Design method for SP sparse channel estimation based on OFDM system

Abstract

The invention discloses a design method for SP sparse channel estimation based on a single-transmitting and single-receiving OFDM (Orthogonal Frequency Division Multiplexing) system. According to the method, selected atoms are re-judged by using a backtracking thought, wrong atoms are deleted, a certain number of support set atoms is kept until iteration is finished, and meanwhile, accurate reconstruction of an original signal is realized by using reconstruction accuracy similar to that of a linear programming optimization method. A simulation experiment verifies that the algorithm has good channel estimation precision, and the position of the channel can be well estimated.

Description

Technical Field

[0001] The invention belongs to the technical field of digital signal processing and provides a design method for SP sparse channel estimation based on an OFDM system. Background Art

[0002] In OFDM systems, due to the orthogonal separation between subcarriers, it can effectively suppress the multipath effect and enhance the signal's anti-interference ability. However, due to the complexity of wireless channels and the existence of noise, the received signals are often subject to various interferences and distortions, which affects the performance and reliability of the system. In order to solve this problem, channel estimation is required, that is, to infer the channel conditions through the received data and compensate and correct the received signals accordingly. Among them, sparse channel estimation technology has attracted widespread attention due to its advantages such as high accuracy and low complexity.

[0003] The SP algorithm is a channel estimation method based on sparse representation and is widely used in OFDM systems. The algorithm uses a dictionary learning method to transform the frequency selective channel into a sparse channel in the time domain, and estimates the sparse channel through iterative approximation. At the same time, the algorithm can also control the balance between estimation accuracy and algorithm complexity by setting a threshold. The sparse channel estimation method based on the SP algorithm can not only improve the anti-interference ability and fault tolerance of the OFDM system, but also reduce the complexity and cost of the system and improve the performance and reliability of the system. Therefore, by utilizing the sparsity of the wireless channel, the compressed sensing technology is introduced into the channel estimation, and the SP algorithm for sparse channel estimation of the OFDM system based on the compressed sensing theory is studied. Summary of the invention

[0004] The purpose of the present invention is to obtain accurate received signals at the receiving end, which requires accurate channel state information. A channel design method introducing the backtracking idea is provided, which is a method for SP sparse channel estimation based on OFDM system.

[0005] The specific steps of the design method for SP sparse channel estimation based on OFDM system provided by the present invention are as follows:

[0006] First, the sparse channel estimation problem in OFDM system can be expressed as:

[0007]

[0008] In the formula, is the received signal vector of P×1 dimension, is a P×L dimensional measurement matrix. In most cases, P<L. is the L×1-dimensional channel vector to be estimated, is a noise signal vector of P×1 dimension; The elements of are all complex numbers, Expressed in real number form:

[0009]

[0010] extract The real and imaginary values ​​of the real number are expressed as:

[0011]

[0012] In the formula, Corresponding to The real part of Corresponding to The imaginary part of The real form of the channel estimation problem is expressed as:

[0013]

[0014] Second, input vector y, measurement matrix A, sparsity K;

[0015] 3. Initialization, residual r0 = y, index set Atomic Set Iteration number t = 1;

[0016] 4. Calculate u=|A T r0|=|<A,r0> |, that is, calculate:

[0017] u= <r0,A l >, 1≤l≤N (5)

[0018] Select the K largest values ​​in u and form a set S with the corresponding column numbers l in matrix A. t (column number set), that is, Λ t =Λ t-1 ∪S t ;

[0019] No. 5. Solution The least squares solution of is:

[0020]

[0021] No. 6. From Select the 2K items with the largest absolute value and record them as The corresponding 2K term in the atomic set is denoted as A tK , the corresponding index sequence number is Λ tK , update the set Λ t =Λ tK ;

[0022] 7. Update residual

[0023] 8. t=t+1, if ||r t ||2≥||r t-1 ||, then Λ t =Λ t-1 , stop the iteration, otherwise return to step 3;

[0024] 9. Reconstruct the signal In Λ t The value at the last iteration is The rest of the elements are 0;

[0025] 10. Estimated value Convert to imaginary form to get the final channel estimate Right now:

[0026]

[0027] The present invention has the following beneficial effects:

[0028] 1. The present invention provides for the first time a design method for SP sparse channel estimation based on OFDM system.

[0029] 2. The present invention utilizes the backtracking idea of ​​the SP algorithm and has a reconstruction accuracy similar to that of the linear programming optimization method to achieve accurate reconstruction of the original signal.

[0030] 3. Simulation experiments have verified that our method has good channel estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of the flow chart of the algorithm of the present invention;

[0032] Figure 2 This is a comparison chart of the mean square error (MSE) of sparse channel estimation for OFDM systems using the SP algorithm and other algorithms;

[0033] Figure 3 This is a comparison chart of the recovery channel accuracy of the SP algorithm and other algorithms for OFDM system sparse channel estimation;

[0034] Figure 4 This is a comparison chart of the recovered channel error rate between the SP algorithm and other algorithms for sparse channel estimation in OFDM systems. DETAILED DESCRIPTION

[0035] First, according to the design requirements, the channel estimation problem in the single-receive and single-transmit OFDM system is transformed into a sparse channel reconstruction problem, which can be expressed as:

[0036]

[0037] Given a measurement matrix A, a sparse signal h, and a Gaussian white noise vector n, an estimate of the channel vector h is obtained from the known vector y and the measurement matrix A by solving the underdetermined equation.

[0038] Second, in each iteration, the backtracking idea is used to judge the existing atoms and remove the wrong atoms, so as to maintain a certain number of support set atoms until the iteration ends.

[0039] In order to verify the effectiveness of the channel estimation design method, computer simulation is carried out.

[0040] Design requirements: This part uses pycharm to implement the design of SP sparse channel estimation based on OFDM system, and simulates and calculates the mean square error MSE of several channel estimation algorithms as the signal-to-noise ratio SNR changes, the accuracy and error rate performance, as follows Figure 2 , 3 As shown in 4, the simulation is based on a single-handed single-transmit OFDM system, and the system parameters are set as follows: transmitting antenna N T =1, receiving antenna N R =1, number of subcarriers N = 512, channel length L = 100, number of pilots P = 64, and number of non-zeros K = 10. After simulation calculation, Figure 2 It can be seen that compared with several other types of algorithms, the SP algorithm has better channel estimation performance, can improve the anti-interference ability of the OFDM system, and reduce the complexity of the system.

Claims

1. A design method for SP sparse channel estimation based on OFDM system, characterized in that The SP algorithm adopts the backtracking idea and has a reconstruction accuracy similar to that of the linear programming optimization method, which can achieve accurate reconstruction of the original signal. The method is carried out in the following steps: First, the sparse channel estimation problem in OFDM system can be expressed as: In the formula, is the received signal vector of P×1 dimension, is a P×L dimensional measurement matrix. In most cases, P<L. is the L×1-dimensional channel vector to be estimated, is a noise signal vector of P×1 dimension; The elements of are all complex numbers, Expressed in real number form: extract The real and imaginary values ​​of the real number are expressed as: In the formula, Corresponding to The real part of Corresponding to The imaginary part of The real form of the channel estimation problem is expressed as: Second, input vector y, measurement matrix A, sparsity K; 3. Initialization, residual r0 = y, index set Atomic Set Iteration number t = 1; 4. Calculate u=|A T r0|=|<A,r0> |, that is, calculate: in= <r0,A l >,1≤l≤N (5) Select the K largest values ​​in u and form a set S with the corresponding column numbers l in matrix A. t (column number set), that is, Λ t =Λ t-1 ∪S t ; No.

5. Solution The least squares solution of is: No.

6. From Select the 2K items with the largest absolute value and record them as The corresponding 2K term in the atomic set is denoted as A tK , the corresponding index sequence number is Λ tK , update the set Λ t =Λ tK ; 7. Update residual 8. t=t+1, if ||r t ||2≥||r t-1 ||, then Λ t =Λ t-1 , stop the iteration, otherwise return to step 3; 9. Reconstruct the signal In Λ t The value at the last iteration is The rest of the elements are 0; 10. Estimated value Convert to imaginary form to get the final channel estimate Right now:

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