OFDM (Orthogonal Frequency Division Multiplexing) system blind Doppler frequency shift estimation method based on correlation coefficient

Abstract

The invention relates to an OFDM (Orthogonal Frequency Division Multiplexing) system blind Doppler frequency shift estimation method based on correlation coefficients, which comprises the following steps of: constructing an OFDM system, dividing each OFDM symbol cyclic prefix into four prefix data intervals according to a multipath fading channel order and a cyclic prefix length, respectively calculating self-correlation functions of a first prefix data interval and a second prefix data interval, and then calculating the correlation coefficients of the first prefix data interval and the second prefix data interval; calculating a normalized self-correlation coefficient of the time domain discrete received signal and taking a corresponding channel order value when the normalized self-correlation coefficient reaches a maximum coefficient value for the first time as a channel order estimation value; calculating a time domain discrete receiving signal difference of the time domain discrete receiving signal between the second prefix data interval and the fourth prefix data interval and an autocorrelation function of the signal difference when the cyclic prefix data is in the second prefix data interval and the delay amount is zero, and calculating a Doppler frequency shift estimation value based on each obtained result; doppler frequency shift estimation in the impulse noise environment is accurately realized, and the adverse effect of Doppler frequency shift on the OFDM system performance in the impulse noise environment is eliminated.

Description

Technical Field

[0001] This invention relates to the field of communications, and more particularly to a blind Doppler frequency shift estimation method for OFDM systems based on correlation coefficients. Background Technology

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology, due to its advantages in resisting inter-symbol interference (ISI) and inter-channel interference (ICI), has been widely used in fields such as underwater acoustic communication and power line carrier communication. Combining OFDM with Non-Orthogonal Multiple Access (NOMA) technology can improve spectrum utilization and has broad application prospects in systems such as 5G and IoT communication. However, in OFDM systems, Doppler shift occurs when there is relative motion between the transmitter and receiver, leading to subcarrier interference and severely affecting the performance of the OFDM system. Therefore, effective estimation and compensation of Doppler shift at the receiver side are necessary to improve the performance of the OFDM system.

[0003] Chinese invention patent application CN102970270A discloses a method for estimating the Doppler frequency offset of an OFDM system in a high-speed mobile environment. A mobile relay is installed on a high-speed moving vehicle to forward communication data between a base station and a mobile station. A finite number of transmission paths exist between the base station and the mobile relay, each path corresponding to a different Doppler frequency offset. By analyzing the Doppler frequency offset between the base station and the mobile relay, the Doppler frequency offset between the base station and the mobile station on the vehicle is obtained. This invention achieves the estimation of multiple Doppler frequency offsets in a high-speed mobile environment. Furthermore, the larger the number of subcarriers Nc, the smaller the mean square error at the same signal-to-noise ratio, meaning the frequency offset estimation is more accurate. Since increasing Nc given Nb essentially increases Na, and Na is equivalent to the number of signal snapshots, increasing Nc can improve the estimation accuracy of the covariance matrix Rd, thus making the frequency offset estimation more accurate.

[0004] However, the Doppler frequency offset estimation method for OFDM systems disclosed in the aforementioned invention patent application CN102970270A has shortcomings: the Doppler frequency offset estimation method is proposed for OFDM signal transmission in Gaussian noise environment, and cannot be applied to Doppler frequency shift estimation in non-Gaussian impulse noise environment such as impulse noise environment, which makes it difficult to eliminate the adverse effects of Doppler frequency shift on OFDM system performance in impulse noise environment. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a blind Doppler frequency shift estimation method for OFDM systems based on correlation coefficients, which addresses the aforementioned prior art. This blind Doppler frequency shift estimation method for OFDM systems based on correlation coefficients can accurately estimate the Doppler frequency shift under impulse noise conditions, thereby eliminating the adverse effects of Doppler frequency shift on OFDM system performance under impulse noise conditions.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problem is: a blind Doppler frequency shift estimation method for OFDM systems based on correlation coefficients, characterized by comprising the following steps:

[0007] Step 1: Construct a system model for the OFDM system; in this OFDM system, it is assumed that an OFDM signal contains N subcarriers, and the time-domain signal of the m-th OFDM symbol transmitted on any of the N subcarriers is labeled as follows:

[0008] n∈[0,N+N cp -1];0≤k≤N-1;1≤m≤M;

[0009] Where, x m (n) represents the nth sampled signal of the mth OFDM symbol, X m (k) represents the k-th QAM-modulated subcarrier contained in the m-th OFDM symbol, N cp This represents the cyclic prefix length of the m-th OFDM symbol; M is the total number of OFDM symbols transmitted on any subcarrier.

