless channel frequency response for the first known CPRS sample sequence in the OFDM symbol at time k; x is X _l (k) For the first known CPRS sample sequence in the OFDM symbol at k time; w (W) _l (k) Additive White Gaussian Noise (AWGN) which is the first known CPRS sample sequence in the OFDM symbol at time k; r is R _l (k) For the frequency domain signal of the first known CPRS sample sequence in the OFDM symbol at time k, x _t (k) Time offset of OFDM symbol at k time, its unit is period, and its size is deltat (k) f _c ，x _f (k) For the frequency offset of the OFDM symbol at time k, T _s K is a positive integer for the sampling time interval;

scalar measurement y of carrier phase according to OFDM first subcarrier at time k _l (k) The expression equation of (2) yields an EKF measurement matrix H as:

wherein H is _l EKF measurement matrix for the l-th subcarrier, T _s Is the sampling interval.

Specifically, in the tracking process of the OFDM carrier phase of the open loop structure and the closed loop structure, the above formula may be used to calculate the measured value of the OFDM carrier phase at each time.

Further, on the basis of the above method embodiment, the obtaining, according to the EKF time update algorithm, a state vector predicted value and a covariance matrix predicted value at a k+1 time based on the state vector estimated value and the covariance matrix estimated value at the k time, and obtaining a scalar predicted value of an OFDM carrier phase at the k+1 time based on the state vector predicted value at the k+1 time and a preset EKF measurement matrix specifically includes:

State vector estimation value of OFDM carrier phase based on k timeAnd a state transition matrix F (k), calculating a state vector predictor of OFDM carrier phase at time k+1 +.>The method comprises the following steps:

wherein DeltaT (k) is the time difference between the moment k+1 and the moment k, and the unit is seconds;

from the covariance matrix estimate P (k|k) at time k and the state transition matrix F (k), the covariance matrix estimate P (k+ 1|k) at time k+1 is calculated as:

P(k+1|k)＝F(k)P(k|k)F ^T (k)+Q(k)

state vector predictor based on time k+1And the EKF measurement matrix H of the first subcarrier _l Obtain scalar predictive value +.of carrier phase of OFDM first sub-carrier at k+1 time>The method comprises the following steps:

wherein,time offset of OFDM symbol for predicted k+1 time; />Frequency offset for the predicted OFDM symbol at time k+1; f (F) ^T (k) The transpose of F (k), Q (k) is the process noise covariance at time k.

Further, on the basis of the above method embodiment, the updating the state vector estimation value and the covariance matrix estimation value of the OFDM carrier phase at time k+1 according to the EKF measurement updating algorithm specifically includes:

state vector predictor from OFDM carrier phase at time k+1An EKF gain matrix K (k+1) at time k+1, a scalar measurement y (k+1) of the OFDM carrier phase at time k+1, and a scalar prediction of the carrier phase at time k+1 ≡k- >Updating the state vector estimate at time k+1 +.>

Updating the covariance matrix estimated value P (k+1|k+1) at the time of k+1 according to the covariance matrix predicted value P (k+ 1|k) at the time of k+1, the EKF gain matrix K (k+1) at the time of k+1 and the EKF measurement matrix H at the time of k+1:

P(k+1|k+1)＝[I-K(k+1)H]P(k+1|k)

wherein K (k+1) =p (k+ 1|k) H ^T ×[HP(k+1|k)H ^T +R _l (k)] ^-1

H ^T Is the transposed matrix of H.

Further, on the basis of the above method embodiment, an estimated value of the time offset of the OFDM symbol at the initial time (k=0)The estimation formula of (2) is as follows:

or alternatively, the first and second heat exchangers may be,

estimation of the time offset of an OFDM symbol at the initial time (k=0)Setting according to an estimated value of the estimated arrival time TOA;

wherein l _j A j-th subcarrier sequence number; l (L) _i Is the i sub-carrier serial number;for the ith subcarrier of the OFDM symbol at time kFrequency domain data; />Conjugation of frequency domain data of the ith subcarrier of the OFDM symbol at k time; />Frequency domain data of the j sub-carrier of the OFDM symbol at k time; />The conjugation of the frequency domain data of the j-th subcarrier of the OFDM symbol at the k moment.

Specifically, in addition to calculating the estimated value of the time offset of the OFDM symbol at the initial time using the above estimation formulaThe TOA can also be estimated according to conventional algorithms and then used to set the initial time offset x _t (0)。

The TOA algorithm is a correlation algorithm utilizing a relation between distance and time between a transmitter and a receiver, and obtains propagation delay of signals between the transmitter and the receiver through a convex optimization theory.

