CoSaMP sparse channel estimation design method based on OFDM system

Abstract

The invention belongs to the technical field of communication, and relates to a CoSaMP sparse channel estimation design method based on an OFDM system. According to the method, a secondary selection strategy is adopted, an atom selection mode of firstly expanding and then deleting is selected for a support set of atoms, unreliable atoms are selected into a candidate set during each iteration, and then the unreliable atoms can be deleted, so that the reconstruction efficiency of the algorithm is improved. A simulation result verifies the effectiveness of the algorithm, the non-zero position and the amplitude of the channel can be accurately estimated, and compared with other traditional algorithms and greedy algorithms, the MSE performance is better.

Description

Technical Field

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

[0002] Orthogonal frequency division multiplexing (OFDM) has high data transmission rate, spectrum utilization and good resistance to multipath fading. In recent years, OFDM communication systems have been widely used in channel estimation problems in wireless communications. The high mobility OFDM system channels encountered in practice often show sparse structural characteristics, and the traditional LS and MMSE algorithms cannot utilize the sparse characteristics of the channel. Therefore, in order to achieve a specific estimation accuracy, a large number of training symbols are required, which reduces the spectrum utilization efficiency. According to current research, compared with traditional estimation algorithms, algorithms that use compressed sensing technology for channel estimation can use fewer pilots to obtain higher channel estimation accuracy, thereby effectively improving spectrum utilization efficiency. Therefore, it is of great significance to study more efficient compressed sensing-based channel estimation algorithms.

[0003] Greedy reconstruction algorithms are widely used in wireless communication systems because of their simple implementation and fast operation. The main idea of ​​the greedy algorithm is to continuously obtain the approximation of the signal through iteration. In each iteration, the greedy algorithm has two basic steps: atom selection and parameter update. The atom selection step means selecting a suitable column vector in the measurement matrix for the reconstruction of the original signal, and the parameter update means obtaining the approximation of the signal in the current iteration through the approximation method. In general, the greedy algorithm continuously iterates to obtain the global optimal solution by selecting the local optimal solution. Therefore, the CoSaMP algorithm for sparse channel estimation of OFDM system based on compressed sensing theory is studied. Summary of the invention

[0004] The purpose of the present invention is to improve the atom selection strategy in the greedy algorithm. The atom support set is selected by first expanding and then deleting the atom selection method. Unreliable atoms are selected into the candidate set in each iteration and can be deleted later, thereby improving the reconstruction efficiency of the algorithm.

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

[0006] First, consider an OFDM system where the channel impulse response from the base station's transmitting antenna to a single user is h = [h(1), h(2), ..., h(L)] T , where L is the length of the channel impulse response, the number of subcarriers is N, the number of pilots is P, and they are located at subcarriers q1, q2, ...q p superior, is the orthogonal pilot sequence of the transmitting antenna, so the frequency domain signal of the receiving antenna is:

[0007] y=diag(x)F L h+n (1)

[0008] In the formula, F L is the P×L partial fast Fourier transform matrix derived from the N-point discrete Fourier transform matrix, and n is the additive white Gaussian noise (AWGN). (1) can be written in matrix form as:

[0009] y=Ah+n (2)

[0010] Because the elements of y, A, h, and n in the above formula are all complex numbers, this design method introduces virtual-real conversion and real-virtual conversion, so that the signal can be more accurate in each iteration. The real and imaginary values ​​of y, A, h, and n are extracted as follows:

[0011]

[0012] Combining the real and imaginary parts, we get the real number problem model:

[0013]

[0014] where y (r) , A (r) 、h (r) 、n (r) Corresponding to the real part values ​​of y, A, h and n respectively, y (i) , A (i) 、h (i) 、n (i) Corresponding to the imaginary values ​​of y, A, h and n respectively; let The real number representation of the channel estimation problem is as follows:

[0015]

