Doppler and channel joint estimation method of OFDM (Orthogonal Frequency Division Multiplexing) system under impulse noise background

Abstract

The invention relates to a Doppler and channel joint estimation method of an OFDM (Orthogonal Frequency Division Multiplexing) system under an impulse noise background, which comprises the following steps of: constructing an OFDM communication system model in which a channel has Doppler frequency shift and a sending signal is an OFDM modulation signal, and then respectively calculating a cyclic autocorrelation function of the sending signal and a cyclic autocorrelation function of a receiving signal in the OFDM communication system model; the method comprises the following steps of: constructing a cyclic correlation matrix equation by using the difference of an OFDM signal, AWGN noise and impulse noise in cyclic correlation function energy distribution, and finally obtaining a Doppler frequency shift estimation value and a channel parameter by solving the matrix equation, thereby realizing Doppler frequency shift and channel estimation of an OFDM system under the impulse noise background. And better robust performance is shown in an impulse noise environment.

Description

Technical Field

[0001] This invention relates to the field of communications, and more particularly to a joint estimation method for Doppler and channel in OFDM systems under impulse noise conditions. Background Technology

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology, due to its advantages in resisting inter-symbol interference and inter-channel interference, has been widely used in various wireless or wired communication systems to support high-speed, high-bandwidth transmission. OFDM-based communication systems (or OFDM systems) provide optimal performance in additive white Gaussian noise (AWGN) environments.

[0003] However, in scenarios such as vehicular networks, smart grids, and underwater acoustic communications, the presence of impulse noise can significantly degrade the performance of OFDM systems. Therefore, channel state information is crucial for OFDM systems to achieve detection and coherent demodulation, and the overall performance of an OFDM system largely depends on the accuracy of channel estimation.

[0004] Chinese invention patent CN103281267B discloses a blind channel estimation method in an OFDM system under impulse noise environment. The process is as follows: First, the OFDM signal received by the receiver of the OFDM system is preprocessed to obtain the preprocessed received signal; then, the autocorrelation function and periodic autocorrelation function of the preprocessed received signal are calculated; next, the periodic autocorrelation function of the preprocessed received signal is subjected to a z-transform of the delay variable to obtain the cyclic spectrum function of the preprocessed received signal; finally, based on some spectral information in the cyclic spectrum function of the preprocessed received signal, the blind estimation of channel information is realized. The advantage is that the computational complexity is low, and only some non-zero spectral information is needed at the OFDM signal receiver to accurately and effectively estimate the channel information under impulse noise environment.

[0005] However, existing channel estimation methods for OFDM systems have shortcomings: channel estimation methods under impulse noise environments do not consider the impact of Doppler shift. Since Doppler shift arises from the relative motion between the transmitter and receiver in a communication system, it disrupts the subcarrier orthogonality of the OFDM system, introducing inter-carrier interference and significantly degrading OFDM system performance. Furthermore, these channel estimation methods rely on prior knowledge of impulse noise models, which cannot satisfy the noise environment conditions of real-world communication. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a joint Doppler and channel estimation method for OFDM systems under impulse noise conditions, which addresses the shortcomings of the prior art. This joint Doppler and channel estimation method for OFDM systems under impulse noise conditions can meet the requirements of impulse noise environments in real communication environments, achieving accurate estimation of the OFDM system channel.

[0007] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a joint Doppler and channel estimation method for OFDM systems under impulse noise background, characterized by comprising the following steps: Step 1: Construct an OFDM communication system model with a channel exhibiting Doppler frequency shift and a transmitted signal being an OFDM modulated signal; Step 2: Calculate the time-varying autocorrelation function of the transmitted signal in the constructed OFDM communication system model, and calculate the cyclic autocorrelation function of the transmitted signal based on the time-varying autocorrelation function; Step 3: Calculate the time-varying autocorrelation function of the received signal in the constructed OFDM communication system model, and calculate the cyclic autocorrelation function of the received signal based on the time-varying autocorrelation function; Step 4: Calculate the estimated Doppler frequency shift of the OFDM communication system based on the obtained cyclic autocorrelation function of the transmitted signal and the cyclic autocorrelation function of the received signal. Step 5: Perform compression transformation on the received signal of the OFDM communication system to obtain the compressed received signal; Step 6: Calculate the autocorrelation function of the received signal after compression transformation, and calculate the cyclic autocorrelation function of the received signal after compression transformation based on the autocorrelation function; Step 7: Based on the obtained cyclic autocorrelation function of the received signal after compression transformation, calculate the first cyclic autocorrelation function corresponding to the cyclic autocorrelation function in its energy concentration region and the cyclic spectrum function of the received signal after compression transformation. Step 8: Calculate the first and second cyclic spectrum functions corresponding to the cyclic spectrum functions of the received signal after compression transformation at the first and second preset variable values, respectively, and calculate the quotient function of the first and second cyclic spectrum functions. Step 9: Calculate the first quotient function corresponding to the transmission signal being at the first preset concentration of its own cyclic correlation energy and the reception signal being at the concentration of its own cyclic correlation energy. Step 10: Process the received signal after compression transformation according to the first cyclic autocorrelation function to construct the first Topplitz matrix and the second Topplitz matrix, and construct the diagonal matrix. Step 11: Based on the first Toplitz matrix, the second Toplitz matrix, and the diagonal matrix, obtain the first matrix expression form corresponding to the first quotient function when the transmitted signal is located at the first preset concentration of its own cyclic correlation energy and the received signal is located at the concentration of its own cyclic correlation energy. Step 12: Based on the first matrix expression of the first quotient function, obtain the second matrix expression of the first quotient function when the transmitted signal is at the second preset concentration of its own cyclic correlation energy and the received signal is at the concentration of its own cyclic correlation energy. Step 13: Based on the obtained first matrix expression and second matrix expression, calculate the comprehensive matrix expression of the first quotient function when the energy of the cyclic autocorrelation function of the transmitted signal is at its energy concentration point; Step 14: Solve the obtained synthesis matrix expression using the minimum mean square error to obtain the channel estimate of the OFDM system under impulse noise background.