Specifically, the EKF receiver for OFDM carrier phase tracking includes the selection of an EKF state vector, the establishment of an EKF state equation and an EKF measurement equation, an EKF iterative update algorithm (including time update and measurement update of estimated state vector and covariance matrix), and the like. The following describes the principles and processes involved in the method provided in this embodiment in detail:

first, an OFDM system transmission model is described:

in an EKF receiver for carrier phase measurement tracking, consider the following uplink or downlink transmission model of an OFDM wireless communication system, as shown in fig. 4:

the OFDM system has N1 sub-carriers with a sub-carrier spacing delta f _SCS ；

N1 symbols X can be transmitted in each OFDM symbol _k ,k∈{0,1,…,N1-1}；

If some OFDM symbol contains CPRS, the OFDM symbol is called CPRS-OFDM symbol, which can be used for tracking carrier phase signal; all reference signals usable for carrier phase measurements are denoted herein by CPRS, including LTE/NR CSI-RS, SSB, PRS, SRS, etc.

Without loss of generality, an OFDM symbol for tracking carrier phase signals is provided to contain L CPRS sample sequences Subcarrier set->Representing the subcarrier locations of the L sequences of CPRS samples in the CPRS-OFDM symbol. In the frequency resource configuration, the EKF does not require a certain mapping pattern of the CPRS sample sequences, i.e., L CPRS sample sequences can be mapped arbitrarily onto the subcarriers in the OFDM symbol.

Each OFDM symbol has a duration of T seconds and a sampling time interval of T _s ＝1/(NΔf _SCS ) Thus, each OFDM symbol includes N (N.gtoreq.N 1) baseband discrete data samples { x } _n The (regardless of cyclic prefix CP) is:

on the time domain resource allocation, the time interval from the CPRS-OFDM symbol starting from the k moment to the CPRS-OFDM symbol starting from the k+1 moment is delta T (k) (seconds); in the EKF receiver of the present embodiment, Δt (k) may be any value. The transmitter may periodically transmit the CPRS-OFDM symbol or may aperiodically transmit the CPRS-OFDM symbol. During the Δt (k) time interval, the receiver can change to the transmitter and vice versa. Thus, the EKF carrier phase tracking method of the present embodiment can be used for FDD and TDD OFDM systems.

It is assumed that the channel remains unchanged, i.e. the transmission channel is quasi-static, for the duration of each OFDM symbol. In carrier phase location, the EKF is required to track the carrier phase of the first transmission path; thus, the present embodiment considers only the first transmission path, and the radio channel frequency response of the first subcarrier can be described as follows:

Wherein g ₀ And τ ₀ Attenuation and propagation delay (in seconds) of the first propagation path, f _c Is the carrier frequency, Δf _SCS Is the subcarrier spacing.

Assume that at the beginning of the CPRS-OFDM symbol (excluding CP) at time k, the time offset and the frequency offset between the signal received by the receiver and the signal generated by the receiver itself are Δt (k) (seconds) and Δf (t) (Hz), respectively. If the normalized frequency offset is denoted by δf, δf=Δf/Δf _SCS . When the interference between sub-carriers is ignored, the received frequency domain signal R of OFDM symbol in the first sub-carrier _l Can be described as:

wherein,g is AWGN noise _l For the first subcarrier channel frequency response, X _l Is the CPRS sample sequence at the first subcarrier position in the CPRS-OFDM symbol.

Specifically, for an EKF receiver based on an open loop architecture OFDM carrier phase tracking, a carrier phase tracking EKF receiver for 5G NR carrier phase positioning includes the following aspects: an EKF state vector, an EKF state equation, an EKF measurement equation, an EKF algorithm, an EKF initialization method, and an EKF closed loop feedback.

Wherein, in order to enable the EKF to realize carrier phase tracking of a 5G NR/4G LTE FDD/TDD multi-carrier system; in the embodiment, the EKF state vector is redesigned, the phase variable of the traditional EKF state vector is removed, the time variable is added, and the EKF state equation and the EKF measurement equation are correspondingly redesigned, so that the EKF state equation and the EKF measurement equation are changed into functions of the time variable; the EKF initialization method and the EKF closed loop feedback are improved, the input of the EKF is modified from traditional amplitude information to phase information, and a prediction equation of the carrier phase and error variance between scalar measured values and scalar predicted values of the carrier phase are modified.

Regarding EKF state vectors:

when designing an EKF receiver, it is first necessary to reasonably select the unknown state vector of the EKF, and the state vector is composed of a plurality of state variables. The present embodiment provides a new EKF state vector, which overcomes the disadvantage that the conventional EKF state vector uses only a single carrier system, so that the EKF state vector is suitable for carrier phase tracking of a 5G NR/4G LTE FDD/TDD multi-carrier system, and details of state variables considered by an EKF receiver are described below, and specifically include the following:

state variable (x) related to carrier phase _t ): the EKF state vector for carrier phase tracking must include state variables associated with the carrier phase. GNSS is a CDMA system, having only one carrier frequency. Thus, in an EKF receiver that GNSS tracks carrier phases, the EKF state typically directly includes the carrier phase of the tracked carrier frequency. In an OFDM system, however, the carrier phases on different subcarriers are different for the same time offset. Instead of the carrier phase, a time offset can then be used as EKF state, i.e. the time difference x between the carrier signal received by the receiver and the carrier signal of the receiver itself _ΔT As an EKF state. X is x _ΔT Comprises two parts of content: first, by the offset Δt between the time of the transmitter and the time of the receiver. One of the main causes of time offset is clock errors caused by oscillator errors between the transmitter and the receiver. In OFDM systems, also commonly referred to as phase noise. Second, the signal propagation delay τ from the transmitter to the receiver. The propagation delay τ is mainly related to the distance between the transmitter and the receiver. To improve the numerical stability (x _ΔT Typically small), where x can be used _t ＝(x _ΔT f _c ) EKF representing time offsetA variable. X is x _t Can also be regarded as corresponding to the carrier frequency f _c Carrier phase, x _t In units of cycles.

