CN114337743B - An improved channel estimation method for SAMP massive MIMO-OFDM system - Google Patents

Abstract

An improved SAMP large-scale MIMO‑OFDM system channel estimation method, which includes the following steps: signal initialization; calculating the absolute value of the inner product of the sensing matrix A and the residual; regularization processing, optimizing the atom set; solving the least squares Solution, update the residual; compare the residual with the double threshold; reconstruct the signal and apply it to large-scale MIMO‑OFDM systems. Compared with the SAMP algorithm, this method significantly reduces the bit error rate and mean square error, which greatly improves the channel estimation performance when the channel sparsity is unknown.

Description

An improved channel estimation method for SAMP massive MIMO-OFDM system

Technical field

The present invention relates to the field of wireless communication technology, and specifically relates to an improved SAMP large-scale MIMO-OFDM system channel estimation method.

Background technique

OFDM technology, due to the advent of the fast Fourier transform method, has reduced the complex calculation amount of OFDM in spectrum orthogonality and promoted the development of OFDM technology. Nowadays, OFDM technology can be widely developed in different communication fields. This is Because OFDM has the advantages of anti-interference ability and improved system capacity. In 2010, the theory of massive MIMO was proposed to expand the scale of base station antennas to hundreds or more to improve spectrum efficiency and achieve better robustness.

The advantage of combining massive MIMO-OFDM technology is that by dividing more orthogonal subcarriers on the broadband spectrum, OFDM effectively improves the anti-interference capability of the massive MIMO system and reduces the technical difficulty of the signal receiving end; and large Scaled MIMO improves the propagation rate of OFDM through the expansion of antenna scale, and the two major technologies make up for their respective shortcomings. Massive MIMO-OFDM systems have technical advantages, but there are some practical factors in obtaining CSI. In an actual communication environment, compared with the transmitted signal, the received signal is affected by the channel environment, resulting in fading and delay. In order to effectively resist interference, the accuracy of obtaining the channel state must be improved.

In massive MIMO-OFDM channels, the number of multipaths is fixed, has a large delay spread and is sparse. Compressed sensing theory was proposed in 2006 and has been widely studied and expanded in the field of communication research.

Compressed sensing signal reconstruction methods include: convex optimization algorithm, greedy algorithm and combination algorithm. Since the computational complexity of the convex optimization algorithm is relatively high, it is difficult to implement in practical applications. The combination algorithm is not as computationally complex as the greedy algorithm, so the greedy algorithm is more widely used. In large-scale MIMO-OFDM systems, channel sparsity is often unknown. Among greedy algorithms, there is a class of algorithms with sparsity adaptive capabilities. Its biggest feature is that it does not require sparsity prior information. The most typical one is Sparse Adaptive Matching Pursuit (SAMP, Sparsity of Adaptive Matching Pursuit) algorithm. However, the step size of traditional SAMP is fixed, and system performance is often deteriorated due to overestimation in channel estimation. Secondly, the residual signal obtained by traditional SAMP is not highly correlated with the atomic set matrix. Therefore, SAMP needs to be improved to improve system performance.

Contents of the invention

In view of the above-mentioned defects in the existing technology, the present invention proposes an improved SAMP large-scale MIMO-OFDM system channel estimation method, setting double thresholds to change the step size, and setting the threshold T1. When the energy difference of the reconstructed signals in adjacent stages is close to the When the threshold is set, it means that the algorithm quickly approaches the reconstructed signal through a large step size; when the threshold T2 is set, when the energy difference of the signal is close to T2, it means that the algorithm gradually approaches the reconstructed signal through a small step size. In addition, regularization processing is proposed to filter the atomic matrix one more time, so that the final residual signal has a better correlation with the atomic set matrix and improves system performance.

