CN110602006A - Channel estimation method under LTE system - Google Patents
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Abstract
The invention provides a channel estimation method under an LTE system, which comprises the steps of firstly carrying out LS least square method channel estimation on a frequency domain at a receiver side to obtain a preliminary channel estimation result, then carrying out MMSE minimum mean square error channel estimation to improve the accuracy of channel estimation, then carrying out IFFT (inverse fast Fourier transform) on the frequency domain channel estimation result, utilizing the time limitation of channel impulse response to carry out truncation on signals except for channel duration, forcibly setting zero, reducing the energy of noise, and finally carrying out FFT (fast Fourier transform) to return to the frequency domain, thereby realizing the improvement of the accuracy of channel estimation. The invention has the beneficial effects that: the mean square error of the channel estimation is greatly reduced, the precision of the channel estimation is improved, and a good effect is obtained.
Description
Technical Field
The present invention relates to a channel estimation method, and in particular, to a channel estimation method in an LTE system.
Background
In the current information society, the development of mobile communication technology is receiving more and more attention. The ultimate goal of the development of mobile communication technology is to enable anyone to communicate with anyone or an object of any kind at any time and any place.
The development of communication technology has passed through the continuous development of the first, second, third and current fourth generation LTE, and even the continuous evolution of the future 5G. The development of communication technology has taught that the most core technology of communication is coding, decoding, modulating and demodulating. However, correct demodulation and decoding of data information first relies on accurate estimation of the radio channel.
The channel estimation can be performed in a time domain or a frequency domain, and in an LTE (Long Term Evolution) system, the channel estimation is generally performed in the frequency domain in consideration of the wideband characteristics and the corresponding complexity of LTE.
Therefore, how to improve the accuracy of channel estimation is an urgent technical problem to be solved by those skilled in the art.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a channel estimation method in an LTE system.
The invention provides a channel estimation method under an LTE system, which comprises the steps of firstly carrying out LS least square method channel estimation on a frequency domain at a receiver side to obtain a preliminary channel estimation result, then carrying out MMSE minimum mean square error channel estimation to improve the accuracy of channel estimation, then carrying out IFFT (inverse fast Fourier transform) on the frequency domain channel estimation result, utilizing the time limitation of channel impulse response to carry out truncation on signals except for channel duration, forcibly setting zero, reducing the energy of noise, and finally carrying out FFT (fast Fourier transform) to return to the frequency domain, thereby realizing the improvement of the accuracy of channel estimation.
As a further improvement of the present invention, the channel estimation method comprises the steps of:
s1, frequency domain equalization;
s2, LS least square method channel estimation;
s3, MMSE minimum mean square error channel estimation;
s4, noise estimation;
s5, time domain truncation.
As a further improvement of the present invention, in step S1, the system equation of the channel estimation is expressed in the form of discrete convolution:
wherein,in order to input the signal, the signal is,the response of the channel impulse is determined,in order to observe the signal(s),for input signalsLength of (d);
expressed in matrix form as follows:
wherein,is composed of
Is the impulse response of the channel;
is an observed signal;
is complex gaussian noise;
according to the property of discrete Fourier transform, multiplying time domain circular convolution by a frequency domain;
to apply frequency domain multiplication, the relationship of the above expressions is first converted to the form of a circular convolution by the following methodCut into lengths ofThen add up:
the observation signal and noise are also treated in the same way:
the signals thus processed are related to the convolution:
expressed in a matrix, then:
andis formed byAnda column vector formed by the arrangement of the column vectors,
within the matrix theory, the matrices are represented in upper case bold and the vectors are represented in lower case bold, and in order to comply with this rule, the expression is used herein、Representing frequency domain signals to avoid confusion, if at allArranged as vectorsHandle barArranged as vectorsThen the discrete fourier transform can be represented by a matrix:
inverse transformation:
whereinA discrete Fourier transform matrix of N points;
note the book，
Equation of pairsDFT conversion is carried out on two sides:
from this, the equation in the frequency domain is expressed as:
wherein,
according to the convolution theorem, the time domain circular convolution corresponds to the frequency domain product,must be a diagonal matrix:
as a further improvement of the present invention, in step S2,
LS least squares channel estimation does not take noise effects into account, so equations in the frequency domainThe method comprises the following steps:
constructing an error vector:
；
where, e is the error vector and,is a received frequency-domain signal that is,is a frequency-domain signal that is transmitted,
is a frequency domain LS least squares method channel estimation,presentation pairEstimating a signal vector;
to minimize the mean square error of the signal estimate, the condition needs to be satisfied:
；
transforming the above equation:
；
the above J-pair matrixCalculating the partial derivatives, and making the partial derivatives zero, then:
；
namely:
therefore, the method comprises the following steps:
thereby obtaining a frequency domain LS least squares channel estimate
As a further improvement of the present invention, in step S3,
MMSE minimum mean square error channel estimation fully considers the influence of noise, further carries out minimum mean square error channel estimation on the basis of completing the preliminary estimation of the channel by an LS least square method,
when MMSE minimum mean square error channel estimation is adopted, orderFor equation in frequency domainConstructing an error vector:
；
where, e is the error vector and,is a characteristic of the frequency domain of the channel,is channel frequency domain MMSE minimum mean square error estimation;
to minimize the mean square error of the signal estimate, the condition needs to be satisfied:
；
transforming the above equation:
；
the above J-pair matrixCalculating the partial derivatives, and making the partial derivatives zero, then:
；
namely:
therefore, the method comprises the following steps:
order to，Represents the noise power, then
Therefore, there are
Wherein, in order to simplify the calculation, the actual engineering realization is considered inIn the calculation of (1) inApproximate substitutionThereby obtaining a frequency domain MMSE minimum mean square error channel estimation
As a further improvement of the present invention, in step S4,
the upper typeIn which there is also a noise termNeed to estimate, in order to estimate, the system noiseThe following calculations were performed:
suppose inOn one OFDM symbolThe received signal on the subcarriers is represented as:
wherein，，Is the number of sub-carriers,represents the m th OFDM symbolThe channel frequency response on the sub-carriers,represents the m th OFDM symbolThe symbols transmitted on the individual sub-carriers,represents the m th OFDM symbolAdditive Gaussian stationary noise on subcarriers with mean of 0 and variance of；
Since the following steps are performed for each subcarrier k, for convenience of description, the subscript k is omitted in the following equation, and the pilot symbol positions are taken as 3 and 10 as examples, that is, the uplink LTE pilot symbol positions:
1) calculating channel frequency response by LS channel estimation、；
2) Calculating channel frequency domain response difference;
3) Calculating a state compensation quantity：;
4) ComputingWherein；
5) ByCalculating；
6) Computing；
7) ComputingAnd thus a noise variance estimate.
As a further improvement of the present invention, in step S5,
obtained by adopting frequency domain MMSE minimum mean square error channel estimation methodThen, more accurate channel estimation is obtained through a time domain truncation processing method;
in a wireless propagation environment, the delay spread of the channel, i.e. the coherence bandwidth, is substantially constant, which can be considered as a known quantity, and is further obtained by the already obtained LS channel estimate:
1) calculating an autocorrelation function of frequency domain channel response according to LS channel estimation;
2) determining a 3db bandwidth of the autocorrelation function;
3) calculating frequency domain correlation bandwidth；
4) Determining root mean square delay spread；
5) According to the Gaussian normal probability distribution, the maximum time delay expansion probability is less thanGet it；
Assuming that the maximum delay spread of the channel has been obtained by channel estimationAccording to an inverse Fourier transformFor frequency domain MMSE minimum mean square error channel estimationAnd (3) carrying out inverse Fourier transform:
wherein,
frequency domain MMSE minimum mean square error channel estimation;
for the purpose of the inverse fourier transformation,
estimating a time domain expression for an MMSE minimum mean square error channel, wherein an N-point discrete sequence is arranged on a time domain and is recorded as follows:，
the prior information of the time delay expansion length of the channel is utilized to exceedSetting the information response outside the length to be zero, and performing time domain truncation to obtain time domain channel estimation after time domain truncation:
,0,0,,0
Time domain channel estimation after time domain truncationBy performing fourier transform, more accurate channel estimation can be achieved:
wherein
The high-precision channel estimation is finally obtained through frequency domain equalization, LS least square method channel estimation, MMSE minimum mean square error channel estimation, inverse Fourier transform, time domain truncation and Fourier transform.
