CN115065578B - DFT channel estimation method based on improved self-adaptive threshold - Google Patents
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Abstract
The invention belongs to the technical field of mobile communication, and particularly relates to a DFT channel estimation method based on an improved self-adaptive threshold, which comprises the following steps: building a wireless channel simulation platform to obtain a noise-containing signal; estimating the channel frequency of the p position by adopting a least square algorithm; adopting Haar wavelet to decompose channel frequency response, reducing noise of the signal after Haar wavelet decomposition through an improved self-adaptive threshold function, and reconstructing the signal after noise reduction to obtain channel frequency response after noise reduction; performing IDFT processing and time domain maximum point selection processing; finally, N-point FFT is carried out to obtain an accurate channel estimation value; the invention designs a processing procedure of maximum value selection based on the traditional DFT algorithm, and simultaneously assists wavelet transformation of the self-adaptive threshold value, thereby solving the problem of estimation accuracy reduction caused by channel noise.
Description
Technical Field
The invention belongs to the technical field of mobile communication, and particularly relates to a DFT channel estimation method based on an improved self-adaptive threshold value.
Background
One can obtain a high data rate and high capacity service regardless of time and place, which is always a key objective of a wireless communication system, which makes efficient use of spectrum a premise. An orthogonal frequency division multiplexing (Orthogonal Frequency Division Multiplexing, OFDM) system is an attractive multi-carrier modulation technique because it divides the overall bandwidth into several overlapping narrowband channels of low bit rate. In order to reduce the influence of the wireless channel on the signal itself, accurate channel estimation needs to be performed at the receiving end.
The conventional channel estimation generally uses an LS algorithm to perform channel estimation, and the conventional LS algorithm has low complexity, but does not consider noise effects. In order to solve the problem that the LS method does not consider the noise influence, a learner proposes a traditional DFT channel estimation method, but the traditional DFT channel estimation method does not consider the noise in the CP length, the improved DFT channel estimation method based on the threshold value is generated in the same way, so that the noise in the CP length is further filtered, and the DFT channel estimation method based on the threshold value has better denoising performance than the traditional DFT channel estimation method in the low signal-to-noise ratio environment, but in the high signal-to-noise ratio environment, useful channel taps are easily filtered into noise by the threshold value in a mistake, and the performance is reduced in the high signal-to-noise ratio environment.
Finally, the prior art problems are: the threshold value is easy to filter the useful channel tap into noise in a high signal-to-noise ratio environment, so that the performance of the channel tap is reduced in the high signal-to-noise ratio environment.
Disclosure of Invention
In order to solve the above technical problems, the present invention proposes a DFT channel estimation method based on an improved adaptive threshold, the method comprising the steps of:
s1: simulating a wireless channel model, wherein a transmitting end transmits signals through the constructed channel model, and a receiving end receives a noise-containing signal Y p ；
S2: from noisy signal Y using LS algorithm p In which the channel frequency response is estimated
S3: decomposing channel frequency response using Haar waveletNoise reduction is carried out on the signals after Haar wavelet decomposition through an improved self-adaptive threshold function, and the noise-reduced signals are reconstructed to obtain noise-reduced channel frequency response +.>
S4: noise-reduced channel frequency responseIDFT processing is carried out to obtain time domain channel response +.>
S5: response to time domain channelMaximum value screening is carried out, and the length of the cyclic prefix is screened to be L CP /8,L CP /2]Time domain channel response->A value;
s6: response to the filtered time domain channelPerforming N-point FFT to obtain accurate channel estimation value
Preferably, the transmitting end transmits signals through the constructed channel model, and the receiving end receives the noise-containing signals Y p ：
Y p ＝H p X p +W p
Wherein Y is p Represents the received p-th frequency domain pilot signal, H p Represents the p-th frequency domain channel response, X p Represents the p-th frequency domain pilot signal transmitted by the transmitting end, W p Representing noise.
Preferably, the LS algorithm is used to obtain an estimate of the channel at the p-position:
wherein,frequency domain channel response obtained for LS algorithm, Y p Representing the received p-th frequency domain pilot signal, X p Represents the p-th frequency domain pilot signal transmitted by the transmitting end, ">X represents p Is the conjugate transpose of (C), H represents the sum of the values of X p And performing conjugate transposition.
