CN-116155658-B - Compressed sensing shallow sea underwater sound channel estimation method based on atomic threshold and backtracking

Abstract

The invention discloses a compressed sensing shallow sea underwater acoustic channel estimation method based on an atomic threshold and backtracking, and relates to the technical field of underwater communication. The method is based on gOMP algorithm, improves gOMP algorithm by setting reasonable atomic screening threshold, introducing backtracking thought and iteration stopping condition based on noise, and applies the improved gOMP algorithm to a compressed sensing channel estimation framework of an underwater acoustic orthogonal frequency division multiplexing system, and provides a gOMP channel estimation method based on the atomic threshold and backtracking.

Inventors

• LIU ZENGLI
• MENG XIYA
• ZHAO XUANZHI

Assignees

• 昆明理工大学

Dates

Publication Date

20260508

Application Date

20221114

Claims (3)

1. 1. A compressed sensing shallow sea underwater sound channel estimation method based on an atomic threshold and backtracking is characterized in that a reasonable atomic threshold is provided for fine screening of atoms based on gOMP algorithm in a compressed sensing channel estimation frame of an underwater sound orthogonal frequency division multiplexing system, and backtracking thought is introduced to eliminate misselected atoms contained in gOMP algorithm; The method specifically comprises the following steps: s0, initializing, and making , , ; Wherein, subscript' "Means an initial value before an iteration, The residual vector is represented as such, The representation matrix is a complex matrix and has a size of , Representation of Is used for the initial value of (a), Indicating the number of pilot sub-carriers, Representing the received signal, i.e. the measurement vector, Representing the set of supports, Representation of Is provided with a set of initial support sets, Representing an empty set; S1, calculating an inner product and taking an absolute value: ; Wherein, the Is a matrix Is the first of (2) The number of columns in a row, The sensing matrix is represented by a matrix of sensors, The matrix is represented as a complex matrix and has a size of , , Represent the first The residual vector of the next iteration, Representation of And (3) with The inner product is made and the vector after the absolute value is taken, The matrix is represented as a real matrix and has a size of , Represent the first Inner product vector of multiple iterations " "Representing the operation of inner product" "Means taking absolute value operation; S2, selecting atoms The largest front of (3) A value of this, this is The value corresponds to Column number of (2) Form a collection ; Wherein, the The number is selected for the atoms and, Is that Maximum of (3) The value corresponds to Is used for the sequence numbers of the columns, For column number The set of the components is formed, Is the first A set of column numbers in the multiple iterations; S3, calculating the atomic threshold value ; S4, carrying out secondary screening on atoms; S5, expanding a supporting set; S6, estimating a channel through least square operation; S7, backtracking when At the time, from Selecting the one with the largest absolute value Column numbers corresponding to the items are recorded as a set Updating a support set And update through support set And Otherwise, directly entering into step S8; s8, updating residual errors: ; s9, judging when the condition is satisfied Or (b) If not, go to step S10, otherwise, let And returns to step S1; s10, outputting the final estimated sparse channel impulse response ; The S3 calculates an atomic threshold value : ; Wherein, the And Respectively the first Inner product vector in multiple iterations Is provided with a first and a second maximum value of (c), Representing the parameters of the compromise factors, and taking the value of [0.2, 0.4]; and S4, carrying out secondary screening on atoms: ; Wherein, the For corresponding to column number Is used to determine the inner product value of (c), Is that Corresponding inner product value Greater than atomic threshold A set of column sequence numbers at the time, Is the first Aggregation in multiple iterations ; The S5 capacity expansion support set comprises: , ; Wherein, the Represents the union, will be Support set for multiple iterations And the first Of multiple iterations Is combined into the first Support set for multiple iterations ; , And Representing the sensing matrices respectively Respectively corresponding to the collection , , A matrix of column vector combinations of (a); the S6 estimates the channel through least square operation: ; Namely: wherein the superscript is " "Conjugate transpose operation of matrix, superscript" "Means the inverse of the matrix, Representing the estimated channel impulse response.
2. 2. The compressed sensing shallow sea water acoustic channel estimation method based on the atomic threshold and backtracking according to claim 1, wherein the step S7 backtracking: When (when) At the time, from Selecting the one with the largest absolute value Column numbers corresponding to the items are recorded as a set Updating a support set And update through support set And Otherwise, directly entering into step S8; Wherein, the Representing the length of the vector.
3. 3. The method for estimating a shallow sea underwater sound channel based on atom threshold and backtracking as set forth in claim 1, wherein said S9 judgment is made when the condition is satisfied Or (b) If not, go to step S10, otherwise, let And returns to step S1; Wherein, the The representation is a function of taking a small value, The L2 norm of the vector is represented, Take the value of , Is the frequency domain noise at the pilot.

