CN110730002B - Combined design method for complex signal measurement matrix and sparse support recovery - Google Patents
Combined design method for complex signal measurement matrix and sparse support recovery Download PDFInfo
- Publication number
- CN110730002B CN110730002B CN201910920294.2A CN201910920294A CN110730002B CN 110730002 B CN110730002 B CN 110730002B CN 201910920294 A CN201910920294 A CN 201910920294A CN 110730002 B CN110730002 B CN 110730002B
- Authority
- CN
- China
- Prior art keywords
- sparse
- complex
- sparse support
- signal
- recovery
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000011084 recovery Methods 0.000 title claims abstract description 92
- 238000000034 method Methods 0.000 title claims abstract description 74
- 239000011159 matrix material Substances 0.000 title claims abstract description 58
- 238000005259 measurement Methods 0.000 title claims abstract description 48
- 238000013461 design Methods 0.000 title claims abstract description 45
- 238000007906 compression Methods 0.000 claims abstract description 11
- 230000006835 compression Effects 0.000 claims abstract description 10
- 238000001514 detection method Methods 0.000 claims description 18
- 238000012549 training Methods 0.000 claims description 18
- 238000013528 artificial neural network Methods 0.000 claims description 14
- 230000000694 effects Effects 0.000 claims description 13
- 230000008569 process Effects 0.000 claims description 13
- 238000004891 communication Methods 0.000 claims description 11
- 239000013598 vector Substances 0.000 claims description 11
- 230000004913 activation Effects 0.000 claims description 10
- 239000000654 additive Substances 0.000 claims description 8
- 230000000996 additive effect Effects 0.000 claims description 8
- 238000005457 optimization Methods 0.000 claims description 4
- 230000008901 benefit Effects 0.000 abstract description 3
- 238000004904 shortening Methods 0.000 abstract description 2
- 230000006870 function Effects 0.000 description 14
- 238000005070 sampling Methods 0.000 description 7
- 210000002569 neuron Anatomy 0.000 description 6
- 238000013135 deep learning Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 5
- 238000005516 engineering process Methods 0.000 description 5
- 238000007476 Maximum Likelihood Methods 0.000 description 3
- 238000013459 approach Methods 0.000 description 3
- 238000012772 sequence design Methods 0.000 description 2
- 102100037599 SPARC Human genes 0.000 description 1
- 101710100111 SPARC Proteins 0.000 description 1
- 230000003044 adaptive effect Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000013527 convolutional neural network Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000009916 joint effect Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000004335 scaling law Methods 0.000 description 1
Images
Classifications
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
- H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/04—Architecture, e.g. interconnection topology
- G06N3/045—Combinations of networks
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
- H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
- H03M7/60—General implementation details not specific to a particular type of compression
- H03M7/6005—Decoder aspects
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Landscapes
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Artificial Intelligence (AREA)
- Biomedical Technology (AREA)
- Biophysics (AREA)
- Computational Linguistics (AREA)
- Data Mining & Analysis (AREA)
- Evolutionary Computation (AREA)
- General Health & Medical Sciences (AREA)
- Molecular Biology (AREA)
- Computing Systems (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Software Systems (AREA)
- Mobile Radio Communication Systems (AREA)
Abstract
The invention relates to a complex signal measurement matrix and sparse support recovery joint design method and application, wherein the method obtains a sparse support recovery result after joint design of the measurement matrix of a sparse complex signal and sparse support recovery, and comprises the following steps: A. performing linear compression on the sparse complex signal by using an encoder of the depth self-encoder to obtain a measurement matrix and real parts and imaginary parts of noisy linear complex observation signals; B. based on the real part and the imaginary part of the noisy linear complex observed signal, obtaining an approximation of a sparse support estimate using a decoder of a depth self-encoder; C. and comparing the approximation of the sparse support estimation with a decision threshold by using hard decision to obtain a sparse support recovery result. Compared with the prior art, the method has the advantages of effectively improving the sparse support recovery performance, shortening the sparse support recovery time and the like.
Description
Technical Field
The invention relates to a measurement matrix design and sparse support recovery technology for sparse complex signals in the field of compressed sensing, in particular to a complex signal measurement matrix and sparse support recovery joint design method and application.
