CN116527457A - Noise reduction sparsity self-adaptive weak orthogonal matching tracking method and system - Google Patents
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Abstract
The invention relates to the technical field of mobile communication, and particularly discloses a noise reduction sparsity self-adaptive weak orthogonal matching tracking method and system, which are used for carrying out channel estimation on an OFDM communication system by combining a compressed sensing theory framework, and particularly carrying out singular value decomposition on a received signal, deleting singular values representing noise, reconstructing a signal without noise, taking the signal as an initial residual error and a sensing matrix to carry out inner product, obtaining projection of each atom on the residual error, adopting a weak selection mode to select corresponding atoms to store the atoms into a dictionary set, and then calculating a reconstructed signal through a least square method, wherein when the energy difference of the reconstructed signals in adjacent stages is stable within a certain range, the reconstructed signal energy tends to be stable, 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 error rate of the whole communication system is lower, and pilot frequency expenditure is reduced, and spectrum resources are saved.
Description
Technical Field
The invention relates to the technical field of mobile communication, in particular to a noise reduction sparsity self-adaptive weak orthogonal matching tracking method and system.
Background
OFDM is a scheme for transmitting by using multiple carriers, and the basic method is to split an original high-speed data stream into a plurality of parallel low-speed data streams at a transmitting end, wherein each low-speed data stream corresponds to a corresponding subcarrier. This is equivalent to dividing the original channel into a number of parallel sub-channels such that the bandwidth of each sub-channel is less than the coherence bandwidth of the channel, thereby providing the ability to combat multipath fading. To combat multipath effects of the wireless channel, OFDM receivers require accurate 2-channel state information (Channel State Information, CSI) to more accurately demodulate the user data. Fig. 1 is a block diagram of channel estimation in an OFDM communication system, where the conventional OFDM channel estimation method does not consider sparseness of a wireless channel and needs to use a large number of pilot signals to detect time-varying characteristics of the channel, resulting in resource waste. The compressed sensing can apply the sparsity of the wireless channel to the channel estimation, so that the reconstructed channel impulse response is more advantageous, some frequency spectrum resources can be saved, and unnecessary pilot frequency overhead is avoided.
Sparse channel estimation algorithms under the framework of compressed sensing theory are 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, finding a locally optimal solution by atomic selection of a known sensing matrix in each iteration, striving to find a globally optimal solution at the end of the algorithm. The algorithm needs to know the sparsity of the signals in the reconstruction process, but in the actual environment, the sparsity of the channels cannot be judged in advance. In addition, in the reconstruction process, the greedy algorithm does not consider the problem of noise in detail, does not have certain anti-noise capability, and therefore the signal reconstruction effect is not good enough, the channel estimation accuracy is not high enough, and the error rate of the whole communication system is high.
Disclosure of Invention
The invention provides a noise reduction sparsity self-adaptive weak orthogonal matching tracking method and a system, which solve the technical problems that: how channel estimation can be performed more accurately in the case where channel sparsity is unclear and the received signal contains noise.
In order to solve the technical problems, the invention provides a noise reduction sparsity self-adaptive weak orthogonal matching tracking method, which comprises the following steps:
s1, reconstructing a received signal vector, namely an observation vector Y in M multiplied by 1, into a Hankel matrix B in M multiplied by M;
s2, carrying out singular value decomposition on the Hankel matrix B, screening out singular values representing useful signals and noise, reserving the singular values representing the useful signals, deleting the singular values representing the noise, and reconstructing an M multiplied by M dimensional signal B' without noise;
s3, taking the signal B' as an initial residual error r 0 Performing inner product with the sensing matrix A to obtain projection of each atom in the sensing matrix A on the residual error;
s4, selecting atoms with projection larger than a fuzzy threshold value and storing the atoms into a dictionary set;
s5, calculating a reconstruction signal through a least square method, and deleting atoms with low correlation in the dictionary set;
s6, updating residual errors between the estimated value of the reconstruction signal and the true value of the received signal;
s7, estimating energy difference of reconstruction signals in adjacent stages, if the energy difference is stable in a set range, completing reconstruction, stopping iteration, turning to a step S8, otherwise, continuing iteration, and turning to a step S3;
s8, outputting an optimal reconstruction signal.