Description

Compressed sensing shallow sea underwater sound channel estimation method based on atomic threshold and backtracking Technical Field The invention relates to the technical field of underwater communication, in particular to a compressed sensing shallow sea underwater sound channel estimation method based on an atomic threshold and backtracking. Background As humans continue to develop and utilize the ocean, underwater communication technologies are also continually improving. Underwater acoustic communication is the only way for high-speed and high-reliability data transmission under water, and is widely applied to the fields of scientific research, military, business and the like, such as submarine data collection, national security defense, offshore oil remote control and the like. The underwater acoustic channel is considered as the most complex channel, wherein the shallow sea underwater acoustic channel is greatly affected by boundary conditions (sea surface and sea bottom) and sea water temperature distribution, so that the shallow sea channel environment is more complex, and is a typical multipath propagation channel with a large time delay. On the premise of realizing underwater acoustic communication in a complex shallow sea environment, accurate Channel State Information (CSI) is obtained through channel estimation, and the channel estimation is also a key of adaptive modulation of a transmitting end, a channel equalization technology and receiver design, and is more an important index for measuring the performance of an underwater communication system and a basis for high-quality recovery of signals. The OFDM system adopts a multi-carrier modulation mode to improve the frequency spectrum utilization rate and the capacity of resisting multipath interference, so that the OFDM system is widely applied to underwater acoustic communication, but due to the time-varying and high-noise characteristics of an underwater channel, a large number of subcarriers are required to transmit pilot frequency information by a traditional Least Square (LS) method, a minimum mean Square error (Minimum Mean Square Error, MMSE) method and other channel estimation methods to ensure the accuracy of channel estimation, spectral resources are seriously occupied, the influence of a frequency domain selective fading channel caused by multipath cannot be effectively eliminated by an interpolation type channel estimation method, the channel frequency domain response at a data position cannot be accurately estimated, and the estimation performance is poor. The underwater sound channel is a sparse channel with a large number of zero taps in time domain response, and the compressed sensing algorithm can fully utilize the sparsity of the channel and obtain a better channel estimation effect by using fewer pilot frequencies. The essence of compressed sensing algorithms for sparse signal reconstruction is the L0 norm optimization problem, which is the non-convex optimization problem of NP-hard. The Basic Pursuit (BP) algorithm and the minimum absolute shrinkage selection operator (LeastAbsolute SHRINKAGE AND Selection Operator, LASSO) replace the L0 norm with the L1 norm, converting the above problem into a convex optimization problem that is easy to solve. The two algorithms improve the estimation accuracy, but the calculation complexity is higher, and the noise influence is not fully considered. The base tracking denoising (Basis Pursuit Denoising, BPDN) algorithm is an improvement of the BP algorithm under the noisy condition, and the original signal is reconstructed by solving the disturbance linear programming problem, but the complexity of the algorithm is greatly influenced by the multipath time delay of a channel, and the complex and changeable underwater sound channel cannot be effectively estimated in time due to overlong running time. The greedy iterative algorithm has high estimation precision, high operation speed, simple hardware implementation and robustness to noise, and is widely applied to underwater acoustic channel estimation. The matching pursuit (Matching Pursuits, MP) algorithm is the earliest proposed classical greedy algorithm that approximates the original signal by multiple iterations, and does not yield an optimal solution every cycle if the residuals are non-orthogonal after vertical projection of the selected atoms. The improved orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm based on the MP algorithm ensures orthogonality between the residual and the selected atoms, and improves estimation accuracy and convergence speed by avoiding repeated selection of the same atoms. In the prior art, some algorithms based on OMP improvement are proposed successively, and a compressed sampling matching Pursuit algorithm (Compressive SAMPLING MATCHING burst, coSaMP) and a regularized orthogonal matching Pursuit algorithm (Regularized Orthogonal Matching Pursuit, ROMP) select a plurality of atoms