State variable (x) related to carrier frequency offset _f ): the state variable x related to frequency offset is typically included in the EKF state vector in consideration of the dynamic mobility of the UE and the difference in carrier frequencies between the transmitter and receiver _f (in Hz). X is x _f Comprises two parts of content: first, the frequency offset Δf between the carrier frequency generated by the transmitter and the carrier frequency generated by the receiver. One of the main causes of time offset is caused by oscillator frequency offset errors between the transmitter and the receiver. In OFDM systems, also commonly referred to as the rate of change of phase noise. Second, doppler frequency f due to relative motion between the transmitter and receiver _d 。

A state variable (x _o ): the EKF state vector may also include a carrier frequency offset rate state for the purpose of improving the accuracy of the carrier frequency offset estimation. The EKF variable x can be used here _o The rate of change of the frequency offset is expressed (in Hz/s). Here we will x _o Set to first order modeling random walk processes, i.e.

Wherein w is _o (t) continuous time Gaussian white noise,is the variance of the gaussian noise.

From the discussion above, the EKF state vector x for tracking the carrier phase of an OFDM signal from a certain transmitter is:

x＝[x _t ,x _f ,x _o ] ^T (5)

wherein the method comprises the steps of

x _t To correspond to f _c Time of carrier phaseOffset (at carrier frequency f _c Is the unit of the period);

x _f is carrier frequency offset (in Hz);

x _o for carrier frequency offset rate of change (in Hz/s)

x _t And x _f Between, and x _f And x _o The relationship between them can be expressed as:

wherein w is _t (t) and w _o (t) modeling as continuous-time gaussian white noise,is the noise w _t Variance of (t),>is the noise w _o (t) variance. And (3) injection: the frequency offset is carrier frequency dependent in nature and thus the frequency offset of each subcarrier in an OFDM system is not the same. However, since the difference in frequency offset of each subcarrier is generally small compared to the subcarrier spacing, in equations (6) and (7), the difference in frequency offset of different subcarriers has been ignored.

Regarding the EKF state equation:

in order to overcome the defect that the traditional EKF state vector only uses a single carrier system, the method is suitable for a 5G NR/4G LTE FDD/TDD multi-carrier system, carrier phase tracking can be carried out on a plurality of subcarrier signals at the same time, and an EKF state equation is redesigned.

Based on the EKF state vector x selected in equation (5), the EKF continuous time state equation tracking carrier phase can be written as:

wherein,

wherein w is _c (t) process noise, which is a continuous time state equation; q (Q) _c A process noise covariance matrix that is a continuous time state equation.

The main reasons for the time offset as mentioned before are clock errors caused by oscillator errors between the transmitter and the receiver and the propagation delay τ of the signal from the transmitter to the receiver. The propagation delay τ is then mainly related to the distance between the transmitter and the receiver.And->The values of (2) require consideration of both the quality of the transmitter and receiver crystal oscillators and the motion dynamics of the UE under consideration.

If it is usedAnd->Represents->And->The transmitter and receiver crystal oscillator error is determined by equation (2)It is known that the number of the components,

wherein f _c Is carrier frequency, { h ₀ ,h _-2 And is the Allen coefficient of variance of the crystal oscillator. { h ₀ ,h _-2 Typical values of } are the following table:

crystal oscillator	h ₀	h _-2
			Low quality temperature compensated crystal oscillator (TCXO)	2×10 ^-19	2×10 ^-20
High quality temperature compensated crystal oscillator (TCXO)	2×10 ^-21	2×10 ^-24
			Constant temperature crystal oscillator (OCXO)	2×10 ^-25	2×10 ^-25

If it is usedAnd->Represents->And->Part of the system which causes errors in the relative position and relative movement of transmitter and receiver, then +. >And->And the relative movement speed and relative acceleration of the transmitter and receiver. It is further assumed that the relative movement speed of the transmitter and the receiver does not exceed v (m/s) and the acceleration does not exceed a (m/s) ² ) There may be

Where c is the speed of light. For example, it may be assumed here that the velocity is less than 6 km/h and the acceleration is less than 0.1 m/s for indoor carrier phase positioning ² 。

