A noise reduction sparseness adaptive weak orthogonal matching pursuit method and system

Abstract

The invention relates to the field of mobile communication technology, and specifically discloses a denoising sparsity adaptive weak orthogonal matching pursuit method and system, which combines a compressed sensing theoretical framework to perform channel estimation on an OFDM communication system, specifically performs singular value decomposition on a received signal, deletes singular values ​​representing noise, reconstructs a noise-free signal, then uses the signal as an initial residual to perform an inner product with a sensing matrix to obtain the projection of each atom on the residual, selects corresponding atoms in a weak selection method and stores them in a dictionary set, then calculates the reconstructed signal by a least square method, and when the energy difference of the reconstructed signals in adjacent stages is stable within a certain range, it indicates that the energy of the reconstructed signal tends to be stable, the reconstruction is completed, and an optimal reconstructed signal is output, so that the accuracy of channel estimation is higher, the acquired channel state information is more accurate, the bit error rate of the entire communication system is lower, and at the same time, the pilot overhead is reduced, and spectrum resources are saved.

Description

Technical Field

[0001] The present invention relates to the field of mobile communication technology, and in particular to a denoising sparsity adaptive weak orthogonal matching tracking method and system. Background Art

[0002] OFDM is a scheme that uses multiple carriers for transmission. The basic method is to split the original high-speed data stream into many parallel low-speed data streams at the transmitting end, and each low-speed data stream corresponds to a corresponding subcarrier. This is equivalent to dividing the original channel into many parallel subchannels, so that the bandwidth of each subchannel is smaller than the coherence bandwidth of the channel, so that it has the ability to resist multipath fading. In order to resist the multipath effect of the wireless channel, the OFDM receiver needs accurate 2-channel state information (CSI) to demodulate user data more accurately. Figure 1 The figure shows the channel estimation block diagram of the OFDM communication system. The traditional OFDM channel estimation method does not take into account the sparsity of the wireless channel and needs to use a large number of pilot signals to detect the time-varying characteristics of the channel, resulting in a waste of resources. Compressed sensing can apply the sparsity of the wireless channel to channel estimation, reconstructing the channel impulse response is more advantageous, and can also save some spectrum resources and avoid unnecessary pilot overhead.

[0003] The sparse channel estimation algorithm under the framework of compressed sensing theory is mainly based on iterative greedy algorithms, such as orthogonal matching pursuit (OMP), regularized orthogonal matching pursuit (ROMP) and compressed sampling matching pursuit (CoSaMP). These greedy algorithms iteratively recover the signal, and in each iteration, they select atoms of the known sensor matrix to find the local optimal solution, and strive to find the global optimal solution at the end of the algorithm. These algorithms require the sparsity of the known signal during the reconstruction process. However, in the actual environment, it is impossible to pre-judge the sparsity of the channel. Moreover, during the reconstruction process, the greedy algorithm does not consider the existence of noise in detail and does not have a certain anti-noise ability, resulting in poor signal reconstruction effect, insufficient channel estimation accuracy, and high bit error rate of the entire communication system. Summary of the invention

[0004] The present invention provides a denoising sparsity adaptive weak orthogonal matching pursuit method and system, which solves the technical problem of how to perform channel estimation more accurately when the channel sparsity is unclear and the received signal contains noise.

[0005] In order to solve the above technical problems, the present invention provides a denoising sparsity adaptive weak orthogonal matching pursuit method, comprising the steps of:

[0006] S1, reconstruct the received signal vector, i.e., the M×1-dimensional observation vector Y, into an M×M-dimensional Hankel matrix B;

[0007] S2, perform singular value decomposition on the Hankel matrix B, and screen out the singular values ​​representing the useful signal and the noise, then retain the singular values ​​representing the useful signal, delete the singular values ​​representing the noise, and finally reconstruct the M×M dimensional signal B' without noise;

[0008] S3, taking the signal B' as the initial residual r0 and performing inner product with the sensing matrix A, and obtaining the projection of each atom in the sensing matrix A on the residual;

[0009] S4, selecting atoms whose projections are greater than the fuzzy threshold value and storing them in the dictionary set;

[0010] S5, calculate the reconstructed signal by the least square method, and delete the atoms with low correlation in the dictionary set;

[0011] S6, updating the residual between the reconstructed signal, i.e., the estimated value, and the received signal, i.e., the true value;

[0012] S7, estimating the energy difference of the reconstructed signals in adjacent stages. If the energy difference is stable within the set range, the reconstruction is completed, the iteration is stopped, and the process goes to step S8; otherwise, the iteration is continued and the process goes to step S3;

[0013] S8. Output the optimal reconstructed signal.