Preferably, the channel frequency response isDecomposing into wavelets, and reducing noise by improving an adaptive threshold, comprising the following steps:
s31: haar wavelet decomposition is carried out on the channel frequency response to obtain detail coefficients and approximate coefficients;
s32: filtering the detail coefficient by adopting a smoothing filter to obtain a smooth impulse response; filtering the approximation coefficients by adopting a high-pass filter to obtain a high-pass impulse response;
s33: filtering the smooth impulse response by adopting a soft threshold method to obtain a smooth impulse response with high-frequency noise removed;
s34: the high-pass impulse response and the smoothed impulse response from which the high-frequency noise is removed form a noise-reduced channel frequency response
Further, the expression for filtering the detail coefficient by using the smoothing filter is as follows:
the expression for filtering the approximation coefficients using a high pass filter is:
where h '(n) is the impulse response of the smoothing filter, g' (n) is the impulse response of the high pass filter, δ (n) is the unit impulse function, and δ (n+1) is the unit impulse function of δ (n) shifted one bit to the left.
Further, the smoothed impulse response is filtered using an improved adaptive threshold function, expressed as:
wherein,wavelet coefficient, w, representing signal wavelet after i-th decomposition processing i Is the untreated wavelet coefficient, |w i I is the absolute value of the unprocessed wavelet coefficient, N is the signal length, lambda i Representing an improved adaptive threshold, e being a natural base.
Further, an improved adaptive threshold lambda is obtained i The process of (1) comprises:
wherein lambda is i A threshold representing the i-th level wavelet decomposition, σ is the noise standard deviation,σ 2 represents the noise variance, P represents the maximum likelihood ratio, p=max (cA), i represents the decomposition scale, cA represents the first layer wavelet decomposition approximation coefficients, R i Representing the high frequency coefficient obtained by the i-th level wavelet decomposition, and mean represents the high frequency coefficient R i And taking a median value.
Preferably, the channel frequency responseAnd (3) performing IDFT transformation:
wherein N is the number of FFT points,for the channel frequency response obtained according to the LS algorithm, k is the frequency domain channel index, n is the time domain channel index, and j is the complex unit.
Preferably, time-domain channel responseThe screening process comprises the following steps:
s51: selecting a time domain channel response having a cyclic prefix length less than a conventional cyclic prefix lengthTime domain channel response greater than the normal cyclic prefix length +.>Zero-set time domain channel response after zero-set>Directly performing accurate channel estimation;
s52: selecting L m Time domain channel response with cyclic prefix length less than conventional cyclic prefix lengthConstructing a minimum heap according to the selected time domain channel response;
s53: respectively comparing the residual time domain channel response with the minimum response value of the minimum pile, and discarding the time domain channel response value when the time domain channel response value is smaller than the minimum response value of the minimum pile; otherwise, the minimum response value of the minimum stack is replaced by the time domain channel response valueAnd updating the minimum heap; until all points are compared, L in the final minimum heap is preserved m Time domain channel responseA value;
s54: for L in the reserved final minimum heap m Time domain channel responseThe value is subjected to simulation screening, and the cyclic prefix length is screened to be L CP /8,L CP /2]Time domain channel response->Values.
Preferably, for the filtered time domain channel responsePerforming DFT conversion to obtain accurate channel estimation value
Wherein N is the number of FFT points,for the time domain channel response after the screening process, k is the frequency domain channel index, n is the time domain channel index, and j is the complex unit.
According to the invention, the detail coefficient and the approximate coefficient can be effectively extracted by transforming the signal into a wavelet domain and decomposing the signal by the wavelet domain, and the detail coefficient is filtered by adopting a smoothing filter to obtain a smooth impulse response; the approximation coefficients are filtered by a high-pass filter to obtain a high-pass impulse response, the smooth impulse response is processed by improved self-adaptive threshold processing, and the high-frequency signal doped with noise is filtered, so that noise interference is reduced to the greatest extent, and the accuracy of channel estimation is improved.
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FIG. 1 is an algorithm flow chart of the method;
fig. 2 is a diagram of simulation effect of channel estimation performance using MATLAB on time domain channel responses of different cyclic prefix lengths.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Noise is widely present in wireless channels, in urban central zones with more buildings, due to the existence of dense buildings and other objects, no direct path exists between a transmitter and a receiver of wireless equipment, meanwhile, the buildings attenuate, reflect, refract and diffract wireless signals, and the characteristics of signal strength, phase and the like are fluctuant due to the movement of the receiver and other reasons, but the strength of the total signal is subject to Rayleigh distribution, so that a channel model can be constructed as a Rayleigh fading channel. In order to better simulate the state of a wireless channel, gaussian noise is added to a signal on the basis of an original Rayleigh fading channel, and a noise-containing Rayleigh channel model is built. Aiming at a channel model in the application scene, the invention provides a DFT channel estimation method based on an improved self-adaptive threshold, which can effectively remove noise in a channel, and the DFT channel estimation method based on the improved self-adaptive threshold is shown in figure 1.