Further, the step S2 specifically includes the steps of:
s21, singular value decomposition is carried out on the Hankel matrix B to obtain B=USV H A diagonal matrix in which S is an M x M dimension can be expressed as s=diag (S 11 ,s 22 ,…s MM ) The element s on the main diagonal 11 ,s 22 ,…s MM Singular values of the called matrix S and satisfying the condition S 11 ≥s 22 ≥…s MM Each of > 0,U and V is a unitary matrix of dimension m×m, and can be expressed as u= (U) 11 ,u 22 ,…u MM )，V＝(v 11 ,v 22 ,…v MM ) Respectively satisfy U H U＝UU H =e and V H V＝VV H =e, E is the identity matrix;
s22, respectively calculating the square sum of all singular valuesSum of squares of the first i singular values
S23, setting a threshold value P according to the sum of squares P p ；
S24, summing the squares of the first i singular values, P i Heel threshold value P p By comparison, if P i Exceeding P p The singular values of the first i representing useful signals are reserved, and the singular values of the rest representing noise are deleted;
s24, updating the singular matrix S to obtain S' =diag (S) 11 ,s 22 ,…,s ii 0, …, 0), updating the unitary matrix U, V resulting in U' = (U) 11 ,u 22 ,…u ii )，V'＝(v 11 ,v 22 ,…v ii )，u 11 ,u 22 ,…u ii For the first i elements, v, in the original unitary matrix U 11 ,v 22 ,…v ii For the first i elements in the original unitary matrix V;
s25, reconstructing a noise-free signal B '=U' S 'V' H 。
Further, in the step S4, the fuzzy threshold value is set as:
λ＝α*max(abs[A T r t-1 ])
wherein, the fuzzy threshold coefficient alpha epsilon (0, 1)]Max () represents maximum value, abs () represents absolute value, r t-1 Representing the residual between the estimated value and the true value at the t-1 th iteration.
Further, in the step S5, the reconstructed signal is calculated by the least square method, specifically adopting the steps of:
s51, constructing an estimation model of a least square method:
wherein,,for the estimated value +.>Sum of squares of error with the true value θ, when +.>Estimated value corresponding to the smallest time +.>The optimal solution is obtained;
s52, constructing a solving model of K sparse signals under the framework of an estimation model of a least square method:
wherein A is t ＝A t-1 ∪a t ，A t Representing the dictionary set at the t-th iteration, A t-1 Representing the dictionary set at the t-1 th iteration, a t Representing the atoms whose projections are above the blur threshold at the t-th iteration and being the column vectors of the perceptual matrix a, I 2 Representative l 2 The norm of the sample is calculated,representing the reconstructed signal estimated at the t-th iteration, θ t Representing a corresponding real signal at the t-th iteration;
s53, solving the solving model to obtain a reconstruction signal
Further, in the step S5, atoms with low relevance in the dictionary set are deleted according to the coefficient of the reconstructed signal, specifically:
using L infinite approximation signal sparsity K to reconstruct signalThe L term with the largest absolute value is selected as +.>And the corresponding atoms in the dictionary set are zeroed and deleted, and the dictionary set is updated at the same time to be expressed as A tL 。
Further, in the step S6, the residual between the estimated value and the true value at the t-th iteration is updated to be
Further, in the step S7, the energy difference is set to be in the range of [0,10 ] -6 )。
Further, in step S1, for the observation vector y= (Y) 1 ,y 2 ,...,y M ) The Hankel matrix B is constructed as:
wherein y is 1 ,y 2 ,...,y M Representing the corresponding element in the observation vector Y.
Further, in step S23, the threshold value P p The method comprises the following steps:
P p ＝0.8P。
the invention also provides a noise reduction sparsity self-adaptive weak orthogonal matching tracking system, which comprises a module for executing the steps S1 to S8 in the method.