The invention has the beneficial effects that: by the scheme, the mean square error of channel estimation is greatly reduced, the precision of the channel estimation is improved, and a good effect is achieved.
Drawings
Fig. 1 is a flowchart of a channel estimation method in an LTE system according to the present invention.
Fig. 2 is a mean square error comparison diagram of the LS channel estimation, MMSE + time domain truncation channel estimation algorithm.
Detailed Description
The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.
As shown in fig. 1, in a channel estimation method in an LTE system, at a receiver, LS least square method channel estimation is performed in a frequency domain to obtain a preliminary channel estimation result, MMSE minimum mean square error channel estimation is performed to improve accuracy of the channel estimation, IFFT inverse transformation is performed on the frequency domain channel estimation result, signals (i.e., noise) outside a channel duration are truncated and forcibly zeroed by using time limitation of channel impulse response, energy of the noise is reduced, and finally FFT transformation is performed to return to the frequency domain, thereby improving accuracy of the channel estimation. Simulation shows that the mean square error of channel estimation is greatly reduced, the precision of channel estimation is improved, and a good effect is achieved.
As shown in fig. 1, a channel estimation method in an LTE system includes the following specific implementation steps:
frequency domain equalization
For a narrow-band system, in a channel estimation algorithm, a large number of zero elements exist in a correlation matrix, and the operation amount of time domain equalization is not large, so that the time domain equalization is feasible. However, in the LTE broadband system, the maximum bandwidth of LTE can reach 20MHz, and in this case, the channel delay is large, and the computation amount of time domain equalization is too large, so the channel estimation of the LTE system generally adopts a frequency domain equalization technology.
In general, the system equation for channel estimation, in the form of a discrete convolution, can be expressed as:
wherein,in order to input the signal, the signal is,the response of the channel impulse is determined,in order to observe the signal(s),for input signalsLength of (d).
In matrix form, the following can be expressed:
wherein,is composed of
Is the impulse response of the channel;
is an observed signal;
is complex gaussian noise.
According to the property of discrete Fourier transform, the convolution of time domain circles corresponds to the multiplication of frequency domains, the convolution operation of the time domain is more complex, and the conversion to the frequency domain is simpler.
To apply frequency domain multiplication, the relationship of the above expressions is first converted to a circular convolution form byCut into lengths ofThen add up:
the observation signal and noise are also treated in the same way:
the signals thus processed are related to the convolution:
expressed in a matrix as
Andis formed byAnda column vector formed by the arrangement of the column vectors,
in the matrix theory, the matrix is generally represented by upper bold and the vector is represented by lower bold, and in order to comply with the rule, the algorithm expression of the invention is expressed by、The frequency domain signal is represented so as not to be confused. If it is at handArranged as vectorsHandle barArranged as vectorsThen the discrete fourier transform can be represented by a matrix:
inverse transform to
WhereinIs a discrete fourier transform matrix of N points.
Note the book，
Equation of pairsDFT conversion is carried out on two sides:
from this, the equation in the frequency domain can be expressed as:
wherein
According to the convolution theorem, the time domain circular convolution corresponds to the frequency domain product,must be a diagonal matrix:
(II) LS least squares channel estimation
LS least squares channel estimation does not take noise effects into account, so the above equation in the frequency domainThe method comprises the following steps:
constructing an error vector:
；
where, e is the error vector and,is a received frequency-domain signal that is,is a frequency-domain signal that is transmitted,is a frequency domain LS least squares method channel estimation,presentation pairEstimating a signal vector;
to minimize the mean square error of the signal estimate, the condition needs to be satisfied:
；
transforming the above equation:
；
the above J-pair matrixCalculating the partial derivatives, and making the partial derivatives zero, then:
；
namely:
therefore, the method comprises the following steps:
thereby obtaining a frequency domain LS least squares channel estimate
(III) MMSE minimum mean square error channel estimation
MMSE minimum mean square error channel estimation fully considers the influence of noise, and further carries out minimum mean square error channel estimation on the basis of completing preliminary estimation of a channel by an LS least square method
When MMSE minimum mean square error channel estimation is adopted, orderFor the above equation in the frequency domainConstructing an error vector:
；
where, e is the error vector and,is a characteristic of the frequency domain of the channel,is channel frequency domain MMSE minimum mean square error estimation;
to minimize the mean square error of the signal estimate, the condition needs to be satisfied:
；
transforming the above equation:
；
the above J-pair matrixCalculating the partial derivatives, and making the partial derivatives zero, then:
；
namely:
therefore, the method comprises the following steps:
order to，Represents the noise power, then
Therefore, there are
Wherein, in order to simplify the calculation, the actual engineering realization is considered inIn the calculation of (1) inApproximate substitutionThereby obtaining a frequency domain MMSE minimum mean square error channel estimation
(IV) noise estimation
Note the above formulaIn which there is also a noise termNeed to estimate, in order to estimate, the system noiseWe can do the following calculations.