[0016] The channel estimation problem in the OFDM system can be transformed into the solution of the minimum l0 norm problem, which is expressed as follows:

[0017]

[0018] Step 2: Input measurement matrix Sensor Matrix Signal sparsity K;

[0019] 3. Initialization: Iteration number t = 1, support set Residual vector Pre-select atoms and calculate inner product vectors Select the largest 2K elements from the inner product vector and put their subscripts into set J;

[0020] The 4th and tth support sets C t =C t-1 ∪J, Indicated in Take out the set C t The elements in are all column vectors of column labels, and the sub-column matrix selected for the tth time where a j express The jth column in ;

[0021] 5. Calculation Least squares solution

[0022] 6. Second selection is from Select K columns from Select the K items with the largest absolute value and denote them as and place it in The corresponding columns are selected to form The corresponding The column numbers in the set C tk , and update the current candidate set C t =C tk ;

[0023] 7. Update residual

[0024] 8. Determine whether the loop ends when t≤K or the residual r t If the value is less than the threshold, return to step 3, otherwise proceed to the next step;

[0025] 9. The estimated channel matrix is:

[0026] 10. Estimated value Convert to imaginary form to get the final estimate As shown in formula (7):

[0027]

[0028] The present invention has the following beneficial effects:

[0029] 1. The present invention provides for the first time a design method for CoSaMP sparse channel estimation based on OFDM system.

[0030] 2. The present invention adopts a secondary selection strategy to eliminate the atoms that are retained but not used in the support set, thereby releasing certain system space resources and improving the reconstruction efficiency of the algorithm.

[0031] 3. The simulation part proves the effectiveness of the algorithm and it has good estimation performance compared with other algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of the algorithm of the present invention;

[0033] Figure 2 is a channel estimation amplitude diagram of the CoSaMP algorithm of the present invention;

[0034] Figure 3 This is a comparison chart of the MSE of sparse channel estimation in OFDM system using CoSaMP algorithm and other algorithms. DETAILED DESCRIPTION

[0035] The specific steps of the design method of CoSaMP sparse channel estimation based on OFDM system provided by the present invention are as follows:

[0036] First, the signal in the OFDM system is converted from virtual to real and from real to virtual to obtain a real number problem model. The channel estimation problem in the system can be converted into the solution of the minimum l0 norm problem.

[0037] Second, we build the CoSaMP algorithm, introduce the backtracking idea, and remove some unnecessary atoms in subsequent iterations;

[0038] Third, use the CoSaMP algorithm to find the non-sparse position and amplitude and estimate the resulting channel matrix;

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

[0040] Design requirements: This part uses pycharm software to implement the design of CoSaMP sparse channel estimation based on OFDM system. The number of subcarriers of OFDM symbol is 512, the number of pilot symbols is 64, and the optimal pilot position inserted on the subcarrier is [5, 10, 13, 22, 29, 48, 57, 68, 86, 89, 100, 103, 122, 126, 130, 141, 150, 154, 162, 165, 169, 175, 178, 181, 185, 189, 209, 214, 2 477,479,488,500]. Assume that the channel follows a Bernoulli Gaussian distribution, the length of the channel impulse response is 200, and the channel sparsity is 14.

[0041] Step 1: Apply virtual-to-real conversion and real-to-virtual conversion to obtain the real number problem model of the signal vector in the OFDM system. The channel estimation problem in the system can be transformed into the solution of the minimum l0 norm problem:

[0042]

[0043] Step 2: Construct the CoSaMP algorithm. Given the signal sparsity K, in each iteration, the signal selects the 2K most matching atoms from the over-complete dictionary set to expand the support set, constructs a sparse approximation to obtain the current sparse estimate, and then selects the K items with the largest absolute value from the current sparse estimate. The remaining atoms are eliminated, the support set is updated, and the vertical component of the signal after decomposition is sent as the residual to the next iteration. When the number of iterations reaches the signal sparsity K or the residual is less than the specified threshold, the iteration is stopped.