The invention provides a noise reduction sparsity self-adaptive weak orthogonal matching tracking method and a system, which are used for carrying out channel estimation on an OFDM communication system by combining a compressed sensing theory framework, and concretely comprises the steps of carrying out singular value decomposition on a received signal, deleting singular values representing noise, reconstructing a signal without noise, taking the signal as an initial residual and a sensing matrix to carry out inner product to obtain projections of all atoms on the residual, adopting a weak selection mode to select a corresponding atom expansion dictionary set, and then adopting a least square method to calculate a reconstructed signal, wherein when the energy difference of the reconstructed signal in an adjacent stage is stable within a certain range, the reconstructed signal energy tends to be stable, reconstruction is completed, the optimal reconstructed signal is output, so that the channel estimation precision is higher, the acquired channel state information is more accurate, the error rate of the whole communication system is lower, and simultaneously, the pilot frequency expenditure is reduced, and the frequency spectrum resource is saved.
Drawings
Fig. 1 is a block diagram of OFDM channel estimation provided in the background of the invention;
fig. 2 is a flowchart of a noise reduction sparsity adaptive weak orthogonal matching pursuit method provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of a mean square error between an estimated channel matrix and an actual channel matrix under different fuzzy threshold coefficients provided by an embodiment of the present invention;
FIG. 4 is a schematic diagram of a mean square error between an estimated channel matrix and an actual channel matrix at different energy threshold ratios provided by an embodiment of the present invention;
FIG. 5 is a schematic diagram of a mean square error between an estimated channel matrix and an actual channel matrix in comparison to other signal reconstruction algorithms provided by an embodiment of the present invention;
fig. 6 is a schematic diagram of error performance of the communication system compared with other signal reconstruction algorithms according to an embodiment of the present invention.
Detailed Description
The following examples are given for the purpose of illustration only and are not to be construed as limiting the invention, including the drawings for reference and description only, and are not to be construed as limiting the scope of the invention as many variations thereof are possible without departing from the spirit and scope of the invention.
In order to perform channel estimation more accurately under the conditions that the channel sparsity is unclear and the received signal contains noise, the embodiment of the invention provides a noise reduction sparsity self-adaptive weak orthogonal matching tracking method, which specifically comprises steps S1 to S8 as shown in the flowchart of fig. 2.
S1, reconstructing a received signal vector, namely an M multiplied by 1 dimension observation vector Y, into an M multiplied by M dimension Hankel matrix B.
In step S1, for the observation vector y= (Y) 1 ,y 2 ,...,y M ) The Hankel matrix B is constructed as:
wherein y is 1 ,y 2 ,…,y M Representing the corresponding element in the observation vector Y.
S2, carrying out singular value decomposition on the Hankel matrix B, screening out singular values representing useful signals and noise, reserving the singular values representing the useful signals, deleting the singular values representing the noise, and finally reconstructing an M multiplied by M dimensional signal B' without noise.
The step S2 specifically comprises the steps of:
s21, singular value decomposition is carried out on the Hankel matrix B to obtain B=USV H A diagonal matrix in which S is an M x M dimension can be expressed as s=diag (S 11 ,s 22 ,…s MM ) The element s on the main diagonal 11 ,s 22 ,…s MM Singular values of the called matrix S and satisfying the condition S 11 ≥s 22 ≥…s MM Each of > 0,U and V is a unitary matrix of dimension m×m, and can be expressed as u= (U) 11 ,u 22 ,…u MM )，V＝(v 11 ,v 22 ,…v MM ) Respectively satisfy U H U＝UU H =e and V H V＝VV H =e, E is the identity matrix;
s22, respectively calculating the square sum of all singular valuesSum of squares of the first i singular values
S23, setting a threshold value P according to the sum of squares P p ；
S24, summing the squares of the first i singular values, P i Heel P p By comparison, if P i Exceeding P p The singular values representing the useful signals are reserved, the singular values representing the noise are deleted, if the singular values are not exceeded, one singular value is added once, and the calculation is continued until P i Exceeding P p ；
S24, updating the singular matrix S to obtain S' =diag (S) 11 ,s 22 ,…,s ii 0, …, 0), updating the unitary matrix U, V resulting in U' = (U) 11 ,u 22 ,…u ii )，V'＝(v 11 ,v 22 ,…v ii )，u 11 ,u 22 ,…u ii For the first i elements, v, in the original unitary matrix U 11 ,v 22 ,…v ii For the first i elements in the original unitary matrix V;
s25, reconstructing a noise-free M x M-dimensional signal B '=U' S 'V' H 。
In step S23, fig. 3 is a schematic diagram showing a Mean Square Error (MSE) between the estimated channel matrix and the actual channel matrix at different energy threshold ratios according to the embodiment of the present invention, as can be seen from fig. 3, the energy threshold ratio delta (P p Setting 0.8 for P) can achieve the optimal effect.