Assume thatAnd->Is independent and->And->Independently, from equations (11) and (12):

may be considered based on the crystal oscillator masses of the transmitter and receiver and the relative positions and relative movements of the transmitter and receiver. For simplicity, a->Can be set to a relative sigma _f Smaller numbers, e.g. assuming sigma ₀ ＝0.01σ _f 。

The discrete-time state equation of the EKF for tracking the carrier phase after the discrete by the EKF continuous-time state equation (8) is:

x(k+1)＝F(k)x(k)+w(k) (14)

wherein:

E[w(i)w ^T (j)]＝Qδ _ij (16)

where Δt (k) (in seconds) represents the time interval between the CPRS-OFDM symbol at time k+1 and the CPRS-OFDM symbol at time k+1, as shown in fig. 4. The process noise matrix Q of the discrete state equation may be calculated based on the following method:

wherein Q is ⁽ⁱ⁾ Is the i derivative of Q.

With respect to the EKF measurement equation

In order to overcome the defect that the traditional EKF state vector only uses a single carrier system, the method is suitable for a 5G NR/4G LTE FDD/TDD multi-carrier system, carrier phase tracking can be carried out on a plurality of subcarrier signals at the same time, and an EKF measurement equation is redesigned.

The frequency domain signal of the first subcarrier can be obtained from equations (3) and (2):

from T _s ＝1/(NΔf _sCS ),δf＝x _f /Δf _SCS ,x _ΔT ＝(Δt+τ ₀ ),x _t ＝x _ΔT f _c Can be obtained

Then, corresponding to the k time (t=t _k ) The measurement equation for carrier phase measurement of CPRS-OFDM symbols can be written as

y(k)＝h(x(k))+v(k) (21)

Wherein the method comprises the steps of

y(k)＝{y _l (k)}；h＝{h _l (k)}；v＝{v _l (k)} (22)

Where v is measurement noise and R represents the covariance matrix of measurement noise v.

Concerning EKF algorithm

The EKF algorithm comprises two steps of time updating and measurement updating, wherein the time updating predicts the EKF state of the next moment based on the EKF state measured at the current moment and mainly comprises an EKF state vector x and an EKF state covariance matrix P; the measurement update is to measure the EKF state at the current time based on the EKF state predicted at the previous time and the output of the measurement matrix at the current time, wherein the EKF state includes an EKF state vector x and an EKF state covariance matrix P.

In the step of time update, the EKF predicts the EKF state at time k+1 based on the state estimate at time k. The EKF time update algorithm is as follows

P(k+1|k)＝F(k)P(k|k)F ^T (k)+Q(k) (28)

Wherein the method comprises the steps ofAnd P (k|k) represents the estimated state vector of the EKF at time k and its covariance matrix, respectively;and P (k+ 1|k) respectively represent EKF based on +.>And the state vector at time k+1 predicted by P (k|k) and its covariance matrix.

In the measurement update step, the EKF updates the state vector of the EKF at time k+1 predicted at time k based on the scalar measurement at time k+1:

K(k+1)＝P(k+1|k)H ^T ×[HP(k+1|k)H ^T +R(k)] ^-1 (30)

P(k+1|k+1)＝[I-K(k+1)H]P(k+1|k) (31)

Wherein the method comprises the steps of

y (k+1) is a scalar measurement of the carrier phase at time k+1;

scalar predicted value for carrier phase at time k+1;

h is the EKF measurement matrix at time k+1.

The measurement matrix H is given by

/>

Due to the modulo 2 pi operation of the phase measurement in equation (24)), the scalar measurement y (k+1) of the measured OFDM carrier phase may differ from the true phase by an integer number of periods. In the measurement updated equation (29), the scalar measurement value y (k+1) and the predicted phase value of the OFDM carrier phase must be correctly determinedDifference of->Based on the predicted state->Predicted carrier phase +.>The method comprises the following steps:

the integer part and the fraction part of (2) are +.>And->If it is assumed that the scalar prediction value of EKF +.>Within 0.5 cycles, can be determined by the following formula>

Finally, the predicted carrier phaseAnd the high-precision position information of each moment of the user terminal can be obtained by a terminal positioning algorithm.

Method for initializing EKF

First, an EKF state quantity is initialized:

from equation (20), it is possible to obtain:

an estimate of the time offset of the OFDM symbol at the initial time (k=0) can be obtained from equation (36)Is an estimation method of (1):

another approach is to estimate the time of arrival (TOA) according to a conventional algorithm and then use the TOA estimate to set the initial time offset x _t (0)。

For the remaining state quantity x of the EKF _f (0),x _o (0) Their initial values are generally not known, and thus their initial estimates may be set to zero. Thus EKF initial State vectorThe method comprises the following steps:

the initial covariance matrix P (0) represents the initial estimateThe uncertainty of (2) can be generally set as follows

Wherein,the initial value may be based on the assumption +.>Is set, for example: set to the square of the maximum error.

In addition, for an EKF receiver based on closed loop structured OFDM carrier phase tracking, an EKF with a closed loop architecture corrects for the effects of time offset, frequency offset and phase noise on the carrier phase of the received data samples with the estimated state quantity.

