Channel estimation method based on compressed sensing and application thereof

Abstract

The invention belongs to the technical field of channel estimation, and particularly relates to a channel estimation method based on compressed sensing and application thereof, in particular to the aspect of sparse channel estimation in the field of short-wave single carrier communication, which comprises the following steps: step 1, a receiver extracts a receiving pilot signal from a receiving signal and generates a local pilot signal at the same time; step 2, generating a sensing matrix by using a local pilot signal, and judging whether the sensing matrix meets an RIP criterion, if so, turning to step 3, otherwise, regenerating the sensing matrix; step 3, establishing a corrected OGOMP reconstruction algorithm; 4, recovering the channel impulse response hP at the pilot frequency by using the corrected OGOMP reconstruction algorithm; and step 5, performing interpolation calculation on the channel impulse response hd of the useful data, and splicing the channel impulse response hP and the channel impulse response hd. The sparse channel estimation method is applied to sparse channel estimation of a short-wave single-carrier system, and the problem that a receiver generates more error bits during decoding due to an OGOMP reconstruction algorithm is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of channel estimation, and specifically relates to a channel estimation method based on compressed sensing and its application, and in particular to sparse channel estimation in the field of shortwave single-carrier communication. Background Art

[0002] In a shortwave single-carrier communication system, the signal received by the receiver will produce fading, multipath effects, and Doppler frequency deviation due to the influence of the shortwave channel, which is not conducive to the demodulation of the receiver. Therefore, the receiving end needs to estimate the channel fading parameters to eliminate the effects of fading and restore the original data sent. Shortwave communication channels are usually time-varying multipath fading channels. Traditional linear channel estimation methods (such as the least squares method) are based on the dense distribution of channel multipaths. A large number of training sequences are required to estimate the channel multipath coefficients, resulting in low spectrum utilization and complex implementation. However, a large number of experiments have shown that multipath channels are sparse, that is, the number of significant multipaths in the channel impulse response is small and scattered. This characteristic can be used to achieve a better estimation method. Channel estimation technology based on compressed sensing can make full use of the prior information of channel sparsity and obtain a more accurate channel estimation result using fewer pilots.

[0003] At present, there is an OGOMP (Optimized Generalized Orthogonal Matching Pursuit) algorithm based on compressed sensing, which implements channel estimation for OFDM (Orthogonal Frequency Division Multiplexing) systems. However, this algorithm has the following defects when applied to sparse channel estimation in shortwave single-carrier systems:

[0004] Under random channel delay, the starting position of the multipath signal in the shortwave single-carrier communication system is not necessarily located at an integer sampling point, which will cause the OGOMP reconstruction algorithm to deviate when selecting dictionary atoms (column vectors in the sensor matrix), resulting in more error bits generated by the receiver during decoding.

[0005] In view of this, the present inventor provides a channel estimation method based on compressed sensing and its application to solve the above technical problems. Summary of the invention

[0006] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and propose a channel estimation method and application based on compressed sensing, aiming to utilize the sparse distribution characteristic of the multipath channel for channel estimation. For sparse multipath channels such as shortwave single-carrier systems, the channel estimation method can reconstruct a more accurate channel impulse response when the pilot length is small, and has certain advantages and prospects for product realization.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] On the one hand, the present invention provides a channel estimation method based on compressed sensing, comprising the following steps:

[0009] Step 1, the receiver extracts a receiving pilot signal from a receiving signal, and the receiver generates a local pilot signal;

[0010] Step 2: Generate a sensor matrix using the local pilot signal, and determine whether the sensor matrix meets the RIP (Restricted Isometry Property) criterion. If so, proceed to step 3; otherwise, regenerate a sensor matrix that meets the RIP criterion.

[0011] Step 3, establishing a modified OGOMP reconstruction algorithm;

[0012] Step 4: Use the modified OGOMP reconstruction algorithm to recover the channel impulse response h at the pilot by receiving the pilot signal and the sensor matrix. P ;

[0013] Step 5: Use the channel impulse response h at the pilot P Interpolation calculation of the channel impulse response h of the useful data d , and h P and h d The channel impulse responses are concatenated in the order of the frame structure to obtain the channel impulse response h of the entire signal.