S3, taking the signal B' as an initial residual error r 0 Inner product is formed with the sensing matrix A to obtain each atom a in the sensing matrix A j (A∈R M×N Each column of A, 1.ltoreq.j.ltoreq.N) projection on the residual.
S4, selecting an atom a with projection larger than a fuzzy threshold value j Store in dictionary set A t 。
In this step S4, the blur threshold value is set as:
λ＝α*max(abs[A T r t-1 ])
wherein, the fuzzy threshold coefficient alpha epsilon (0, 1)]Max () represents maximum value, abs () represents absolute value, r t-1 Representing the residual between the estimated value and the true value at the t-1 th iterationAnd (3) difference.
FIG. 4 is a schematic diagram of a Mean Square Error (MSE) between an estimated channel matrix and an actual channel matrix under different fuzzy threshold coefficients, and it can be obtained that as a signal-to-noise ratio (SNR) increases, the MSE gradually decreases, and the fuzzy threshold coefficient alpha (i.e. alpha) is too large or too small to interfere with the selection of atoms, so that the channel cannot be estimated correctly, when the fuzzy threshold coefficient alpha is between 0.2 and 0.4, the channel estimation error is relatively large in other ranges, wherein the optimal coefficient value is 0.3, and the mean square error can be optimized, so that the example alpha is set to 0.3;
s5, calculating a reconstruction signal through a least square method, and deleting atoms with low dictionary set correlation.
In step S5, a reconstructed signal is calculated by a least square method, specifically comprising the steps of:
s51, constructing an estimation model of a least square method:
wherein,,reconstruction signal, i.e. estimate +.>Sum of squares of error with the received signal, i.e. the true value θ, when +.>Estimated value corresponding to the smallest time +.>The optimal solution is obtained;
s52, constructing a solving model of K sparse signals under the framework of an estimation model of a least square method:
wherein A is t ＝A t-1 ∪a t ，A t Representing the dictionary set at the t-th iteration, A t-1 Representing the dictionary set at the t-1 th iteration, a t Representing the atoms whose projections are above the blur threshold at the t-th iteration and being the column vectors of the perceptual matrix a,representing the reconstructed signal estimated at the t-th iteration, θ t Representing the corresponding real signal at the t-th iteration, I 2 Representative l 2 Norms, l 2 The norm represents the sum of squares of all element modulus values; "K sparse" here means that for a vector of length J (actually referred to as a J-dimensional discrete signal), only K of its J element values are non-zero, where K < J, this vector is said to be K sparse;
s53, solving the solving model to obtain a reconstruction signal
In step S5, atoms with low relevance in the dictionary set are deleted, specifically: using L infinite approximation signal sparsity K to reconstruct signalThe L term with the largest absolute value is selected as +.>And the corresponding atoms in the dictionary set are zeroed and deleted, and the dictionary set is updated at the same time to represent A tL . Ensuring that the size of the dictionary set does not expand by employing a weak selection ensures that the size of the dictionary set remains unchanged.
And S6, updating residual errors between the estimated value and the true value.
The residual error between the estimated value and the true value at the t-th iteration is updated as follows:
s7, estimating the energy difference of the reconstructed signals of the adjacent stagesIf the energy difference is +>Stabilize within a set range ([ 0, 10) -6 ) If yes, stopping iteration, turning to step S7, otherwise, continuing iteration, and enabling +.>L=l+1, t=t+1, and go to step S3. In this step S7, if the number of iterations has reached the maximum number of iterations M, the iteration is stopped.
S8, outputting an optimal reconstruction signal
The embodiment of the invention also provides a noise reduction sparsity self-adaptive weak orthogonal matching tracking system, which comprises a module for executing the steps S1 to S8.
Fig. 5 is a schematic diagram of a Mean Square Error (MSE) between an estimated channel matrix and an actual channel matrix in comparison with other signal reconstruction algorithms provided by an embodiment of the present invention, where NR-SA-SWOMP represents the method provided by the present invention, and OMP, ROMP, coSaMP is described in the background section, and represents orthogonal matching pursuit, regularized orthogonal matching pursuit, and compressed sample matching pursuit, respectively. As is evident from fig. 5, the mean square error between the channel matrix of the present invention and the actual channel matrix is greatly reduced in other methods.
Fig. 6 is a schematic diagram of Bit Error Rate (BER) of a communication system compared with other signal reconstruction algorithms according to an embodiment of the present invention. As is apparent from fig. 6, the error rate of the communication system of the method provided by the present invention is greatly reduced compared with other methods.
In summary, the method and system for adaptive weak orthogonal matching pursuit of noise reduction sparsity provided by the embodiments of the present invention combine with a compressed sensing theory framework to perform channel estimation on an OFDM communication system, specifically, perform singular value decomposition on a received signal, delete singular values representing noise, reconstruct a signal without noise, then use the signal as an initial residual error and an inner product of a sensing matrix to obtain projections of each atom on the residual error, select a corresponding atom in a weak selection manner and store the selected atom in a dictionary set, then calculate a reconstructed signal by a least square method, and when an energy difference of the reconstructed signal in an adjacent stage is stable within a certain range, it is explained that the energy of the reconstructed signal is stable, the reconstruction is completed, and an optimal reconstructed signal is output, so that the accuracy of channel estimation is higher (the effect is shown in fig. 5), the obtained channel state information is more accurate, the error rate of the whole communication system is lower (the effect is shown in fig. 6), and pilot frequency overhead is reduced, and spectrum resources are saved.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (10)
1. A noise reduction sparsity self-adaptive weak orthogonal matching tracking method is characterized by comprising the following steps:
s1, reconstructing a received signal vector, namely an observation vector Y in M multiplied by 1, into a Hankel matrix B in M multiplied by M;
s2, carrying out singular value decomposition on the Hankel matrix B, screening out singular values representing useful signals and noise, reserving the singular values representing the useful signals, deleting the singular values representing the noise, and reconstructing an M multiplied by M dimensional signal B' without noise;
s3, taking the signal B' as an initial residual error r 0 Performing inner product with the sensing matrix A to obtain projection of each atom in the sensing matrix A on the residual error;
s4, selecting atoms with projection larger than a fuzzy threshold value and storing the atoms into a dictionary set;
s5, calculating a reconstruction signal through a least square method, and deleting atoms with low correlation in the dictionary set;
s6, updating residual errors between the estimated value of the reconstruction signal and the true value of the received signal;
s7, estimating energy difference of reconstruction signals in adjacent stages, if the energy difference is stable in a set range, completing reconstruction, stopping iteration, turning to a step S8, otherwise, continuing iteration, and turning to a step S3;
s8, outputting an optimal reconstruction signal.