Let the sequence of data samples corresponding to the CPRS OFDM symbol starting at time k+2 be denoted as { x } _n (k+2) } (n=0, 1, …, N-1). For EKF receiver in closed loop configuration, { x _n The carrier phase of the (k+2) } sequence will be { x over the data samples prior to FFT using equation (40) based on the EKF state predicted at time k+2 _n Phase rotation is performed to form a new data sample sequence { z }, a new data sample sequence { z _n (k+2) } as an input sequence of the FFT:

wherein,

z _n (k+2) phase rotated data samples;

prediction-based time offset- >Is of the phase rotation of (a)

The EKF receiver of the closed-loop structure has the same steps as the EKF receiver of the open-loop structure, including EKF state, time update and measurement update of the EKF algorithm, and EKF initialization. The difference is that: since the EKF of the closed loop structure uses the predicted time offsetFor a received sequence of data samples { x } _n (k+2) } phase rotated, +.>Instead of the calculation of equation (34), the calculation of equation (42) below is used:

while the prior art does not disclose an EKF design method suitable for real-time tracking of carrier phase of an OFDM wireless network (LTE, 5G NR), the present embodiment proposes a real-time tracking method for carrier phase positioning of an OFDM wireless network based on EKF, and the steps of an EKF receiver for tracking OFDM carrier phase of a corresponding open loop structure and closed loop structure are as follows, in combination with the implementation procedure of the above specific formula:

step1: for baseband discrete data samples { x } _n FFT transforming to obtain frequency domain signals corresponding to sub-carriers with known CPRS sample sequence in OFDM symbolAs in equation (19);

step2: will beCPRS sample sequence known thereto +. >Performing a correlation calculation to obtain a scalar measurement of its phase +.>As in equation (23);

step3: according to EKF time updating algorithm, using state estimation value based on k timeAnd covariance matrix P (k|k)Predicting the state vector at time k+1 +.>And a covariance matrix P (k+ 1|k) as in equations (27) and (28);

step4: based on the predicted state vectorThe carrier phase is predicted and is marked as +.>As in equation (34);

step5: calculating the difference between the scalar measurement value and the scalar prediction value of the acquired carrier phase at the time k+1, and recording asAs in equation (35);

step6: based on EKF measurement update algorithms (29) - (31)P (k+ 1|k)Updating the state vector estimate +.>And covariance matrix P (k+1|k+1);

step7: and repeating Step3 to Step6, calculating scalar measurement values and state vector prediction values of the carrier phase at each moment, and obtaining estimated values of the carrier phase, thereby completing tracking of the carrier phase. .

As shown in fig. 3, the EKF receiver for OFDM carrier phase tracking based on a closed loop structure includes the following steps:

step1 to Step6: the method is identical to Step1 to Step6 of OFDM carrier phase tracking based on an open loop structure;

step7: EKF state vector estimation at k+1 is first utilized at k+2 Value feedback correction is performed on pre-FFT incoming data samples (baseband discrete data samples { x }, by time and frequency offset _n -j) introduced effects, such as equation (40);

Fig. 5 shows a schematic structural diagram of a tracking device for an ofdm carrier phase according to the present embodiment, where the device includes: a value acquisition module 501 and a tracking module 502, wherein:

the value obtaining module 501 is configured to obtain a state vector predicted value of an orthogonal frequency division multiplexing OFDM carrier phase and a scalar measurement value of the OFDM carrier phase at each time;

the tracking module 502 is configured to obtain a state vector estimated value of the OFDM carrier phase based on the state vector predicted value of the OFDM carrier phase at each time and the scalar measurement value of the OFDM carrier phase, and track the OFDM carrier phase.

Specifically, the value obtaining module 501 obtains a state vector predicted value of an orthogonal frequency division multiplexing OFDM carrier phase and a scalar measurement value of the OFDM carrier phase at each time; the tracking module 502 obtains a state vector estimated value of the OFDM carrier phase based on the state vector predicted value of the OFDM carrier phase at each time and the scalar measurement value of the OFDM carrier phase, and tracks the OFDM carrier phase.

The tracking device for the ofdm carrier phase in this embodiment may be used to execute the above method embodiment, and the principle and technical effects of the tracking device are similar, and are not described herein again.

Referring to fig. 6, the electronic device includes: a processor (processor) 601, a memory (memory) 602, and a bus 603;

wherein,

the processor 601 and the memory 602 perform communication with each other through the bus 603;

the processor 601 is configured to call program instructions in the memory 602 to perform the following method:

Further, on the basis of the foregoing embodiment, the obtaining the state vector estimation value of the OFDM carrier phase based on the state vector prediction value of the OFDM carrier phase at each time and the scalar measurement value of the OFDM carrier phase, and tracking the OFDM carrier phase specifically includes:

wherein k is a positive integer.

