A sparsity tracking dynamic compressive sensing adaptive channel equalization method

Abstract

The application discloses a sparse degree tracking dynamic compressive sensing adaptive channel equalization method. Aiming at a fast time-varying long multi-path wireless communication channel, the method mainly solves the problem of insufficient tap support set tracking performance of an existing dynamic compressive sensing adaptive channel equalizer. The implementation process is divided into two stages: 1) a training stage, based on a received signal and a pilot sequence, an adaptive filtering algorithm is combined with a data multiplexing technology to train a full-tap equalizer, so that tap coefficients reach a convergence state; 2) a symbol detection stage, a sparse degree tracking dynamic compressive sensing algorithm is used to track the equalizer tap support set and coefficient values simultaneously and estimate data symbols. The application applies the sparse degree tracking dynamic compressive sensing method to adaptive equalization, realizes dynamic tracking of the equalizer tap support set and coefficient values to better adapt to environmental changes, and has high practical application value.

Description

Technical Field

[0001] This invention belongs to the field of adaptive channel equalization, specifically relating to a sparse tracking dynamic compressed sensing adaptive channel equalization method. Background Technology

[0002] The long multipath effect of wireless channels leads to severe inter-symbol interference (ISI) in received signals, posing a challenge to reliable data transmission. Equalization techniques can effectively suppress ISI and are a key technology at the receiver end. Currently, there are two main types of equalizer design: Channel-Estimation-Based Equalizer (CEE) and Direct Adaptive Equalizer (DAE). Compared to CEE, DAE has gained widespread attention due to its lower complexity and better environmental tracking capabilities.

[0003] Adaptive channel equalizers exhibit sparsity, meaning that a small portion of the equalizer taps consume most of the energy. Leveraging this characteristic, sparse adaptive filtering algorithms can effectively improve equalization performance. For example, equalization based on the Improved Proportionate Normalized Minimum Symbol Error Rate (IPNMSER) ​​algorithm has been applied and validated.

[0004] Dynamic compressed sensing is an emerging branch of compressed sensing, designed to handle time-varying sparse signals where the support set changes over time. This suitability for signals that dynamically change over time gives it advantages in various applications. Currently, dynamic greedy algorithms in dynamic compressed sensing have been applied to adaptive channel equalization. In this method, the equalizer tap coefficients are the sparse signal to be reconstructed. By iteratively tracking the support set of the equalizer tap vector and using an adaptive filtering algorithm to update the coefficient values ​​on the support set, efficient tracking of the equalizer coefficients and data symbol detection are achieved. Compared to traditional adaptive equalization, adaptive equalization based on dynamic compressed sensing can reduce the dimension from the full tap dimension to the support set dimension, thereby reducing the computational complexity of the equalizer and improving convergence speed. However, existing methods require pre-setting the sparsity of the equalizer, i.e., the size of the support set. In time-varying channel environments, this method has insufficient performance in tracking the equalizer support set and cannot dynamically track equalizer support sets of variable size. Summary of the Invention

[0005] This invention proposes a sparse-trackable (ST) dynamic compressed sensing adaptive channel equalization method to solve the problems of the inability to track the number of taps at the symbol level and the high computational complexity of sparse adaptive channel equalization.

[0006] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0007] A sparse tracking dynamic compressed sensing adaptive channel equalization method includes the following steps:

[0008] (1) Determine the number of transmitter branches N, and denote the transmitted symbol block on the nth branch as x. n =[x n,1 ,…,x n,K ] T Its length is K, including K p pilot symbols and K d A data symbol, x n,k This represents the k-th transmitted symbol on the n-th branch;

[0009] (2) Determine the number of receiver branches M, and denote the receiver block on the m-th branch as y. m =[y m,1 ,…,y m,K+L-1 ] T Where L represents the channel length, y m,k This represents the k-th received symbol on the m-th branch;

[0010] (3) Determine the parameters of the adaptive decision feedback equalizer, including the feedforward FF equalizer length parameter K1 and its corresponding adaptive update step size μ. w The length parameter K2 of the feedback FB equalizer and its corresponding adaptive update step size μ f Data reuse DR times N dr Initialize the equalizer;

[0011] (4) Based on the received signal and pilot sequence, a sparse adaptive filtering algorithm combined with data multiplexing technology is used to train the full-tap adaptive decision feedback equalizer.