Background
Compressed sensing presents two key challenges: 1) Designing a measurement matrix which can reduce the signal dimension and simultaneously keep as much sparse information as possible; 2) Sparse support of sparse signals is restored from downsampled linear measurements based on a given measurement matrix. Classical measurement matrix design methods are based on Restricted Isometry Property (RIP) property analysis of the matrix. J. candes in article "The restricted isometry property and its implications for compressed sensing" indicates: when the measurement matrix satisfies the RIP property, the signal can be successfully recovered. Although the determination of the RIP properties of the matrix is NP-difficult, R.G. Baraniak, in the article "Model-based compressive sensing", states that the sub-Gaussian matrix has a high probability of having RIP properties. The RIP-property based design approach does not utilize signal sparse patterns and does not necessarily provide better linear compression. Tibshirani uses LASSO method to recover sparse signal in article Regression shrinkage and selection via the LASSO; liu and W.Yu perform sparse signal recovery in article "Massive connectivity with massive MIMO-Part I: device activity detection and channel estimation" using the AMP method; the Group LASSO algorithm was derived from Yuan and Y.Lin in article "Model selection and estimation in regression with grouped variables" using the Group sparsity improvement LASSO algorithm. Note that neither LASSO nor AMP methods can utilize sparse patterns of sparse signals, and the Group LASSO algorithm can utilize signal sparse patterns to improve sparse signal recovery performance, but is only suitable for specific sparse patterns, and has poor expansibility.
Sparse support recovery refers to estimating the position of non-zero elements of a sparse signal based on noisy linear observations of the sparse signal. The measurement matrix and recovery method designed for sparse signal recovery are not necessarily applicable to sparse support recovery. Most current sparse support recovery methods focus on recovery of sparse support under a given measurement matrix, for example, m.j. Wainwright derives conditions that can successfully recover sparse support with known sparse signal sparsity by using an exhaustive method in the article "Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting", but the exhaustive method is too complex and has limited application in practice. M.J. Wainwright, another article "Sharp thresholds for high-dimensional and noisy sparsity recovery usingl 1 -constrained quadratic programming (LASSO) "sparse support recovery using LASSO-based optimization methods. Lee et al in article "Subspace methods for joint sparse recovery" address the sparse support recovery problem using a heuristic algorithm that has a complexity lower than LASSO but is less performing. Note that none of these sparse support recovery methods takes into account the design of the measurement matrix and cannot utilize the sparse pattern of the sparse signal.
Sparse signal recovery and sparse support recovery are widely applied to the field of image sampling recovery. In the process of sampling and restoring the image, the original image is transmitted or stored after being sampled, and then the original image is restored, wherein the restoration of the original image corresponds to the sparse signal restoration problem in the compressed sensing field. In order to fully utilize the sparse pattern of the image signal, some works use a deep learning method to achieve restoration of the image signal. Mousavi and R.G.Baraniak consider the recovery of real image signals based on deep learning in article "Learning to invert: signal recovery via deep convolutional networks", and Y.Yang et al consider the recovery of complex image signals based on deep learning in article "ADMM-CSNet: A deep learning approach for image compressive sensing". To further improve the performance of image signal recovery, some work contemplates the use of a self-encoder and generation of a countermeasure network (GAN) to implement a joint design of image signal sampling and recovery methods. Mousavi et al in the article "deep codec: adaptive sensing and recovery via deep convolutional neural networks" considered a joint design of a nonlinear sampling and recovery method for a real image signal, and W.Shi et al in the article "Deep networks for compressed image sensing" studied a joint design of a linear sampling and recovery method for a real image signal. Note that the first two image signal recovery methods based on deep learning do not consider the design of the image sampling process, and the last two image signal sampling and recovery joint design methods are only applicable to real image signals and cannot be extended to measurement matrix and sparse support recovery joint design of sparse complex signals.
