US20210377079A1 - Time-frequency block-sparse channel estimation method based on compressed sensing - Google Patents
Time-frequency block-sparse channel estimation method based on compressed sensing Download PDFInfo
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- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
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- H04L25/024—Channel estimation channel estimation algorithms
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/0204—Channel estimation of multiple channels
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/0224—Channel estimation using sounding signals
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- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
- H04L25/025—Channel estimation channel estimation algorithms using least-mean-square [LMS] method
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- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2647—Arrangements specific to the receiver only
- H04L27/2655—Synchronisation arrangements
- H04L27/2689—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
- H04L27/2695—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation with channel estimation, e.g. determination of delay spread, derivative or peak tracking
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- H04L5/00—Arrangements affording multiple use of the transmission path
- H04L5/0001—Arrangements for dividing the transmission path
- H04L5/0003—Two-dimensional division
- H04L5/0005—Time-frequency
- H04L5/0007—Time-frequency the frequencies being orthogonal, e.g. OFDM(A), DMT
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- H04B7/00—Radio transmission systems, i.e. using radiation field
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- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
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- H04L5/00—Arrangements affording multiple use of the transmission path
- H04L5/003—Arrangements for allocating sub-channels of the transmission path
- H04L5/0048—Allocation of pilot signals, i.e. of signals known to the receiver
Definitions
- the disclosure relates to the field of pilot-assisted channel estimation in a wireless communication system, and in particular, to a time-frequency block-sparse channel estimation method based on compressed sensing.
- Massive multiple-input and multiple-output is a key technology in next-generation 5G mobile cellular network communications and can improve the system capacity and spectrum utilization.
- MIMO massive multiple-input and multiple-output
- the acquisition and accuracy of channel state information become key issues.
- the frequency-division duplexing (FDD) system can provide more efficient communication with low delay and dominates the current wireless communication. Therefore, it is necessary to study more effective channel estimation of the FDD system.
- a channel In a massive MIMO system, a channel has block sparsity of its time domain, frequency domain, and spatial domain. With respect to this sparsity structure, in recent years, many authors have applied the compressed sensing theory to pilot-assisted channel estimation to achieve better performance. However, these algorithms all require a specified threshold condition to ensure the algorithm reconstruction precision, and for different occasions, the threshold is different. Therefore, how to determine the size of the threshold becomes a difficult issue.
- the disclosure addresses the issue of channel estimation of an FDD downlink massive MIMO system which remains unsolved in the related art, and provides a time-frequency block-sparse channel estimation method based on compressed sensing which can quickly and accurately recover massive MIMO channel information of which the sparsity degree is unknown.
- the disclosure provides a time-frequency block-sparse channel estimation method based on compressed sensing, where an orthogonal frequency-division multiplexing (OFDM) system of a downlink frequency-division duplexing (FDD) massive MIMO channel model is initialized, supposing M antennas are disposed at a base station end and U single-antenna users are simultaneously served, and let there be N subcarriers in the OFDM system, where N P subcarriers are used to transmit pilot signals, and L is a maximum path delay, considering observing in R adjacent OFDM symbols.
- OFDM orthogonal frequency-division multiplexing
- FDD downlink frequency-division duplexing
- the method Based on a time-frequency block sparsity and a compressed sensing framework of a massive MIMO channel, the method includes the following steps.
- Y ⁇ N P ⁇ R is a reception signal matrix
- H ⁇ N P ⁇ R is a channel matrix
- V ⁇ N P ⁇ R is a noise matrix
- Step 2 A sparse signal estimation value ⁇ tilde over (H) ⁇ is solved by a compressed sensing method according to the channel model obtained in Step 1 to further calculate an index set ⁇ tilde over ( ⁇ ) ⁇ k .
- Step 1 of the disclosure further includes the following.
- the channel model is established, since N P ⁇ LM, it is determined that the channel model is an underdetermined equation, and since a joint sparsity structure is present in the massive MIMO channel, it is determined to reconstruct a high-dimensional channel H from a low-dimensional vector Y by a channel estimation method based on compressed sensing.
- the compressed sensing method in Step 2 specifically includes the following.
- the method includes the following steps.