A DFT channel estimation method based on an improved adaptive threshold value specifically comprises the following steps:
s1: for the dense urban central zone of the building, a wireless channel model is simulated, a transmitting end transmits signals through the built channel model, and a receiving end receives a noise-containing signal Y p ；
S2: from noisy signal Y using LS algorithm p In which the channel frequency response is estimated
S3: decomposing channel frequency response using Haar waveletNoise reduction is carried out on the signals after Haar wavelet decomposition through an improved self-adaptive threshold function, and the noise-reduced signals are reconstructed to obtain noise-reduced channel frequency response +.>
S4: performing IDFT on the result obtained in S34 to obtain time domain channel response
S5: response to time domain channelMaximum value screening is carried out, and the length of the cyclic prefix is screened to be L CP /8,L CP /2]Time domain channel response->A value;
s6: for time domain channel response after screening processingPerforming N-point FFT to obtain accurate channel estimation value
Obtaining noisy signal Y p ：
Y p ＝H p X p +W p
Wherein Y is p Representing the received firstp frequency domain pilot signals, H p Represents the p-th frequency domain channel response, X p Represents the p-th frequency domain pilot signal transmitted by the transmitting end, W p Representing noise.
Estimating channel frequency response using LS algorithm
Wherein,frequency domain channel response obtained for LS algorithm, Y p Representing the received p-th frequency domain pilot signal, X p Represents the p-th frequency domain pilot signal transmitted by the transmitting end, ">X represents p Is the conjugate transpose of (C), H represents the sum of the values of X p And performing conjugate transposition.
In response to channel frequencyPerforming wavelet transformation, and performing adaptive threshold noise reduction on the signal after wavelet transformation decomposition to obtain the noise reduced channel frequency response +.>The method specifically comprises the following steps:
s31: haar wavelet decomposition is carried out on the channel frequency response to obtain detail coefficients and approximate coefficients;
s32: filtering the detail coefficient by adopting a smoothing filter to obtain a smooth impulse response; filtering the approximation coefficients by adopting a high-pass filter to obtain a high-pass impulse response;
s33: filtering the smooth impulse response by adopting a soft threshold method to obtain a smooth impulse response with high-frequency noise removed;
s34: reconstructing the high-pass impulse response and the smooth impulse response without high-frequency noise to obtain the channel frequency response after noise reduction
Preferably, haar wavelets are used, which better decompose the estimates obtained above into detail coefficients and approximation coefficients, smoothing filters can be used to obtain approximation coefficients, similar detail coefficients are obtained using high pass filters, smoothing filter impulse responses h '(n), high pass filter impulse responses g' (n);
the expression for filtering the detail coefficients using a smoothing filter is:
the expression for filtering the approximation coefficients using a high pass filter is:
where h '(n) is the impulse response of the smoothing filter, g' (n) is the impulse response of the high pass filter, δ (n) is the unit impulse function, and δ (n+1) is the unit impulse function of δ (n) shifted one bit to the left.
Further, the hard threshold function has a discontinuous abrupt point at the threshold λ in terms of threshold mode selection, resulting in oscillation when the signal is reconstructed. Although the soft threshold function is continuous, the difference between the wavelet coefficients and the threshold coefficient λ results in a deviation between the reconstructed signal and the original signal, and thus a modified wavelet threshold function is used for the threshold filtering, where the modified wavelet threshold function is formulated as:
wherein,wavelet coefficient, w, representing signal wavelet after i-th decomposition processing i Is the untreated wavelet coefficient, |w i I is the absolute value of the unprocessed wavelet coefficient, N is the signal length, lambda i Representing an improved adaptive threshold, e being a natural base.