[0014] Furthermore, in step 3, the modified OGOMP reconstruction algorithm is established as follows:

[0015] Step 3.1, input the received signal y, the M×N sensing matrix Φ and the sparsity K, and set the number of atoms selected in each iteration to S (S≤K, SK≤M);

[0016] Step 3.2, data initialization, including initializing the residual r0 = y, the index set of the selected atoms in the sensor matrix Iteration number t = 0;

[0017] Step 3.3, atom selection, iteration number t=t+1, calculate the residual error of each selected atom, select the index corresponding to the smallest S residual errors, and update the index set, denoted as Π;

[0018] Step 3.4, index correction, determine whether the first column index in the current index set Π is 1, if it is 1, go to step 3.5, otherwise, set the first column index to 1 and go to step 3.5;

[0019] Step 3.5, atomically refine and update the index set;

[0020] Step 3.6: Estimate the sparse vector and update the residual. If the iteration meets the set conditions, stop the iteration and output the recovered sparse vector, i.e., the channel impulse response h at the pilot. P , otherwise, go to step 3.3.

[0021] Furthermore, step 3.5 specifically includes the following:

[0022] If the number of indexes in the current index set Π is less than K, then let the further updated index set Λ t =Π, otherwise, calculate the sparse vector right Find the absolute value and sort from large to small, keep The indices corresponding to the largest K values ​​in {j1,j2,…,j K}∈Π, update the index set Λ t ={j1,j2,…,j K}.

[0023] Furthermore, in step 3.6, the setting condition is t≥min(K,M / S).

[0024] Furthermore, in step 4, the specific process is as follows:

[0025] Assuming that the channel impulse response remains stable within the pilot time range, the pilot signal in the received signal can be expressed as:

[0026]

[0027] Among them, y P (n) represents the received pilot signal, x P (n) represents the local pilot signal, z(n) represents random noise, h P (l) represents the channel impulse response, L represents the number of channel multipaths, and N represents the pilot length. Ignoring noise, the above formula is written in matrix form as follows:

[0028]

[0029] That is: y P ≈X P ·h P (3)

[0030] Among them, X P represents the sensing matrix, h P represents the channel impulse response at the pilot.

[0031] Furthermore, in step 5, the interpolation calculation uses linear interpolation.

[0032] On the other hand, the present invention also provides an application of the channel estimation method as described above in sparse channel estimation of a shortwave single-carrier system.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1) The present invention proposes a channel estimation method based on compressed sensing, which optimizes the OGOMP reconstruction algorithm to obtain a modified OGOMP reconstruction algorithm, and uses the algorithm to perform channel estimation, thereby improving the problems of large resource consumption and low spectrum utilization in traditional channel estimation algorithms.

[0035] 2) A channel estimation method based on compressed sensing is applied to sparse channel estimation of a shortwave single-carrier system. When the starting position of the multipath signal is at a non-integer sampling point, the receiver has very few error bits during the decoding process, which solves the problem that the OGOMP reconstruction algorithm has deviations in selecting dictionary atoms, thereby causing the receiver to generate more error bits during decoding. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings are incorporated in and constitute a part of this specification and, together with the description, serve to explain the principles of the present invention.