- the iteration stop condition is adaptively determined based on the residual by using channel time-frequency block sparsity while there is no threshold parameter and the sparsity degree is unknown, which achieves more accurate channel estimation performance than conventional matching pursuit algorithms. Simulation shows that the algorithm can quickly and accurately recover massive MIMO channel information of which the sparsity degree is unknown.
- FIG. 1 is a diagram showing normalized mean square errors (NMSE) at different signal-to-noise ratios (SNR) of an embodiment of the disclosure and comparative embodiments.
- NMSE normalized mean square errors
- SNR signal-to-noise ratios
- FIG. 2 is a diagram showing normalized mean square errors at different transmitting antenna quantities of the embodiment of the disclosure and the comparative embodiments.
- the channel estimation method includes the following steps.
- Y ⁇ N P ⁇ R is a reception signal matrix
- H ⁇ LM ⁇ R is a channel matrix
- V ⁇ N P ⁇ R is a noise matrix
- N P ⁇ LM the channel model is an underdetermined equation, but a joint sparsity structure is present in the massive MIMO channel, and a high-dimensional channel H may be reconstructed from a low-dimensional vector Y by a channel estimation method based on compressed sensing.
- Step 2 A sparse signal estimation value ⁇ tilde over (H) ⁇ is solved by a compressed sensing method according to the channel model obtained in Step 1 to further calculate an index set ⁇ tilde over ( ⁇ ) ⁇ k .
- the compressed sensing method in Step 2 specifically includes the following.
- the step size s is 2
- a threshold parameter ⁇ of the algorithm reconstruction precision is all 0.001
- normalized least mean square errors of channel estimation algorithms at different signal-to-noise ratios are calculated, and the result is shown in FIG. 1 .
- the step size s is 2
- the threshold parameter ⁇ of the algorithm reconstruction precision is all 0.001
- normalized least mean square errors of channel estimation algorithms at different transmitting antennas of the base station are calculated, and the result is shown in FIG. 2 .
- the normalized least mean square error is defined as follows:
- N e represents an operation count of the algorithm at each signal-to-noise ratio, and herein, N e is 20.
- the proposed gBAMP algorithm can detect the minimum precision achieved by the reconstruction and automatically end the reconstruction process without the constraint of the threshold parameter ⁇ .
- the experimental result shows that the algorithm achieves good performance close to that of the exact-LS algorithm and is superior to other algorithms.
- the precision of channel reconstruction is affected, and the reason lies in that the increase in the antenna quantity leads to pilot insufficiency.
- the reconstruction by the SAMP-Block algorithm fails at the threshold parameter.
- the proposed gBAMP algorithm exhibits better performance, and exhibits optimal performance in both precision and stability that are even better than those of the exact-LS algorithm.
- the time-frequency block-sparse channel estimation method based on compressed sensing in the embodiment of the disclosure i.e., a generalized block adaptive gBAMP algorithm, has good reconstruction performance and is applicable to occasions requiring pilot-assisted channel estimation of a wireless communication system.
- Simulation shows that the method of the disclosure can quickly and accurately recover massive MIMO channel information of which a sparsity degree is unknown.
Abstract
A time-frequency block-sparse channel estimation method based on compressed sensing includes the following steps. Step 1: A channel model is established. Step 2: According to the channel model obtained in Step 1, a sparse signal estimation value is solved by a compressed sensing method to further calculate an index set. Step 3: According to the index set obtained in Step 2, a channel matrix estimation value is solved. The method provides a generalized block adaptive gBAMP algorithm, which uses time-frequency joint block sparsity of a massive MIMO system to further optimize selection of an index set in an algorithm iteration process to improve stability of the algorithm. Then, without a specified threshold parameter, based on an F norm, an adaptive iteration stop condition is determined based on a residual, and the validity of the method is proved.
Description
- This application claims the priority benefit of China application serial no. 202010454893.2, filed on May 26, 2020. The entirety of the above-mentioned patent application is hereby incorporated by reference herein and made a part of this specification.
- The disclosure relates to the field of pilot-assisted channel estimation in a wireless communication system, and in particular, to a time-frequency block-sparse channel estimation method based on compressed sensing.
- Massive multiple-input and multiple-output (MIMO) is a key technology in next-generation 5G mobile cellular network communications and can improve the system capacity and spectrum utilization. However, in a massive MIMO system, as the antenna quantity at the base station end and the number of users in a cell increase, the acquisition and accuracy of channel state information become key issues. Compared with the time-division duplexing (TDD) system, the frequency-division duplexing (FDD) system can provide more efficient communication with low delay and dominates the current wireless communication. Therefore, it is necessary to study more effective channel estimation of the FDD system.