An improved SAMP massive MIMO-OFDM system channel estimation method, including the following steps:

S1. Signal initialization, including initializing signal residuals and support sets and sizes, setting the initial step size and number of iterations;

S2. Calculate the absolute value of the inner product of the sensing matrix A and the residual to obtain a set of absolute values;

S3. Regularize the set obtained in S2, filter and optimize the atomic set, and obtain an updated set;

S4. Based on the set updated in S3, solve the least squares solution of the set and update the residual;

S5. Set a double threshold, and compare the residual after S4 updated with the double threshold; the double threshold includes threshold T1 and threshold T2; when the energy difference of the reconstructed signal in adjacent stages is close to the threshold T1, it means that the large step size is used to quickly approach Reconstruct the signal; when the energy difference of the signal is close to the threshold T2, it means that the reconstructed signal is gradually approached through a small step size; adjust the step size and support set size according to the structure of the comparison between the residual and the double threshold, and return to S2 for iteration;

S6. Complete the iteration, realize signal reconstruction, complete channel estimation, and apply it to large-scale MIMO-OFDM systems.

Further, signal initialization in S1 includes the following steps:

S11. Residual r ₀ =y;

S12, support set Size L = s, that is, the support set size is equal to the initial step size;

S13. Set the initial step size s;

S14. Set the number of iterations t.

Further, S2 calculates the absolute value of the inner product of the sensing matrix A and the residual, which specifically includes the following steps:

S21. Calculate the absolute value u=abs(A ^T r _t-1 ) of the inner product of the sensing matrix A and the residual;

S22. Select the L maximum values in u and correspond one-to-one to the column subscript j in A to form a set S _K .

Further, regularization processing in S3 and optimizing the atomic set specifically include the following steps:

S31. Regularization processing: optimize atoms in S _K , and the atoms are the selected L maximum values of u, so that they satisfy |u _i |≤2|u _j |;

S32. Update the set C _t =F _t-1 ∪S _K ,A _t =A _t-1 ∪{a _j }, where j∈S _K , a _j represents the j-th column of matrix A.

Further, in S4, the least squares solution is solved and the residual update includes the following steps:

S41, least squares solution

S42. Select the L item with the largest absolute value from h: The corresponding column L in A _t is denoted as A _TL , and the corresponding column L in F _t is denoted as F _tL ;

S43. Update residuals:

Further, the comparison of residuals and double thresholds in S5 includes the following steps:

S51. If T1 is satisfied: Execute step S52; otherwise execute step S53;

S52. If T2 is satisfied: Execute step S53; otherwise, change the step size s=s/2, increase the size of F to L+s, t=t+1, and return to step S2;

S53. If ||r _n || ₂ ≥||r _t-1 || ₂ is satisfied, then the step size s=s/2, C _t =C _t-1 , t=t+1, return to step S2; otherwise , enter step S54;

S54. If ||r _n || ₂ ≤10 ^-6 is satisfied, enter S6; otherwise, C _t =F _tL , r _t =r _n , t = t+1, the size of F increases to L+s, and return to S2.

Further, the application of reconstructed signals in S6 to large-scale MIMO-OFDM systems includes the following steps:

S61. Reconstruct the signal to be estimated There are non-zero items at F _tL , whose values are the last iteration/>

S62. Apply the improved SAMP method to large-scale MIMO-OFDM.

The beneficial effects achieved by the present invention are: an improved SAMP large-scale MIMO-OFDM system channel estimation method is proposed. Compared with the SAMP algorithm, the bit error rate and mean square error are greatly reduced, and the channel sparsity is unknown. channel estimation performance in the case of .

Description of drawings

Figure 1 is a schematic flow diagram of an improved SAMP in an embodiment of the present invention.

Figure 2 is a schematic diagram comparing bit error rates in an embodiment of the present invention.

FIG. 3 is a schematic diagram of the comparison of normalized mean square errors in the embodiment of the present invention.