Sparse signal recovery and sparse support recovery are also widely used in the field of machine type communications. The mass machine type communication is one of three application scenes of 5G, and compared with the other two application scenes, the 5G research and standardization process for the mass machine type communication is relatively lagged. Currently, mass machine type communications involve unlicensed large-scale access (grant-free massive access) and passive access (unsourced multiple access). In unlicensed large-scale access, different non-orthogonal pilot sequences are allocated to devices in advance, one pilot sequence can be allocated to each device to characterize its identity information, and multiple pilot sequences can be allocated to each device to characterize its identity information and a small amount of information that may be transmitted. The active equipment simultaneously transmits pilot frequency, and the receiving end detects the transmitted pilot frequency according to the received pilot frequency signal. Detection of transmitted pilots in unlicensed large-scale access corresponds to measurement matrix design and sparse support recovery for complex signals in the compressed sensing field. Liu and W.Yu use AMP method for device activity detection in article "Massive connectivity with massive MIMO-Part I: device activity detection and channel estimation"; caire et al use maximum likelihood estimation (ML) for device liveness detection in article "Improved scaling law for activity detection in Massive MIMO systems". E.Larsson et al in the article Grant-free massive MTC-Enabled massive MIMO: A Compressive Sensing Approach, use M-AMP algorithm to realize device activity detection and embedded information recovery; yu et al in article "Covariance based joint activity and data detection for massive random access with massive MIMO" utilize a modified maximum likelihood estimation (ML) algorithm to achieve device liveness detection and embedded information recovery. Note that none of these methods of achieving device activity detection consider joint design of pilot sequences and device activity detection, and do not take full advantage of sparse patterns of sparse signals. In passive access, all devices use the same message codebook, and the active devices send one codeword in the message codebook at the same time. The receiving end detects the list of the transmitted messages according to the received codeword signals. The recovery of the message list corresponds to the measurement matrix design and sparse support recovery problem for complex signals in the compressed sensing field. Polyanskiy uses ALOHA algorithm to realize the recovery of the message list in article A perspective on massive random-access; caire et al uses maximum likelihood estimation (ML) in article "Massive MIMO unsourced random access" to effect retrieval of the list of transmitted messages; fengler et al in article "SPARCs for unsourced random access" uses the AMP algorithm for recovery of transmitted information messages; vem et al uses the LASSO algorithm in article "A user-independent serial interference cancellation based coding scheme for the unsourced random access Gaussian channel" for retrieval of the list of messages sent. Similar to algorithms for device activity detection in unlicensed large-scale access technologies, none of these algorithms for message list recovery in passive access consider joint design of message codebook and message list recovery and do not take full advantage of sparse patterns of sparse signals.
In summary, the current measurement matrix design and sparse support recovery method for sparse complex signals cannot fully utilize the relationship between the sparse pattern or linear compression of the sparse complex signals and the sparse support recovery, and the accuracy of the sparse support recovery is limited and the speed is low.
Disclosure of Invention
The invention overcomes the defects in the prior art and provides a complex signal measurement matrix and sparse support recovery joint design method and application.
The aim of the invention can be achieved by the following technical scheme:
a complex signal measurement matrix and sparse support recovery joint design method is provided, and the method obtains a sparse support recovery result after joint design of the measurement matrix of the sparse complex signal and the sparse support recovery, and comprises the following steps:
A. performing linear compression on the sparse complex signal by using an encoder of the depth self-encoder to obtain a measurement matrix and real parts and imaginary parts of noisy linear complex observation signals;
B. based on the real part and the imaginary part of the noisy linear complex observed signal, obtaining an approximation of a sparse support estimate using a decoder of a depth self-encoder;
C. and comparing the approximation of the sparse support estimation with a decision threshold by using hard decision to obtain a sparse support recovery result.
Further, the process of linearly compressing the sparse complex signal by the encoder is specifically:
from noisy linear complex observed signals
And measuring matrix->
Sparse complex signal->
And additive complex noise->
Is to be noisy linear complexThe Y real and imaginary parts of the observed signal are expressed as:
Re(Y)＝Re(A)Re(X)-Im(A)Im(X)+Re(Z)
Im(Y)＝Im(A)Re(X)+Re(A)Im(X)+Im(Z)
wherein ,
representing a complex set, re () and Im () representing real and imaginary parts of the respective complex numbers, respectively;
and utilizing a standard neural network structure to realize linear compression of the sparse complex signal according to the two real number equivalence relations.
Respectively representing real matrixes Re (A) and Im (A) of L multiplied by N by using two convolution layers consisting of L convolution kernels with the channel number of 1 and the size of N multiplied by 1, wherein the weights in the convolution kernels are in one-to-one correspondence with elements in Re (A) and Im (A); multiplying the real part Re (X) and the imaginary part Im (X) of X with Re (A) and Im (A) respectively to obtain Re (A) Re (X), re (A) Im (X), im (A) Re (X) and Im (A) Im (X); the real part Re (Y) of the noisy linear complex observation signal is obtained by subtracting the Im (A) Im (X) from Re (A) Re (X) and adding Re (Z), and the imaginary part Im (Y) of the noisy linear complex observation signal is obtained by adding Re (A) Im (X) from Im (A) Re (X) and adding Im (Z). To embody a linear relationship of y=ax+y, the encoder does not use an activation function.