[0008] Improved, in the joint Doppler and channel estimation method for the OFDM system under impulse noise background, the OFDM communication system model is constructed as follows: In this OFDM communication system model, each OFDM symbol contains M Each subcarrier, the transmitted signal is marked as x ( n The received signal is marked as y ( n ); where: transmitting signal x ( n ) is represented as: , n∈[0, M + N CP -1]; X ( i ) represents the i-th subcarrier from QPSK modulation. N CP This indicates the length of the cyclic prefix CP added to the OFDM symbol as a guard interval; Received signal y ( n ) is represented as: ;in, l ∈[0, L h ], ; or ( n )= I ( n )+ v ( n ), , I (n )= B ( n ) G ( n ); e = f d / Δ f = Mf d / f s ; f d =| vf c cos( i )| / c ;Δ f = f s / M ; h ( l ) represents the first in the OFDM communication system l The coefficients of the path, L h This represents the maximum path order of a multipath channel in an OFDM communication system. or ( n The ) represents the noise signal of the OFDM communication system. This noise signal includes impulse noise and independent, identically distributed additive white Gaussian noise as background noise. The time-varying variance of the channel impulse response. I ( n ) represents impulse noise signal, v ( n ) represents independent and identically distributed additive white Gaussian noise. B ( n ) represents a Bernoulli random process. G ( n ) indicates that the mean is 0 and the variance is Complex Gaussian white noise, e This represents the normalized Doppler frequency shift. f d This refers to the Doppler frequency shift caused by the channel in the OFDM communication system. f s Δ is the sampling frequency. f For subcarrier spacing, c At the speed of light, i It is the angle between the direction of arrival of the wave and the direction of motion of the signal receiving end.

[0009] Furthermore, in the joint Doppler and channel estimation method for the OFDM system under the impulsive noise background, the time-varying autocorrelation function and cyclic autocorrelation function of the transmitted signal are calculated as follows: ; ; in, R x ( n , t (to send a signal) x ( n The time-varying autocorrelation function of E[ x ( n ) x * ( n+t )]express x ( n ) x * ( n+ t ) expectations, x * ( n+t (to send a signal) x ( n The conjugate of ) t To delay, Indicates subcarrier X ( i The variance of ) d ( t () represents the discrete-time unit impulse function, also known as the discrete Dirac delta function. the Represents a delay variable. R x ( n , t ) is in the variable n Periodic functions on P This indicates the periodic function R x ( n , t The cycle of ); ; , ;in, C x ( k , t (to send a signal) x ( n The cyclic autocorrelation function of ) k Indicates the cycle frequency.

[0010] Further improvements are made to the joint Doppler and channel estimation method for OFDM systems under impulse noise background. In step 3, the received signal... y ( n The time-varying autocorrelation function of ) is denoted as R yy* ( n , t ): ; Δτ= l 1- l 2, R ηη* ( n , t )= R II* ( n , t )+ R vv* ( n , t ); in, R yy* ( n , t (received signal) y ( n The time-varying autocorrelation function of ) y * ( n+t (received signal) y ( n )exist- t Delayed conjugate, e The normalized Doppler frequency shift in the channel of the OFDM communication system model. R II* ( n , t () is an impulse noise signal I ( n The time-varying autocorrelation function of ) R vv* ( n , t (This is) an additive white Gaussian noise signal. v ( n The time-varying autocorrelation function of ). ; ; C η ( k , t )= C I ( k , t )+C v ( k , t ); in, C y ( k , t (received signal) y ( n The cyclic autocorrelation function of ) C x ( k , t () is the signal being sent. x ( n The cyclic autocorrelation function of ) C I ( k , t () is an impulse noise signal I ( n The cyclic autocorrelation function of ) C v ( k , t () is an additive white Gaussian noise signal v ( n The cyclic autocorrelation function of ).