Detailed ways

The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

The present invention discloses an improved SAMP large-scale MIMO-OFDM system channel estimation method. In the traditional SAMP algorithm, the step size is fixed. When the sparsity is small and the step size is too large, the SAMP method will suffer from too few iterations. As a result, the reconstruction accuracy is reduced; there is overestimation. Secondly, the residual signal obtained by traditional SAMP is not well correlated with the atomic set matrix, which will affect the output performance of the system. Therefore, the present invention proposes an improved SAMP method with double threshold regularization and uses it in large-scale MIMO-OFDM. Compared with traditional SAMP, the bit error rate and mean square error are greatly reduced, which greatly improves the performance in sparse channels. Performance of channel estimation when degree is unknown.

In a massive MIMO-ODM system, it is assumed that there are M antennas at the transmitting end and U single-antenna users at the receiving end. Express the channel impulse response between the mth transmitting antenna and a certain user in the kth OFDM symbol:

h _m,k =[h _m,k (0),h _m,k (1),...,h _m,k (L-1)] ^T

Among them, L is the total number of tap delay lines in the discrete-time channel model, and h _m,k (l) is the complex gain on the l-th tap. For sparse channels, vector h = [h(0), h(1),..., h(L-1)] ^T has only a few non-zero values. If the number of non-zero elements is K, it is called a vector h is K sparse. Consider that the number of subcarriers is N, and the mth transmitting antenna of the base station transmits a pilot signal of p _m . For a certain user, the receiving sequence can be expressed in the frequency domain as:

Among them, P = diag{p _m } is a diagonal matrix with p _m as its diagonal. The DFT matrix F is the NxN discrete Fourier transform matrix. F _L is the partial matrix of the first L columns of F. And F _L|Ω is some rows of F _L selected according to the pilot sequence position set Ω, and n is additive Gaussian white noise. The above equation can be further simplified as:

y＝Θh+n

Among them, Θ=[P ₁ F _L|Ω ,P ₂ F _L|Ω ,...,P _M F _L|Ω ] is a P×ML matrix is an equivalent channel impulse response vector of size M×1.

In the above formula, y and Θ are known signals to the signal receiving end. We need to estimate the vector h from the formula, and then estimate the channel frequency response H according to H = Wh. We can find that estimating h from the above formula is a typical sparse signal reconstruction problem, which can be completed using a CS-based reconstruction algorithm.

Compressed sensing theory mainly includes three parts: sparse representation of signals, design of observation matrix, and reconstruction algorithm.

Sparse representation of signal: If the length of signal h is N, it can be expressed as:

In the formula, c _i is the projection coefficient of the signal h on the basis vector Ψ. The signal x can be expressed in vector form: x=Ψc.

In the formula, Ψ=[Ψ ₁ , Ψ ₂ , Ψ ₃ , ..., Ψ _N ] is a matrix form in which Ψ _i is written as N×N. c is the representation of signal h in the Ψ domain. If the number K of non-zero elements in c is much smaller than the length N of the signal, that is, K << N, then the signal x is compressible or sparse in the Ψ domain, and the signal can be expressed as a K sparse signal.

Design of observation matrix: Compressed sensing theory shows that for a signal x of length N, if its coefficients under a certain basis matrix Ψ are K sparse, then M (M＜＜N) can be selected from the signal x through the observation matrix ) samples, ensuring that the signal x of length N or the coefficients under the basis matrix Ψ can be recovered from them. Usually, an M×N-dimensional observation matrix O that is not related to the base matrix Ψ is used to linearly transform the signal x, and M samples are obtained, which can be expressed by the following formula: y=Ox=OΨc=Ac.

Among them, y is an M×1 observation vector, which is a vector composed of M sample values, O is an M×N-dimensional observation matrix, and A=OΨ is an M×N-dimensional measurement matrix.

An improved SAMP massive MIMO-OFDM system channel estimation method, including the following steps:

S1. Signal initialization details are as follows:

S11. Residual r ₀ =y;

S12, support set Size L = s;

S13. Initial step size s=5;

S14. Number of iterations t=1.