- In a massive MIMO system, a channel has block sparsity of its time domain, frequency domain, and spatial domain. With respect to this sparsity structure, in recent years, many scholars have applied the compressed sensing theory to pilot-assisted channel estimation to achieve better performance. However, these algorithms all require a specified threshold condition to ensure the algorithm reconstruction precision, and for different occasions, the threshold is different. Therefore, how to determine the size of the threshold becomes a difficult issue.
- The disclosure addresses the issue of channel estimation of an FDD downlink massive MIMO system which remains unsolved in the related art, and provides a time-frequency block-sparse channel estimation method based on compressed sensing which can quickly and accurately recover massive MIMO channel information of which the sparsity degree is unknown.
- The technical solutions adopted to solve the technical problems herein are as follows.
- The disclosure provides a time-frequency block-sparse channel estimation method based on compressed sensing, where an orthogonal frequency-division multiplexing (OFDM) system of a downlink frequency-division duplexing (FDD) massive MIMO channel model is initialized, supposing M antennas are disposed at a base station end and U single-antenna users are simultaneously served, and let there be N subcarriers in the OFDM system, where NP subcarriers are used to transmit pilot signals, and L is a maximum path delay, considering observing in R adjacent OFDM symbols.
- Based on a time-frequency block sparsity and a compressed sensing framework of a massive MIMO channel, the method includes the following steps.
- Step 1: A pilot signal and a reception signal of a transmitting end are inputted, and a channel model is established as Y=ΨH+V according to the signal,
-
- Step 2: A sparse signal estimation value {tilde over (H)} is solved by a compressed sensing method according to the channel model obtained in
Step 1 to further calculate an index set {tilde over (Γ)}k. - Step 3: A channel matrix estimation value {tilde over (H)}{tilde over (Γ)}
k is solved according to the index set {tilde over (Γ)}k obtained inStep 2, i.e., {tilde over (H)}{tilde over (Γ)}k =Ψ{tilde over (Γ)}k †Y, where a superscript “†” represents a pseudoinverse, i.e., Ψ{tilde over (Γ)}k † represents a pseudoinverse with respect to Ψ{tilde over (Γ)}k , and after a baseband signal is demodulated, data information of the transmitting end is outputted according to the obtained channel matrix estimation value {tilde over (H)}{tilde over (Γ)}k . - Further,
Step 1 of the disclosure further includes the following. - After the channel model is established, since NP<<LM, it is determined that the channel model is an underdetermined equation, and since a joint sparsity structure is present in the massive MIMO channel, it is determined to reconstruct a high-dimensional channel H from a low-dimensional vector Y by a channel estimation method based on compressed sensing.
- Further, the compressed sensing method in
Step 2 specifically includes the following. - Parameters are inputted as a measurement value Y, a sensing matrix Ψ, a step size S, and a maximum path delay L; a residual vector ν0=Y is initialized, a signal estimation value H=Ø∈ LM×T is reconstructed, an index set Γ=Ø, let an initial iteration count k=1, and a step size count I=1 is updated. The method includes the following steps.
- Step 201: A projection coefficient of each column of the sensing matrix on the residual vector is calculated, i.e., Z=ΨHνk−1.
-
- Step 203: The index set updated: Γk L=Γk−1 L∪{arg max ({tilde over (Z)},S)}.
- Step 204: The index set Γk L is extended to Γk Li=Γk L+iL, 1≤i≤M, and the index sets are merged, Γk=Γk L∪Γk L2 . . . ∪Γk LM.
- Step 205: The estimation value of the channel H is solved by a least squares method: ĤΓ
k k=ΨΓk †Y. -
- Step 207: An index set is obtained: Γk L=arg max (
H Γk k,S). - Step 208: The index set
Γ k L is extended toΓ k Li=Γ k L+iL, 1≤i≤M, and the index sets are merged,Γ k=Γ k L ∪Γ k L2 . . . ∪Γ k LM. - Step 209: The estimation value of the channel H is solved by a least squares method: {tilde over (H)}
Γ k k=ΨΓ k †Y. - Step 210: The residual is updated: ν′k=Y−Ψ{tilde over (H)}
Γ k k. - Step 211: If ∥ν′k∥F>∥νk−1∥F, then {tilde over (Γ)}k={circumflex over (Γ)}k and operation is stopped.