[0012] (5) Using the full-tap adaptive decision feedback equalizer obtained in step (4) as the initial value, data symbol detection is performed, and sparse tracking dynamic compressed sensing technology is used to dynamically track the tap support set and coefficient values ​​of the partial tap adaptive decision feedback equalizer.

[0013] Preferably, in step (2), the received signal at time k on the m-th receiving branch is represented as follows:

[0014]

[0015] Where x n,k-l h represents the transmitted symbol of the nth transmit branch. n,m,k (l) represents the l-th tap of the subchannel between the n-th transmit branch and the m-th receive branch at time k, where n m,k This indicates additive noise.

[0016] Preferred: In step (4), based on the received signal and pilot symbol, the estimation of the k-th transmitted symbol of the n-th transmit branch output by the full-tap adaptive decision feedback equalizer is as follows:

[0017]

[0018] in This represents the received signal vector, with zeros padded to any portion exceeding the actual received sequence. Let be the decision symbol vector, where

[0019]

[0020] During the training phase, Using known pilot symbols;

[0021] w n,k and f n,k The coefficient vectors of the FF equalizer and the FB equalizer, respectively, corresponding to the nth transmit branch at time k, are updated using a sparse adaptive filtering algorithm; the equalizer training process repeats N times on the pilot signal block. dr After training, the feedforward FF equalizer is obtained. and FB equalizer The lengths are L w =M(K1+1), L f =NK2-1; and Provides an initial equilibrium vector for data symbol detection.

[0022] Preferred method: In step (5), based on the Sparse Adaptive Orthogonal Matching Pursuit (SpAdOMP) dynamic compressed sensing algorithm, a sparsity tracking mechanism is introduced to dynamically adjust the equalizer tap support set. The specific implementation method is as follows:

[0023] First, the candidate support set and coefficient values ​​of the equalizer taps are dynamically updated. Let the sizes of the support sets of the FF and FB equalizers at time k be respectively... and The initial values ​​are set as follows: and Let the proxy signal vectors corresponding to the FF and FB equalizers at time k be respectively The lengths are L w ,L f The initial values ​​are set to zero vectors, and at time k... The update equation is:

[0024]

[0025]

[0026] in, The signal is a residual signal with an initial value v. n,0 =x n,1 0 < λ ≤ 1 is the forgetting factor. Representing the received signal vector u at time k-1 respectively k-1 and the decision symbol vector d k-1 The conjugate;

[0027] based on Sparsity information at time k and Determine the following support set

[0028]

[0029] Where supp(·) represents the support set retrieval operation; based on The candidate support set for calculating the equalizer vector at time k is as follows:

[0030]

[0031]

[0032] Preferred method: In step (5), a sparse adaptive filtering algorithm is used to update the tap coefficients of the partial tap adaptive decision feedback equalizer on the support set. The specific implementation method is as follows:

[0033] Obtain candidate support set Subsequently, an adaptive filtering algorithm is used to optimize the partial tap adaptive decision feedback equalizer. and The equalizer coefficients at the corresponding positions in the vector are updated, while the coefficients at other positions remain unchanged; definition for Central support set The vector formed by corresponding elements is defined as follows: for Central support set A vector formed by corresponding elements;

[0034] The tap coefficients of the upper part of the support set adaptive decision feedback equalizer are updated using the IPNMSER algorithm as follows:

[0035]