[0037] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0038] Figure 1 is a flow chart of a channel estimation method of the present invention;

[0039] Figure 2 The iterative process of the OGOMP reconstruction algorithm modified by the present invention;

[0040] Figure 3 is the mean square error of the corrected OGOMP and LS channel estimation in Experiment 1 of the present invention;

[0041] Figure 4 is the bit error rate of the OGOMP and LS channel estimation corrected in Experiment 1 of the present invention;

[0042] Figure 5 This is a schematic diagram of four channel delays in Experiment 2 of the present invention;

[0043] Figure 6 The channel estimation performance of the modified OGOMP algorithm and the modified GOMP algorithm are compared under the sampling rate of 9600 Hz in Experiment 2 of the present invention, when the starting position of the delayed signal corresponds to 19.2 sampling points;

[0044] Figure 7 The channel estimation performance of the modified OGOMP algorithm and the modified GOMP algorithm are compared under the sampling rate of 9600 Hz in Experiment 2 of the present invention, when the starting position of the delayed signal corresponds to 18.91 sampling points;

[0045] Figure 8 The channel estimation performance of the modified OGOMP algorithm and the modified GOMP algorithm are compared under the sampling rate of 9600 Hz in Experiment 2 of the present invention, when the starting position of the delayed signal corresponds to 17.47 sampling points;

[0046] Fig. 9 The channel estimation performance of the modified OGOMP algorithm and the modified GOMP algorithm are compared under the sampling rate of 9600 Hz in Experiment 2 of the present invention, when the starting position of the delayed signal corresponds to 18.62 sampling points;

[0047] Fig.10 BER curves of OGOMP channel estimation before and after correction under different pilot lengths in Experiment 3 of the present invention. DETAILED DESCRIPTION

[0048] Here, exemplary embodiments will be described in detail, and the embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are only examples consistent with some aspects of the present invention described in detail in the appended claims.

[0049] On the one hand, see Figure 1-2 The embodiment of the present invention provides a channel estimation method based on compressed sensing, comprising the following steps:

[0050] Step 1, the receiver extracts a receiving pilot signal from a receiving signal, and the receiver generates a local pilot signal;

[0051] Step 2: Generate a sensor matrix using the local pilot signal, and determine whether the sensor matrix meets the RIP criterion. If yes, proceed to step 3; otherwise, regenerate a sensor matrix that meets the RIP criterion.

[0052] Step 3, establishing a modified OGOMP reconstruction algorithm;

[0053] Step 4: Use the modified OGOMP reconstruction algorithm to recover the channel impulse response h at the pilot by receiving the pilot signal and the sensor matrix. P ;

[0054] Step 5: Use the channel impulse response h at the pilot P Interpolation calculation of the channel impulse response h of the useful data d , and hP and h d The channel impulse responses are concatenated in the order of the frame structure to obtain the channel impulse response h of the entire signal.

[0055] Furthermore, in step 3, the modified OGOMP reconstruction algorithm is established as follows:

[0056] Step 3.1, input the received signal y, the M×N sensing matrix Φ and the sparsity K, and set the number of atoms selected in each iteration to S (S≤K, SK≤M);

[0057] Among them, the M×N sensor matrix Φ represents that the received signal y is an N-dimensional signal, which is mapped into an M-dimensional space;

[0058] Step 3.2, data initialization, including initializing the residual r0 = y, the index set of the selected atoms in the sensor matrix Iteration number t = 0, index set Ω = {1, 2, ..., N} of all atoms in the sensing matrix; Step 3.3, atom selection, iteration number t = t + 1, calculate the residual error of each selected atom, select the index corresponding to the smallest S residual errors, and update the index set, denoted as Π;

[0059] Specifically, t=t+1, add index sets Ω\Λ one by one t-1 Each index in (represents the column number of the unselected atoms in the sensing matrix Φ) is indexed into Γ, that is, Γ = Λ t-1 ∪i,i∈Ω\Λ t-1 , and calculate the corresponding residual error in is Φ Γ The pseudo-inverse matrix of i The index i corresponding to the value i ,i2,…,i m ; The updated index set is Π=Λ t-1 ∪{i1,i2,…,i m};

[0060] Step 3.4, index correction, determine whether the first column index in the current index set Π is 1, if it is 1, go to step 3.5, otherwise, set the first column index to 1 and go to step 3.5;

[0061] Step 3.5, atomically refine and update the index set;

[0062] Step 3.6: Estimate the sparse vector and update the residual. If the iteration meets the set conditions, stop the iteration and output the recovered sparse vector, i.e., the channel impulse response h at the pilot. P , otherwise, go to step 3.3.