Further, the adaptive threshold lambda is improved i The process of (1) comprises:
based on the relative variation of signal noise on different wavelet scales, an adaptive threshold is constructed by maximum likelihood ratio P and noise difference, expressed as:
the maximum likelihood ratio P suppresses the influence of the signal wavelength on the threshold value selection to be too large and too small, and the maximum likelihood ratio P is expressed as:
P＝max(cA)
threshold lambda i With decomposition scale i and noise varianceIs reduced by an increase in the noise variance +.>The standard deviation of the high frequency signal noise, expressed as:
wherein lambda is i Threshold representing level i wavelet decomposition, σ is noise standard deviation, σ 2 Represents the noise variance, P represents the maximum likelihood ratio, i represents the decomposition scale, cA represents the first layer wavelet decomposition approximation coefficient, R i Representing the high frequency coefficient obtained by the decomposition of the ith level wavelet, and mean represents the high frequencyCoefficient R i And taking a median value.
Preferably, the noise-reduced channel frequency responsePerforming IDFT to obtain time domain channel response +.>
Wherein N is the number of FFT points,for the channel frequency response obtained according to the LS algorithm, k is the frequency domain channel index, n is the time domain channel index, and j is the complex unit.
Preferably, the time domain channel response with a cyclic prefix length less than the length of a conventional cyclic prefix (the conventional cyclic prefix length is 4.7 mu s) is selectedThen respond to the selected time domain channel +.>Performing time domain maximum value selection processing to obtain time domain channel response +.>
Step one: selecting a time domain channel response having a cyclic prefix length less than a conventional cyclic prefix lengthTime domain channel response +.>Zero-set time domain channel response after zero-set>Directly performing accurate channel estimation;
further, selecting a time domain channel response having a cyclic prefix length less than a conventional cyclic prefix lengthTime domain channel response greater than the normal cyclic prefix length +.>Setting zero:
wherein,representing a time domain channel response with a cyclic prefix length less than a conventional cyclic prefix length, L CP Representing the cyclic prefix length, n being the time domain channel index;
step two: time domain channel response to a selected cyclic prefix length less than a conventional cyclic prefix lengthPerforming maximum value selection processing on the selected +.>Sorting by heap sorting according to absolute value, and keeping the sorted data +.>L with the maximum absolute value m The specific steps include;
s521: front L m Time domain messages having a cyclic prefix length less than a conventional cyclic prefix lengthTrack responseConstructing a minimum heap by points;
s522: from L < th > m Starting at +1, starting to compare with the top of the smallest heap, and discarding it when this point is smaller than the top of the heap; when it is larger, replace the top with this point and recursively adjust the minimum heap from top to bottom; until all points are compared, L in the final minimum heap is preserved m Time domain channel responseA dot;
s523: for L in the reserved final minimum heap m Time domain channel responseSimulation screening is carried out on the values to obtain the most suitable time domain channel response +.>Values.
Further, with respect to time domain channel responseSelecting: if the time domain channel response->Too much noise is left due to the too large cyclic prefix length; if the time domain channel response->The cyclic prefix length of (2) is small and useful channel estimation information will be lost, thus the time domain channel response +.>Is that the choice of (a) will affect the performance of the estimation method;
simulating performance of a proposed channel estimation method using MATLABIndeed, time domain channel responses of different sizes are selectedAnd taking Bit Error Rate (BER) as a performance measure, FIG. 2 shows that time domain channel responses of different magnitudes are selected +.>The performance results of the improved process;
figure one shows if the time domain channel responseToo many or too few, the error probability BER will be high because reserving too many points will preserve too much noise, while reserving too few points will result in losing useful channel estimation information, the effect of which is more serious, the lowest points of the three curves from top to bottom are 15, 20 and 24, respectively; in summary, the selected time domain channel response has an important influence on the performance, not too much or too little, and the time domain channel response is selected according to the simulation result>At [ L ] CP /8,L CP /2]The effect is better.