[0036] in They are respectively The supplement, Represents the scale matrix Central support set A diagonal matrix formed by corresponding elements. Depend on Calculations show that Represents the scale matrix Central support set A diagonal matrix formed by corresponding elements. Depend on Calculations show that I n,k For error indicators;

[0037] Next, a new support set is obtained based on the updated equalizer vector. and as follows

[0038]

[0039]

[0040] get Then, the sign estimation is made as follows:

[0041]

[0042] Finally, the sparsity of the equalizer is updated for symbol estimation at time k+1. The update equation is as follows:

[0043]

[0044] in This indicates the rounding up operation. and Let these represent the sparsity measures of the tap vectors of the FF and FB equalizers at time k, respectively, and the calculation formula is as follows:

[0045]

[0046] Where ζ is a small positive number; repeat step (5) until all data symbols have been detected.

[0047] Beneficial effects: This invention employs data reuse technology, which effectively improves the training quality of the full-tap adaptive equalizer. In the data symbol detection stage, it uses sparse tracking dynamic compressed sensing technology. Compared with existing dynamic compressed sensing technology, this technology can achieve dynamic tracking of the support set and coefficient values ​​of the sparse equalizer, thereby enabling the equalizer to better adapt to environmental changes. In practical applications, it reduces complexity while also achieving certain performance gains. Attached Figure Description

[0048] Figure 1 The amplitude diagram of the estimated Channel Impulse Response (CIR) is shown.

[0049] Figure 2 A flowchart of the sparse tracking adaptive equalizer;

[0050] Figure 3 Comparison of the number of equalizer taps between SpAdOMP-IPNMSER-DAE (an adaptive equalizer with fixed sparsity) and ST-SpAdOMP-IPNMSER-DAE (an adaptive equalizer with dynamic compressed sensing IPNMSER based on sparsity tracking).

[0051] Figure 4 A comparison chart of the bit error rate (BER) of SpAdOMP-IPNMSER-DAE and ST-SpAdOMP-IPNMSER-DAE;

[0052] Figure 5 A comparison chart of the mean squared error (MSE) of SpAdOMP-IPNMSER-DAE and ST-SpAdOMP-IPNMSER-DAE. Detailed Implementation

[0053] The present invention provides a sparse tracking dynamic compressed sensing adaptive channel equalization method, comprising the following steps:

[0054] (1) Determine the number of transmitter branches N, where the last transmitted symbol block on the nth branch is x. n =[x n,1 ,…,x n,K ] T Its length is K, including K p pilot symbols and K d One data symbol;

[0055] (2) Determine the number of receiver branches M, and denote the receiver block on the m-th branch as y. m =[y m,1 ,…,y m,K+L-1] T , where L represents the channel length;

[0056] (3) Determine the parameters of the adaptive decision feedback equalizer, including the feedforward (FF) equalizer length parameter K1 and the feedback (FB) equalizer length parameter K2, as well as their corresponding adaptive update step size μ. w and μ f Data reuse (DR) times N dr Initialize the equalizer;

[0057] (4) Based on the pilot sequence, the full-tap equalizer is trained by using a sparse adaptive filtering algorithm combined with data reuse technology. The same pilot block is used to repeat the training multiple times, and the number of repetitions is the number of data reuses.

[0058] (5) Using the full tap equalizer obtained in step (4) as the initial value, perform data symbol detection and use sparse tracking dynamic compressed sensing technology to dynamically track the equalizer tap support set and coefficient values.

[0059] In step (2), the received signal at time k on the m-th receiving branch is represented as follows:

[0060]

[0061] Where x n,k-l h represents the transmitted symbol of the nth transmit branch. n,m,k (l) represents the l-th tap of the subchannel between the n-th transmit branch and the m-th receive branch at time k, where n m,k This indicates additive noise.