Further, the approximate acquisition process of the sparse support estimation specifically includes:
inputting the real part and the imaginary part of the noisy linear complex observation signal into T 1 The +2 layer fully connected neural network derives an approximation of the sparse support estimate, where T 1 Is a non-negative integer.
The sparse support (X) is a set of positions where the non-zero rows of the sparse complex signal X are located, and can be a sparse support vector
Representation of->
To indicate a function.
Approximation for sparse support estimation
Representation of->
Alpha is alpha n Is a approximation of (a).
Further, another described process for obtaining an approximation of the sparse support estimate is specifically:
will YY H As an approximation of the covariance matrix of the noisy linear complex observed signal, where Y H Representing the conjugate transpose of the noisy linear complex observed signal. Obtaining the approximate real and imaginary parts of the covariance matrix of the noisy linear complex observed signal from the real and imaginary parts of the noisy linear complex observed signal:
Re(YY H )＝Re(Y)Re(Y T )+Im(Y)Im(Y T )
Im(YY H )＝Im(Y)Re(Y T )-Re(Y)Im(Y T )
wherein YT Representing a transpose of the noisy linear complex observed signal.
Inputting the approximate real part and imaginary part of the covariance matrix of the noisy linear complex observed signal into T 2 Approximation of sparse support estimation obtained by +2 layer fully connected neural network
wherein T2 Is a non-negative integer.
Further, in the fully-connected neural network, the hidden layer adopts a linear rectifying unit as an activation function, and the output layer adopts sigmoid as an activation function.
Further, when the depth self-encoder performs training, the encoder and the decoder in the depth self-encoder are jointly trained by taking the cross entropy of the sparse support in the training samples and the approximation of the sparse support estimate obtained by the depth self-encoder as a loss function.
Further, the loss function expression is:
its corresponding training samples are denoted (X) (i) ,Z (i) ,α (i) ) I=1, …, I represents the number of training samples, X (i) 、Z (i) and α(i) The true sparse support vectors of the sparse complex signal, the additive complex noise and the sparse complex signal corresponding to the sample i are respectively represented,
the representation will (X (i) ,Z (i) ) True sparse support vector alpha obtained after depth self-encoder is input (i) Is a good approximation of the estimate of (a).
Further, the hard decision process specifically includes:
decision threshold gamma for hard decisions * E (0, 1) is obtained by the following optimization method:
wherein ,PE And (gamma) represents a sparse support recovery error rate measurement when the decision threshold is gamma epsilon (0, 1), and the sparse support recovery error rate measurement can be obtained based on training samples. Approximation of sparse support
Each element of gamma is equal to gamma * Comparing to obtain sparse support estimation
wherein />
The invention also provides a pilot sequence and equipment activity detection joint design method in unlicensed large-scale access (grant-free massive access) aiming at machine type communication, which is realized based on the complex signal measurement matrix and sparse support recovery joint design method.
The invention also provides a combined design method for recovering the message codebook and the message list in the passive access (unsourced multiple access) aiming at the machine type communication, which is realized based on the combined design method for recovering the complex signal measurement matrix and the sparse support.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention realizes the joint optimization of the measurement matrix and the sparse support recovery based on the depth self-encoder, and effectively improves the performance of the sparse support recovery;
2. the invention excavates the characteristic of the signal sparse pattern by means of a data driving method, and effectively improves the performance of sparse support recovery;
3. the invention uses the characteristic that the neural network can perform parallel computation, thereby greatly shortening the time for sparse support recovery;
4. the method can be used for pilot sequence design and equipment activity detection in the unlicensed large-scale access aiming at machine type communication, and improves detection accuracy and detection speed.
5. The invention can be used for message codebook design and message list recovery in the passive access technology aiming at machine type communication, and improves recovery accuracy and recovery speed.