Further, on the basis of the foregoing embodiment, the obtaining the scalar predicted value of the OFDM carrier phase at the time k+1 according to the state vector predicted value of the OFDM carrier phase at the time k+1, calculating a difference between the scalar measured value of the OFDM carrier phase at the time k+1 and the scalar predicted value of the OFDM carrier phase at the time k+1, and updating the state vector estimated value and the covariance matrix estimated value of the OFDM carrier phase at the time k+1 according to the extended kalman filter EKF measurement update algorithm, and then further includes:

the baseband discrete data samples at time k+2 are phase rotated based on the state vector estimate of the OFDM carrier phase at time k+1 to correct the baseband discrete data samples at time k+2 by the time and frequency offset.

Further, on the basis of the above embodiment, the phase rotation is performed on the baseband discrete data sample at the k+2 time according to the state vector estimated value at the k+1 time to correct the baseband discrete data sample at the k+2 time by the time and frequency offset, which specifically includes:

wherein,is made of->Calculated phase rotation +.>j is the unit imaginary number; x is x _n (k+2) is the nth known CPRS sample sequence in the OFDM symbol at time k+2; n is the number of baseband discrete data samples contained in each OFDM symbol; />For the predicted time offset of the OFDM symbol at time k+2, Δt (k+2) is the time offset between the signal received by the receiver at the beginning of the OFDM symbol at time k+2 and the signal generated by the receiver itself; f (f) _c K is a positive integer for the carrier frequency.

Further, on the basis of the foregoing embodiment, the acquiring the state vector predicted value of the orthogonal frequency division multiplexing OFDM carrier phase and the scalar measurement value of the OFDM carrier phase at each time specifically includes:

Further, on the basis of the foregoing embodiment, the performing correlation calculation on the known carrier phase reference signal CPRS sample sequence in the OFDM symbol carried at the k time and the frequency domain signal of the subcarrier corresponding to the sample sequence at the k time to obtain a scalar measurement value of the OFDM carrier phase at the k time specifically includes:

/>

Wherein δf is the normalized frequency deviation; h is a _o Attenuation for the first transmission path; n is the number of baseband discrete data samples contained in each OFDM symbol; j is the unit imaginary number; f (f) _c Is the carrier frequency; l is the sequence number of the subcarrier in the known CPRS sample sequence; Δf _SCS Is the subcarrier spacing of an OFDM system; Δt (k) is the signal received by the receiver at the beginning of the OFDM symbol at time k and the receiver is self-containedTime offset between the body-generated signals; τ ₀ (k) Time offset generated by Doppler in channel transmission for the OFDM symbol at k time; g _l (k) A wireless channel frequency response for the first known CPRS sample sequence in the OFDM symbol at time k; x is X _l (k) For the first known CPRS sample sequence in the OFDM symbol at k time; w (W) _l (k) Additive White Gaussian Noise (AWGN) which is the first known CPRS sample sequence in the OFDM symbol at time k; r is R _l (k) For the frequency domain signal of the first known CPRS sample sequence in the OFDM symbol at time k, x _t (k) For the time offset of the OFDM symbol at time k, x _f (k) For the frequency offset of the OFDM symbol at time k, T _s K is a positive integer for the sampling time interval;

Further, on the basis of the foregoing embodiment, the obtaining, according to the EKF time update algorithm, a state vector predicted value and a covariance matrix predicted value at a k+1 time based on the state vector estimated value and the covariance matrix estimated value at the k+1 time, and obtaining a scalar predicted value of an OFDM carrier phase at the k+1 time based on the state vector predicted value at the k+1 time and a preset EKF measurement matrix specifically includes:

wherein DeltaT (k) is the time difference between the time of k+1 and the time of k;

P(k+1|k)＝F(k)P(k|k)F ^T (k)+Q(k)

Further, on the basis of the foregoing embodiment, the updating the state vector estimation value and the covariance matrix estimation value of the OFDM carrier phase at time k+1 according to the EKF measurement updating algorithm specifically includes:

P(k+1|k+1)＝[I-K(k+1)H]P(k+1|k)

wherein K (k+1) =p (k+ 1|k) H ^T ×[HP(k+1|k)H ^T +R _l (k)] ^-1

H ^T Is the transposed matrix of H.

Further, on the basis of the above embodiment, the estimated value of the time offset of the OFDM symbol at the initial time isThe estimation formula of (2) is as follows:

or alternatively, the first and second heat exchangers may be,

estimation of time offset of OFDM symbol at initial timeSetting according to an estimated value of the estimated arrival time TOA;

wherein l _j A j-th subcarrier sequence number; l (L) _i Is the i sub-carrier serial number;frequency domain data of the ith subcarrier of the OFDM symbol at k time; />Conjugation of frequency domain data of the ith subcarrier of the OFDM symbol at k time; />Frequency domain data of the j sub-carrier of the OFDM symbol at k time; />The conjugation of the frequency domain data of the j-th subcarrier of the OFDM symbol at the k moment.

The present embodiments disclose a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, are capable of performing the method of:

The electronic device in this embodiment may be used to execute the above method embodiment, and the principle and technical effects of the electronic device are similar, and are not described herein again.