S2 calculates the absolute value of the inner product of the sensing matrix A and the residual as follows:

S21. Calculate the absolute value u=abs(A ^T r _t-1 ) of the inner product of the sensing matrix A and the residual;

S22. Select the L maximum values in u and correspond one-to-one to the column subscript j in A to form a set S _K .

S3 regularization processing, optimizing the atomic collective includes the following steps:

S31. Regularization processing (improving the correlation between the residual signal and the atomic set matrix): further screen the atomic set in step 2, and optimize the atomic set in S _K to satisfy |u _i |≤2|u _j |;

S32. Update the set C _t =F _t-1 ∪S _K ,A _t =A _t-1 ∪{a _j }, where j∈S _K .

S4 solves the least squares solution and updates the residuals specifically including the following steps:

S41, least squares solution

S42. Select the L item with the largest absolute value from h: The corresponding column L in A _t is denoted as A _TL , and the corresponding column L in F _t is denoted as F _tL ;

S43. Update residuals:

The comparison of S5 residual and double threshold specifically includes the following steps:

S51. If condition 1T1 is met: (Indicating that the step size is not much different from the sparsity), execute step S52; otherwise, (indicating that the step size needs to be adjusted, a large step size quickly approaches the reconstructed target signal), execute step S53;

S52. If condition 2T2 is met: (Indicating that the estimation accuracy reaches the standard), execute step S53; otherwise (explaining overestimation, reducing the step size and gradually approaching), change the step size s=s/2, increase the size of F to L+s, t=t+1, and return Step S2;

S53. If ||r _n || ₂ ≥||r _t-1 || ₂ (explaining overestimation, reduce the step size), then the step size s=s/2, C _t =C _t-1 , t =t+1, return to step S2; otherwise, enter step S54;

S54. If ||r _n || ₂ ≤10 ^-6 (stop iteration threshold, which can also be understood as within the error range), enter S61; otherwise, C _t =F _tL ,r _t =r _n ,t=t+ 1. Increase the size of F to L+s and return to S2;

S6. Reconstructing the signal and applying it to the large-scale MIMO-OFDM system specifically includes the following steps:

S61. Reconstruction There are non-zero items at F _tL , whose values are the last iteration/>

S62. Apply the improved SAMP method to large-scale MIMO-OFDM. And compare the bit error rate and normalized mean square error with traditional SAMP.

In the massive MIMO-OFDM system, the multipath Rayleigh fading channel is used, the duplex mode FDD is used, the number of transmitting antennas is 128, the number of receiving antennas is 1, the number of subcarriers is 1024, and the number of pilots is 256. The initial step size is 5 in both SAMP and improved SAMP. The performance comparison is bit error rate and normalized mean square error, and the abscissas are signal-to-noise ratio. The formula is as follows:

Bit error rate:

Normalized mean square error:

The general flow chart of this method is shown in Figure 1. The comparison diagram of the bit error rate between this method and the traditional SAMP in the system is shown in Figure 2. The comparison diagram of the normalized mean square error between this method and the traditional SAMP in the system is shown in Figure 3. Show. Through the comparison between Figure 2 and Figure 3, this method is significantly better than the traditional SAMP method.

To sum up, the improved SAMP large-scale MIMO-OFDM system channel estimation method proposed by the present invention significantly reduces the bit error rate and mean square error compared with traditional SAMP, which greatly improves the channel sparsity. Performance of channel estimation in unknown situations.

In addition, the present invention also provides a brand-new idea for related research on channel estimation and provides a reference for other related issues in the same field. It can be used as a basis for expansion, extension and in-depth research, and has very broad application prospects. .

The above are only preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above-mentioned embodiments. Any equivalent modifications or changes made by those of ordinary skill in the art based on the disclosure of the present invention should be included. within the scope of protection stated in the claims.