2. The noise reduction sparsity adaptive weak orthogonal matching pursuit method according to claim 1, wherein the step S2 specifically includes the steps of:
s21, singular value decomposition is carried out on the Hankel matrix B to obtain B=USV H A diagonal matrix in which S is an M x M dimension can be expressed as s=diag (S 11 ,s 22 ,…s MM ) The element s on the main diagonal 11 ,s 22 ,…s MM Singular values of the called matrix S and satisfying the condition S 11 ≥s 22 ≥…s MM Each of > 0,U and V is a unitary matrix of dimension m×m, and can be expressed as u= (U) 11 ,u 22 ,…u MM )，V＝(v 11 ,v 22 ,…v MM ) Respectively satisfy U H U＝UU H =e and V H V＝VV H =e, E is the identity matrix;
s22, respectively calculating the square sum of all singular valuesSum of squares of the first i singular values
S23, setting a threshold value P according to the sum of squares P p ；
S24, the first i singular valuesSum of squares P of values i Setting threshold value P p By comparison, if P i Exceeding P p The singular values of the first i representing useful signals are reserved, and the singular values of the rest representing noise are deleted;
s24, updating the singular matrix S to obtain S' =diag (S) 11 ,s 22 ,…,s ii 0, 0), update the unitary matrix U, V to U' = (U) 11 ,u 22 ,…u ii )，V'＝(v 11 ,v 22 ,…v ii )，u 11 ,u 22 ,…u ii For the first i elements, v, in the original unitary matrix U 11 ,v 22 ,…v ii For the first i elements in the original unitary matrix V;
s25, reconstructing a noise-free signal B '=U' S 'V' H 。
3. The noise reduction sparsity adaptive weak orthogonal matching pursuit method of claim 2, wherein in the step S4, the ambiguity threshold value is set to:
λ＝α*max(abs[A T r t-1 ])
wherein, the fuzzy threshold coefficient alpha epsilon (0, 1)]Max () represents maximum value, abs () represents absolute value, r t-1 Representing the residual between the estimated value and the true value at the t-1 th iteration.
4. The adaptive weak orthogonal matching pursuit method of noise reduction sparsity according to claim 3, wherein in the step S5, a reconstructed signal is calculated by a least square method, specifically comprising the steps of:
s51, constructing an estimation model of a least square method:
wherein,,for the estimated value +.>Sum of squares of error with the true value θ, when +.>Estimated value corresponding to the smallest time +.>The optimal solution is obtained;
s52, constructing a solving model of K sparse signals under the framework of an estimation model of a least square method:
wherein A is t ＝A t-1 ∪a t ，A t Representing the dictionary set at the t-th iteration, A t-1 Representing the dictionary set at the t-1 th iteration, a t Representing the atoms whose projections are above the blur threshold at the t-th iteration and being the column vectors of the perceptual matrix a, I 2 Representative l 2 The norm of the sample is calculated,representing the reconstructed signal estimated at the t-th iteration, θ t Representing a corresponding real signal at the t-th iteration;
s53, solving the solving model to obtain a reconstruction signal
5. The adaptive weak orthogonal matching pursuit method of claim 4, wherein in the step S5, atoms with low dictionary set correlation are deleted, specifically:
sparseness of signal by L infinite approximationDegree K, at reconstruction signalThe L term with the largest absolute value is selected as +.>And the corresponding atoms in the dictionary set are zeroed and deleted, and the dictionary set is updated at the same time to be expressed as A tL 。
6. The method according to claim 5, wherein in the step S6, the residual between the estimated value and the true value at the time of updating the t-th iteration is
7. The method of claim 1, wherein in the step S7, the energy difference is set to be in a range of 0,10 -6 )。
8. The noise reduction sparsity adaptive weak orthogonal matching pursuit method of claim 1, wherein in step S1, for an observation vector y= (Y 1 ,y 2 ,...,y M ) The Hankel matrix B is constructed as:
wherein y is 1 ,y 2 ,…,y M Representing the corresponding element in the observation vector Y.
9. The method for adaptive weak orthogonal matching pursuit of noise reduction sparsity according to claim 2, wherein in step S23, the threshold value P is p The method comprises the following steps:
P p ＝0.8P。
10. a noise reduction sparsity self-adaptive weak orthogonal matching tracking system is characterized in that: comprising means for performing the steps S1 to S8 of any of claims 1 to 9.
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