The present embodiment provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the method of:

The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.

From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.

It should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for tracking the phase of an orthogonal frequency division multiplexing carrier, comprising:

based on the state vector predicted value of the OFDM carrier phase and the scalar measurement value of the OFDM carrier phase at each moment, obtaining a state vector estimated value of the OFDM carrier phase, and tracking the OFDM carrier phase;

the method for tracking the OFDM carrier phase specifically includes the steps of:

Wherein k is a positive integer.

2. The method for tracking an OFDM carrier phase according to claim 1, wherein the steps of obtaining a scalar predicted value of an OFDM carrier phase at time k+1 from a state vector predicted value of the OFDM carrier phase at time k+1, calculating a difference between a scalar measured value of the OFDM carrier phase at time k+1 and the scalar predicted value of the OFDM carrier phase at time k+1, updating the state vector estimated value and the covariance matrix estimated value of the OFDM carrier phase at time k+1 according to an extended kalman filter EKF measurement update algorithm, and then:

3. The method for tracking the carrier phase of the orthogonal frequency division multiplexing according to claim 2, wherein the phase rotation is performed on the baseband discrete data sample at the k+2 time according to the state vector estimation value at the k+1 time to correct the baseband discrete data sample at the k+2 time by the time and frequency offset, specifically comprising:

wherein,is made of->Calculated phase rotation +.>j is the unit imaginary number; x is x _n (k+2) is the nth known CPRS sample sequence in the OFDM symbol at time k+2; n is the number of baseband discrete data samples contained in each OFDM symbol; />For prediction ofTime offset of OFDM symbol at time k+2; f (f) _c Is the carrier frequency; k is a positive integer.

4. The method for tracking an OFDM carrier phase according to claim 1, wherein the step of obtaining the state vector predicted value of the OFDM carrier phase and the scalar measurement value of the OFDM carrier phase at each time specifically includes:

5. The method for tracking an OFDM carrier phase according to claim 4, wherein the correlating the sample sequence of the CPRS of the known carrier phase reference signal in the OFDM symbol carried at the k time with the frequency domain signal of the subcarrier corresponding to the sample sequence at the k time to obtain the scalar measurement value of the OFDM carrier phase at the k time specifically comprises:

For the frequency domain signal R _l (k) And corresponding known CPRS sample sequence X _l (k) Proceeding withCorrelation calculation to obtain scalar measurement y of carrier phase of OFDM first subcarrier at k moment _l (k)：

Wherein δf is the normalized frequency deviation; h is a ₀ Attenuation for the first transmission path; n is the number of baseband discrete data samples contained in each OFDM symbol; j is the unit imaginary number; f (f) _c Is the carrier frequency; l is the sequence number of the subcarrier in the known CPRS sample sequence; Δf _SCS Is the subcarrier spacing of an OFDM system; Δt (k) is the time offset between the signal received by the receiver at the beginning of the OFDM symbol at time k and the signal generated by the receiver itself; τ ₀ (k) Time offset generated by Doppler in channel transmission for the OFDM symbol at k time; g _l (k) A wireless channel frequency response for the first known CPRS sample sequence in the OFDM symbol at time k; x is X _l (k) For the first known CPRS sample sequence in the OFDM symbol at k time; w (W) _l (k) Additive White Gaussian Noise (AWGN) which is the first known CPRS sample sequence in the OFDM symbol at time k; r is R _l (k) For the frequency domain signal of the first known CPRS sample sequence in the OFDM symbol at time k, x _t (k) For the time offset of the OFDM symbol at time k, x _f (k) For the frequency offset of the OFDM symbol at time k, T _s K is a positive integer for the sampling time interval;

H＝{H _l }；

wherein H is _l EKF measurement matrix for the l-th subcarrier, T _s In order to sample the time interval of the time,for the subcarrier locations of the sequence of L CPRS samples in the CPRS-OFDM symbol.

6. The method for tracking an OFDM carrier phase according to claim 5, wherein the obtaining, according to the EKF time update algorithm, a state vector predictor and a covariance matrix predictor at a k+1 time based on the state vector estimator and the covariance matrix estimator at the k+1 time, and obtaining a scalar predictor of the OFDM carrier phase at the k+1 time based on the state vector predictor at the k+1 time and a preset EKF measurement matrix specifically includes:

P(k+1|k)＝F(k)P(k|k)F ^T (k)+Q(k)

7. The method for tracking an OFDM carrier phase according to claim 6, wherein updating the state vector estimate and the covariance matrix estimate of the OFDM carrier phase at time k+1 according to an extended kalman filter EKF measurement update algorithm comprises:

state vector predictor from OFDM carrier phase at time k+1An EKF gain matrix K (k+1) at time k+1, a scalar measurement y (k+1) of the OFDM carrier phase at time k+1, and a scalar prediction of the carrier phase at time k+1 Updating the state vector estimate at time k+1 +.>

P(k+1|k+1)＝[I-K(k+1)H]P(k+1|k)

wherein K (k+1) =p (k+ 1|k) H ^T ×[HP(k+1|k)H ^T +R _l (k)] ^-1

H ^T The transposed matrix of H, and I is the identity matrix.