[0011] Compared with the prior art, the advantages of this invention are as follows: The Doppler and channel joint estimation method for OFDM systems under impulse noise background of this invention constructs an OFDM communication system model with Doppler frequency shift in the channel and OFDM modulated signal in the transmitted signal. Then, it calculates the estimated Doppler frequency shift of the OFDM communication system by calculating the cyclic autocorrelation function of the transmitted signal and the cyclic autocorrelation function of the received signal in the OFDM communication system model. Based on the obtained Doppler frequency shift estimate, the received signal of the OFDM communication system is subjected to compression transformation and cyclic spectrum calculation processing in sequence to obtain the cyclic spectrum function of the received signal after compression transformation and the quotient function of the first cyclic spectrum function and the second cyclic spectrum function corresponding to the first preset variable value and the second preset variable value, respectively. The quotient function is calculated when the transmitted signal is at the first preset concentration of its own cyclic correlation energy and the received signal is at the same cyclic correlation energy concentration. The first quotient function corresponding to the energy concentration point is obtained by constructing a first Topplitz matrix and a second Topplitz matrix based on the first cyclic autocorrelation function, and then constructing a diagonal matrix. Based on the two Topplitz matrices and the diagonal matrix, the first matrix expression of the first quotient function when the transmitted signal is at a first preset concentration point of its own cyclic autocorrelation energy and the received signal is at a concentration point of its own cyclic autocorrelation energy is obtained. Furthermore, the second matrix expression of the first quotient function when the transmitted signal is at a second preset concentration point of its own cyclic autocorrelation energy and the received signal is at a concentration point of its own cyclic autocorrelation energy is obtained. Based on the two obtained second matrix expressions, the comprehensive matrix expression of the first quotient function when the cyclic autocorrelation function energy of the transmitted signal is at its energy concentration point is calculated. Finally, the minimum mean square error is used to solve the obtained comprehensive matrix expression to obtain the channel estimate of the OFDM system under impulse noise background. Thus, by performing compression transformation (CT) processing on the received signal of the OFDM system to suppress the adverse effects of impulse noise on channel estimation performance, and then utilizing the differences in the energy distribution of the cyclic correlation function of the OFDM signal, AWGN noise and impulse noise, a cyclic correlation matrix equation is constructed. Finally, by solving the matrix equation, the Doppler frequency shift estimate and channel parameters are obtained, realizing the Doppler frequency shift and channel estimation of the OFDM system under the background of impulse noise, and exhibiting better robust performance in the impulse noise environment. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating the joint Doppler and channel estimation method for an OFDM system under impulse noise background in an embodiment of the present invention. Figure 2 The amplitude diagram of the cyclic autocorrelation function of the OFDM signal; Figure 3 The amplitude diagram of the cyclic correlation function of the OFDM signal after compression transformation; Figure 4 The amplitude plot of the cyclic autocorrelation function for impulse noise; Figure 5 The amplitude diagram of the cyclic autocorrelation function of the impulse noise after compression transformation; Figure 6 This is a schematic diagram comparing the MSE (mean square error of channel estimation) of the Doppler and channel joint estimation method with other channel estimation methods in this embodiment of the invention. Figure 7 This is a schematic diagram showing the curves of MSE as a function of signal-to-interference-plus-noise ratio under different impulse noise models for the Doppler and channel joint estimation method in this embodiment of the invention. Detailed Implementation

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0014] This embodiment provides a joint Doppler and channel estimation method for OFDM systems under impulse noise background. See also Figure 1 As shown, the joint Doppler and channel estimation method for an OFDM system under impulse noise background in this embodiment includes the following steps 1-14:

[0015] Step 1: Construct an OFDM communication system model where the channel exhibits Doppler frequency shift and the transmitted signal is an OFDM modulated signal; wherein, in this OFDM communication system model, each OFDM symbol contains M subcarriers, and the transmitted signal is labeled as... x ( n The received signal is marked as y ( n );in: Send signal x ( n ) is represented as: , n∈[0, M + N CP -1]; X ( i ) represents the i-th subcarrier from QPSK modulation. N CP This indicates the length of the cyclic prefix CP added to the OFDM symbol as a guard interval; Received signal y ( n ) is represented as: ;in, l ∈[0, L h ], ; or ( n )= I ( n )+ v (n ), , I ( n )= B ( n ) G ( n ); e = f d / Δ f = Mf d / f s ; f d =| vf c cos( i )| / c ;Δ f = f s / M。

[0016] h ( l ) represents the first in the OFDM communication system l The coefficients of the path, L h This represents the maximum path order of a multipath channel in an OFDM communication system. or ( n The ) represents the noise signal of the OFDM communication system. This noise signal includes impulse noise and independent, identically distributed additive white Gaussian noise as background noise. The time-varying variance of the channel impulse response. I ( n ) represents impulse noise signal, v ( n ) represents independent and identically distributed additive white Gaussian noise. B ( n ) represents a Bernoulli random process. G ( n ) indicates that the mean is 0 and the variance is Complex Gaussian white noise, e This represents the normalized Doppler frequency shift. f d This refers to the Doppler frequency shift caused by the channel in the OFDM communication system. f s Δ is the sampling frequency. f For subcarrier spacing, c At the speed of light, iThis is the angle between the arriving wave and the direction of motion of the signal receiver. The arriving wave refers to the radio wave (electromagnetic wave) transmitted from the transmitting antenna and reaching the receiving antenna after propagation. The direction of motion usually refers to the direction of the receiver's velocity vector; in mobile communication, it is generally assumed that the receiver is moving (e.g., in vehicles or handheld devices), so this is the direction of the receiver's motion.

[0017] Step 2: Calculate the time-varying autocorrelation function of the transmitted signal in the constructed OFDM communication system model, and calculate the cyclic autocorrelation function of the transmitted signal based on this time-varying autocorrelation function; transmitted signal x ( n The time-varying autocorrelation function of is denoted as R x ( n , t Send signal x ( n The cyclic autocorrelation function of is denoted as . C x ( k , t ); ; ; in, R x ( n , t (to send a signal) x ( n The time-varying autocorrelation function of E[ x ( n ) x * ( n+t )]express x ( n ) x * ( n+ t ) expectations, x * ( n+t (to send a signal) x ( n The conjugate of ) t To delay, Indicates subcarrier X ( i The variance of ) d ( t () represents the discrete-time unit impulse function, also known as the discrete Dirac delta function. the Represents a delay variable. R x ( n , t ) is in the variablen Periodic functions on P This indicates the periodic function R x ( n , t The cycle of ); ; , ; in, k This represents the cycle frequency. See the graph for the amplitude of the cyclic autocorrelation function of the OFDM signal (i.e., the transmitted signal). Figure 2 As shown, M =32, L =8.

[0018] Step 3: Calculate the received signal in the constructed OFDM communication system model. y ( n The time-varying autocorrelation function of the signal is used to calculate the received signal based on this time-varying autocorrelation function. y ( n The cyclic autocorrelation function of the received signal. y ( n The time-varying autocorrelation function of ) is denoted as R yy* ( n , t ): ; Δτ= l 1- l 2, R ηη* ( n , t )= R II* ( n , t )+ R vv* ( n , t ); in, R yy* ( n , t (received signal) y ( n The time-varying autocorrelation function of ) y * ( n+t (received signal) y ( n )exist- t Delayed conjugate, e The normalized Doppler frequency shift in the channel of the OFDM communication system model.R II* ( n , t () is an impulse noise signal I ( n The time-varying autocorrelation function of ) R vv* ( n , t (This is) an additive white Gaussian noise signal. v ( n The time-varying autocorrelation function of ). ; ; C η ( k , t )= C I ( k , t )+ C v ( k , t ); in, C y ( k , t (received signal) y ( n The cyclic autocorrelation function of ) C x ( k , t () is the signal being sent. x ( n The cyclic autocorrelation function of ) C I ( k , t () is an impulse noise signal I ( n The cyclic autocorrelation function of ) C v ( k , t () is an additive white Gaussian noise signal v ( n The cyclic autocorrelation function of ).

[0019] like Figure 2 As shown, the signal is sent. x ( n The cyclic autocorrelation function of ) only exists in k= 0 and t =± M Additive white Gaussian noise v ( nThe cyclic autocorrelation function of ) is C v ( k , t )= d ( k ) d ( t The cyclic autocorrelation function C v ( k , t The non-zero value of ) has one and only k= 0 and t =0; for impulse noise I ( n ), C I ( k , t )exist t =0 has non-zero values, and in t =0 and k= 0, there is an impulse pulse. Based on the above characteristics, consider special conditions. k= 0 and t =± M ,get C I ( 0 , ± M )= C v ( 0 , ± M )=0, received signal y ( n The cyclic autocorrelation function of ) is C y ( 0 , t ): , t =± M ; Among them, when hour, C x ( 0 , t The value is always zero. In general, for any condition satisfying this condition... l 1 ≠ l 2 ∈{0,1,…, L h -1} condition, Both are true. Therefore, when t ∈{ 0 , ± M} at that time, Therefore, in Γ( 0 , t In the expression, for t ∈{± M} , can be obtained C x ( 0 , τ+ l 1 - l 2 ) = 0, therefore Γ( 0 , ± M )=0, thus receiving the signal. y ( n ) cyclic autocorrelation function C y ( 0 , t This can be further simplified to: .

[0020] Step 4, based on the obtained transmitted signal x ( n The cyclic autocorrelation function and received signal y ( n The Doppler frequency shift estimate of the OFDM communication system is calculated by using the cyclic autocorrelation function of . The Doppler frequency shift estimate is denoted as . : , T Represents any integer.

[0021] Step 5: Receive signals from the OFDM communication system. y ( n The signal undergoes compression transformation (CT processing) to obtain the compressed received signal; the compressed received signal is denoted as... r ( n ): ; p> 0; s This is the scale parameter.

[0022] Step 6: Calculate the received signal after compression and transformation. r ( n The autocorrelation function of the signal is used to calculate the received signal after compression transformation based on the autocorrelation function. r ( n The cyclic autocorrelation function of the received signal after compression transformation; where the received signal after compression transformation r ( n The autocorrelation function of ) is denoted as R r ( n , t The received signal after compression and transformation r ( n The cyclic autocorrelation function of ) is denoted asC r ( k , t ): ; , l 1= l - L , Q = l 1+ t , ; in, r * ( n+t The received signal after compression conversion r ( n The conjugate of ) Impulse noise signal I ( n The autocorrelation function after compression transformation. Additive white Gaussian noise signal v ( n The autocorrelation function after compression transformation; ; ; ; in, Impulse noise signal I ( n The cyclic autocorrelation function after compression transformation. Additive white Gaussian noise signal v ( n The cyclic autocorrelation function after compression transformation. C x ( k , Q The period is P The periodic function. Wherein, the compressed OFDM signal (i.e., the received signal) is a periodic function. y ( n In ) x ( n The amplitude plot of the cyclic autocorrelation function of the compressed signal is shown in [reference needed]. Figure 3 As shown, s =6.

[0023] After the compression transform (CT processing) in step 6, the received signal is correlated with coefficient A and does not change the autocorrelation function and cyclic autocorrelation function of the OFDM signal. In other words, this compression transform processing of the received signal ensures phase preservation of the transmitted signal (i.e., the OFDM signal), thus maintaining the cyclic stationary characteristics of the signal before and after the compression transform processing. As shown in step 5, for received signals exceeding the threshold, the output after compression transform processing will attenuate rapidly, effectively suppressing weak noise and strong impulse noise. The cyclic correlation energy distribution of the OFDM signal remains unchanged before and after the compression transform processing; for example... Figure 3 As shown, C x ( k , Q ) is a periodic function that recurs periodically with respect to its cyclic frequency. P It undergoes periodic changes, and the non-zero components only exist in Q =- M ,0, M These three places.

[0024] Step 7: Based on the obtained cyclic autocorrelation function of the received signal after compression transformation, calculate the first cyclic autocorrelation function corresponding to this cyclic autocorrelation function within its energy concentration region, and the cyclic spectrum function of the received signal after compression transformation. Wherein, the received signal after compression transformation... r ( n The first cyclic autocorrelation function is labeled as : ; Wherein, periodic function C x ( k , Q The energy concentration area is Q ∈[- M , M ].like Figure 4 , Figure 5 As shown, the cyclic correlation energy distribution of impulse noise changes before and after compression transformation. k =0 and t When =0, it satisfies C I ( k , t )≠0. However, the cyclic correlation energy distribution of the additive white Gaussian noise signal remains unchanged before and after compression transformation, and similarly in k =0 and t When =0, it satisfies C v ( k , t )≠0. Furthermore, in k ≠0 and t When ≠0, it satisfies Thus, the received signal is compressed and transformed. r ( n The cyclic spectrum function of the first cyclic autocorrelation function can be transformed into: ; ; ; ; .

[0025] in, S r ( k , z The received signal after compression conversion r ( n The cyclic spectrum function of ) The cyclic spectrum function representing the channel impulse response, z represents z Variables during the transformation process; Indicates sending signal x ( n The cyclic spectrum function of ) express The conjugate of z * It is the conjugate of z.

[0026] Step 8: Calculate the received signal after compression and transformation. r ( n The cyclic spectrum functions of are the first and second cyclic spectrum functions corresponding to the first and second preset variable values, respectively, and the quotient function between the first and second cyclic spectrum functions is calculated. Where: ; ; ; in, S r ( k , z 1) is the cyclic spectrum function of the received signal after compression transformation. S r ( k , z ) in the first preset variable value z The first cyclic spectral function corresponding to 1, S r ( k , z 2) is the cyclic spectrum function of the received signal after compression transformation. S r ( k , z) in the second preset variable value z The second cyclic spectral function corresponding to time 2. The first cyclic spectral function S r ( k , z 1) With the second cyclic spectral function S r ( k , z 2) Quotient function.

[0027] Step 9: Calculate the quotient function when sending the signal. x ( n Located at the first preset concentration point of its own cycle-related energy and receiving signals y ( n The first quotient function corresponding to the location of its own cycle-related energy concentration. This first quotient function is denoted as... : ; Among them, sending signals x ( n The first preset concentration point of the self-circulating related energy is... t = M Receive signal y ( n The region where the energy related to the self-cycle is concentrated is the interval. t ∈[ ML h , M+L h ]; express C r ( k , M+t ) conjugate.

[0028] Step 10: Receive the signal after compression and transformation. r ( n The first cyclic autocorrelation function of the matrix is ​​processed to construct the first and second Topplitz matrices, and a diagonal matrix is ​​also constructed; wherein, the first Topplitz matrix is ​​denoted as... The second Toplitz matrix is ​​labeled as The diagonal matrix is ​​labeled as D k : ; ; ; Among them, the first Toplitz matrix For the corresponding The matrix, the second Topplitz matrix For the corresponding Matrix; diagnosis [] represents the symbol for a diagonal matrix.

[0029] Step 11: Based on the first Toplitz matrix, the second Toplitz matrix, and the diagonal matrix, obtain the first quotient function in the transmitted signal. x ( n Located at the first preset concentration point of its own cycle-related energy and receiving signals y ( n The first matrix expression form corresponding to the location of the self-cyclic related energy concentration. The first matrix expression form of the first quotient function is: .

[0030] Step 12: Based on the first matrix expression of the obtained first quotient function, obtain the first quotient function in the transmitted signal. x ( n (The signal is located at the second preset concentration point of its own cycle-related energy and receives signals.) y ( n The second matrix expression form corresponding to the location of the self-cyclic related energy concentration. The second matrix expression form of the first quotient function is as follows: Among them, sending signals x ( n The second preset concentration point of the self-circulating related energy is t =- M。

[0031] Step 13: Based on the obtained first and second matrix expressions, calculate the comprehensive matrix expression of the first quotient function when the energy of the cyclic autocorrelation function of the transmitted signal is at its energy concentration point. The comprehensive matrix expression is as follows: ; where the energy concentration of the cyclic autocorrelation function energy of the transmitted signal is t = M and t =- M。

[0032] Step 14: Solve the obtained synthesis matrix expression using the minimum mean square error to obtain the channel estimate of the OFDM system under impulse noise background. The obtained channel estimate of the OFDM system under this impulse noise background is denoted as... h : h= [ h 0 , h 1 ,…, h Lh ] T ;[ h0 , h 1 ,…, h Lh ] T For matrix [ h 0 , h 1 ,…, h Lh The transpose of ] h 0 Indicates channel h ( l The 0th order channel coefficient, h 1 Indicates channel h ( l The first-order channel coefficients, h Lh Indicates channel h ( l ) L h Channel coefficients of order 1.

[0033] Furthermore, this embodiment also simulates the joint Doppler and channel estimation method of the OFDM system under impulse noise background of the invention. Specifically, the simulation process adopts a standard OFDM configuration, with a subcarrier number of... M =64, OFDM symbol number is 128, the modulation scheme of the transmitted signal is QPSK, the channel impulse response is h1=[0.65 0.2-0.2j 0.15+0.005j0.25-0.1j 0.19+0.1j]; DFS value is [0.0045 0.0075 0.0090 0.0105 0.0120 0.01350.0150 0.0180]; the impulse noise model is Bernoulli-Gaussian model; cyclic prefix length is... N cp =16, which is consistent with common standards such as IEEE 802.11a, and ensures its robustness against inter-symbol interference in multipath channels. QPSK modulation is chosen to balance spectral efficiency and noise immunity. Impulse noise is introduced through a Bernoulli-Gaussian model, with an occurrence probability of... p =10%; the intensity of impulse noise is determined by the interference-to-noise ratio (INR) = 5 dB and the scale parameter. s =6 control; sampling frequency f s Setting it to 60kHz is sufficient to fully sample the OFDM signal bandwidth; carrier frequency f cThe frequency was set to 5.9 GHz, a commonly used frequency band for vehicle-to-everything (V2X) communication; the relative speed v was variable to simulate different movement scenarios, covering a range from 0 km / h to 250 km / h; all results were obtained by averaging 1000 independent runs. In the comparative methods, a distortion-constrained group-sparse recursive least squares channel estimation method (referred to as "distortion-constrained channel estimation method") was adopted, utilizing the channel group sparsity and impulse noise characteristics to improve estimation performance.

[0034] Figure 6 The graphs show the mean square error (MSE) of various channel estimation methods as a function of SINR (signal-to-noise ratio) under the condition of Doppler frequency shift DFS = 0.0045. Figure 6 As shown, the MSE values ​​of all channel estimation methods decrease with increasing SINR. The proposed Doppler and channel joint estimation method in this embodiment consistently outperforms the distortion-constrained method across the entire SINR range. At a SINR of 3 dB, the MSE of the proposed Doppler and channel joint estimation method is 0.142 lower than that of the distortion-constrained method, and even the unprocessed method shows a significant advantage with an MSE approximately 0.07804 lower. These results highlight the effectiveness of the proposed Doppler and channel joint estimation method in suppressing impulse noise under complex channel conditions. While the performance gap between the various channel estimation methods narrows at a SINR of 18 dB, the proposed Doppler and channel joint estimation method still maintains a sustained MSE advantage of approximately 0.001567. This continuous improvement is attributed to the fact that the proposed Doppler and channel joint estimation method effectively preserves the inherent sparse structure of the channel by performing a compression transformation (CT compression transformation) on the received signal of the OFDM communication system. In contrast, distortion-constrained channel estimation methods are more sensitive to distortion in sparse channels, especially under low SINR conditions. Overall, these simulation results quantitatively demonstrate the superiority and robustness of the proposed joint Doppler and channel estimation method in this embodiment.

[0035] in addition, Figure 7 The curves showing the mean square error (MSE) of the channel estimation method as a function of SINR under different impulse noise models are presented. To verify the robustness of the proposed joint Doppler and channel estimation method under different impulse noise conditions, simulations were performed using the Bernoulli-Gaussian (BL) model, the α-stable distribution model, and the Middleton Class-A model. When the impulse noise follows an α-stable distribution, the parameters are set to α=1.5 and γ=0.1; for the Middleton Class-A model, the parameter A=1.8. Figure 7The results show that the MSE of all channel estimation methods gradually decreases as the SINR increases. Furthermore, the proposed Doppler and channel joint estimation method in this embodiment is robust under different impulse noise models, with a significantly lower MSE than the distortion-constrained channel estimation method. The distortion-constrained channel estimation method performs poorly under Middleton type A models and is not included in the results. Figure 7 As shown in the figure, the performance of the distortion-constrained channel estimation method is limited by the assumptions of sparse channel and impulse noise modeling, while the Doppler and channel joint estimation method proposed in this embodiment overcomes this limitation.