[0062] In step (4), based on the received signal and pilot symbol, the estimate of the k-th transmitted symbol of the n-th transmit branch output by the full-tap adaptive equalizer is as follows:

[0063]

[0064] in This represents the received signal vector, with zeros padded to any portion exceeding the actual received sequence. Let be the decision symbol vector, where

[0065]

[0066] During the training phase, Known pilot symbols can be used;

[0067] w n,k and f n,kLet N be the coefficient vectors of the FF equalizer and the FB equalizer, respectively, corresponding to the nth transmit branch at time k. These are updated using a sparse adaptive filtering algorithm. To ensure convergence, the equalizer training process is repeated N times on the pilot signal block. dr After training, a full-tap FF equalizer was obtained. and FB equalizer The lengths are L w =M(K1+1), L f =NK2-1. and Provides an initial equilibrium vector for data symbol detection;

[0068] In step (5), based on the SpAdOMP dynamic compressed sensing algorithm, a sparsity tracking mechanism is introduced to dynamically adjust the equalizer tap support set, and a sparse adaptive filtering algorithm is used to update the equalizer tap coefficients. The specific implementation method is as follows:

[0069] First, the candidate support set and coefficient values ​​of the equalizer taps are dynamically updated. Let the sizes of the support sets of the FF and FB equalizers at time k be respectively... and Set its initial value and Let the proxy signal vectors of the FF and FB equalizers at time k be respectively The lengths are L w ,L f Its initial value is set to zero vector, at time k The update equation is:

[0070]

[0071]

[0072] in, The signal is a residual signal with an initial value v. n,0 =x n,1 0 < λ ≤ 1 is the forgetting factor; based on Sparsity information at time k and Determine the following support set

[0073]

[0074] Where supp(·) represents the support set retrieval operation; based on The candidate support set for calculating the equalizer vector at time k is as follows:

[0075]

[0076]

[0077] Obtain candidate support set Then, an adaptive filtering algorithm is used to adjust the full-tap equalizer. and The equalizer coefficients at the corresponding positions in the vector are updated, while the tap coefficients at other positions remain unchanged. Definition for Central support set The vector formed by corresponding elements is similar to the definition. Without loss of generality, the IPNMSER algorithm is used to update the equalizer tap coefficients on the support set as follows:

[0078]

[0079] in They are respectively The supplement, Represents the scale matrix Central support set The vector formed by the corresponding elements above, Depend on Calculations show that A similar definition is possible, I n,k This serves as an error indicator. Next, a new support set is obtained based on the updated full-tap equalizer vector. and as follows

[0080]

[0081]

[0082] get Then, a sign estimate can be made as follows:

[0083]

[0084] It is clear that the estimation only involves the coefficients on the support set and does not require all coefficients, thus reducing the equilibrium complexity.

[0085] Finally, the sparsity of the equalizer is updated for symbol estimation at time k+1. The update equation is as follows:

[0086]

[0087] in This indicates the rounding up operation. and Let these represent the sparsity measures of the tap vectors of the FF and FB equalizers at time k, respectively, and the calculation formula is as follows:

[0088]

[0089] Where ζ is a small positive number; after the update and The dynamic update of the equalizer tap support set and coefficient values ​​at time k+1 is performed by repeating the three-step update in step (5) until the detection of data symbols is completed.

[0090] The present invention will be further explained and described below with reference to the embodiments.

[0091] The method of this invention was verified using sea trial data from a dual-transmit, quad-receive MIMO single-carrier underwater acoustic communication system. The sea trial transmission distance was 2 km, the carrier frequency was 17 kHz, and the symbol period was 0.2 ms. Channel coding employed a low-density parity-check code with a code rate of 1 / 2, and the symbol modulation scheme was QPSK. One transmission block contained K = 1024 QPSK symbols, where the pilot symbol length K... p =200, data symbol length K d =824. Figure 1 The channel estimation results are shown, with a channel length of approximately L = 70 symbol periods. The workflow of the method of this invention is as follows: Figure 2 As shown. The equalizer length parameters are set to K1 = 40 and K2 = 50 respectively. Under this setting, the lengths of the full-tap FF and FB equalizers are L respectively. w =164, L f =99.