[0010] The time-domain discrete-received signal corresponding to the m-th OFDM symbol on any subcarrier after transmission through the OFDM system channel is denoted as y. m (n):

[0011] y m (n)=r m (n)+I m (n)+u m (n);

[0012]

[0013] Where, r m (n) represents the channel output signal, I m (n) represents the impulse noise signal, u m (n) represents an independent and identically distributed Gaussian white noise signal; impulse noise signal I m (n) and Gaussian white noise signal u m (n) represents mutually independent noise signals; The Gaussian white noise signal u mThe variance of (n);

[0014] L h f represents the maximum channel order of the multipath channel within the OFDM system, ε represents the normalized Doppler frequency shift, and f d For Doppler frequency shift, Δf is the subcarrier spacing of the OFDM symbol, f s h is the sampling frequency. l This represents the channel coefficient of the l-th path in a multipath channel;

[0015] B(n) is a Bernoulli random process, P(B(n)) is the probability density function of the Bernoulli random process B(n); G(n) is a random process with a mean of 0 and a variance of 0. Gaussian white noise; impulse noise signal I m The autocorrelation function of (n) is denoted as

[0016]

[0017] Step 2: Divide the cyclic prefix of each OFDM symbol located in the time domain and having a preset cyclic prefix length into four prefix data intervals; wherein the preset cyclic prefix length is N+N. cp The four prefix data intervals are labeled as the first prefix data interval C1, the second prefix data interval C2, the third prefix data interval C3, and the fourth prefix data interval C4, respectively; the first prefix data interval C1 = [0,L... h -1], the second prefix data interval C2 = [L h N cp -1], the third prefix data interval C3 = C1 + N, the fourth prefix data interval C4 = C2 + N;

[0018] Wherein, the first prefix data interval C1 represents the data portion of the cyclic prefix data of the m-th OFDM symbol that suffers from inter-symbol interference, the second prefix data interval C2 represents the remaining data portion of the cyclic prefix data of the m-th OFDM symbol that does not suffer from inter-symbol interference, the third prefix data interval C3 represents the copy portion located in the m-th OFDM symbol and corresponding to the first prefix data interval C1, and the fourth prefix data interval C4 represents the copy portion located in the m-th OFDM symbol and corresponding to the second prefix data interval C2;

[0019] Where, when the cyclic prefix data cp∈C1, the channel output signal r m (n) is represented as follows:

[0020]

[0021] Among them, S' m-1(n) represents the inter-symbol interference value of the m-th OFDM symbol caused by the (m-1)-th OFDM symbol;

[0022] Step 3: Calculate the autocorrelation function of the time-domain discrete received signal within the first prefix data interval in the OFDM system; where:

[0023]

[0024] in, For the time-domain discrete received signal y m (n) is the autocorrelation function corresponding to the first prefix data interval C1, and U(·) is the step function;

[0025] Step 4: Calculate the autocorrelation function of the time-domain discrete received signal within the second prefix data interval in the OFDM system; where:

[0026] For cyclic prefix data cp∈C2 and delay τ=N, the time-domain discrete received signal y m The autocorrelation function corresponding to (n) is labeled as

[0027]

[0028] in, This represents the time-domain signal x corresponding to the delay τ = N. m The autocorrelation function of (n);

[0029] For cyclic prefix data cp∈C2 and delay τ=0, the time-domain discrete received signal y m The autocorrelation function corresponding to (n) is labeled as

[0030]

[0031] in, This represents the time-domain signal x corresponding to the delay τ = 0. m The autocorrelation function of (n), The impulse noise I corresponding to the delay τ = 0. m The autocorrelation function of (n), The Gaussian white noise u corresponding to the delay τ = 0 m The autocorrelation function of (n);

[0032] Step 5: Calculate the normalized autocorrelation coefficient of the time-domain discrete received signal based on the autocorrelation function of the first prefix data interval corresponding to the obtained time-domain discrete received signal and the autocorrelation function of the second prefix data interval corresponding to the obtained time-domain discrete received signal; where:

[0033]

[0034] Where Rate(a) represents the discrete-time received signal y. m The normalized autocorrelation coefficient of (n); Represents the discrete-time received signal y m (n) The autocorrelation function of the data interval containing the cyclic prefix data a. Represents the discrete-time received signal y m The autocorrelation function of (n);

[0035] Step 6: Calculate the channel order value corresponding to the first time the normalized autocorrelation coefficient of the discrete-time received signal reaches its maximum value, and use this channel order value as the channel order estimate; wherein, the channel order value corresponding to the first time the normalized autocorrelation coefficient of the discrete-time received signal reaches its maximum value is denoted as...