[0014] Furthermore, the step S2 specifically includes the steps of:

[0015] S21. Decompose the Hankel matrix B into B = USV H , where S is an M×M dimensional diagonal matrix and can be expressed as S=diag(s 11 ,s 22 ,…s MM ), the elements s on its main diagonal 11 ,s 22 ,…s MM It is called the singular value of the matrix S and satisfies the condition s 11 ≥s 22 ≥…s MM >0, U and V are M×M dimensional unitary matrices, which can be expressed as U=(u 11 ,u 22 ,…u MM ), V=(v 11 ,v 22 ,…v MM ), respectively satisfying U H U=UU H =E and V H V=VVH =E, E is the unit matrix;

[0016] S22, calculate the sum of squares of all singular values ​​separately and the sum of the squares of the first i singular values

[0017] S23, setting a threshold value P according to the square sum P p ;

[0018] S24, sum the squares of the first i singular values ​​P i Threshold value P p For comparison, if P i More than P p , then the first i singular values ​​representing useful signals are retained, and the remaining singular values ​​representing noise are deleted;

[0019] S24, update the singular matrix S to obtain S'=diag(s 11 ,s 22 ,…,s ii ,0,…,0), update the unitary matrix U,V to get U'=(u 11 ,u 22 ,…u ii ), V'=(v 11 ,v 22 ,…v ii ),u 11 ,u 22 ,…u ii is the first i elements in the original unitary matrix U, v 11 ,v 22 ,…v ii is the first i elements in the original unitary matrix V;

[0020] S25, reconstruct the noise-free signal B'=U'S'V' H .

[0021] Further, in step S4, the fuzzy threshold value is set to:

[0022] λ=α*max(abs[A T r t-1 ])

[0023] Among them, the fuzzy threshold coefficient α∈(0,1], max() means taking the maximum value, abs() means taking the absolute value, r t-1 It represents the residual between the estimated value and the true value at the t-1th iteration.

[0024] Furthermore, in step S5, the reconstructed signal is calculated by the least square method, specifically using the following steps:

[0025] S51. Construct the estimation model of least squares method:

[0026]

[0027] in, For estimated value The sum of squared errors between the true value θ and The estimated value corresponding to the minimum This is the optimal solution;

[0028] S52. Construct a solution model for K sparse signals under the framework of the least squares estimation model:

[0029]

[0030] Among them, A t =A t-1 ∪a t , A t Represents the dictionary set at the tth iteration, A t-1 represents the dictionary set at the t-1th iteration, a t represents the atoms whose projection is greater than the blur threshold at the tth iteration and is the column vector of the perception matrix A, || ||2 represents the l2 norm, represents the reconstructed signal estimated at the tth iteration, θ t represents the real signal corresponding to the tth iteration;

[0031] S53, solving the solution model to obtain a reconstructed signal

[0032] Furthermore, in step S5, atoms with low correlation in the dictionary set are deleted according to the coefficients of the reconstructed signal, specifically:

[0033] Use L to infinitely approximate the sparsity K of the signal, and reconstruct the signal The L term with the largest absolute value is selected and recorded as And set the corresponding atoms in the dictionary set to zero and delete them, while updating the dictionary set as A tL .

[0034] Further, in step S6, the residual between the estimated value and the true value at the tth iteration is updated as

[0035] Furthermore, in step S7, the setting range of the energy difference is [0,10 -6 ).

[0036] Furthermore, in step S1, for the observation vector Y=(y1, y2, ..., y M), the Hankel matrix B is constructed as:

[0037]

[0038] Among them, y1,y2,...,y M Represents the corresponding element in the observation vector Y.