- Step 212: If ∥ν′k∥F=∥νk−1∥F, then I=I+1, S=S×I, {circumflex over (Γ)}k=
Γ k. - Step 213: If ∥ν′k∥F<∥νk−1∥F, then νk=ν′k, Γk L=
Γ k L. - Step 214: k=k+1, Step 201 to Step 214 are repeated until the stop condition is satisfied.
- In the time-frequency block-sparse channel estimation method based on compressed sensing of the disclosure, with respect to an FDD downlink massive MIMO system, the iteration stop condition is adaptively determined based on the residual by using channel time-frequency block sparsity while there is no threshold parameter and the sparsity degree is unknown, which achieves more accurate channel estimation performance than conventional matching pursuit algorithms. Simulation shows that the algorithm can quickly and accurately recover massive MIMO channel information of which the sparsity degree is unknown.
- The disclosure will be further described below with reference to the accompanying drawings and embodiments.
-
FIG. 1 is a diagram showing normalized mean square errors (NMSE) at different signal-to-noise ratios (SNR) of an embodiment of the disclosure and comparative embodiments. -
FIG. 2 is a diagram showing normalized mean square errors at different transmitting antenna quantities of the embodiment of the disclosure and the comparative embodiments. - To make the objectives, technical solutions, and advantages of the disclosure more apparent, the disclosure will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the disclosure and are not intended to limit the disclosure.
- In an embodiment of the disclosure, an FDD downlink massive MIMO system is considered, in which an antenna quantity of a base station is M=20, and U=6 single-antenna users are simultaneously served. A total number of subcarriers of OFDM symbols is N=4096, where NP=100 subcarriers are used to transmit pilot signals. Pilots are placed all in the same manner; namely, they are distributed randomly and the pilots among different antennas are orthogonal to each other. A channel length L is 160, and a TU-6 channel model is adopted, where a number of paths S=6, path delays are respectively 0.0, 0.2, 0.5, 1.6, 2.3, 5, and path gains are respectively −3, 0, −2, −6, −8, −10. Let a coherence time T of the channel be T=4 OFDM symbols. Based on a time-frequency block sparsity and a compressed sensing framework of a massive MIMO channel, the channel estimation method includes the following steps.
- Step 1: A pilot signal and a reception signal of a transmitting end are inputted, and a channel model is established as Y=ΨH+V according to the signal.
- where Y∈ N
P ×R is a reception signal matrix, H∈ LM×R is a channel matrix, Ψ=∈ NP ×LM is a pilot matrix, V∈ NP ×R is a noise matrix; since NP<<LM, the channel model is an underdetermined equation, but a joint sparsity structure is present in the massive MIMO channel, and a high-dimensional channel H may be reconstructed from a low-dimensional vector Y by a channel estimation method based on compressed sensing. - Step 2: A sparse signal estimation value {tilde over (H)} is solved by a compressed sensing method according to the channel model obtained in
Step 1 to further calculate an index set {tilde over (Γ)}k. - The compressed sensing method in
Step 2 specifically includes the following. - Parameters are inputted as a measurement value Y, a sensing matrix Ψ, a step size S, and a maximum path delay L; a residual vector ν0=Y is initialized, a signal estimation value H=Ø∈ LM×T is reconstructed, an index set Γ=Ø, letting an initial iteration count k=1, and a step size count I=1 is updated; the method includes the following steps.
- Step 201: A projection coefficient of each column of the sensing matrix on the residual vector is calculated, i.e., Z=ΨHνk−1.
-
- Step 203: The index set is updated: Γk L=Γk−1 L∪{arg max ({tilde over (Z)}, S)}.
- Step 204: The index set Γk L is extended to Γk Li=Γk L+iL, 1≤i≤M, and the index sets are merged, Γk=Γk L∪Γk L2 . . . ∪Γk LM.