[0044] Step 3: Use the CoSaMP algorithm to find the non-sparse position and amplitude and estimate the resulting channel matrix

[0045] The estimated amplitude diagram of the non-zero position obtained is as follows Figure 2 As shown, in order to reflect the availability of the CoSaMP algorithm, a sparse signal of size 200 is generated, and the algorithm of the present invention is used for reconstruction simulation. It can be seen from the figure that the algorithm can accurately reconstruct the sparse signal of length 200, and accurately estimate the non-zero position of the channel and the signal amplitude. In order to further objectively evaluate the performance of the CoSaMP sparse channel estimation algorithm based on the OFDM system, this paper evaluates the channel estimation performance of the CoSaMP algorithm through the relationship curve between the mean square error MSE and the signal-to-noise ratio SNR. It is reflected in the curve that the mean square error decreases with the increase of the signal-to-noise ratio. Compared with the LS and OMP algorithms, the algorithm of the present invention shows better estimation performance. Overall, the mean square error of the CoSaMP algorithm is lower than that of the OMP algorithm at the same signal-to-noise ratio, and the difference between the two in the low signal-to-noise ratio area is greater than that in the high signal-to-noise ratio area. It can be seen from the figure that the use of the secondary selection strategy improves the estimation accuracy.

Claims

1. A design method for CoSaMP sparse channel estimation based on OFDM system, characterized in that In order to eliminate the atoms that are retained but not used in the support set, release certain system space resources, and improve the reconstruction efficiency of the algorithm, the method is carried out according to the following steps: First, consider an OFDM system where the channel impulse response from the base station's transmitting antenna to a single user is h = [h(1), h(2), ..., h(L)] T , where L is the length of the channel impulse response, the number of subcarriers is N, the number of pilots is P, and they are located at subcarriers q1, q2, ...q p superior, is the orthogonal pilot sequence of the transmitting antenna, so the frequency domain signal of the receiving antenna is: y=diag(x)F L h+n (1) In the formula, F L is the P×L partial fast Fourier transform matrix derived from the N-point discrete Fourier transform matrix, and n is the additive white Gaussian noise (AWGN). (1) can be written in matrix form as: y=Ah+n (2) Because the elements of y, A, h, and n in the above formula are all complex numbers, this design method introduces virtual-real conversion and real-virtual conversion, so that the signal can be more accurate in each iteration. The real and imaginary values ​​of y, A, h, and n are extracted as follows: Combining the real and imaginary parts, we get the real number problem model: where y (r) , A (r) 、h (r) 、n (r) Corresponding to the real part values ​​of y, A, h and n respectively, y (i) , A (i) 、h (i) 、n (i) Corresponding to the imaginary values ​​of y, A, h and n respectively; let The real number representation of the channel estimation problem is as follows: The channel estimation problem in the OFDM system can be transformed into the solution of the minimum l0 norm problem, which is expressed as follows: Step 2: Input measurement matrix Sensor Matrix Signal sparsity K; 3. Initialization: Iteration number t = 1, support set Residual vector Pre-select atoms and calculate inner product vectors Select the largest 2K elements from the inner product vector and put their subscripts into set J; The 4th and tth support sets C t =C t-1 ∪J, Indicated in Take out the set C t The elements in are all column vectors of column labels, and the sub-column matrix selected for the tth time where a j express The jth column in ; 5. Calculation Least squares solution 6. Second selection is from Select K columns from Select the K items with the largest absolute value and denote them as and place it in The corresponding columns are selected to form The corresponding The column numbers in the set C tk , and update the current candidate set C t =C tk ; 7. Update residual 8. Determine whether the loop ends when t≤K or the residual r t If the value is less than the threshold, return to step 3, otherwise proceed to the next step; 9. The estimated channel matrix is:

10. Estimated value Convert to imaginary form and get the final estimate As shown in formula (7):

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