Drawings
FIG. 1 is a schematic block diagram of a method of the present invention;
FIG. 2 is a schematic diagram of an encoder for implementing sparse complex signal linear compression;
FIG. 3 is a schematic diagram of a decoder for implementing complex signal sparse support recovery;
FIG. 4 is a schematic diagram of another decoder for implementing complex signal sparse support recovery;
fig. 5 is a schematic diagram of a hard decision process.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
The embodiment provides a complex signal measurement matrix and sparse support recovery joint design method. As shown in fig. 1, the method is implemented based on a joint design framework of sparse complex signal measurement matrix design and sparse support recovery, the framework comprises a depth self-encoder and a hard decision module, the depth self-encoder comprises an encoder and a decoder, the encoder is used for realizing linear compression of the sparse complex signal to design the measurement matrix, the decoder is used for approximating sparse support recovery of the sparse complex signal, and the hard decision module is used for converting an output result of the depth self-encoder into a sparse support recovery result.
The complex signal measurement matrix and sparse support recovery joint design method specifically comprises the following steps:
A. performing linear compression on the sparse complex signal by using an encoder of the depth self-encoder to obtain a measurement matrix and real parts and imaginary parts of noisy linear complex observation signals;
B. based on the real part and the imaginary part of the noisy linear complex observed signal, obtaining an approximation of a sparse support estimate using a decoder of a depth self-encoder;
C. and performing hard decision comparison on the approximation of the sparse support estimation and a decision threshold by using hard decision to obtain a sparse support recovery result.
The method for designing the measurement matrix by linearly compressing the sparse complex signal by the encoder of the depth self-encoder is specifically based on the real part and the imaginary part of the sparse complex signal, the complex measurement matrix and the additive complex noise to represent the real part and the imaginary part of the noisy linear complex observed signal.
Order the
and />
Representing the complex measurement matrix, the sparse complex signal, the additive complex noise and the noisy linear complex observation signal respectively, and L× N, N × M, L ×M representing the size of each matrix, the following two real relationships are obtained from the complex relationship Y=AX+Z：
Re(Y)＝Re(A)Re(X)-Im(A)Im(X)+Re(Z)
Im(Y)＝Im(A)Re(X)+Re(A)Im(X)+Im(Z)
wherein ,
representing a complex set, re (-) and Im (-) represent the real and imaginary parts of the corresponding complex, respectively.
The real and imaginary parts of the noisy linear complex observed signal are characterized by a neural network based on two real relationships. As shown in the encoder structure of fig. 2, two convolution layers consisting of L number of channels of 1 and size n×1 are used to respectively represent l×n real matrices Re (a) and Im (a), and weights in the convolution cores are in one-to-one correspondence with elements in Re (a) and Im (a); multiplying the real part Re (X) and the imaginary part Im (X) of X with Re (A) and Im (A) respectively to obtain Re (A) Re (X), re (A) Im (X), im (A) Re (X) and Im (A) Im (X); the real part Re (Y) of the noisy linear complex observation signal is obtained by subtracting the Im (A) Im (X) from Re (A) Re (X) and adding Re (Z), and the imaginary part Im (Y) of the noisy linear complex observation signal is obtained by adding Re (A) Im (X) from Im (A) Re (X) and adding Im (Z). To embody a linear relationship of y=ax+z, the encoder does not use an activation function.
The method for recovering the sparse support of the decoder approximate sparse complex signal by using the depth self-encoder specifically comprises the following two steps:
1) As shown in FIG. 3, the real and imaginary parts of the noisy linear complex observed signal are directly input to T 1 The +2 layer fully connected neural network derives an approximation of the sparse support estimate, where T 1 Is a non-negative integer. The sparse support (X) is a set of positions where the non-zero rows of the sparse complex signal X are located, and can be a sparse vector
Representation of wherein
To indicate a function. Approximation of sparse support estimate>
Representation of->
Alpha is alpha n Is a approximation of (a). The first layer of the fully-connected neural network is an input layer, and the number of neurons is set to be 2ML so as to input a real part Re (Y) and an imaginary part Im (Y) of a noisy linear complex observation signal; intermediate T 1 The layer is a hidden layer, T 1 The size of each layer and the number of the neurons of each layer can be selected according to specific conditions; the last layer is the output layer, and the number of neurons is set to N to output an approximation of the sparse support estimate. To output an approximation of the sparse support estimate lying within the (0, 1) interval, an intermediate T 1 The layer uses a linear rectifying unit (RELU) as an activation function to discard negative values, and the output layer uses sigmoid as an activation function to limit the output value to within the (0, 1) interval.