[0063] Furthermore, step 3.5 specifically includes the following:

[0064] If the number of indexes in the current index set Π is less than K, then let the further updated index set Λ t =Π, otherwise, calculate the sparse vector right Find the absolute value and sort from large to small, keep The indices corresponding to the largest K values ​​in {j1,j2,…,j K}∈Π, update the index set Λ t ={j1,j2,…,j K}.

[0065] Furthermore, in step 3.6, the sparse vector is estimated and the residual is updated:

[0066] When t≥min(K,M / S), stop the iteration and output the recovered sparse vector, which is only in Λ t There are values ​​at the position, which are the last iteration Denotes the selection of index set Λ from the sensor matrix Φ t The corresponding atoms form a matrix and then conjugate it.

[0067] Furthermore, in step 4, the specific process is as follows:

[0068] In the process of radio wave propagation, shortwave communication will be affected by multipath effects, fading, Doppler frequency shift, etc., causing signal distortion. Fading is divided into slow fading and fast fading, and fast fading has obvious frequency selectivity. For frequency selective fading channels, it is assumed that the transmitter, receiver and reflector are stationary or slowly moving during the analyzed time, and the number, position and characteristics of the reflectors are also fixed, then the characteristics of multiple signal paths are also fixed, and the equivalent channel impulse response remains constant during the analyzed time. Therefore, it can be assumed that the channel impulse response remains stable within the pilot time range. At this time, the pilot signal in the received signal can be expressed as:

[0069]

[0070] Among them, y P (n) represents the received pilot signal, x P (n) represents the local pilot signal, z(n) represents random noise, h P (l) represents the channel impulse response, L represents the number of channel multipaths, and N represents the pilot length. Ignoring noise, the above formula is written in matrix form as follows:

[0071]

[0072] That is: y P ≈X P ·h P (3)

[0073] The key to applying compressed sensing technology to sparse multipath channel estimation is to find a sensing matrix that corresponds to the known information in the actual system and satisfies the RIP criterion. P is a convolution matrix of the Toeplitz structure (except for the first row and the first column, each element is the same as the element in its upper left corner). This matrix has been proven to meet the RIP criterion under certain conditions and can restore sparse signals with a higher probability in compressed sensing. Therefore, X P The matrix serves as a sensing matrix.

[0074] In this embodiment, let L = N, h P The sparsity is 2, that is, there are two paths.

[0075] The sparse vector h is recovered by using the received pilot signal and the modified OGOMP reconstruction algorithm. P ,h P The two non-zero value elements contained correspond to the channel impulse responses of the two-path channels at the current pilot.

[0076] Furthermore, in step 5, the interpolation calculation uses linear interpolation.

[0077] On the other hand, the present invention also provides an application of the channel estimation method as described above in sparse channel estimation of a shortwave single-carrier system.

[0078] Specifically, this embodiment is applied to a channel estimation module in a shortwave single-carrier receiver and can be implemented through hardware on an FPGA.

[0079] In order to further illustrate the effect of the present invention, the present invention has done the following simulation experiment:

[0080] This embodiment sets up three simulation experiments:

[0081] (1) Compare the channel estimation performance of the traditional LS algorithm and the modified OGOMP reconstruction algorithm under the same pilot length;

[0082] (2) Analyze the applicability of the modified OGOMP reconstruction algorithm channel estimation algorithm under the conditions of the same pilot length and different channel delays;

[0083] (3) Under the conditions of the same channel delay and different pilot lengths, the channel estimation results of the OGOMP channel estimation algorithm before and after correction are compared.

[0084] All three experiments use mean square error (MSE) and bit error rate (BER) to evaluate the estimation results.

[0085] The calculation formulas for the mean square error MSE and bit error rate BER are as follows:

[0086]

[0087] h represents the ideal channel impulse response, represents the channel impulse response estimate, N t Indicates the number of transmitted bits, N w Indicates the number of error bits.