[0092] During the experimental training phase, the improved proportionally normalized minimum symbol rate (IPNMSER) ​​algorithm was used to track the equalizer coefficients. The step size parameter of IPNMSER-DAE was set to μ. w =μ f =0.2; In the symbol detection stage, a sparse-tracking dynamic compressed sensing IPNMSER adaptive equalizer ST-SpAdOMP-IPNMSER-DAE is used for symbol estimation, with a forgetting factor λ = 0.99 and ζ = 10. -12 The initial size of the tap support set for FF and FB equalizers is... The experiment used the SpAdOMP-IPNMSER-DAE adaptive equalizer with fixed sparsity as a control, with the tap support set sizes of its FF and FB equalizers fixed at 110 and 20, respectively. The experiment was set to reuse data N times. dr =0,2,4,6. A total of 5 bursts of data transmission were processed, each burst containing 50 blocks, for a total of 250 blocks. Performance metrics included bit error rate (BER) and mean squared error of symbol estimation (MSE).

[0093] Figure 3The number of FF equalizer taps in a block was compared between SpAdOMP-IPNMSER-DAE and ST-SpAdOMP-IPNMSER-DAE. For generalization, blocks 25 and 50 of the 5th burst were selected as examples. For SpAdOMP-IPNMSER-DAE, the number of equalizer taps is always a preset 110, so only one curve is shown in the figure. However, the number of taps in ST-SpAdOMP-IPNMSER-DAE changes dynamically. It can be seen that the number of taps in ST-SpAdOMP-IPNMSER-DAE is less than that in SpAdOMP-IPNMSER-DAE in both different blocks, indicating that the proposed new scheme has lower complexity. Furthermore, the number of taps in ST-SpAdOMP-IPNMSER-DAE varies significantly across different blocks, indicating that the proposed scheme can adapt to changes in channel conditions.

[0094] Figure 4 The BER of SpAdOMP-IPNMSER-DAE and ST-SpAdOMP-IPNMSER-DAE were compared. It can be seen that the BER of both equilibrium schemes increases with N. dr While increasing, decreasing overall, ST-SpAdOMP-IPNMSER-DAE has better BER performance than SpAdOMP-IPNMSER-DAE, especially in N. dr When = 0, it indicates that ST-SpAdOMP-IPNMSER-DAE has a greater performance advantage under limited training conditions.

[0095] Figure 5 The MSE evolution curves of ST-SpAdOMP-IPNMSER-DAE and SpAdOMP-IPNMSER-DAE were compared. It can be seen that during the training phase, i.e., the first 200 iterations, ST-SpAdOMP-IPNMSER-DAE converges slightly faster. However, during the data detection phase, ST-SpAdOMP-IPNMSER-DAE generally achieves a lower MSE.