[0039] Further, in step S23, the threshold value P p Set to:

[0040] P p =0.8P.

[0041] The present invention also provides a denoising sparsity adaptive weak orthogonal matching pursuit system, comprising a module for executing steps S1 to S8 in the above method.

[0042] The present invention provides a denoising sparsity adaptive weak orthogonal matching pursuit method and system, which combines the compressed sensing theoretical framework to perform channel estimation on an OFDM communication system, specifically, performing singular value decomposition on a received signal, deleting the singular values ​​representing noise, reconstructing a noise-free signal, and then using the signal as an initial residual to perform an inner product with a sensing matrix to obtain the projection of each atom on the residual, using a weak selection method to select a corresponding atomic expansion dictionary set, and then calculating the reconstructed signal by a least squares method. When the energy difference of the reconstructed signals in adjacent stages is stable within a certain range, it indicates that the reconstructed signal energy tends to be stable, the reconstruction is completed, and the optimal reconstructed signal is output, so that the channel estimation accuracy is higher, the acquired channel state information is more accurate, the bit error rate of the entire communication system is lower, and at the same time, the pilot overhead is reduced, saving spectrum resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is an OFDM channel estimation block diagram provided by the background technology of the present invention;

[0044] Figure 2 It is a flow chart of a denoising sparsity adaptive weak orthogonal matching pursuit method provided by an embodiment of the present invention;

[0045] Figure 3 It is a schematic diagram of the mean square error between the estimated channel matrix and the actual channel matrix under different fuzzy threshold coefficients provided by an embodiment of the present invention;

[0046] Figure 4 is a schematic diagram of the mean square error between the estimated channel matrix and the actual channel matrix under different energy threshold ratios provided by an embodiment of the present invention;

[0047] Figure 5is a schematic diagram of the mean square error between the estimated channel matrix and the actual channel matrix in comparison with other signal reconstruction algorithms provided by an embodiment of the present invention;

[0048] Figure 6 It is a schematic diagram of the error performance of a communication system provided by an embodiment of the present invention in comparison with other signal reconstruction algorithms. DETAILED DESCRIPTION

[0049] The following specifically illustrates the implementation mode of the present invention in conjunction with the accompanying drawings. The embodiments are provided for illustrative purposes only and cannot be understood as limiting the present invention. The accompanying drawings are provided for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0050] In order to perform channel estimation more accurately when the channel sparsity is unclear and the received signal contains noise, an embodiment of the present invention provides a denoising sparsity adaptive weak orthogonal matching pursuit method, such as Figure 2 As shown in the flowchart, it specifically includes steps S1 to S8.

[0051] S1. Reconstruct the received signal vector, i.e., the M×1-dimensional observation vector Y, into an M×M-dimensional Hankel matrix B.

[0052] In step S1, for the observation vector Y=(y1, y2, ..., y M ), the Hankel matrix B is constructed as:

[0053]

[0054] Among them, y1,y2,…,y M Represents the corresponding element in the observation vector Y.

[0055] S2. Perform singular value decomposition on the Hankel matrix B and screen out the singular values ​​representing the useful signal and the noise. Then, retain the singular values ​​representing the useful signal and delete the singular values ​​representing the noise. Finally, reconstruct the M×M dimensional signal B' without noise.

[0056] Step S2 specifically includes the following steps:

[0057] S21. Decompose the Hankel matrix B into B = USV H , where S is an M×M dimensional diagonal matrix and can be expressed as S=diag(s 11 ,s 22 ,…s MM ), the elements s on its main diagonal 11 ,s 22 ,…s MMIt is called the singular value of the matrix S and satisfies the condition s 11 ≥s 22 ≥…s MM >0, U and V are M×M dimensional unitary matrices, which can be expressed as U=(u 11 ,u 22 ,…u MM ), V=(v 11 ,v 22 ,…v MM ), respectively satisfying U H U=UU H =E and V H V=VV H =E, E is the unit matrix;

[0058] S22, calculate the sum of squares of all singular values ​​separately and the sum of the squares of the first i singular values

[0059] S23, setting a threshold value P according to the square sum P p ;

[0060] S24, sum the squares of the first i singular values ​​P i Follow P p For comparison, if P i More than P p , then the first i singular values ​​representing useful signals are retained, and the remaining singular values ​​representing noise are deleted. If it does not exceed, a singular value is added at a time and the calculation continues until P i More than P p ;

[0061] S24, update the singular matrix S to obtain S'=diag(s 11 ,s 22 ,…,s ii ,0,…,0), update the unitary matrix U,V to get U'=(u 11 ,u 22 ,…u ii ), V'=(v 11 ,v 22 ,…v ii ),u 11 ,u 22 ,…u ii is the first i elements in the original unitary matrix U, v 11 ,v 22 ,…v ii is the first i elements in the original unitary matrix V;

[0062] S25, reconstruct the noise-free M×M-dimensional signal B'=U'S'V' H .

[0063] In step S23, Figure 3 is a schematic diagram of the mean square error (MSE) between the estimated channel matrix and the actual channel matrix under different energy threshold ratios provided by an embodiment of the present invention, Figure 3 It can be seen that the energy threshold ratio delta(P p / P) is set to 0.8 to achieve the best effect.

[0064] S3, take the signal B' as the initial residual r0 and do the inner product with the perception matrix A to obtain each atom in the perception matrix A j (A∈R M×N , the projection of each column of A, 1≤j≤N) on the residual.

[0065] S4. Select atom a whose projection is greater than the fuzzy threshold value. j Store in dictionary set A t .

[0066] In step S4, the fuzzy threshold is set to:

[0067] λ=α*max(abs[A T r t-1 ])

[0068] Among them, the fuzzy threshold coefficient α∈(0,1], max() means taking the maximum value, abs() means taking the absolute value, r t-1 It represents the residual between the estimated value and the true value at the t-1th iteration.

[0069] Figure 4 The figure is a schematic diagram of the mean square error (MSE) between the estimated channel matrix and the actual channel matrix under different fuzzy threshold coefficients. It can be concluded that as the signal-to-noise ratio (SNR) increases, the MSE gradually decreases. The fuzzy threshold coefficient α (i.e., alpha) that is too large or too small cannot interfere with the selection of atoms and thus cannot correctly estimate the channel. When the fuzzy threshold coefficient α is between 0.2 and 0.4, it has better performance. In other ranges, the channel estimation error is large. The best coefficient value is 0.3, which can make the mean square error optimal, so α is set to 0.3 in this example;

[0070] S5. Calculate the reconstructed signal by the least squares method and delete the atoms with low correlation in the dictionary set.

[0071] In step S5, the reconstructed signal is calculated by the least square method, specifically using the following steps:

[0072] S51. Construct the estimation model of least squares method:

[0073]

[0074] in, The reconstructed signal is the estimated value The sum of squared errors between the received signal, i.e., the true value θ, is The estimated value corresponding to the minimum This is the optimal solution;

[0075] S52. Construct a solution model for K sparse signals under the framework of the least squares estimation model:

[0076]

[0077] Among them, A t =A t-1 ∪a t , A t Represents the dictionary set at the tth iteration, A t-1 represents the dictionary set at the t-1th iteration, a t represents the atoms whose projection is greater than the blur threshold at the tth iteration and is the column vector of the perception matrix A, represents the reconstructed signal estimated at the tth iteration, θ t represents the real signal corresponding to the t-th iteration, || ||2 represents the l2 norm, and the l2 norm represents the square root of the sum of the squares of the modulus values ​​of all elements; here "K-sparse" means that for a vector of length J (actually refers to a J-dimensional discrete signal), only K of its J element values ​​are non-zero, where K<<J, and the vector is called K-sparse;

[0078] S53, solving the solution model to obtain a reconstructed signal

[0079] In step S5, the atoms with low correlation in the dictionary are deleted. Specifically, L is used to infinitely approximate the sparsity K of the signal. The L term with the largest absolute value is selected and recorded as And set the corresponding atoms in the dictionary set to zero and delete them, while updating the dictionary set, indicating that A tL . Ensure that the size of the dictionary set does not expand due to the use of weak selection to ensure that the size of the dictionary set remains unchanged.