Suppose inOn one OFDM symbolThe received signal on the subcarriers is represented as:
wherein，，Is the number of sub-carriers,represents the m th OFDM symbolThe channel frequency response on the sub-carriers,represents the m th OFDM symbolThe symbols transmitted on the individual sub-carriers,represents the m th OFDM symbolAdditive Gaussian stationary noise on subcarriers with mean of 0 and variance of。
Since the following steps are performed for each subcarrier k, for convenience of description, the subscript k is omitted in the following equation, and the pilot symbol positions are taken as 3 and 10 as examples (uplink LTE pilot symbol positions):
1) calculating channel frequency response by LS channel estimation、；
2) Calculating channel frequency domain response difference;
3) Calculating a state compensation quantity：;
4) ComputingWherein；
5) ByCalculating；
6) Computing；
7) ComputingAnd thus a noise variance estimate.
(V) time domain truncation
Obtained by adopting frequency domain MMSE minimum mean square error channel estimation methodAnd then, more accurate channel estimation can be obtained by a time domain truncation processing method.
Note that there is actually also information that can be used to reduce the impact of burst noise, and in a wireless propagation environment, the delay spread of the channel, i.e. the coherence bandwidth, is substantially constant, which can be considered as a known quantity, and is further obtained by the already obtained LS channel estimation:
1) computation of autocorrelation function of frequency domain channel response from LS channel estimation
2) Determining the 3db bandwidth of an autocorrelation function
3) Calculating frequency domain correlation bandwidth
4) Determining root mean square delay spread
5) According to the Gaussian normal probability distribution, the maximum time delay expansion probability is less thanGet it
Assuming that the maximum delay spread of the channel has been obtained by channel estimationAccording to an inverse Fourier transformFor frequency domain MMSE minimum mean square error channel estimationAnd (3) carrying out inverse Fourier transform:
wherein,
minimum mean square error channel estimation for frequency domain MMSE
Is an inverse Fourier transform
Estimating a time domain expression for an MMSE minimum mean square error channel, wherein an N-point discrete sequence is arranged on a time domain and is recorded as follows:
the prior information of the time delay expansion length of the channel is utilized to exceedSetting the information response outside the length to be zero, and performing time domain truncation to obtain time domain channel estimation after time domain truncation:
,0,0,,0
Time domain channel estimation after time domain truncationBy performing fourier transform, more accurate channel estimation can be achieved:
wherein
The high-precision channel estimation is finally obtained through frequency domain equalization, LS least square method channel estimation, MMSE minimum mean square error channel estimation, inverse Fourier transform, time domain truncation and Fourier transform.
As shown in fig. 1, it is a block diagram of a specific implementation of the method of the present invention, and the specific implementation is as follows:
(one) LS least squares channel estimation
According toAnd performing LS channel estimation, wherein the obtained LS channel estimation result is used for noise estimation, frequency domain channel response autocorrelation calculation and coefficient generation of MMSE channel estimation.
(II) noise estimation
And according to the received signal and the LS channel estimation result, applying the noise estimation method to estimate the noise variance for MMSE coefficient generation.
MMSE estimation module
And generating an MMSE coefficient for MMSE channel estimation according to the LS channel estimation result, the frequency domain channel response correlation function calculated by the LS channel estimation result and the noise variance estimation.