2) As shown in FIG. 4, YY is H As an approximation of the covariance matrix of the noisy linear complex observed signal, where Y H Representing the conjugate transpose of the noisy linear complex observed signal. First based on the following equivalence relation:
Re(YY H )＝Re(Y)Re(Y T )+Im(Y)Im(Y T )
Im(YY H )＝Im(Y)Re(Y T )-Re(Y)Im(Y T )
obtaining an approximate real part Re (YY) of a covariance matrix of the noisy linear complex observed signal from the real part Re (Y) and the imaginary part Im (Y) of the noisy linear complex observed signal H ) And imaginary part Im (YY) H ) Y in equivalence relation T Representing a transpose of the noisy linear complex observed signal. Re (YY) H ) And Im (YY) H ) Inputting T as shown in FIG. 4 2 The +2 layer fully connected neural network gets an approximation of the sparse support estimate, where T 2 Is a non-negative integer. The first layer of the fully-connected neural network is an input layer, and the number of neurons is set to be 2L 2 With the input of an approximated real part Re (YY) of a noisy linear complex observed signal covariance matrix H ) And imaginary part Im (YY) H ) The method comprises the steps of carrying out a first treatment on the surface of the Intermediate T 2 The layer is hiddenLayer T 2 The size of each layer and the number of the neurons of each layer can be selected according to specific conditions; the last layer is the output layer, and the number of neurons is set to N to output an approximation of the sparse support estimate. To output an approximation of the sparse support estimate lying within the (0, 1) interval, an intermediate T 2 The layer uses a linear rectifying unit (RELU) as an activation function to discard negative values, and the output layer uses sigmoid as an activation function to limit the output value to within the (0, 1) interval.
When training a depth self-encoder, an encoder and a decoder in the depth self-encoder are jointly trained with the cross entropy of the sparse support in the training samples and the approximation of the sparse support estimate obtained by the depth self-encoder as a loss function. Training samples are denoted as (X) (i) ,Z (i) ,α (i) ) I=1, …, I denotes the number of training samples, where X (i) 、Z (i) and α(i) The true sparse support vectors of the sparse complex signal, the additive complex noise and the sparse complex signal corresponding to the sample i are respectively represented,
the representation will (X (i) ,Z (i) ) True sparse support vector alpha obtained after depth self-encoder is input (i) Is a good approximation of the estimate of (a). The corresponding loss function expression of the training sample is:
when training is completed, a complex measurement matrix a can be obtained based on the weights of the encoder.
The approximation of the sparse support estimation is compared with a decision threshold by utilizing hard decision, and the process for obtaining the sparse support recovery result comprises the following steps:
as shown in fig. 5, when the input sparsity supports an approximation of the estimation
N element->
Greater than or equal to decision threshold gamma * At this time, the sparse support estimate of the output +.>
N element->
Judging as 1; approximation of sparse support estimate when input +.>
N element->
Less than decision threshold gamma * At this time, the sparse support estimate of the output +.>
N element->
And judging as 0. Wherein, the judgment threshold gamma * The acquisition method of (a) comprises the following steps: selecting U training samples (X) (u) ,Z (u) ,α (u) ) U=1, …, U, where X (u) 、Z (u) and α(u) And respectively representing the sparse complex signal, the additive complex noise and the true sparse support vector of the sparse complex signal corresponding to the sample u. By using
The representation will (X (u) ,Z (u) ) Inputting a true sparse support vector alpha obtained after a trained depth self-encoder (u) Approximation of the estimate of (1) with ∈ ->
Sparse support estimation representing a decision threshold of γ. Selecting an appropriate sparse support recovery error rate metric P E (gamma) to measure alpha (u) U=1, …, U and +.>
Distinction when the decision threshold is gamma e (0, 1), decision threshold gamma used in hard decision * Decision threshold for minimizing sparse support recovery error rate metric, i.e., gamma * ＝argmin γ∈(0,1) P E (γ)。
The complex signal measurement matrix and sparse support recovery joint design method can be conveniently applied to pilot sequence design and equipment activity detection in the unlicensed large-scale access technology aiming at machine type communication and message codebook design and message list recovery in the passive access technology.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the technical personnel in the field according to the inventive concept are within the protection scope determined by the present invention.