[0080] S6. Update the residual between the estimated value and the true value.

[0081] The residual between the estimated value and the true value at the tth iteration is updated as:

[0082]

[0083] S7. Estimating the energy difference of the reconstructed signals in adjacent stages If the energy difference Stable in the set range ([0,10 -6 ), the reconstruction is completed, the iteration is stopped, and the process goes to step S7; otherwise, the iteration continues. L=L+1, t=t+1, and go to step S3. In step S7, if the number of iterations has reached the maximum number of iterations M, the iteration is stopped.

[0084] S8. Output the optimal reconstruction signal

[0085] An embodiment of the present invention further provides a denoising sparsity adaptive weak orthogonal matching pursuit system, comprising a module for executing the above steps S1 to S8.

[0086] Figure 5 This is a schematic diagram of the mean square error (MSE) between the estimated channel matrix and the actual channel matrix in comparison with other signal reconstruction algorithms provided by the embodiment of the present invention, where NR-SA-SWOMP represents the method provided by the present invention, and OMP, ROMP, and CoSaMP are introduced in the background technology section, representing orthogonal matching pursuit, regularized orthogonal matching pursuit, and compressed sampling matching pursuit, respectively. Figure 5 It can be clearly seen that the mean square error between the channel matrix of the present invention and the actual channel matrix is ​​greatly reduced compared with other methods.

[0087] Figure 6 FIG. 1 is a schematic diagram of the bit error rate (BER) of a communication system compared with other signal reconstruction algorithms provided by an embodiment of the present invention. Figure 6 It can be clearly seen that the bit error rate of the communication system of the method provided by the present invention is greatly reduced compared with other methods.

[0088] In summary, the embodiment of the present invention provides a denoising sparsity adaptive weak orthogonal matching pursuit method and system, which combines the compressed sensing theoretical framework to perform channel estimation on the OFDM communication system, specifically, the received signal is subjected to singular value decomposition, the singular values ​​representing the noise are deleted, and a noise-free signal is reconstructed. Then, this signal is used as the initial residual to perform an inner product with the sensing matrix to obtain the projection of each atom on the residual, and the corresponding atoms are selected by a weak selection method and stored in a dictionary set. Then, the reconstructed signal is calculated by the least squares method. When the energy difference of the reconstructed signals in adjacent stages is stable within a certain range, it indicates that the energy of the reconstructed signal tends to be stable, the reconstruction is completed, and the optimal reconstructed signal is output, so that the accuracy of the channel estimation is higher (the effect is as follows: Figure 5 As shown), the channel state information obtained is more accurate and the bit error rate of the entire communication system is lower (the effect is as shown Figure 6 As shown), it also reduces pilot overhead and saves spectrum resources.

[0089] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A denoising sparsity adaptive weak orthogonal matching pursuit method, characterized in that: Includes steps: S1, reconstruct the received signal vector, i.e., the M×1-dimensional observation vector Y, into an M×M-dimensional Hankel matrix B; S2, perform singular value decomposition on the Hankel matrix B, and screen out the singular values ​​representing the useful signal and the noise, then retain the singular values ​​representing the useful signal, delete the singular values ​​representing the noise, and finally reconstruct the M×M dimensional signal B' without noise; S3, taking the signal B' as the initial residual r0 and performing inner product with the sensing matrix A, and obtaining the projection of each atom in the sensing matrix A on the residual; S4, selecting atoms whose projections are greater than the fuzzy threshold value and storing them in the dictionary set; S5, calculating the reconstructed signal by the least square method, and deleting atoms with low correlation in the dictionary set; S6, updating the residual between the reconstructed signal, i.e., the estimated value, and the received signal, i.e., the true value; S7, estimating the energy difference of the reconstructed signals in adjacent stages. If the energy difference is stable within the set range, the reconstruction is completed, the iteration is stopped, and the process goes to step S8. Otherwise, the iteration continues, and the process goes to step S5. S8. Output the optimal reconstructed signal.

2. A denoising sparsity adaptive weak orthogonal matching pursuit method according to claim 1, characterized in that: The step S2 specifically includes the following steps: S21. Decompose the Hankel matrix B into B = USV H , where S is an M×M dimensional diagonal matrix and can be expressed as S=diag(s 11 ,s 22 ,…s MM ), the elements s on its main diagonal 11 ,s 22 ,…s MM It is called the singular value of the matrix S and satisfies the condition s 11 ≥s 22 ≥…s MM >0, U and V are M×M dimensional unitary matrices, which can be expressed as U=(u 11 ,u 22 ,…u MM ), V=(v 11 ,v 22 ,…v MM ), respectively satisfying U H U=UU H =E and V H V=VV H =E, E is the unit matrix; S22, calculate the sum of squares of all singular values ​​separately and the sum of the squares of the first i singular values S23, setting a threshold value P according to the square sum P p ; S24, sum the squares of the first i singular values ​​P i Set the threshold value P p For comparison, if P i More than P p , then the first i singular values ​​representing useful signals are retained, and the remaining singular values ​​representing noise are deleted; S24, update the singular matrix S to obtain S'=diag(s 11 ,s 22 ,…,s ii ,0,…,0), update the unitary matrix U,V to get U'=(u 11 ,u 22 ,…u ii ), V'=(v 11 ,v 22 ,…v ii ),u 11 ,u 22 ,…u ii is the first i elements in the original unitary matrix U, v 11 ,v 22 ,…v ii is the first i elements in the original unitary matrix V; S25, reconstruct the noise-free signal B'=U'S'V' H .

3. A denoising sparsity adaptive weak orthogonal matching pursuit method according to claim 2, characterized in that: In step S4, the fuzzy threshold is set to: λ=α*max(abs[A T r t-1 ]) Among them, the fuzzy threshold coefficient α∈(0,1], max() means taking the maximum value, abs() means taking the absolute value, r t-1 It represents the residual between the estimated value and the true value at the t-1th iteration.

4. A denoising sparsity adaptive weak orthogonal matching pursuit method according to claim 3, characterized in that: In step S5, the reconstructed signal is calculated by the least square method, specifically using the following steps: S51. Construct the estimation model of least squares method: in, For estimated value The sum of squared errors between the true value θ and The estimated value corresponding to the minimum This is the optimal solution; S52. Construct a solution model for K sparse signals under the framework of the least squares estimation model: Among them, A t =A t-1 ∪a t , A t Represents the dictionary set at the tth iteration, A t-1 represents the dictionary set at the t-1th iteration, a t represents the atoms whose projection is greater than the blur threshold at the tth iteration and is the column vector of the perception matrix A, || ||2 represents the l2 norm, represents the reconstructed signal estimated at the tth iteration, θ t represents the real signal corresponding to the tth iteration; S53, solving the solution model to obtain a reconstructed signal 5. A denoising sparsity adaptive weak orthogonal matching pursuit method according to claim 4, characterized in that: In step S5, atoms with low correlation in the dictionary are deleted, specifically: Use L to infinitely approximate the sparsity K of the signal, and reconstruct the signal The L term with the largest absolute value is selected and recorded as And set the corresponding atoms in the dictionary set to zero and delete them, while updating the dictionary set as A tL .

6. A denoising sparsity adaptive weak orthogonal matching pursuit method according to claim 5, characterized in that: In step S6, the residual between the estimated value and the true value at the tth iteration is updated as 7. The denoising sparsity adaptive weak orthogonal matching pursuit method according to claim 1, characterized in that: In step S7, the energy difference is set in the range of [0,10 -6 ).

8. The denoising sparsity adaptive weak orthogonal matching pursuit method according to claim 1, characterized in that: In step S1, for the observation vector Y=(y1, y2, ..., y M ), the Hankel matrix B is constructed as: Among them, y1,y2,...,y M Represents the corresponding element in the observation vector Y.

9. The denoising sparsity adaptive weak orthogonal matching pursuit method according to claim 2, characterized in that: In step S23, the threshold value P p Set to: P p =0.8P。

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