- Step 205: The estimation value of the channel H is solved by a least squares method: ĤΓ
k k=ΨΓk †Y. -
- Step 207: An index set is obtained:
Γ k L=arg max (H Γk k, S). - Step 208: The index set
Γ k L is extended toΓ k Li=Γ k L+iL, 1≤i≤M, and the index sets are merged,Γ k=Γ k L∪Γ k L2 . . . ∪Γ k LM. - Step 209: The estimation value of the channel H is solved by a least squares method: {tilde over (H)}
Γ k k=ΨΓ k †Y. - Step 210: The residual is updated: ν′k=Y−Ψ{tilde over (H)}
Γ k k. - Step 211: If ∥ν′k∥F>∥νk−1∥F, then {tilde over (Γ)}k={circumflex over (Γ)}k and operation is stopped.
- Step 212: If ∥ν′k∥F=∥νk−1∥F, then I=I+1, S=S×I, {circumflex over (Γ)}k=
Γ k. - Step 213: If ∥ν′k∥F<∥νk−1∥F, then νk=ν′k, Γk L=
Γ k L. - Step 214: k=k+1; Step 201 to Step 214 are repeated until the stop condition is satisfied.
- Step 3: According to the index set {tilde over (Γ)}k obtained in
Step 2, a channel matrix estimation value {tilde over (H)}{tilde over (Γ)}k may be solved, i.e., {tilde over (H)}{tilde over (Γ)}k =Ψ{tilde over (Γ)}k †Y, where a superscript “†” represents a pseudoinverse, i.e., Ψ{tilde over (Γ)}k † represents a pseudoinverse with respect to Ψ{tilde over (Γ)}k , and according to the obtained channel matrix estimation value {tilde over (H)}{tilde over (Γ)}k , after a baseband signal is demodulated, data information of the transmitting end is outputted. - To evaluate the performance of the disclosure, when the antenna quantity M is 16, the step size s is 2, and a threshold parameter μ of the algorithm reconstruction precision is all 0.001, normalized least mean square errors of channel estimation algorithms at different signal-to-noise ratios are calculated, and the result is shown in
FIG. 1 . - To further evaluate the performance of the disclosure, when the signal-to-noise ratio is 20 dB, the step size s is 2, the threshold parameter μ of the algorithm reconstruction precision is all 0.001, normalized least mean square errors of channel estimation algorithms at different transmitting antennas of the base station are calculated, and the result is shown in
FIG. 2 . - The normalized least mean square error is defined as follows:
-
- where Ne represents an operation count of the algorithm at each signal-to-noise ratio, and herein, Ne is 20.
- According to
FIG. 1 , in the embodiment of the disclosure, with the generalized adaptive mechanism introduced, the proposed gBAMP algorithm can detect the minimum precision achieved by the reconstruction and automatically end the reconstruction process without the constraint of the threshold parameter μ. The experimental result shows that the algorithm achieves good performance close to that of the exact-LS algorithm and is superior to other algorithms. - According to
FIG. 2 , as the antenna quantity increases, the precision of channel reconstruction is affected, and the reason lies in that the increase in the antenna quantity leads to pilot insufficiency. The reconstruction by the SAMP-Block algorithm fails at the threshold parameter. However, in the embodiment of the disclosure, when the antenna quantity is 16 more, the proposed gBAMP algorithm exhibits better performance, and exhibits optimal performance in both precision and stability that are even better than those of the exact-LS algorithm. - The time-frequency block-sparse channel estimation method based on compressed sensing in the embodiment of the disclosure, i.e., a generalized block adaptive gBAMP algorithm, has good reconstruction performance and is applicable to occasions requiring pilot-assisted channel estimation of a wireless communication system.
- Simulation shows that the method of the disclosure can quickly and accurately recover massive MIMO channel information of which a sparsity degree is unknown.
- It will be understood that modifications and variations may be made by persons skilled in the art according to the above description, and all such modifications and variations are intended to be included within the scope of the disclosure as defined in the appended claims.
Claims (3)
1. A time-frequency block-sparse channel estimation method based on compressed sensing, wherein an orthogonal frequency-division multiplexing (OFDM) system of a downlink frequency-division duplexing (FDD) massive MIMO channel model is initialized, supposing M antennas are disposed at a base station end and U single-antenna users are simultaneously served, and let there be N subcarriers in the OFDM system, wherein NP subcarriers are used to transmit pilot signals, and L is a maximum path delay, considering observing in R adjacent OFDM symbols, the method comprising:
Step 1: inputting a pilot signal and a reception signal of a transmitting end, and establishing a channel model as Y=ΨH+V according to the signal,
wherein Y∈ N P ×R is a reception signal matrix, H∈ LM×R is a channel matrix, Ψ∈ N P ×LM is a pilot matrix, V∈ N P ×R is a noise matrix;
Step 2: solving a sparse signal estimation value {tilde over (H)} by a compressed sensing method according to the channel model obtained in Step 1 to further calculate an index set {tilde over (Γ)}k; and
Step 3: solving a channel matrix estimation value {tilde over (H)}{tilde over (Γ)} k according to the index set {tilde over (Γ)}k obtained in Step 2, i.e., {tilde over (H)}{tilde over (Γ)} k =Ψ{tilde over (Γ)} k †Y, wherein a superscript “†” represents a pseudoinverse, i.e., Ψ{tilde over (Γ)} k † represents a pseudoinverse with respect to Ψ{tilde over (Γ)} k , and after a baseband signal is demodulated, outputting data information of the transmitting end according to the obtained channel matrix estimation value {tilde over (H)}{tilde over (Γ)} k .
2. The time-frequency block-sparse channel estimation method based on compressed sensing according to claim 1 , wherein Step 1 further comprises:
after establishing the channel model, since NP<<LM, determining that the channel model is an underdetermined equation, and since a joint sparsity structure is present in the massive MIMO channel, determining to reconstruct a high-dimensional channel H from a low-dimensional vector Y by a channel estimation method based on compressed sensing.
3. The time-frequency block-sparse channel estimation method based on compressed sensing according to claim 1 , wherein the compressed sensing method in Step 2 specifically comprises:
inputting parameters as a measurement value Y, a sensing matrix W, a step size S, and a maximum path delay L; initializing a residual vector ν0=Y, reconstructing a signal estimation value H=Ø∈ LM×T, an index set r=0, letting an initial iteration count k=1, and updating a step size count I=1, the method comprising:
Step 201: calculating a projection coefficient of each column of the sensing matrix on the residual vector, i.e., Z=ΨHνk−1;
Step 202: converting a matrix Z∈ LM×R into a matrix {circumflex over (Z)} of L×RM by joint sparsity of the channel, and summing {circumflex over (Z)} by row to obtain {circumflex over (Z)}=Σi RM∥{circumflex over (Z)}∥F 2∈ L×1;
Step 203: updating the index set: Γk L=Γk−1 L∪{arg max ({tilde over (Z)},S)};
Step 204: extending the index set Γk L to Γk Li=Γk L+iL, 1≤i≤M, and merging the index sets, Γk=Γk L∪Γk L2 . . . ∪Γk LM;
Step 205: solving the estimation value of the channel H by a least squares method: ĤΓ k k=ΨΓ k †Y;
Step 206: converting a matrix ĤΓ k k∈ LM×R into a matrix H̆Γ k k of L×RM, and summing H̆Γ k k by row to obtain H Γ k k=Σi RMH̆Γ k k∈ L×1;
Step 207: obtaining an index set: Γ k L=arg max (H Γ k k, S);
Step 208: extending the index set Γ k L to Γ k Li=Γ k L+iL, 1≤i≤M, and merging the index sets, Γ k=Γ k L∪Γ k L2 . . . ∪Γ k LM;
Step 209: solving the estimation value of the channel H by a least squares method: {tilde over (H)} Γ k k=Ψ Γ k †Y;
Step 210: updating the residual: ν′k=Y−Ψ{tilde over (H)} Γ k k;
Step 211: if ∥ν′k∥F>∥νk−1∥F, then {tilde over (Γ)}k={circumflex over (Γ)}k and stopping operation;
Step 212: if ∥ν′k∥F=∥νk−1∥F, then I=I+1, S=S×I, {circumflex over (Γ)}k=Γ k;
Step 213: if ∥ν′k∥F<∥νk−1∥F, then νk=ν′k, Γk L=Γ k L; and
Step 214: k=k+1, repeating Step 201 to Step 214 until the stop condition is satisfied.
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CN114330455A (en) * | 2022-01-05 | 2022-04-12 | 哈尔滨工业大学 | Steel rail acoustic emission signal rapid high-precision reconstruction method based on compressed sensing |
CN117278367A (en) * | 2023-11-23 | 2023-12-22 | 北京中关村实验室 | Distributed compressed sensing sparse time-varying channel estimation method |
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