[0096] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A sparse tracking dynamic compressed sensing adaptive channel equalization method, characterized in that, Includes the following steps: (1) Determine the number of transmitter branches N, and denote the transmitted symbol block on the nth branch as x. n =[x n,1 ,…,x n,K ] T Its length is K, including K p pilot symbols and K d A data symbol, x n,k This represents the k-th transmitted symbol on the n-th branch; (2) Determine the number of receiver branches M, and denote the receiver block on the m-th branch as y. m =[y m,1 ,…,y m,K+L-1 ] T Where L represents the channel length, y m,k This represents the k-th received symbol on the m-th branch; (3) Determine the parameters of the adaptive decision feedback equalizer, including the feedforward FF equalizer length parameter K1 and its corresponding adaptive update step size μ. w The length parameter K2 of the feedback FB equalizer and its corresponding adaptive update step size μ f Data reuse DR times N dr Initialize the equalizer; (4) Based on the received signal and pilot sequence, a sparse adaptive filtering algorithm combined with data multiplexing technology is used to train the full-tap adaptive decision feedback equalizer. (5) Using the full-tap adaptive decision feedback equalizer obtained in step (4) as the initial value, perform data symbol detection, and use sparse tracking dynamic compressed sensing technology to dynamically track the tap support set and coefficient values ​​of the partial tap adaptive decision feedback equalizer. In step (4), based on the received signal and pilot symbol, the estimate of the k-th transmitted symbol of the n-th transmit branch output by the full-tap adaptive decision feedback equalizer is as follows: in This represents the received signal vector, with zeros padded to any portion exceeding the actual received sequence. Let be the decision symbol vector, where During the training phase, Using known pilot symbols; w n,k and f n,k The coefficient vectors of the FF equalizer and the FB equalizer, respectively, corresponding to the nth transmit branch at time k, are updated using a sparse adaptive filtering algorithm; the equalizer training process repeats N times on the pilot signal block. dr After training, the feedforward FF equalizer is obtained. and FB equalizer The lengths are L w =M(K1+1), L f =NK2-1; and Provides an initial equilibrium vector for data symbol detection; In step (5), based on the sparse adaptive orthogonal matching pursuit SpAdOMP dynamic compressed sensing algorithm, a sparsity tracking mechanism is introduced to dynamically adjust the equalizer tap support set. The specific implementation method is as follows: First, the candidate support set and coefficient values ​​of the equalizer taps are dynamically updated. Let the sizes of the support sets of the FF and FB equalizers at time k be respectively... and The initial values ​​are set as follows: and Let the proxy signal vectors corresponding to the FF and FB equalizers at time k be respectively The lengths are L w ,L f The initial values ​​are set to zero vectors, and at time k... The update equation is: in, The signal is a residual signal with an initial value v. n,0 =x n,1 0 < λ ≤ 1 is the forgetting factor. Representing the received signal vector u at time k-1 respectively k-1 and the decision symbol vector d k-1 Conjugate; based on Sparsity information at time k and Determine the following support set Where supp(·) represents the support set retrieval operation; based on The candidate support set for calculating the equalizer vector at time k is as follows:

2. The sparse tracking dynamic compressed sensing adaptive channel equalization method according to claim 1, characterized in that: In step (2), the received signal at time k on the m-th receiving branch is represented as follows: Where x n,k-l h represents the transmitted symbol of the nth transmit branch. n,m,k (l) represents the l-th tap of the subchannel between the n-th transmit branch and the m-th receive branch at time k, where n m,k This indicates additive noise.

3. The sparse tracking dynamic compressed sensing adaptive channel equalization method according to claim 1, characterized in that: In step (5), a sparse adaptive filtering algorithm is used to update the tap coefficients of the partial tap adaptive decision feedback equalizer on the support set. The specific implementation method is as follows: Obtain candidate support set Subsequently, an adaptive filtering algorithm is used to optimize the partial tap adaptive decision feedback equalizer. and The equalizer coefficients at the corresponding positions in the vector are updated, while the coefficients at other positions remain unchanged; definition for Central support set The vector formed by corresponding elements is defined as follows: for Central support set A vector formed by corresponding elements; The tap coefficients of the upper part of the support set adaptive decision feedback equalizer are updated using the IPNMSER algorithm as follows: in They are respectively The supplement, Represents the scale matrix Central support set A diagonal matrix formed by corresponding elements. Depend on Calculations show that Represents the scale matrix Central support set A diagonal matrix formed by corresponding elements. Depend on Calculations show that I n,k For error indicators; Next, a new support set is obtained based on the updated equalizer vector. and as follows get Then, the sign estimation is made as follows: Finally, the sparsity of the equalizer is updated for symbol estimation at time k+1. The update equation is as follows: in This indicates the rounding up operation. and Let these represent the sparsity measures of the tap vectors of the FF and FB equalizers at time k, respectively, and the calculation formula is as follows: Where ζ is a positive number; repeat step (5) until all data symbols have been detected.

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