Compressed sensing channel estimation algorithm for embedded systems

Abstract

The present invention discloses a compressed sensing channel estimation algorithm suitable for embedded systems, which is characterized by comprising the following steps: S1, initializing a residual vector, an index set and a support set; S2, calculating the inner product of the residual vector and a sensing matrix to find the best matching vector; S3, updating the index set and the support set; S4, estimating the channel response by using the least squares method; S5, updating the residual vector; S6, judging whether a preset iteration stop condition is met; if so, stopping the iteration and outputting the current latest channel response; if not, returning to step S2 with the current latest residual vector to continue the iteration.

Description

Technical Field

[0001] The present invention relates to the field of communications, in particular to the field of channel estimation, and in particular to a compressed sensing channel estimation algorithm suitable for embedded systems. Background Art

[0002] The development and exploration of marine resources cannot be achieved without the support of underwater communication technology. Underwater acoustic communication is the primary method for achieving medium- and long-distance underwater communication. Compared to wireless communications on land, underwater wireless communications face a more complex marine environment. During ocean propagation, underwater sound is subject to multiple reflections from the sea surface and seabed, resulting in complex multipath effects. Because the speed of sound underwater is only approximately 1500 m / s, the Doppler effect caused by the motion of the medium is significant, making it more sensitive to the relative motion of the sender and receiver. Fluctuations in the ocean temperature profile caused by seasons, weather, and ocean currents further complicate the propagation of sound, and the channel exhibits significant time-varying characteristics. The complex and variable nature of underwater acoustic channels, coupled with their limited bandwidth, make them one of the most challenging channels currently. Orthogonal frequency division multiplexing (OFDM) technology effectively improves spectrum utilization and mitigates intersymbol interference, making it widely used in underwater acoustic communication systems. After a signal passes through a complex and variable underwater acoustic channel, its amplitude, phase, and frequency will change, requiring channel estimation to compensate. Accurate channel estimation can improve communication reliability.

[0003] Existing channel estimation algorithms mostly use least squares (LS) and minimum mean square error (MMSE) estimation, which are inaccurate in time-varying channels with multipath and Doppler effects. Compressed sensing technology can effectively estimate multipath distribution and has a certain degree of Doppler resistance, resulting in better channel estimation in real-world marine environments. Representative compressed sensing algorithms fall into two main categories: convex optimization algorithms, such as basis pursuit (BP) and interior point methods; and greedy algorithms, such as matching pursuit (MP), orthogonal matching pursuit (OMP), adaptive matching pursuit (SAMP), and compressed sampling matching pursuit (CoSaMP). However, these compressed sensing algorithms generally have high computational complexity, making them difficult to implement on existing embedded systems and difficult to meet the real-time communication requirements.

[0004] Collecting and processing real-world signals is an essential component of information technology. The traditional signal acquisition process involves sampling, compression, storage, and reconstruction. The sampling rate must be greater than twice the signal bandwidth (Nyquist's sampling theorem), otherwise signal distortion will occur. However, during the compression process, a large amount of sampled data is discarded, wasting sampling resources. Compressed sensing is a new data acquisition and processing method that can accurately recover the original data from a small number of observation samples. Compressed sensing theory exploits the sparsity of signals, extracting low-dimensional data from the original signal using a pre-designed observation matrix. This reduces the sampling frequency during the sampling process, significantly reducing the burden on signal processing and storage systems.

[0005] The Orthogonal Matching Pursuit (OMP) algorithm is a greedy algorithm that has a faster computation speed than convex optimization algorithms. However, since the OMP algorithm requires multiple iterations, the computing resources of existing embedded systems are difficult to meet the computational requirements of the OMP channel estimation algorithm, affecting real-time communication. Summary of the Invention

[0006] In view of this, the present invention proposes a compressed sensing channel estimation algorithm suitable for embedded systems to solve the problem that the existing OMP channel estimation algorithm is difficult to be quickly implemented on embedded systems.

[0007] In order to solve the above problems, the present invention proposes the following technical solutions:

[0008] A compressed sensing channel estimation algorithm suitable for embedded systems includes the following steps: S1, initializing a residual vector, an index set, and a support set; S2, calculating the inner product of the residual vector and a sensing matrix to find the best matching vector; S3, updating the index set and the support set; S4, estimating the channel response by the least squares method; S5, updating the residual vector; S6, judging whether a preset iteration stop condition is met; if so, stopping the iteration and outputting the current latest channel response; if not, returning to step S2 with the current latest residual vector to continue the iteration.

[0009] Furthermore, step S1 includes: initializing the residual vector r0=y, index set Support set Iteration count i=1; y represents an OFDM frequency domain signal.

[0010] Furthermore, searching for the best matching vector in step S2 includes: searching for an index j*=argmax|<r i-1 ,a j >|;where r i-1 It is a newly defined collection used to store the index obtained from the previous iteration; a j are all column vectors of the perception matrix.

[0011] Furthermore, step S3 includes: updating the index set to γ i =γ i-1 ∪j*, update the support set to Ψ i =Ψ i-1 ∪a j* ;a j* is the column vector corresponding to j*.

[0012] Furthermore, step S4 includes: S41, optimizing the pilot insertion so that the perception matrix of compressed sensing becomes a diagonal matrix; S42, avoiding the inversion operation through the properties of the diagonal matrix to simplify the least squares method; S43, simplifying the least squares method by using the property that the sum of the squares of the column vector elements of the Fourier transform matrix is ​​a constant, and obtaining the predicted channel response through the least squares method.

[0013] Furthermore, step S41 includes: inserting pilot P=diag(x(0), x(1), ..., x(n)), and the sensing matrix A is a diagonal matrix:

[0014]

[0015] Wherein, N is the number corresponding to each OFDM subcarrier frequency, x(N) is the data corresponding to the N frequency, and w is a sine wave.

[0016] Furthermore, step S42 includes: simplifying the least squares method by the diagonal matrix A, and making the parameters of the least squares method of the orthogonal matching pursuit algorithm Ψ i is the support set of the i-th iteration, by selecting the sequence number γ in A ik The elemental composition of γ ik is the corresponding column vector of A; that is

[0017]

[0018] Among them, A γ Represents the selection of sequence number γ in A ik The set consists of elements, k represents the sparsity.

[0019] Furthermore, step S43 includes: since each column vector of the Fourier transform matrix is ​​composed of bases of different frequencies, the bases of the Fourier transform are orthogonal, therefore The simplified least squares method is:

[0020]

[0021] in, represents the channel response estimated by the iterative step i, y represents the OFDM frequency domain signal, h p represents the time domain channel response corresponding to the pilot, Ap Represents the observation matrix corresponding to the pilot.

[0022] Furthermore, step S5 includes: updating the residual vector using the estimated channel response

[0023] The present invention further provides a computer-readable storage medium having a computer program stored thereon, which can implement the steps of the aforementioned compressed sensing channel estimation algorithm when executed by a processor.

[0024] The present invention utilizes the OMP algorithm for compressed sensing-based underwater acoustic channel estimation. By modifying the pilot insertion method and transforming the sensing matrix into a diagonal matrix, the least squares inversion process in the OMP algorithm is simplified, allowing for rapid implementation on embedded systems. The proposed channel estimation algorithm reduces computational complexity, enabling the deployment of compressed sensing algorithms on embedded systems, minimizing system resource consumption and ensuring real-time communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a flow chart of a compressed sensing channel estimation algorithm applicable to embedded systems according to an embodiment of the present invention.

[0026] Figure 2 It is a comparison diagram of the actual channel response and the channel response estimated by the present invention.

[0027] Figure 3 is the performance of different channel estimation algorithms in multipath Doppler channels.

[0028] Figure 4 This is a time-consuming comparison of different channel estimation algorithms. DETAILED DESCRIPTION

[0029] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0030] An embodiment of the present invention proposes a compressed sensing channel estimation algorithm suitable for embedded systems. The algorithm is based on compressed sensing and improves the OMP algorithm (orthogonal matching pursuit algorithm). Subsequently, EmOMP (improved OMP algorithm) represents the compressed sensing channel estimation algorithm suitable for embedded systems proposed by the present invention.

[0031] The algorithm of the embodiment of the present invention is applicable to OFDM-based communication technology. In the process of implementing OFDM communication, it is necessary to model the channel estimation. Taking an OFDM system with K subcarriers as an example, its channel estimation model is:

[0032] y=XH+W (1)

[0033] Where y represents the OFDM frequency domain signal, H and W are the frequency domain channel response and noise vector respectively, and X represents the data transmission matrix.

[0034] Through fast Fourier transform (FFT), equation (1) can be rewritten as:

[0035] y=XFh+W (2)

[0036] Where h is the corresponding time domain channel response, and F represents the Fourier transform matrix with dimension N×N.

[0037] Due to the severe attenuation of the underwater acoustic channel, only a few propagation paths can successfully reach the receiver. Therefore, h is usually regarded as a sparse matrix, in which only a small number of entries are non-zero, and the rest are almost close to zero. The data transmission matrix X = diag{x(0),…,x(N)}, where x(0) to x(N) represent the OFDM frequency domain difference points. In order to perform channel estimation, it is necessary to add pilot signals P to the data transmission matrix X. Let the pilot selection matrix be P:

[0038]

[0039] In formula (3), the position where the pilot is added is 1, and the other 0 parts are used to transmit data;

[0040] Then the received pilot is:

[0041] y p =X p F p h+W p =PXP T PFh+PW (4)

[0042] Among them, X p 、F p 、W p X, F, and W represent the pilot positions respectively, that is, except for h which is an unknown quantity, all others are known quantities. h can be obtained through the channel estimation method, thereby completing the estimation of the channel.

[0043] Figure 1 This is a basic flow chart of the compressed sensing channel estimation algorithm according to an embodiment of the present invention. Figure 1 The algorithm of the embodiment of the present invention includes the following steps S1 to S6:

[0044] Step S1, perform parameter initialization: set the initial value of the residual vector r0 = y, initialize the index set Initialize support set Iteration count i=1.

[0045] Step S2: Calculate the inner product of the residual vector and the perception matrix to find the best matching vector. T PF; residual vector is r i Indicates that the residual vector at the time of initialization is recorded as r0, and the index j*=argmax|<r i-1 ,a j >|;where r i-1 It is a newly defined set used to store the index obtained from the previous iteration. The index is the maximum value of the residual; a j are all column vectors of the perception matrix.

[0046] Step S3: Update the index set to γ i =γ i-1 ∪j*, update the support set to Ψ i =Ψ i-1 ∪a j* ;a j* is the column vector corresponding to j*.

[0047] Step S4: Estimate the channel response using the least squares method. In this step, the pilot insertion is first optimized to transform the compressed sensing perception matrix into a diagonal matrix. Then, the properties of the diagonal matrix are used to simplify the least squares method in the OMP. The property that the sum of the squares of the column vector elements of the Fourier transform matrix is ​​a constant is used to avoid the complex inversion process in the least squares method and simplify the least squares solution process. Finally, the simplified least squares method is used to estimate the time domain channel response.

[0048] In the embodiment of the present invention, a pilot insertion method of P=diag(x(0), x(1), …, x(n)) is selected, which also makes the perception matrix of compressed sensing become a diagonal matrix, that is:

[0049]

[0050] Among them, x(N) is the data corresponding to frequency N, and w is a sine wave.

[0051] By simplifying the least squares method with the diagonal matrix A, the parameters of the least squares method of the OMP algorithm are Ψ i is the support set of the i-th iteration, by selecting the sequence number γ in A ik The elemental composition of γ ik is the corresponding column vector of A; that is:

[0052]

[0053] Among them, A γ Represents the selection of sequence number γ in A ik The set consists of elements, k represents the sparsity.

[0054] The solution process is simplified by using the property that the sum of squares of the column vector elements of the Fourier transform matrix is ​​a constant. Since each column vector of the Fourier transform matrix is ​​composed of bases of different frequencies, the bases of the Fourier transform are orthogonal, so The simplified least squares method is:

[0055]

[0056] in, represents the channel response estimated at the i-th iterative step, h p represents the time domain channel response corresponding to the pilot, A p Represents the observation matrix corresponding to the pilot.

[0057] Step S5: Update the residual vector using the estimated channel response

[0058] Step S6: Update the loop number i. If the preset stop condition is met, for example, if i≥K, stop the loop and output the current latest channel response; otherwise, return to step S2 with the current latest residual vector to continue execution.

[0059] Among greedy algorithms, the SAMP algorithm does not require setting the channel sparsity (K) and is more robust and stable. However, its strict stopping condition leads to uncertain running time, making it unsuitable for communication systems with high real-time requirements. The CoSaMP algorithm is more stable than OMP and has improved accuracy, but the number of atoms selected in each iteration is 2*K times that of the OMP algorithm, which requires higher computing resources.

[0060] Figure 2 This is a comparison diagram of the real channel response and the channel response estimated by the present invention. It compares the real channel response and the channel response estimated by the EmOMP of the present invention, and illustrates that the improved OMP of the present invention is very accurate in estimating the channel. Figure 3 The figure shows the performance of different channel estimation algorithms in a multipath Doppler channel. This figure shows simulation results for a scenario with a relative velocity of 1.75 m / s and strong multipath. It shows that the improved OMP (EmOMP), OMP, and CoSaMP algorithms perform similarly. In the presence of strong noise, the improved OMP algorithm achieves significantly better estimation accuracy than the LS algorithm. Figure 4This figure compares the runtime of different channel estimation algorithms, analyzed using MATLAB software. The improved OMP algorithm demonstrates a significant speed advantage over other algorithms. Field measurements show that the improved OMP algorithm reduces computational effort by 30.5% compared to the traditional OMP algorithm, 66.3% compared to CoSaMP, and 683.3 times compared to SAMP.

[0061] Another embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, can implement the steps of the compressed sensing channel estimation algorithm applicable to embedded systems in the aforementioned embodiment. Based on this understanding, the technical solution of the present invention can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, USB flash drive, mobile hard disk, etc.), including a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of the present application.

[0062] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. Those skilled in the art will recognize that several equivalent substitutions or obvious variations can be made without departing from the scope of the present invention, and that any equivalent performance or application should be considered to fall within the scope of protection of the present invention.

Claims

1. A compressed sensing channel estimation algorithm suitable for embedded systems, characterized in that: The steps include: S1, initialize the residual vector, index set and support set; S2. Calculate the inner product of the residual vector and the perception matrix to find the best matching vector; S3, update the index set and support set; S4, estimating the channel response by the least squares method; S5, update the residual vector; S6. Determine whether a preset iteration stop condition is reached; If it is reached, the iteration stops and the latest channel response is output; If not reached, return to step S2 and continue iteration with the current latest residual vector; Step S4 includes: S41, optimizing the pilot insertion so that the perception matrix of the compressed sensing becomes a diagonal matrix; S42. By using the properties of diagonal matrices, we can avoid inversion operations and simplify the least squares method. S43. Use the property that the sum of squares of the elements of the column vector of the Fourier transform matrix is ​​a constant to simplify the least squares method, and calculate the predicted channel response through the least squares method.

2. The compressed sensing channel estimation algorithm according to claim 1, wherein: Step S1 includes: initializing the residual vector r0=y, index set Support set Iteration count i=1; y represents an OFDM frequency domain signal.

3. The compressed sensing channel estimation algorithm according to claim 2, wherein: Searching for the best matching vector in step S2 includes: Find index j*=argmax|<r i-1 ,a j >|;where r i-1 It is a newly defined collection used to store the index obtained from the previous iteration; a j are all column vectors of the perception matrix.

4. The compressed sensing channel estimation algorithm according to claim 3, wherein: Step S3 includes: updating the index set to γ i =γ i-1 ∪j*, update the support set to Ψ i =Ψ i-1 ∪a j* ;a j* is the column vector corresponding to j*.

5. The compressed sensing channel estimation algorithm according to claim 1, wherein: Step S41 includes: Insert pilot P = diag(x(0), x(1), ..., x(n)), and the sensing matrix A is a diagonal matrix: Wherein, N is the number corresponding to each OFDM subcarrier frequency, x(N) is the data corresponding to the N frequency, and w is a sine wave.

6. The compressed sensing channel estimation algorithm according to claim 5, wherein: Step S42 includes: By simplifying the least squares method with the diagonal matrix A, the parameters of the least squares method of the orthogonal matching pursuit algorithm are Ψ i is the support set of the i-th iteration, by selecting the sequence number γ in A ik The elemental composition of γ ik is the corresponding column vector of A; that is Among them, A γ Represents the selection of sequence number γ in A ik The set consists of elements, k represents the sparsity.

7. The compressed sensing channel estimation algorithm according to claim 6, wherein: Step S43 includes: Since each column vector of the Fourier transform matrix is ​​composed of bases of different frequencies, the bases of the Fourier transform are orthogonal, so The simplified least squares method is: in, represents the channel response estimated by the iterative step i, y represents the OFDM frequency domain signal, h p represents the time domain channel response corresponding to the pilot, A p Represents the observation matrix corresponding to the pilot.

8. The compressed sensing channel estimation algorithm according to claim 7, wherein: Step S5 includes: using the estimated channel response to update the residual vector 9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it can implement the steps of the compressed sensing channel estimation algorithm according to any one of claims 1 to 8.

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