Preferably, the time domain channel response is screened outPerforming DFT conversion to obtain accurate channel estimation value
Wherein N is the number of FFT points,after the screening treatmentK is a frequency domain channel index, n is a time domain channel index, and j is a complex unit.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (6)
1. A DFT channel estimation method based on an improved adaptive threshold, comprising the steps of:
s1: acquiring a noise-containing signal Y according to a wireless channel model p ；
S2: from noisy signal Y using LS algorithm p In which the channel frequency response is estimated
S3: decomposing channel frequency response using Haar waveletNoise reduction is carried out on the signals after Haar wavelet decomposition through an improved self-adaptive threshold function, and the noise-reduced signals are reconstructed to obtain noise-reduced channel frequency response +.>
S31: haar wavelet decomposition is carried out on the channel frequency response to obtain detail coefficients and approximate coefficients;
s32: filtering the detail coefficient by adopting a smoothing filter to obtain a smooth impulse response; filtering the approximation coefficients by adopting a high-pass filter to obtain a high-pass impulse response;
s33: filtering the smooth impulse response by adopting an improved self-adaptive threshold function to obtain a smooth impulse response with high-frequency noise removed;
the smoothed impulse response is filtered using an improved adaptive threshold function, expressed as:
wherein,wavelet coefficient lambda representing signal wavelet after i-th decomposition processing i Threshold, w, representing level i wavelet decomposition i Is the untreated wavelet coefficient, |w i The I is the absolute value of an unprocessed wavelet coefficient, N is the signal length, and e is a natural base number;
obtaining an improved adaptive threshold lambda i The process of (1) comprises:
wherein lambda is i A threshold representing the i-th level wavelet decomposition, σ is the noise standard deviation,σ 2 represents the noise variance, P represents the maximum likelihood ratio, p=max (cA), i represents the decomposition scale, cA represents the first layer wavelet decomposition approximation coefficients, R i Representing the high frequency coefficient obtained by the i-th level wavelet decomposition, and mean represents the high frequency coefficient R i Taking a median value;
s34: reconstructing the high-pass impulse response and the smooth impulse response without high-frequency noise to obtain the channel frequency response after noise reduction
S4: noise-reduced channel frequency responseAt the IDFTObtaining the time domain channel response +.>
S5: response to time domain channelMaximum value screening is carried out, and the length of the cyclic prefix is screened to be L CP /8,L Cp /2]Time domain channel response->A value;
s51: selecting a time domain channel response having a cyclic prefix length less than a conventional cyclic prefix lengthTime domain channel response greater than the normal cyclic prefix length +.>Setting zero;
s52: selecting L m Time domain channel response with cyclic prefix length less than conventional cyclic prefix lengthConstructing a minimum heap according to the selected time domain channel response;
s53: respectively comparing the residual time domain channel response with the minimum response value of the minimum pile, and discarding the time domain channel response value when the time domain channel response value is smaller than the minimum response value of the minimum pile; otherwise, the minimum response value of the minimum stack is replaced by the time domain channel response value, and the minimum stack is updated; until all points are compared, L in the final minimum heap is preserved m Time domain channel responseA value;
s54: for L in the reserved final minimum heap m Time domain channel responseThe value is subjected to simulation screening to obtain the cyclic prefix length of [ L ] CP /8,L CP /2]Time domain channel response->A value;
s6: response to the screened time domain channelPerforming N-point DFT to obtain accurate channel estimation value +.>
2. The method of claim 1, wherein the transmitting end transmits signals through a channel model and the receiving end receives the noisy signal Y p The expression of (2) is:
Y p ＝H p X p +W p
wherein Y is p Represents the received p-th frequency domain pilot signal, H p Represents the p-th frequency domain channel response, X p Represents the p-th frequency domain pilot signal transmitted by the transmitting end, W p Representing noise.
3. The improved adaptive threshold based DFT channel estimation method as recited in claim 1, wherein the LS algorithm is used to obtain the estimated value of the channel at the p-position:
wherein,frequency domain channel response obtained for LS algorithm, Y p Representing the received p-th frequency domain pilot signal, X p Represents the p-th frequency domain pilot signal transmitted by the transmitting end, ">X represents p Is the conjugate transpose of (C), H represents the sum of the values of X p And performing conjugate transposition.
4. The improved adaptive threshold based DFT channel estimation method as recited in claim 1, wherein the expression for filtering the detail coefficients using a smoothing filter is:
the expression for filtering the approximation coefficients using a high pass filter is:
where h '(n) is the impulse response of the smoothing filter, g' (n) is the impulse response of the high pass filter, δ (n) is the unit impulse function, and δ (n+1) is the impulse function of δ (n) shifted one bit to the left.
5. The improved adaptive threshold based DFT channel estimation method as recited in claim 1, wherein the channel frequency responseAnd carrying out IDFT conversion, wherein the expression is as follows:
wherein N is the number of FFT points,for the channel frequency response obtained according to the LS algorithm, k is the frequency domain channel index, n is the time domain channel index, and j is the complex unit.
6. A DFT channel estimation method based on improved adaptive threshold as set forth in claim 1 wherein,performing DFT conversion to obtain accurate channel estimation value +.>
Wherein N is the number of FFT points,for the time domain channel response after the screening process, k is the frequency domain channel index, n is the time domain channel index, and j is the complex unit.
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