[0088] Experiment 1

[0089] This simulation experiment compares the performance of the modified OGOMP reconstruction algorithm with the traditional LS channel estimation algorithm. The parameter settings are shown in Table 1. The simulation results are shown in Figure 3 and Figure 4 shown.

[0090] Table 1 Experiment 1 simulation parameter settings

[0091]

[0092] Depend on Figure 3 It can be seen that the mean square error of channel estimation of the modified OGOMP reconstruction algorithm and the LS algorithm gradually decreases with the increase of the signal-to-noise ratio; the mean square error of channel estimation of the modified OGOMP reconstruction algorithm is lower than that of the traditional LS algorithm. Figure 4 It is found that under the same pilot length, the bit error rate of the modified OGOMP reconstruction algorithm is lower than that of the LS algorithm, and when the pilot length is reduced from 48 symbols to 36 symbols, the performance of the modified OGOMP algorithm decays by about 4dB, while the performance of the LS algorithm decays by about 8dB.

[0093] This shows that: 1) when the pilot length is short, the performance of the modified OGOMP channel estimation algorithm is significantly better than that of the LS algorithm; 2) the pilot length has a greater impact on LS channel estimation. If the algorithm wants to obtain a better estimation effect, the pilot length must be increased. However, this will bring about a large pilot overhead and waste certain frequency band resources.

[0094] Experiment 2

[0095] In the case that other simulation parameters in Experiment 1 remain unchanged, four representative channel delays are selected for Experiment 2, which are two critical values ​​close to integer sampling points: 2ms (i.e., at a sampling rate of 9600Hz, the starting position of the delay signal corresponds to 19.2 sampling points) and 1.97ms (i.e., 18.91 sampling points), and two intermediate values ​​close to the center between adjacent integer sampling points: 1.82ms (i.e., 17.47 sampling points) and 1.94ms (i.e., 18.62 sampling points). Figure 5The same correction method is used for the GOMP algorithm to compare the channel estimation performance of the modified OGOMP (pilot length is 36 symbols) algorithm and the modified GOMP (pilot length is 48 symbols) algorithm.

[0096] Depend on Figure 6 to Figure 9 It can be seen that under the same pilot length, the performance of the modified OGOMP reconstruction algorithm is better than that of the modified GOMP reconstruction algorithm; the modified OGOMP reconstruction algorithm can achieve channel estimation performance comparable to that of the GOMP reconstruction algorithm with 48 pilot symbols using only 36 pilot symbols. In the case of the two boundary delays of 2ms and 1.97ms, the performance of the OGOMP (36) channel estimation is close to that of the GOMP (48), and when the channel delay is two intermediate delays, the performance of the OGOMP (36) is better than that of the GOMP (48), with a gain of about 2dB, which can save about 4.63% of the pilot overhead. Therefore, the modified OGOMP channel estimation algorithm is more applicable. This is because the OGOMP algorithm adopts a better atom selection scheme in the sense of minimum residual error and deletes multiple selected erroneous atoms through atom refinement, which can better approximate the original sparse signal. Therefore, the OGOMP algorithm has a smaller pilot overhead under the approximately same estimation performance.

[0097] Experiment 3

[0098] This simulation experiment is carried out under 2ms channel delay. The pilot length is set as shown in Table 2. Other parameter values ​​are the same as those in Experiment 1. The simulation results are shown in Fig.10 As shown, the numbers "48", "36" and "32" in the figure represent the number of pilot symbols.

[0099] Table 2 Frame structure of Experiment 3

[0100]

[0101]

[0102] from Fig.10 It can be observed from the bit error rate curve that under the condition of the same pilot length, the bit error rate of the modified OGOMP reconstruction algorithm is lower, and the longer the pilot length, the better the channel estimation performance; and the performance of the modified OGOMP (36) is better than that of the unmodified OGOMP (48) and OGOMP (36).