[0036] Step 7: Based on the periodicity of the OFDM signal, calculate the time-domain discrete received signal difference between the second and fourth prefix data intervals; whereby this time-domain discrete received signal difference is denoted as Δy. m (n):

[0037]

[0038] △I m (n)=I m (n+N)-I m (n);

[0039] △u m (n)=u m (n+N)-u m (n);

[0040] in:

[0041] y m (n) represents the received signal of the discrete-time received signal in the second prefix data interval, y m (n+N) represents the received signal of the time-domain discrete received signal in the fourth prefix data interval;

[0042] I m (n) represents the impulse noise signal in the second prefix data interval, I m (n+N) represents the impulse noise in the fourth prefix data interval, ΔI m (n) represents the signal difference between two impulse noise signals;

[0043] u m(n) represents the Gaussian white noise signal in the second prefix data interval, I m (n+N) represents the Gaussian white noise signal in the fourth prefix data interval; △u m (n) represents the signal difference between two Gaussian white noise signals;

[0044] Step 8: Calculate the autocorrelation function of the obtained time-domain discrete received signal difference when the cyclic prefix data is within the second prefix data interval and the delay is zero; where:

[0045]

[0046] in, The difference Δy between the received discrete-time signals represents the difference in the time domain. m (n) The autocorrelation function of the cyclic prefix data in the second prefix data interval and with zero delay;

[0047] Step 9: Based on the autocorrelation function of the obtained discrete-time received signal within the second prefix data interval, the autocorrelation function of the discrete-time received signal difference when the cyclic prefix data is within the second prefix data interval and the delay is zero, and the obtained channel order estimate, calculate the Doppler frequency shift estimate of the OFDM system; where:

[0048]

[0049] in, This represents the estimated Doppler frequency shift of the OFDM system.

[0050] Improved, in the OFDM system blind Doppler frequency shift estimation method based on correlation coefficient, after step 9, the method further includes: calculating the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation in the following manner:

[0051] Step a1: Establish a likelihood function with a preset number of sample symbols; wherein, the likelihood function is expressed as follows:

[0052]

[0053] Where f(y,θ) represents the likelihood function of the time-domain discrete received signal y(n) with respect to the parameter θ, x(nl) represents the time-domain discrete transmitted signal on the multipath fading channel in the OFDM system, and I(n) represents the impulse noise signal on the multipath fading channel in the OFDM system;

[0054] Step a2: Based on the established likelihood function, calculate the Fisher information matrix corresponding to the likelihood function; the Fisher information matrix is ​​calculated as follows:

[0055]

[0056] Among them, J 11 (θ) is the Fisher information matrix corresponding to the likelihood function;

[0057] Step a3: Based on the Fisher information matrix corresponding to the obtained likelihood function, calculate the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation; wherein, the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation is denoted as...

[0058]

[0059] Wherein, SNR is the signal-to-noise ratio on the multipath fading channel within the OFDM system.

[0060] Compared with the prior art, the advantages of this invention are as follows: The OFDM system blind Doppler frequency shift estimation method based on correlation coefficient, after constructing the OFDM system, divides the cyclic prefix of each OFDM symbol into four prefix data intervals according to the order of the multipath fading channel and the cyclic prefix length. After calculating the autocorrelation function of the first and second prefix data intervals respectively, the normalized autocorrelation coefficient of the time-domain discrete received signal is calculated, and the channel order value corresponding to the first time the normalized autocorrelation coefficient reaches its maximum value is used as the channel order estimate. The time-domain discrete received signal between the second and fourth prefix data intervals is then calculated. The time-domain discrete received signal difference and its autocorrelation function when the cyclic prefix data is within the second prefix data interval and the delay is zero are obtained. Further, based on the respective autocorrelation functions of the obtained time-domain discrete received signal within the second prefix data interval, the autocorrelation function of the time-domain discrete received signal difference when the cyclic prefix data is within the second prefix data interval and the delay is zero, and the obtained channel order estimate, the Doppler frequency shift estimate of the OFDM system is calculated. This accurately achieves Doppler frequency shift estimation under impulse noise conditions, eliminating the adverse effects of Doppler frequency shift on OFDM system performance under impulse noise conditions. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the blind Doppler frequency shift estimation method for OFDM systems based on correlation coefficients in an embodiment of the present invention;