Claims (6)

1. An improved SAMP massive MIMO-OFDM system channel estimation method, which is characterized by: including the following steps: S1. Signal initialization, including initializing signal residuals and support sets and sizes, setting the initial step size and number of iterations; S2. Calculate the absolute value of the inner product of the sensing matrix A and the residual to obtain a set of absolute values; S3. Regularize the set obtained in S2, filter and optimize the atomic set, and obtain an updated set; S4. Based on the set updated in S3, solve the least squares solution of the set and update the residual; S5. Set a double threshold, and compare the residual after S4 updated with the double threshold; the double threshold includes threshold T ₁ and threshold T ₂ ; when the energy difference of the reconstructed signal in adjacent stages is close to the threshold T ₁ , it means that the big step has been passed. The reconstructed signal is quickly approached for a long time; when the energy difference of the signal is close to the threshold T ₂ , it means that the reconstructed signal is gradually approximated through a small step size; the step size and support set size are adjusted according to the structure of comparing the size of the residual with the double threshold, and return to S2 for iteration ; The comparison of residuals and double thresholds in S5 includes the following steps: S51. If T ₁ is satisfied: Execute step S52; otherwise execute step S53;/> is the least squares solution; S52. If T ₂ is satisfied: Execute step S53; otherwise, change the step size s=s/2, increase the size of the support set F to L+s, t=t+1, and return to step S2; s is the initial step size, t is the number of iterations; S53. If ||r _n || ₂ ≥||r _t-1 || ₂ is satisfied, then the step size s=s/2, C _t =C _t-1 , t=t+1, return to step S2; otherwise , enter step S54; r _n is the residual, the set C _t = F _t-1 ∪S _K , S _K is the absolute value of the inner product of the sensing matrix A and the residual. The L maximum values in u correspond to A The set composed of column subscript j; S54. If ||r _n || ₂ ≤10 ^-6 is satisfied, enter S6; otherwise, C _t =F _tL , r _t =r _n , t = t+1, the size of F increases to L+s, and return to S2; Among them, from the least squares solution Select the maximum absolute value of L term, and the corresponding L column in F _t is recorded as F _tL ; S6. Complete the iteration, realize signal reconstruction, complete channel estimation, and apply it to large-scale MIMO-OFDM systems. 2. An improved SAMP massive MIMO-OFDM system channel estimation method according to claim 1, characterized in that: signal initialization in S1 includes the following steps: S11. Residual error r ₀ =y, where y is the M*1-dimensional observation vector; S12, support set Size L = s, that is, the support set size is equal to the initial step size; S13. Set the initial step size s; S14. Set the number of iterations t. 3. An improved SAMP massive MIMO-OFDM system channel estimation method according to claim 2, characterized in that S2 calculates the absolute value of the inner product of the sensing matrix A and the residual specifically includes the following steps: S21. Calculate the absolute value u=abs(A ^T r _t-1 ) of the inner product of the sensing matrix A and the residual; S22. Select the L maximum values in u and correspond one-to-one to the column subscript j in A to form a set S _K . 4. An improved SAMP massive MIMO-OFDM system channel estimation method according to claim 3, characterized in that the regularization processing in S3 and optimizing the atomic set specifically include the following steps: S31. Regularization processing: optimize atoms in S _K , and the atoms are the selected L maximum values of u, so that they satisfy |u _i |≤2|u _j |; S32. Update the set C _t =F _t-1 ∪S _K ,A _t =A _t-1 ∪{a _j }, where j∈S _K , a _j represents the j-th column of matrix A. 5. An improved SAMP massive MIMO-OFDM system channel estimation method according to claim 4, characterized in that, in S4, solving the least squares solution and updating the residual includes the following steps: S41, least squares solution S42. Select the L item with the largest absolute value from h: The corresponding column L in A _t is denoted as A _TL , and the corresponding column L in F _t is denoted as F _tL ; S43. Update residuals: 6. An improved SAMP massive MIMO-OFDM system channel estimation method according to claim 5, characterized in that, reconstructing the signal in S6 and applying it to the massive MIMO-OFDM system includes the following steps: S61. Reconstruction There are non-zero items at F _tL , whose values are the last iteration/> S62. Apply the improved SAMP method to large-scale MIMO-OFDM.