(IV) time domain truncation
And performing inverse Fourier transform on the frequency domain channel estimation result obtained by MMSE channel estimation to obtain time domain channel estimation.
Determining the bandwidth of the correlation function 3db according to the frequency domain channel response correlation function, and calculating the root mean square delay spreadDetermining the maximum delay spreadAnd performing time domain truncation on the obtained time domain channel estimation.
And performing Fourier transform on the time domain channel after time domain truncation to finally obtain high-precision frequency domain channel estimation.
As shown in fig. 2, the mean square error comparison of the LS channel estimation, MMSE + time domain truncation channel estimation algorithm is also consistent with the expected result, the LS channel estimation does not consider the influence of noise factors, and therefore the mean square error of the channel estimation is maximum; the MMSE channel estimation fully considers the influence of noise factors, the mean square error of the channel estimation is smaller, but the time delay expansion of the channel is not considered in the MMSE channel estimation, so the channel estimation is still not accurate enough, and the MMSE + time domain truncation channel estimation algorithm fully utilizes the time delay expansion information of the channel and carries out time domain truncation processing on the basis of the MMSE channel estimation, so the accuracy of the channel estimation is further improved, and the high-precision frequency domain channel estimation is obtained.
Simulation shows that the mean square error of channel estimation is greatly reduced, the precision of channel estimation is improved, and a good effect is achieved.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (7)
1. A channel estimation method under an LTE system is characterized in that: at the receiver side, firstly, LS least square method channel estimation is carried out on a frequency domain to obtain a primary channel estimation result, then MMSE minimum mean square error channel estimation is carried out to improve the accuracy of channel estimation, then IFFT inverse transformation is carried out on the frequency domain channel estimation result, signals beyond the channel duration are truncated by utilizing the time limitation of channel impulse response, zero is forcibly set, the energy of noise is reduced, and finally FFT transformation is carried out to return to the frequency domain, so that the accuracy of channel estimation is improved.
2. The channel estimation method under the LTE system according to claim 1, wherein: the channel estimation method comprises the following steps:
s1, frequency domain equalization;
s2, LS least square method channel estimation;
s3, MMSE minimum mean square error channel estimation;
s4, noise estimation;
s5, time domain truncation.
3. The channel estimation method under the LTE system according to claim 2, wherein: in step S1, the system equation for channel estimation is expressed in the form of discrete convolution:
wherein,in order to input the signal, the signal is,the response of the channel impulse is determined,in order to observe the signal(s),for input signalsLength of (d);
expressed in matrix form as follows:
wherein,is composed of
Is the impulse response of the channel;
is an observed signal;
is complex gaussian noise;
according to the property of discrete Fourier transform, multiplying time domain circular convolution by a frequency domain;
to apply frequency domain multiplication, the relationship of the above expressions is first converted to the form of a circular convolution by the following methodCut into lengths ofThen add up:
the observation signal and noise are also treated in the same way:
the signals thus processed are related to the convolution:
expressed in a matrix, then:
andis formed byAnda column vector formed by the arrangement of the column vectors,
within the matrix theory, the matrices are represented in upper case bold and the vectors are represented in lower case bold, and in order to comply with this rule, the expression is used herein、Representing frequency domain signals to avoid confusion, if at allArranged as vectorsHandle barArranged as vectorsThen the discrete fourier transform can be represented by a matrix:
inverse transformation:
whereinA discrete Fourier transform matrix of N points;
note the book，
Equation of pairsDFT conversion is carried out on two sides:
from this, the equation in the frequency domain is expressed as:
wherein,
according to the convolution theorem, the time domain circular convolution corresponds to the frequency domain product,must be a diagonal matrix:
。
4. the channel estimation method under the LTE system according to claim 3, wherein: in the step S2, in step S2,
LS least squares channel estimation does not take noise effects into account, so equations in the frequency domainThe method comprises the following steps:
constructing an error vector:
；
where, e is the error vector and,is a received frequency-domain signal that is,is a frequency-domain signal that is transmitted,
is a frequency domain LS least squares method channel estimation,presentation pairEstimating a signal vector;
to minimize the mean square error of the signal estimate, the condition needs to be satisfied:
；
transforming the above equation:
；
the above J-pair matrixCalculating the partial derivatives, and making the partial derivatives zero, then:
；
namely:
therefore, the method comprises the following steps:
thereby obtaining a frequency domain LS least squares channel estimate。
5. The channel estimation method under LTE system according to claim 4, characterized in that: in the step S3, in step S3,
MMSE minimum mean square error channel estimation fully considers the influence of noise, further carries out minimum mean square error channel estimation on the basis of completing the preliminary estimation of the channel by an LS least square method,
when MMSE minimum mean square error channel estimation is adopted, orderFor equation in frequency domainConstructing an error vector:
；
where, e is the error vector and,is a characteristic of the frequency domain of the channel,is channel frequency domain MMSE minimum mean square error estimation;
to minimize the mean square error of the signal estimate, the condition needs to be satisfied:
；
transforming the above equation:
；
the above J-pair matrixCalculating the partial derivatives, and making the partial derivatives zero, then:
；
namely:
therefore, the method comprises the following steps:
order to，Represents the noise power, then
Therefore, there are
Wherein, in order to simplify the calculation, the actual engineering realization is considered inIn the calculation of (1) inApproximate substitutionThereby obtaining a frequency domain MMSE minimum mean square error channel estimation。
6. The channel estimation method under the LTE system according to claim 5, wherein: in the step S4, in step S4,
the upper typeIn which there is also a noise termNeed to estimate, in order to estimate, the system noiseThe following calculations were performed:
suppose inOn one OFDM symbolThe received signal on the subcarriers is represented as:
wherein，，Is the number of sub-carriers,represents the m th OFDM symbolThe channel frequency response on the sub-carriers,represents the m th OFDM symbolThe symbols transmitted on the individual sub-carriers,represents the m < th >On OFDM symbolAdditive Gaussian stationary noise on subcarriers with mean of 0 and variance of；
Since the following steps are performed for each subcarrier k, for convenience of description, the subscript k is omitted in the following equation, and the pilot symbol positions are taken as 3 and 10 as examples, that is, the uplink LTE pilot symbol positions:
1) calculating channel frequency response by LS channel estimation、；
2) Calculating channel frequency domain response difference;
3) Calculating a state compensation quantity：;
4) ComputingWherein；
5) ByCalculating；
6) Computing；
7) ComputingAnd thus a noise variance estimate.
7. The channel estimation method under the LTE system according to claim 6, wherein: in the step S5, in step S5,
obtained by adopting frequency domain MMSE minimum mean square error channel estimation methodThen, more accurate channel estimation is obtained through a time domain truncation processing method;
in a wireless propagation environment, the delay spread of the channel, i.e. the coherence bandwidth, is substantially constant, which can be considered as a known quantity, and is further obtained by the already obtained LS channel estimate:
1) calculating an autocorrelation function of frequency domain channel response according to LS channel estimation;
2) determining a 3db bandwidth of the autocorrelation function;
3) calculating frequency domain correlation bandwidth；
4) Determining root mean square delay spread；
5) According to the Gaussian normal probability distribution, the maximum time delay expansion probability is less thanGet it；
Assuming that the maximum delay spread of the channel has been obtained by channel estimationAccording to an inverse Fourier transformFor frequency domain MMSE minimum mean square error channel estimationAnd (3) carrying out inverse Fourier transform:
wherein,
frequency domain MMSE minimum mean square error channel estimation;
for the purpose of the inverse fourier transformation,
estimating a time domain expression for an MMSE minimum mean square error channel, wherein an N-point discrete sequence is arranged on a time domain and is recorded as follows:，
the prior information of the time delay expansion length of the channel is utilized to exceedSetting the information response outside the length to be zero, and performing time domain truncation to obtain time domain channel estimation after time domain truncation:
,0,0,,0
Time domain channel estimation after time domain truncationBy performing fourier transform, more accurate channel estimation can be achieved:
wherein
The high-precision channel estimation is finally obtained through frequency domain equalization, LS least square method channel estimation, MMSE minimum mean square error channel estimation, inverse Fourier transform, time domain truncation and Fourier transform.
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