[0036] Although preferred embodiments of the present invention have been described in detail above, it should be clearly understood that various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A joint Doppler and channel estimation method for OFDM systems under impulse noise background, characterized in that, Includes the following steps: Step 1: Construct an OFDM communication system model with a channel exhibiting Doppler frequency shift and a transmitted signal being an OFDM modulated signal; Step 2: Calculate the time-varying autocorrelation function of the transmitted signal in the constructed OFDM communication system model, and calculate the cyclic autocorrelation function of the transmitted signal based on the time-varying autocorrelation function; Step 3: Calculate the time-varying autocorrelation function of the received signal in the constructed OFDM communication system model, and calculate the cyclic autocorrelation function of the received signal based on the time-varying autocorrelation function; Step 4: Calculate the estimated Doppler frequency shift of the OFDM communication system based on the obtained cyclic autocorrelation function of the transmitted signal and the cyclic autocorrelation function of the received signal. Step 5: Perform compression transformation on the received signal of the OFDM communication system to obtain the compressed received signal; Step 6: Calculate the autocorrelation function of the received signal after compression transformation, and calculate the cyclic autocorrelation function of the received signal after compression transformation based on the autocorrelation function; Step 7: Based on the obtained cyclic autocorrelation function of the received signal after compression transformation, calculate the first cyclic autocorrelation function corresponding to the cyclic autocorrelation function in its energy concentration region and the cyclic spectrum function of the received signal after compression transformation. Step 8: Calculate the first and second cyclic spectrum functions corresponding to the cyclic spectrum functions of the received signal after compression transformation at the first and second preset variable values, respectively, and calculate the quotient function of the first and second cyclic spectrum functions. Step 9: Calculate the first quotient function corresponding to the transmission signal being at the first preset concentration of its own cyclic correlation energy and the reception signal being at the concentration of its own cyclic correlation energy. Step 10: Process the received signal after compression transformation according to the first cyclic autocorrelation function to construct the first Topplitz matrix and the second Topplitz matrix, and construct the diagonal matrix. Step 11: Based on the first Toplitz matrix, the second Toplitz matrix, and the diagonal matrix, obtain the first matrix expression form corresponding to the first quotient function when the transmitted signal is located at the first preset concentration of its own cyclic correlation energy and the received signal is located at the concentration of its own cyclic correlation energy. Step 12: Based on the first matrix expression of the first quotient function, obtain the second matrix expression of the first quotient function when the transmitted signal is at the second preset concentration of its own cyclic correlation energy and the received signal is at the concentration of its own cyclic correlation energy. Step 13: Based on the obtained first matrix expression and second matrix expression, calculate the comprehensive matrix expression of the first quotient function when the energy of the cyclic autocorrelation function of the transmitted signal is at its energy concentration point; Step 14: Solve the obtained synthesis matrix expression using the minimum mean square error to obtain the channel estimate of the OFDM system under impulse noise background.

2. The joint Doppler and channel estimation method for OFDM systems under impulse noise background according to claim 1, characterized in that, The OFDM communication system model is constructed as follows: In this OFDM communication system model, each OFDM symbol contains M Each subcarrier, the transmitted signal is marked as x ( n The received signal is marked as y ( n );in: Send signal x ( n ) is represented as: , n∈[0, M + N CP -1]; X ( i ) represents the i-th subcarrier from QPSK modulation. N CP This indicates the length of the cyclic prefix CP added to the OFDM symbol as a guard interval; Received signal y ( n ) is represented as: ;in, l ∈[0, L h ], ; η ( n ) = I ( n )+ v ( n ), , I ( n ) = B ( n ) G ( n ); ε = f d / Δ f = M f d / f s ; f d =| vf c cos( θ )| / c ;Δ f = f s / M ; h ( l ) represents the first in the OFDM communication system l The coefficients of the path, L h This represents the maximum path order of a multipath channel in an OFDM communication system. η ( n The ) represents the noise signal of the OFDM communication system. This noise signal includes impulse noise and independent, identically distributed additive white Gaussian noise as background noise. The time-varying variance of the channel impulse response. I ( n ) represents impulse noise signal, v ( n ) represents independent and identically distributed additive white Gaussian noise. B ( n ) represents a Bernoulli random process. G ( n ) indicates that the mean is 0 and the variance is Complex Gaussian white noise, ε This represents the normalized Doppler frequency shift. f d This refers to the Doppler frequency shift caused by the channel in the OFDM communication system. f s Δ is the sampling frequency. f For subcarrier spacing, c At the speed of light, θ It is the angle between the direction of arrival of the wave and the direction of motion of the signal receiving end.

3. The joint Doppler and channel estimation method for OFDM systems under impulse noise background according to claim 2, characterized in that, In step 2, the time-varying autocorrelation function and cyclic autocorrelation function of the transmitted signal are calculated as follows: ； ； in, R x ( n , τ (to send a signal) x ( n The time-varying autocorrelation function of E[ x ( n ) x * ( n+τ )]express x ( n ) x * ( n+τ ) expectations, x * ( n+τ (to send a signal) x ( n The conjugate of ) τ To delay, Indicates subcarrier X ( i The variance of ) δ ( τ () represents the discrete-time unit impulse function, also known as the discrete Dirac delta function. τ′ Represents a delay variable. R x ( n , τ ) is in the variable n Periodic functions on P This indicates the periodic function R x ( n , τ The cycle of ); ； , ;in, C x ( k , τ (to send a signal) x ( n The cyclic autocorrelation function of ) k Indicates the cycle frequency.

4. The joint Doppler and channel estimation method for OFDM systems under impulse noise background as described in claim 3, characterized in that, In step 3, the time-varying autocorrelation function and cyclic autocorrelation function of the received signal are calculated as follows: Received signal y ( n The time-varying autocorrelation function of ) is denoted as R yy* ( n , τ ): ； Δτ= l 1- l 2, R ηη* ( n , τ )= R II* ( n , τ )+ R vv* ( n , τ ); in, y * ( n+τ (received signal) y ( n )exist- τ Delayed conjugate, ε The normalized Doppler frequency shift in the channel of the OFDM communication system model. R II* ( n , τ () is an impulse noise signal I ( n The time-varying autocorrelation function of ) R vv* ( n , τ (This is) an additive white Gaussian noise signal. v ( n The time-varying autocorrelation function of the received signal; y ( n The cyclic autocorrelation function of ) is denoted as C y ( k , τ ): ； ； C η ( k , τ )= C I ( k , τ )+ C v ( k , τ )； in, C x ( k , τ () is the signal being sent. x ( n The cyclic autocorrelation function of ) C I ( k , τ () is an impulse noise signal I ( n The cyclic autocorrelation function of ) C v ( k , τ () is an additive white Gaussian noise signal v ( n The cyclic autocorrelation function of ).

5. The joint Doppler and channel estimation method for OFDM systems under impulse noise background according to claim 4, characterized in that, In step 4, the Doppler frequency shift estimate is calculated as follows: ;in, This is the estimated value of the Doppler frequency shift. T Represents any integer.

6. The joint Doppler and channel estimation method for OFDM systems under impulse noise background according to claim 5, characterized in that, In step 5, the calculation method for the received signal after compression transformation is as follows: ;σ>0; where, r ( n ) represents the received signal after compression transformation, and σ is the scale parameter; In step 6, the autocorrelation function of the received signal after compression transformation is calculated as follows: ； ， l 1= l - L ， Q = l 1 + τ ， ； in, R r ( n , τ The received signal after compression conversion r ( n The autocorrelation function of ) r * ( n+τ The received signal after compression conversion r ( n The conjugate of ) Impulse noise signal I ( n The autocorrelation function after compression transformation. Additive white Gaussian noise signal v ( n The autocorrelation function after compression transformation; In step 6, the cyclic autocorrelation function of the received signal after compression transformation is calculated as follows: ； ； ； in, C r ( k , τ The received signal after compression conversion r ( n The cyclic autocorrelation function of ) Impulse noise signal I ( n The cyclic autocorrelation function after compression transformation. Additive white Gaussian noise signal v ( n The cyclic autocorrelation function after compression transformation. C x ( k , Q The period is P A periodic function.

7. The joint Doppler and channel estimation method for OFDM systems under impulse noise background as described in claim 6, characterized in that, In step 7, the first cyclic autocorrelation function and cyclic spectrum function of the received signal after compression transformation are calculated as follows: ； in, For the received signal after compression transformation r ( n The first cyclic autocorrelation function, periodic function C x ( k , Q The energy concentration area is Q ∈[- M , M The cyclic correlation energy distribution of impulse noise changed before and after compression transformation. k =0 and τ When =0, it satisfies C I ( k , τ The cyclic correlation energy distribution of the additive white Gaussian noise signal remains unchanged before and after compression transformation. k =0 and τ When =0, it satisfies C v ( k , τ )≠0; in k ≠0 and τ When ≠0, it satisfies The received signal after compression and transformation r ( n The cyclic spectrum function of the first cyclic autocorrelation function is transformed into: ； ； ； ； ； in, S r ( k , z The received signal after compression conversion r ( n The cyclic spectrum function of ) The cyclic spectrum function representing the channel impulse response, z represents z Variables during the transformation process; Indicates sending signal x ( n The cyclic spectrum function of ) express The conjugate of z * It is the conjugate of z.

8. The joint Doppler and channel estimation method for OFDM systems under impulse noise background according to claim 7, characterized in that, In step 8, the calculation methods for the first cyclic spectrum function corresponding to the first preset variable value and the second cyclic spectrum function corresponding to the second preset variable value of the compressed and transformed received signal are as follows: ； ； ； in, S r ( k , z 1) is the cyclic spectrum function of the received signal after compression transformation. S r ( k , z ) in the first preset variable value z The first cyclic spectral function corresponding to 1, S r ( k , z 2) is the cyclic spectrum function of the received signal after compression transformation. S r ( k , z ) in the second preset variable value z The second cyclic spectral function corresponding to time 2. The first cyclic spectral function S r ( k , z 1) With the second cyclic spectral function S r ( k , z 2) Quotient function.

9. The joint Doppler and channel estimation method for OFDM systems under impulse noise background according to claim 8, characterized in that, In step 9, the first quotient function is calculated as follows: ； in, The first quotient function is used to send signals. x ( n The first preset concentration point of the self-circulating related energy is... τ = M Receive signal y ( n The region where the energy related to the self-cycle is concentrated is the interval. τ ∈[ ML h , M+L h ]; express C r ( k , M+τ ) conjugate.

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