[0062] Figure 2 This is a schematic diagram of the OFDM signal in each OFDM symbol in an embodiment of the present invention;

[0063] Figure 3 This is a schematic diagram of the Cramer-Rao lower bound for the Doppler frequency shift estimation of the OFDM system obtained from simulation in an embodiment of the present invention. Detailed Implementation

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0065] This embodiment provides a blind Doppler frequency shift estimation method for OFDM systems based on correlation coefficients. See also... Figure 1 As shown, the blind Doppler frequency shift estimation method for OFDM systems based on correlation coefficients in this embodiment includes the following steps:

[0066] Step 1: Construct a system model of the OFDM system; wherein the system model of the OFDM system includes an OFDM transmit signal and a time-domain discrete receive signal, the OFDM transmit signal contains several subcarriers, and the OFDM symbol transmitted on any of these subcarriers has a cyclic prefix; specifically:

[0067] Assuming an OFDM signal contains N subcarriers, the time-domain signal representation of the m-th OFDM symbol transmitted on any of these N subcarriers is as follows:

[0068] n∈[0,N+N cp -1];0≤k≤N-1;m>1;

[0069] Where, x m (n) represents the nth sampled signal of the mth OFDM symbol, X m (k) represents the k-th QAM-modulated subcarrier contained in the m-th OFDM symbol, N cp This represents the cyclic prefix length of the m-th OFDM symbol; M is the total number of OFDM symbols transmitted on any subcarrier.

[0070] The time-domain discrete-received signal corresponding to the m-th OFDM symbol on any subcarrier after transmission through the OFDM system channel is denoted as y. m (n):

[0071] y m (n)=r m (n)+I m (n)+u m (n);

[0072]

[0073] Where, r m (n) represents the channel output signal, I m (n) represents the impulse noise signal, u m (n) represents an independent and identically distributed Gaussian white noise signal; impulse noise signal I m (n) and Gaussian white noise signal u m (n) represents mutually independent noise signals; The Gaussian white noise signal u m The variance of (n); for h l Variance of the channel impulse response;

[0074] L h f represents the maximum channel order of the multipath channel within the OFDM system, ε represents the normalized Doppler frequency shift, and f d For Doppler frequency shift, Δf is the subcarrier spacing of the OFDM symbol, f s h is the sampling frequency. l This represents the channel coefficient of the l-th path in a multipath channel;

[0075] B(n) is a Bernoulli random process, P(B(n)) is the probability density function of the Bernoulli random process B(n); G(n) is a random process with a mean of 0 and a variance of 0. Gaussian white noise; impulse noise signal I m The autocorrelation function of (n) is denoted as

[0076] τ is the delay amount;

[0077] Step 2: Divide the cyclic prefix of each OFDM symbol located in the time domain and having a preset cyclic prefix length into four prefix data intervals; wherein the preset cyclic prefix length is N+N. cp The four prefix data intervals are labeled as the first prefix data interval C1, the second prefix data interval C2, the third prefix data interval C3, and the fourth prefix data interval C4, respectively; the first prefix data interval C1 = [0,L... h -1], the second prefix data interval C2 = [L h N cp -1], the third prefix data interval C3 = C1 + N, the fourth prefix data interval C4 = C2 + N;

[0078] Wherein, the first prefix data interval C1 represents the data portion of the cyclic prefix data of the m-th OFDM symbol that suffers inter-symbol interference; the second prefix data interval C2 represents the remaining data portion of the cyclic prefix data of the m-th OFDM symbol that does not suffer inter-symbol interference; the third prefix data interval C3 represents the copy portion of the m-th OFDM symbol corresponding to the first prefix data interval C1; and the fourth prefix data interval C4 represents the copy portion of the m-th OFDM symbol corresponding to the second prefix data interval C2. Specifically, the OFDM signal in each OFDM symbol is described in [reference needed]. Figure 2 As shown;

[0079] Specifically, when the cyclic prefix data cp∈C1, that is, when the cyclic prefix data cp is located within the first prefix data interval C1, the channel output signal r m (n) is represented as follows:

[0080]

[0081] Among them, S' m-1 (n) represents the inter-symbol interference value of the m-th OFDM symbol caused by the (m-1)-th OFDM symbol;

[0082] Step 3: Calculate the discrete-time received signal y in the OFDM system. m (n) The autocorrelation function corresponding to the first prefix data interval C1; where:

[0083]

[0084] in, For the time-domain discrete received signal y m (n) is the autocorrelation function corresponding to the first prefix data interval C1, and U(·) is the step function;

[0085] Step 4: Calculate the discrete-time received signal y in the OFDM system. m (n) The autocorrelation function corresponding to the second prefix data interval C2; where:

[0086] For a cyclic prefix data cp ∈ C2 and a delay τ = N, that is, when the cyclic prefix data cp is located within the second prefix data interval C2 and the delay τ = N, the time-domain discrete received signal y m The autocorrelation function corresponding to (n) is labeled as

[0087]

[0088] in, This represents the time-domain signal x corresponding to the delay τ = N. m The autocorrelation function of (n);

[0089] For the cyclic prefix data cp∈C2 and the delay τ=0, that is, when the cyclic prefix data cp is located within the second prefix data interval C2 and the delay τ=0, the time-domain discrete received signal y m The autocorrelation function corresponding to (n) is labeled as

[0090]

[0091] in, This represents the time-domain signal x corresponding to the delay τ = 0. m The autocorrelation function of (n), The impulse noise I corresponding to the delay τ = 0. m The autocorrelation function of (n), The Gaussian white noise u corresponding to the delay τ = 0 m The autocorrelation function of (n);

[0092] Step 5: Based on the autocorrelation function of the first prefix data interval corresponding to the obtained time-domain discrete received signal. and the respective correlation functions of the second prefix data intervals corresponding to the obtained time-domain discrete received signals. and Calculate the normalized autocorrelation coefficient of the discrete-time received signal; where:

[0093]

[0094] Where Rate(a) represents the discrete-time received signal y. m The normalized autocorrelation coefficient of (n); Represents the discrete-time received signal y m (n) The autocorrelation function of the data interval containing the cyclic prefix data a. Represents the discrete-time received signal y m The autocorrelation function of (n); for example, when the cyclic prefix data a = 0,

[0095] Step 6: Calculate the channel order value corresponding to the first time the normalized autocorrelation coefficient of the discrete-time received signal reaches its maximum value, and use this channel order value as the channel order estimate; wherein, the channel order value corresponding to the first time the normalized autocorrelation coefficient of the discrete-time received signal reaches its maximum value is denoted as...

[0096] In other words, by comparing the normalized autocorrelation coefficients of the discrete received signal in the time domain and finding the channel order value corresponding to the maximum value of the normalized autocorrelation coefficient, the channel order value found is used as the channel order estimate.

[0097] Step 7: Based on the periodicity of the OFDM signal, calculate the time-domain discrete received signal difference between the second and fourth prefix data intervals; whereby this time-domain discrete received signal difference is denoted as Δy. m (n):

[0098]

[0099] △I m (n)=I m(n+N)-I m (n);

[0100] △u m (n)=u m (n+N)-u m (n);

[0101] in:

[0102] y m (n) represents the received signal of the discrete-time received signal in the second prefix data interval C2, y m (n+N) represents the received signal of the time-domain discrete received signal in the fourth prefix data interval C4;

[0103] I m (n) represents the impulse noise signal in the second prefix data interval C2, I m (n+N) represents the impulse noise in the fourth prefix data interval C4, ΔI m (n) represents the signal difference between two impulse noise signals;

[0104] u m (n) represents the Gaussian white noise signal in the second prefix data interval C2, I m (n+N) represents the Gaussian white noise signal in the fourth prefix data interval C4; △u m (n) represents the signal difference between two Gaussian white noise signals;

[0105] Step 8: Calculate the autocorrelation function of the obtained time-domain discrete received signal difference when the cyclic prefix data is within the second prefix data interval and the delay is zero; where:

[0106]

[0107] in, The difference Δy between the received discrete-time signals represents the difference in the time domain. m (n) The autocorrelation function of the cyclic prefix data in the second prefix data interval and with zero delay;

[0108] Step 9: Based on the autocorrelation function of the obtained discrete-time received signal within the second prefix data interval, the autocorrelation function of the discrete-time received signal difference when the cyclic prefix data is within the second prefix data interval and the delay is zero, and the obtained channel order estimate, calculate the Doppler frequency shift estimate of the OFDM system; where:

[0109]

[0110] in, arg[·] represents the estimated Doppler frequency shift of the OFDM system, and arg[·] refers to the phase angle function.

[0111] To evaluate the estimation performance of the OFDM system blind Doppler frequency shift estimation method in this embodiment, the OFDM system blind Doppler frequency shift estimation method in this embodiment further includes, after step 9, the following process: calculating the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation according to steps a1 to a3:

[0112] Step a1: Establish a likelihood function with a preset number of sample symbols; wherein, the likelihood function is expressed as follows:

[0113]

[0114] Where f(y,θ) represents the likelihood function of the time-domain discrete received signal y(n) with respect to the parameter θ, x(nl) represents the time-domain discrete transmitted signal on the multipath fading channel in the OFDM system, and I(n) represents the impulse noise signal on the multipath fading channel in the OFDM system;

[0115] Step a2: Based on the established likelihood function f(y,θ), calculate the Fisher information matrix corresponding to the likelihood function f(y,θ); wherein, the Fisher information matrix is ​​calculated as follows:

[0116]

[0117] Among them, J 11 (θ) is the Fisher information matrix corresponding to the likelihood function; where the Fisher information matrix and its calculation method are common knowledge in this technical field, and will not be elaborated here;

[0118] Step a3: Based on the Fisher information matrix corresponding to the obtained likelihood function, calculate the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation; wherein, the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation is denoted as...

[0119]

[0120] Wherein, SNR is the signal-to-noise ratio on the multipath fading channel within the OFDM system.

[0121] Simulation experiment:

[0122] To compare the Doppler frequency shift estimation performance of the OFDM system blind Doppler frequency shift estimation method (defined as CORRE) based on correlation coefficient proposed in this embodiment with the traditional OFDM system blind Doppler frequency shift estimation method (defined as CYCL) based on cyclostationarity, the following computer simulation analysis was also performed in this embodiment:

[0123] During the simulation, the power-normalized 7th-order channel impulse response is h1 = [1 + 0.2 - 0.2j + 0.15 + 0.05j + 0.25 - 0.1j + 0.19 + 0.1j - 0.46 + 0.12j + 0.35 - 0.17j + 0.46 - 0.29j]. The channel impulse response follows a complex Gaussian distribution, and the impulse noise follows a Bernoulli-Gaussian model. The cyclic prefix length N... cp =16, number of subcarriers N=64, OFDM signal uses 4-QAM modulation, sampling frequency fs=60kHz, 10000 independent runs are performed, each run contains M=128 OFDM symbols; the true value of Doppler frequency shift DFS is [0.0045 0.0075 0.0090 0.0105 0.0120 0.0135 0.0150 0.0180].

[0124] To measure the estimation performance of the blind Doppler frequency shift estimation method for the OFDM system in this embodiment, we define the normalized mean square error (NMSE) of the Doppler frequency shift estimate of the OFDM system as:

[0125]

[0126] in, ε represents the estimated Doppler frequency shift of the OFDM system, Num represents the true Doppler frequency shift of the OFDM system, and Num is the number of independent runs.

[0127] The simulation results show that, compared with the traditional blind Doppler frequency shift estimation method for OFDM systems, the correlation coefficient-based blind Doppler frequency shift estimation method for OFDM systems in this embodiment has a lower normalized mean square error and is closer to the Cramer-Rao lower bound (CRLB). This indicates that the correlation coefficient-based blind Doppler frequency shift estimation method for OFDM systems can accurately estimate the Doppler frequency shift under impulse noise conditions and eliminate the adverse effects of Doppler frequency shift on the performance of OFDM systems under impulse noise conditions.

[0128] 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 blind Doppler frequency shift estimation method for OFDM systems based on correlation coefficients, characterized in that, Includes the following steps: Step 1: Construct a system model of the OFDM system; wherein, the system model of the OFDM system includes an OFDM transmit signal and a time-domain discrete receive signal, the OFDM transmit signal contains several subcarriers, and the OFDM symbol transmitted on any of the several subcarriers has a cyclic prefix; Step 2: Divide the cyclic prefix of each OFDM symbol located in the time domain and having a preset cyclic prefix length into four prefix data intervals; wherein, the four prefix data intervals include a first prefix data interval, a second prefix data interval, a third prefix data interval, and a fourth prefix data interval; and, the first prefix data interval represents the data portion of the cyclic prefix data of any OFDM symbol that suffers from inter-symbol interference; the second prefix data interval represents the remaining data portion of the cyclic prefix data of any OFDM symbol that does not suffer from inter-symbol interference; the third prefix data interval represents the copied portion of any OFDM symbol that corresponds to the first prefix data interval; the fourth prefix data interval represents the copied portion of any OFDM symbol that corresponds to the second prefix data interval. Step 3: Calculate the autocorrelation function of the time-domain discrete received signal in the OFDM system within the first prefix data interval; Step 4: Calculate the autocorrelation function of the time-domain discrete received signal in the second prefix data interval within the OFDM system; Step 5: Calculate the normalized autocorrelation coefficient of the time-domain discrete received signal based on the autocorrelation function of the first prefix data interval corresponding to the obtained time-domain discrete received signal and the autocorrelation function of the second prefix data interval corresponding to the obtained time-domain discrete received signal. Step 6: Calculate the channel order value corresponding to the first time the normalized autocorrelation coefficient of the time-domain discrete received signal reaches its maximum value, and use this channel order value as the channel order estimate. Step 7: Based on the periodicity of the OFDM signal, calculate the time-domain discrete received signal difference between the second prefix data interval and the fourth prefix data interval. Step 8: Calculate the autocorrelation function of the time-domain discrete received signal difference when the cyclic prefix data is within the second prefix data interval and the delay is zero; Step 9: Calculate the Doppler frequency shift estimate of the OFDM system based on the autocorrelation function of the obtained discrete time-domain received signal within the second prefix data interval, the autocorrelation function of the difference of the discrete time-domain received signal when the cyclic prefix data is within the second prefix data interval and the delay is zero, and the obtained channel order estimate.

2. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 1, characterized in that, The system model of the OFDM system constructed in step 1 is as follows: In this OFDM system, assuming an OFDM signal contains N subcarriers, the time-domain signal of the m-th OFDM symbol transmitted on any of these N subcarriers is labeled as follows: n∈[0,N+N cp -1];0≤k≤N-1;1≤m≤M; Where, x m (n) represents the nth sampled signal of the mth OFDM symbol, X m (k) represents the k-th QAM-modulated subcarrier contained in the m-th OFDM symbol, N cp This represents the cyclic prefix length of the m-th OFDM symbol; M is the total number of OFDM symbols transmitted on any subcarrier. The time-domain discrete-received signal corresponding to the m-th OFDM symbol on any subcarrier after transmission through the OFDM system channel is denoted as y. m (n): y m (n)=r m (n)+I m (n)+u m (n); I m (n)=B(n)G(n); Where, r m (n) represents the channel output signal, I m (n) represents the impulse noise signal, u m (n) represents an independent and identically distributed Gaussian white noise signal; impulse noise signal I m (n) and Gaussian white noise signal u m (n) represents mutually independent noise signals; The Gaussian white noise signal u m The variance of (n); L h f represents the maximum channel order of the multipath channel within the OFDM system, ε represents the normalized Doppler frequency shift, and f d For Doppler frequency shift, Δf is the subcarrier spacing of the OFDM symbol, f s h is the sampling frequency. l This represents the channel coefficient of the l-th path in a multipath channel; B(n) is a Bernoulli random process, P(B(n)) is the probability density function of the Bernoulli random process B(n); G(n) is a random process with a mean of 0 and a variance of 0. Gaussian white noise; impulse noise signal I m The autocorrelation function of (n) is denoted as 3. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 2, characterized in that, The division of the four prefix data intervals in step 2 is as follows: the preset cyclic prefix length is set to N+N. cp The four prefix data intervals are labeled as the first prefix data interval C1, the second prefix data interval C2, the third prefix data interval C3, and the fourth prefix data interval C4, respectively; the first prefix data interval C1 = [0,L... h -1], the second prefix data interval C2 = [L h N cp -1], the third prefix data interval C3 = C1 + N, the fourth prefix data interval C4 = C2 + N; Where, when the cyclic prefix data cp∈C1, the channel output signal r m (n) is represented as follows: Among them, S' m-1 (n) represents the inter-symbol interference value of the m-th OFDM symbol caused by the (m-1)-th OFDM symbol.

4. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 3, characterized in that, In step 3, the autocorrelation function of the time-domain discrete received signal within the first prefix data interval in the OFDM system is calculated as follows: in, For the time-domain discrete received signal y m (n) is the autocorrelation function corresponding to the first prefix data interval C1, and U(·) is the step function.

5. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 4, characterized in that, In step 4, the autocorrelation function of the time-domain discrete received signal within the second prefix data interval in the OFDM system is calculated as follows: For cyclic prefix data cp∈C2 and delay τ=N, the time-domain discrete received signal y m The autocorrelation function corresponding to (n) is labeled as in, This represents the time-domain signal x corresponding to the delay τ = N. m The autocorrelation function of (n); For cyclic prefix data cp∈C2 and delay τ=0, the time-domain discrete received signal y m The autocorrelation function corresponding to (n) is labeled as in, This represents the time-domain signal x corresponding to the delay τ = 0. m The autocorrelation function of (n), The impulse noise I corresponding to the delay τ = 0. m The autocorrelation function of (n), The Gaussian white noise u corresponding to the delay τ = 0 m The autocorrelation function of (n).

6. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 5, characterized in that, In step 5, the normalized autocorrelation coefficient of the time-domain discrete received signal is calculated as follows: Where Rate(a) represents the discrete-time received signal y. m The normalized autocorrelation coefficient of (n); Represents the discrete-time received signal y m (n) The autocorrelation function of the data interval containing the cyclic prefix data a. Represents the discrete-time received signal y m The autocorrelation function of (n).

7. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 6, characterized in that, In step 7, the time-domain discrete received signal difference between the second prefix data interval and the fourth prefix data interval is calculated as follows: △I m (n)=I m (n+N)-I m (n);△u m (n)=u m (n+N)-u m (n); in: △y m (n) represents the time-domain discrete received signal difference; y m (n) represents the received signal of the discrete-time received signal in the second prefix data interval, y m (n+N) represents the received signal of the time-domain discrete received signal in the fourth prefix data interval; I m (n) represents the impulse noise signal in the second prefix data interval, I m (n+N) represents the impulse noise in the fourth prefix data interval, ΔI m (n) represents the signal difference between two impulse noise signals; u m (n) represents the Gaussian white noise signal in the second prefix data interval, I m (n+N) represents the Gaussian white noise signal in the fourth prefix data interval; △u m (n) represents the signal difference between two Gaussian white noise signals.

8. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 7, characterized in that, In step 8, the autocorrelation function of the time-domain discrete received signal difference when the cyclic prefix data is within the second prefix data interval and the delay is zero is calculated as follows: in, The difference Δy between the received discrete-time signals represents the difference in the time domain. m (n) is the autocorrelation function of the cyclic prefix data in the second prefix data interval and with zero delay.

9. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 8, characterized in that, The Doppler frequency shift estimate of the OFDM system is calculated as follows: in, This represents the estimated Doppler frequency shift of the OFDM system.

10. The method for blind Doppler frequency shift estimation of OFDM systems based on correlation coefficients according to claim 9, characterized in that, Following step 9, the process further includes: calculating the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation according to steps a1 to a3 as follows: Step a1: Establish a likelihood function with a preset number of sample symbols; wherein, the likelihood function is expressed as follows: Where f(y,θ) represents the likelihood function of the time-domain discrete received signal y(n) with respect to the parameter θ, x(nl) represents the time-domain discrete transmitted signal on the multipath fading channel in the OFDM system, and I(n) represents the impulse noise signal on the multipath fading channel in the OFDM system; Step a2: Based on the established likelihood function, calculate the Fisher information matrix corresponding to the likelihood function; the Fisher information matrix is ​​calculated as follows: Among them, J 11 (θ) is the Fisher information matrix corresponding to the likelihood function; Step a3: Based on the Fisher information matrix corresponding to the obtained likelihood function, calculate the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation; wherein, the Cramer-Rao lower bound of the OFDM system Doppler frequency shift estimation is denoted as... Wherein, SNR is the signal-to-noise ratio on the multipath fading channel within the OFDM system.

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