[0103] In summary, for sparse multipath channels such as shortwave single-carrier communication systems, the OGOMP channel estimation scheme based on compressed sensing is superior to the traditional LS channel estimation; compared with the GOMP algorithm, the algorithm used in the present invention can reconstruct a more accurate channel impulse response when the pilot length is small, and has certain advantages.

[0104] The above description is only a specific embodiment of the present invention, so that those skilled in the art can understand or implement the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention.

[0105] It should be understood that the present invention is not limited to what has been described above and that various modifications and changes may be made without departing from its scope. The scope of the present invention is limited only by the appended claims.

Claims

1. A channel estimation method based on compressed sensing, characterized in that: The following steps are involved: Step 1, the receiver extracts a receiving pilot signal from a receiving signal, and the receiver generates a local pilot signal; Step 2: Generate a sensor matrix using the local pilot signal, and determine whether the sensor matrix meets the RIP criterion. If yes, proceed to step 3; otherwise, regenerate a sensor matrix that meets the RIP criterion. Step 3, establishing a modified OGOMP reconstruction algorithm; Step 4: Use the modified OGOMP reconstruction algorithm to recover the channel impulse response h at the pilot by receiving the pilot signal and the sensor matrix. P ; Step 5: Use the channel impulse response h at the pilot P Interpolation calculation of the channel impulse response h of the useful data d , and h P and h d The channel impulse responses are concatenated in the order of the frame structure to obtain the channel impulse response h of the entire signal.

2. The channel estimation method based on compressed sensing according to claim 1, characterized in that: In step 3, the modified OGOMP reconstruction algorithm is established as follows: Step 3.1, input the received signal y, the M×N sensing matrix Φ and the sparsity K, and set the number of atoms selected in each iteration to S (S≤K, SK≤M); Step 3.2, data initialization, including initializing the residual r0 = y, the index set of the selected atoms in the sensor matrix Iteration number t = 0; Step 3.3, atom selection, iteration number t=t+1, calculate the residual error of each selected atom, select the index corresponding to the smallest S residual errors, and update the index set, denoted as Π; Step 3.4, index correction, determine whether the first column index in the current index set Π is 1, if it is 1, go to step 3.5, otherwise, set the first column index to 1 and go to step 3.5; Step 3.5, atomically refine and update the index set; Step 3.6: Estimate the sparse vector and update the residual. If the iteration meets the set conditions, stop the iteration and output the recovered sparse vector, that is, the channel impulse response h at the pilot. P , otherwise, go to step 3.

3.

3. The channel estimation method based on compressed sensing according to claim 2, characterized in that: Step 3.5 specifically includes the following: If the number of indexes in the current index set Π is less than K, then let the further updated index set Λ t =Π, otherwise, calculate the sparse vector right Find the absolute value and sort from large to small, keep The indices corresponding to the largest K values ​​in {j1,j2,…,j K }∈Π, update the index set Λ t ={j1,j2,…,j K }.

4. The channel estimation method based on compressed sensing according to claim 2, characterized in that: In step 3.6, the setting condition is t≥min(K,M / S).

5. The channel estimation method based on compressed sensing according to claim 1, characterized in that: In step 4, the specific process is as follows: Assuming that the channel impulse response remains stable within the pilot time range, the pilot signal in the received signal can be expressed as: Among them, y P (n) represents the received pilot signal, x P (n) represents the local pilot signal, z(n) represents random noise, h P (l) represents the channel impulse response, L represents the number of channel multipaths, and N represents the pilot length. Ignoring noise, the above formula is written in matrix form as follows: That is: y P ≈X P ·h P (3) Where X P represents the sensing matrix, h P represents the channel impulse response at the pilot.

6. The channel estimation method based on compressed sensing according to claim 1, characterized in that: In step 5, the interpolation calculation uses linear interpolation.

7. An application of the channel estimation method according to any one of claims 1 to 6 in sparse channel estimation of a shortwave single-carrier system.

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