Claims (8)
1. A complex signal measurement matrix and sparse support recovery joint design method is characterized in that the method obtains a sparse support recovery result after joint design of the measurement matrix of a sparse complex signal and sparse support recovery, and the method comprises the following steps:
A. performing linear compression on the sparse complex signal by using an encoder of the depth self-encoder to obtain a measurement matrix and real parts and imaginary parts of noisy linear complex observation signals;
B. based on the real part and the imaginary part of the noisy linear complex observed signal, obtaining an approximation of a sparse support estimate using a decoder of a depth self-encoder;
C. comparing the approximation of the sparse support estimation with a decision threshold by using hard decision to obtain a sparse support recovery result;
the linear compression process of the sparse complex signal by using the encoder specifically comprises the following steps:
from noisy linear complex observed signals
And measuring matrix->
Sparse complex signal->
And additive complex noise->
The complex relation y=ax+z of the noisy linear complex observation signal Y is expressed as:
Re(Y)＝Re(A)Re(X)-Im(A)Im(X)+Re(Z)
Im(Y)＝Im(A)Re(X)+Re(A)Im(X)+Im(Z)
wherein ,
representing a complex set, re () and Im () representing real and imaginary parts of the respective complex numbers, respectively;
according to the two real number equivalence relations, linear compression of sparse complex signals is achieved through a standard neural network structure;
the approximate acquisition process of the sparse support estimation specifically comprises the following steps:
inputting the real part and the imaginary part of the noisy linear complex observation signal into a T1+2 layer fully connected neural network to obtain the approximation of sparse support estimation, wherein T1 is a non-negative integer;
sparse support (X) is a set of positions where non-zero rows of a sparse complex signal X are located, and a sparse support vector is adopted
Representation of->
Is an indication function;
approximation for sparse support estimation
Representation of->
Alpha is alpha n Is a approximation of (a).
2. The joint design method of complex signal measurement matrix and sparse support recovery according to claim 1, wherein the approximate acquisition process of the sparse support estimation specifically further comprises:
will YY H As an approximation of the covariance matrix of the noisy linear complex observed signal, Y, Y T Representing a noisy linear complex observed signal and its conjugate transpose, deriving from real and imaginary parts of the noisy linear complex observed signal an approximated real and imaginary part of a noisy linear complex observed signal covariance matrix:
Re(YY H )＝Re(Y)Re(Y T )+Im(Y)Im(Y T )
Im(YY H )＝Im(Y)Re(Y T )-Re(Y)Im(Y T )
inputting the approximate real part and imaginary part of the covariance matrix of the noisy linear complex observed signal into T 2 Approximation of sparse support estimation obtained by +2 layer fully connected neural network
wherein T2 Is a non-negative integer.
3. The joint design method of complex signal measurement matrix and sparse support recovery according to claim 1 or 2, wherein in the fully connected neural network, a linear rectifying unit is adopted as an activation function by a hidden layer, and a sigmoid is adopted as an activation function by an output layer.
4. The joint design method of complex signal measurement matrix and sparse support recovery of claim 1, wherein the depth self-encoder performs training by jointly training the encoder and decoder in the depth self-encoder with the approximate cross entropy of the sparse support in the training samples and the sparse support estimate obtained by the depth self-encoder as a loss function.
5. The joint design method of complex signal measurement matrix and sparse support recovery of claim 4, wherein the loss function expression is:
its corresponding training samples are denoted (X) (i) ，Z (i) ，α (i) ) I=1, a method of treating a subject suffering from a disorder, I, I represents the number of training samples, X (i) 、Z (i) and α(i) The true sparse support vectors of the sparse complex signal, the additive complex noise and the sparse complex signal corresponding to the sample i are respectively represented,
the representation will (X (i) ，Z (i) ) True sparse support vector alpha obtained after depth self-encoder is input (i) Is a good approximation of the estimate of (a).
6. The method for jointly designing the complex signal measurement matrix and the sparse support recovery according to claim 1, wherein the hard decision process is specifically:
decision threshold gamma for hard decisions * E (0, 1) is obtained by the following optimization method:
wherein ,PE (gamma) represents a sparse support recovery error rate metric for a decision threshold gamma e (0, 1) and can be obtained based on training samples;
approximation of sparse support estimates
Each element of gamma is equal to gamma * Comparing to obtain sparse support recovery result
wherein />
7. A pilot sequence and device activity detection joint design method in unlicensed large-scale access for machine-type communication, characterized in that the method is implemented based on the complex signal measurement matrix and sparse support recovery joint design method according to any one of claims 1-6.