8. The method for tracking an OFDM carrier phase according to claim 5 or 6, wherein an estimated value of a time offset of an OFDM symbol at an initial time is calculatedThe estimation formula of (2) is as follows:

or alternatively, the first and second heat exchangers may be,

wherein l _j A j-th subcarrier sequence number; l (L) _i Is the i sub-carrier serial number;at time kFrequency domain data of an ith subcarrier of the OFDM symbol; />Conjugation of frequency domain data of the ith subcarrier of the OFDM symbol at k time; />Frequency domain data of the j sub-carrier of the OFDM symbol at k time; />Conjugation of frequency domain data for j-th subcarrier of k-time OFDM symbol, < >>For the subcarrier locations of the sequence of L CPRS samples in the CPRS-OFDM symbol.

9. An apparatus for tracking the phase of an orthogonal frequency division multiplexing carrier, comprising:

the tracking module is used for obtaining a state vector estimated value of the OFDM carrier phase based on the state vector predicted value of the OFDM carrier phase at each moment and the scalar measured value of the OFDM carrier phase and tracking the OFDM carrier phase;

Wherein k is a positive integer.

10. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor, when executing the program, performs the method of:

wherein k is a positive integer.

11. The electronic device of claim 10, wherein the steps of obtaining the scalar predicted value of the OFDM carrier phase at time k+1 from the state vector predicted value of the OFDM carrier phase at time k+1, calculating a difference between the scalar measured value of the OFDM carrier phase at time k+1 and the scalar predicted value of the OFDM carrier phase at time k+1, and updating the state vector estimated value and the covariance matrix estimated value of the OFDM carrier phase at time k+1 according to an extended kalman filter EKF measurement update algorithm, further comprise:

12. The electronic device of claim 11, wherein the phase rotating the baseband discrete data samples at time k+2 based on the state vector estimate at time k+1 to correct the baseband discrete data samples at time k+2 by a time and frequency offset, comprises:

wherein,is made of->Calculated phase rotation +.>j is the unit imaginary number; x is x _n (k+2) is the nth known CPRS sample sequence in the OFDM symbol at time k+2; n is the number of baseband discrete data samples contained in each OFDM symbol; />For the predicted time offset of the OFDM symbol at time k+2, Δt (k+2) is the time offset between the signal received by the receiver at the beginning of the OFDM symbol at time k+2 and the signal generated by the receiver itself; f (f) _c Is the carrier frequency; k is a positive integer.

13. The electronic device according to claim 10, wherein the obtaining the state vector predictor of the orthogonal frequency division multiplexing OFDM carrier phase and the scalar measure of the OFDM carrier phase for each time instant specifically comprises:

14. The electronic device of claim 13, wherein the correlating the known carrier phase reference signal CPRS sample sequence in the OFDM symbol carried at the k time with the frequency domain signal of the subcarrier corresponding to the sample sequence at the k time to obtain the scalar measurement value of the OFDM carrier phase at the k time specifically comprises:

H＝{H _l }；

15. The electronic device of claim 14, wherein the obtaining, according to the EKF time update algorithm, the state vector predictor and the covariance matrix predictor at the k+1 time based on the state vector estimator and the covariance matrix estimator at the k time, and obtaining the scalar predictor of the OFDM carrier phase at the k+1 time based on the state vector predictor at the k+1 time and the pre-set EKF measurement matrix specifically includes:

P(k+1|k)＝F(k)P(k|k)F ^T (k)+Q(k)

16. The electronic device of claim 15, wherein the updating the state vector estimate and the covariance matrix estimate of the OFDM carrier phase at time k+1 according to the extended kalman filter EKF measurement update algorithm, specifically comprises:

P(k+1|k+1)＝[I-K(k+1)H]P(k+1|k)

wherein K (k+1) =p (k+ 1|k) H ^T ×[HP(k+1|k)H ^T +R _l (k)] ^-1

H ^T The transposed matrix of H, and I is the identity matrix.

17. The electronic device of claim 14 or 15, wherein the estimated value of the time offset of the OFDM symbol at the initial time instantThe estimation formula of (2) is as follows:

or alternatively, the first and second heat exchangers may be,

wherein l _j A j-th subcarrier sequence number; l (L) _i Is the i sub-carrier serial number;frequency domain data of the ith subcarrier of the OFDM symbol at k time; />Conjugation of frequency domain data of the ith subcarrier of the OFDM symbol at k time; />Frequency domain data of the j sub-carrier of the OFDM symbol at k time; />Conjugation of frequency domain data for j-th subcarrier of k-time OFDM symbol, < >>For the subcarrier locations of the sequence of L CPRS samples in the CPRS-OFDM symbol.

18. A non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor implements the method of tracking an orthogonal frequency division multiplexing carrier phase according to any of claims 1 to 8.