8. A method of joint design of message codebook and message list restoration in passive access for machine type communication, characterized in that the method is implemented based on the complex signal measurement matrix and sparse support restoration joint design method as claimed in any one of claims 1-6.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910920294.2A CN110730002B (en) | 2019-09-26 | 2019-09-26 | Combined design method for complex signal measurement matrix and sparse support recovery |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910920294.2A CN110730002B (en) | 2019-09-26 | 2019-09-26 | Combined design method for complex signal measurement matrix and sparse support recovery |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110730002A CN110730002A (en) | 2020-01-24 |
| CN110730002B true CN110730002B (en) | 2023-06-16 |
Family
ID=69219485
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910920294.2A Active CN110730002B (en) | 2019-09-26 | 2019-09-26 | Combined design method for complex signal measurement matrix and sparse support recovery |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110730002B (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103250352A (en) * | 2011-01-10 | 2013-08-14 | 上海贝尔股份有限公司 | Method and apparatus for measuring and recovering sparse signals |
| CN109818645A (en) * | 2019-02-20 | 2019-05-28 | 西华大学 | CSI feedback method is superimposed with what supported collection assisted based on signal detection |
-
2019
- 2019-09-26 CN CN201910920294.2A patent/CN110730002B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103250352A (en) * | 2011-01-10 | 2013-08-14 | 上海贝尔股份有限公司 | Method and apparatus for measuring and recovering sparse signals |
| CN109818645A (en) * | 2019-02-20 | 2019-05-28 | 西华大学 | CSI feedback method is superimposed with what supported collection assisted based on signal detection |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110730002A (en) | 2020-01-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Shlezinger et al. | DeepSIC: Deep soft interference cancellation for multiuser MIMO detection | |
| CN109412993B (en) | Full-duplex cognitive underwater acoustic communication signal detection method capable of inhibiting self-interference based on deep learning | |
| CN110429965B (en) | Method for detecting uplink signal of large-scale multi-input multi-output system | |
| CN110166391B (en) | Baseband precoding MSK signal demodulation method based on deep learning under impulse noise | |
| Hasan et al. | The role of deep learning in NOMA for 5G and beyond communications | |
| Winkelbauer et al. | Rate-information-optimal Gaussian channel output compression | |
| Shlezinger et al. | Deep soft interference cancellation for MIMO detection | |
| CN114239749A (en) | Modulation identification method based on residual shrinkage and bidirectional long-short term memory network | |
| CN114268388A (en) | Channel estimation method based on improved GAN network in large-scale MIMO | |
| Qing et al. | ELM-based superimposed CSI feedback for FDD massive MIMO system | |
| Alawad et al. | A deep learning-based detector for IM-MIMO-OFDM | |
| CN110730002B (en) | Combined design method for complex signal measurement matrix and sparse support recovery | |
| Liu et al. | Scalable compressive sensing-based multi-user detection scheme for Internet-of-Things applications | |
| Wang et al. | Compressive sensing based user activity detection and channel estimation in uplink NOMA systems | |
| Wang et al. | Exploiting temporal side information in massive IoT connectivity | |
| Wu et al. | A CNN architecture for learning device activity from MMV | |
| Fu et al. | Scalable extraction based semantic communication for 6G wireless networks | |
| CN109639603A (en) | Low complexity compression channel perception estimation method based on pilot tone | |
| Plabst et al. | Efficient non-linear equalization for 1-bit quantized cyclic prefix-free massive MIMO systems | |
| Wang et al. | Blind recognition method for non-cooperative communication signals based on aerial computing | |
| Sun et al. | RBM based cooperative Bayesian compressive spectrum sensing with adaptive threshold | |
| Dai et al. | Power allocation for multiple transmitter-receiver pairs under frequency-selective fading based on convolutional neural network | |
| Xie et al. | Detection Algorithm Based on Deep Learning for the Multi-user MIMO-NOMA System | |
| Raja et al. | Improved ICA based multi-user detection of DS-CDMA | |
| Jiang et al. | Adaptive semantic video conferencing for ofdm systems |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |