Sparsity tracking dynamic compressed sensing adaptive channel equalization method

Abstract

The invention discloses a sparsity tracking dynamic compressed sensing adaptive channel equalization method. For a fast time-varying multi-path wireless communication channel, the problem that the tracking performance of a tap support set of an existing dynamic compressed sensing self-adaptive channel equalizer is insufficient is mainly solved. The implementation process is divided into two stages: 1) a training stage: based on a received signal and a pilot frequency sequence, training a full-tap equalizer by adopting an adaptive filtering algorithm in combination with a data multiplexing technology to enable a tap coefficient to reach a convergence state; and 2) a symbol detection stage: simultaneously tracking an equalizer tap support set and a coefficient value by adopting a sparsity tracking dynamic compressed sensing algorithm, and estimating a data symbol. According to the method, the sparsity tracking dynamic compressed sensing method is applied to adaptive equalization, dynamic tracking of the tapped support set and the coefficient value of the equalizer is achieved so as to better adapt to environmental changes, and the method has high practical application value.

Description

Technical Field

[0001] The invention belongs to the field of adaptive channel equalization, and in particular relates to a sparsity tracking dynamic compressed sensing adaptive channel equalization method. Background Art

[0002] The long multipath effect of wireless channels causes serious inter-symbol interference in the received signal, which poses a challenge to reliable data transmission. Equalization technology can effectively suppress inter-symbol interference and is a key technology at the receiving end. There are currently two main types of equalizer design methods: Channel-Estimation-Based Equalizer (CEE) and Direct Adaptive Equalizer (DAE). Compared with CEE, DAE has attracted widespread attention due to its advantages such as lower complexity and good environment tracking capabilities.

[0003] Adaptive channel equalizers have a sparse characteristic, which means that a small number of equalizer taps occupy most of the energy. Taking advantage of this characteristic, the sparse adaptive filtering algorithm can effectively improve the equalization performance. For example, the equalization based on the Improved Proportionate Normalized Minimum Symbol Error Rate (IPNMSER) ​​algorithm has been applied and verified.

[0004] Dynamic compressed sensing technology is a newly emerging branch in the field of compressed sensing, which aims to process time-varying sparse signals whose signal support sets change over time. This characteristic of being applicable to signals that change dynamically in the time dimension makes it stand out in many application fields. At present, dynamic greedy algorithms in dynamic compressed sensing have been applied in adaptive channel equalization. In this method, the tap coefficients of the equalizer are the sparse signals to be reconstructed. By iteratively tracking the support set of the tap vector of the equalizer, 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 obtained. Compared with traditional adaptive equalization, adaptive equalization based on dynamic compressed sensing can be reduced from the dimension of the full tap to the dimension of the support set, thereby reducing the computational complexity of the equalizer and improving the convergence speed. However, the existing method requires the sparsity of the equalizer, that is, the size of the support set, to be set in advance. In a time-varying channel environment, this method has insufficient support set tracking performance for the equalizer and cannot dynamically track the support set of the equalizer with a variable size. Summary of the invention

[0005] The present invention proposes a sparsity-trackable (ST) dynamic compressed sensing adaptive channel equalization method to solve the problem that the number of sparse adaptive channel equalization taps cannot be tracked at the symbol level and the computational complexity is high.

[0006] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

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

[0008] (1) Determine the number of branches N at the transmitting end. The transmitted symbol block on the nth branch is denoted as x. n =[x n,1 ,…,x n,K ] T , whose length is K, including K p pilot symbols and K d data symbols, x n,k represents the kth transmitted symbol on the nth branch;

[0009] (2) Determine the number of receiving branches M, and the received block on the mth branch is denoted as y m =[y m,1 ,…,y m,K+L-1 ] T , where L represents the channel length, y m,k represents the kth received symbol on the mth branch;

[0010] (3) Determine the adaptive decision feedback equalizer parameters, including the feedforward FF equalizer length parameter K 1 and its corresponding adaptive update step size μ w and the post-feedback FB equalizer length parameter K 2 and its corresponding adaptive update step size μ f , data multiplexing 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 for data symbol detection, the sparsity 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 the kth moment on the mth receiving branch is expressed as follows

[0014]

[0015] where x n,k-l represents the transmitted symbol of the nth transmitting branch, h n,m,k (l) represents the lth tap of the subchannel between the nth transmitting branch and the mth receiving branch at time k, n m,k represents additive noise.

[0016] Preferably: in step (4), based on the received signal and the pilot symbol, the estimation of the kth transmitted symbol of the nth transmit branch output by the full-tap adaptive decision feedback equalizer is as follows:

[0017]

[0018] in Represents the received signal vector, and the part beyond the actual received sequence is padded with zeros. is the decision symbol vector, where

[0019]

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

[0021] w n,k and f n,k The FF equalizer coefficient vector and FB equalizer coefficient vector corresponding to the nth transmitting branch at time k are updated using the sparse adaptive filtering algorithm; the equalizer training process is repeated N times on the pilot signal block. dr After the training, the feedforward FF equalizer is obtained. and FB equalizer The lengths are L w =M(K 1 +1), L f =NK 2 -1; and Provides an initial equalization vector for data symbol detection.

[0022] Preferably: 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 tap support set of the equalizer. The specific implementation method is as follows:

[0023] First, the candidate support set and coefficient value of the equalizer tap are dynamically updated. The size of the FF and FB equalizer support sets at time k are and Set the initial values ​​to and The proxy signal vectors corresponding to the FF and FB equalizers at time k are The lengths are L w ,L f , set the initial values ​​to zero vector, k time The update equation is:

[0024]

[0025]

[0026] in, is the residual signal, the initial value v n,0 =x n,1 , 0<λ≤1 is the forgetting factor, They represent the received signal vector u at time k-1 respectively k-1 and the decision symbol vector d k-1 conjugation of;

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

[0028]

[0029] Where supp(·) represents the operation of obtaining the support set; based on The candidate support set of the equalizer vector at time k is calculated as follows

[0030]

[0031]

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

[0033] Get the candidate support set Afterwards, an adaptive filtering algorithm is used to adaptively filter some taps of the decision feedback equalizer. and The equalizer coefficients at the corresponding positions of the vector are updated, while the coefficients at other positions remain unchanged; define for Middle support set The vector consisting of the corresponding elements on for Middle support set The vector consisting of the corresponding elements on ;

[0034] The IPNMSER algorithm is used to update the tap coefficients of the partial tap adaptive decision feedback equalizer on the support set as follows

[0035]

[0036] in They are The complement of Represents the scale matrix Middle support set The diagonal matrix consisting of the corresponding elements on Depend on Calculated, Represents the scale matrix Middle support set The diagonal matrix consisting of the corresponding elements on Depend on Calculated, I n,k is the error indicator;

[0037] Next, we obtain a new support set based on the updated equalizer vector and as follows

[0038]

[0039]

[0040] get After that, the symbol estimation is as follows

[0041]

[0042] Finally, the equalizer sparsity is updated for symbol estimation at the k+1th moment, and the update equation is as follows:

[0043]

[0044] in Indicates rounding up operation. and They represent the sparsity measure of the FF and FB equalizer tap vectors at time k, respectively, and the calculation formula is:

[0045]

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

[0047] Beneficial effects: The present invention adopts data multiplexing technology to effectively improve the training quality of the full-tap adaptive equalizer. In the data symbol detection stage, the sparsity tracking dynamic compressed sensing technology is adopted. Compared with the existing dynamic compressed sensing technology, this technology can realize the dynamic tracking of the support set and coefficient values ​​of the sparse equalizer, so that the equalizer can better adapt to environmental changes, reduce the complexity in practical applications, and obtain certain performance gains. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is the estimated channel impulse response (CIR) amplitude diagram;

[0049] Figure 2 Workflow diagram of adaptive equalizer for sparsity tracking;

[0050] Figure 3 It is a comparison chart of the tap number changes of the FF equalizer of the fixed sparsity adaptive equalizer SpAdOMP-IPNMSER-DAE and the sparsity tracking dynamic compressed sensing IPNMSER adaptive equalizer ST-SpAdOMP-IPNMSER-DAE;

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

[0052] Figure 5 This is a comparison chart of the mean square error (MSE) of SpAdOMP-IPNMSER-DAE and ST-SpAdOMP-IPNMSER-DAE. DETAILED DESCRIPTION

[0053] A sparsity tracking dynamic compressed sensing adaptive channel equalization method of the present invention comprises the following steps:

[0054] (1) Determine the number of branches N at the transmitting end. The symbol block sent on the nth branch is x. n =[x n,1 ,…,x n,K ] T , whose length is K, including K p pilot symbols and K d data symbols;

[0055] (2) Determine the number of receiving branches M, and the received block on the mth branch is denoted as y m =[y m,1 ,…,y m,K+L-1] T , where L represents the channel length;

[0056] (3) Determine the adaptive decision feedback equalizer parameters, including the feedforward (FF) equalizer length parameter K 1 and the length parameter K of the feedback (FB) equalizer 2 , and 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, a sparse adaptive filtering algorithm combined with data multiplexing technology is used to train the full-tap equalizer. The same pilot block is used to repeat multiple training times. The number of repetitions is the number of data multiplexing times.

[0058] (5) Using the full-tap equalizer obtained in step (4) as the initial value, data symbol detection is performed, and sparsity tracking dynamic compressed sensing technology is used to dynamically track the tap support set and coefficient values ​​of the equalizer.

[0059] In step (2), the received signal at the kth time on the mth receiving branch is expressed as follows:

[0060]

[0061] where x n,k-l represents the transmitted symbol of the nth transmitting branch, h n,m,k (l) represents the lth tap of the subchannel between the nth transmitting branch and the mth receiving branch at time k, n m,k represents additive noise.

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

[0063]

[0064] in Represents the received signal vector, and the part beyond the actual received sequence is padded with zeros. is the decision symbol vector, where

[0065]

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

[0067] w n,k and fn,k The FF equalizer coefficient vector and FB equalizer coefficient vector corresponding to the nth transmitting branch at time k are updated using the sparse adaptive filtering algorithm. To ensure convergence, the equalizer training process is repeated N times on the pilot signal block. dr After the training, we get the full-tap FF equalizer. and FB equalizer The lengths are L w =M(K 1 +1), L f =NK 2 -1. and Providing an initial equalization 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 tap support set of the equalizer, and a sparse adaptive filtering algorithm is used to update the tap coefficients of the equalizer. The specific implementation method is as follows:

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

[0070]

[0071]

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

[0073]

[0074] Where supp(·) represents the operation of obtaining the support set; based on The candidate support set of the equalizer vector at time k is calculated as follows

[0075]

[0076]

[0077] Get the candidate support set Afterwards, an adaptive filtering algorithm is used to filter the full-tap equalizer. and The equalizer coefficients at the corresponding positions of the vector are updated, while the tap coefficients at the other positions remain unchanged. for Middle support set The vector of corresponding elements is similarly defined Without loss of generality, the IPNMSER algorithm is used to update the tap coefficients of the equalizer on the support set as follows:

[0078]

[0079] in They are The complement of Represents the scale matrix Middle support set The vector consisting of the corresponding elements on , Depend on Calculated, It can be defined similarly, I n,k is the error indicator. Next, a new support set is obtained based on the updated full-tap equalizer vector. and as follows

[0080]

[0081]

[0082] get After that, the symbol estimation can be done as follows

[0083]

[0084] Obviously, the estimation only involves the coefficients on the support set instead of all coefficients, thus reducing the complexity of equalization.

[0085] Finally, the equalizer sparsity is updated for symbol estimation at the k+1th moment, and the update equation is as follows:

[0086]

[0087] in Indicates rounding up operation. and They represent the sparsity measure of the FF and FB equalizer tap vectors at time k, respectively, and the calculation formula is:

[0088]

[0089] where ζ is a small positive number; after the update and For the dynamic update of the tap support set and coefficient value of the equalizer at time k+1, the three-step update of step (5) is repeated in sequence until the detection of the data symbol is completed.

[0090] The present invention will be further explained below in conjunction with the embodiments.

[0091] The method of the present invention is verified by using the sea trial data of MIMO single-carrier underwater acoustic communication with two transmissions and four receptions. The sea trial transmission distance is 2km, the carrier frequency is 17kHz, and the symbol period is 0.2ms. The channel coding adopts a low-density parity check code with a code rate of 1 / 2, and the symbol modulation mode is QPSK. A transmission block contains K = 1024 QPSK symbols, where the pilot symbol length is K p =200, data symbol length K d =824. Figure 1 The channel estimation result is shown, and the channel length is about L=70 symbol periods. The working process of the method of the present invention is as follows Figure 2 As shown. The equalizer length parameters are set to K 1 =40, K 2 =50. Under this setting, the lengths of the full-tap FF and FB equalizers are L w =164,L f =99.

[0092] In the experimental training phase, the improved proportional normalized minimum symbol error rate IPNMSER algorithm is used to track the equalizer coefficients, and the step size parameter of IPNMSER-DAE is set to μ w =μ f =0.2; in the symbol detection stage, the dynamic compressed sensing IPNMSER adaptive equalizer ST-SpAdOMP-IPNMSER-DAE with sparsity tracking is used for symbol estimation, with the forgetting factor λ=0.99 and ζ=10 -12 , the initial size of the tap support set of FF and FB equalizers is The experiment uses the fixed sparsity adaptive equalizer SpAdOMP-IPNMSER-DAE as a control, and the tap support set sizes of its FF and FB equalizers are fixed to 110 and 20 respectively. dr = 0, 2, 4, 6. A total of 5 burst transmission data were processed, each burst contained 50 blocks, a total of 250 blocks, and the performance measurement indicators included the bit error rate BER and the symbol estimation mean square error MSE.

[0093] Figure 3 The number of FF equalizer taps in a block of SpAdOMP-IPNMSER-DAE and ST-SpAdOMP-IPNMSER-DAE is compared. The 25th and 50th blocks of the 5th burst are selected as examples for demonstration without loss of generality. For SpAdOMP-IPNMSER-DAE, the number of equalizer taps is always the preset 110, so only one curve is shown in the figure. The number of taps of ST-SpAdOMP-IPNMSER-DAE changes dynamically. It can be seen that the number of taps of ST-SpAdOMP-IPNMSER-DAE on two different blocks is less than that of SpAdOMP-IPNMSER-DAE, indicating that the proposed new scheme has lower complexity; in addition, there is a large difference in the number of taps of ST-SpAdOMP-IPNMSER-DAE on 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 are compared. It can be seen that the BER of the two equalization schemes increases with N dr The BER performance of ST-SpAdOMP-IPNMSER-DAE is better than that of SpAdOMP-IPNMSER-DAE, especially in N dr = 0, indicating 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 are compared. It can be seen that in the training phase, that is, within the first 200 iterations, the convergence speed of ST-SpAdOMP-IPNMSER-DAE is slightly faster. In the data detection phase, ST-SpAdOMP-IPNMSER-DAE can obtain a lower MSE overall.

[0096] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A sparsity tracking dynamic compressed sensing adaptive channel equalization method, characterized in that: The steps include: (1) Determine the number of branches N at the transmitting end. The transmitted symbol block on the nth branch is denoted as x. n =[x n,1 ,…,x n,K ] T , whose length is K, including K p pilot symbols and K d data symbols, x n,k represents the kth transmitted symbol on the nth branch; (2) Determine the number of receiving branches M, and the received block on the mth branch is denoted as y m =[y m,1 ,…,y m,K+L-1 ] T , where L represents the channel length, y m,k represents the kth received symbol on the mth branch; (3) Determine the adaptive decision feedback equalizer parameters, including the feedforward FF equalizer length parameter K1 and its corresponding adaptive update step size μ w And the post-feedback FB equalizer length parameter K2 and its corresponding adaptive update step size μ f , data multiplexing 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 for data symbol detection, the sparsity 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.

2. The sparsity tracking dynamic compressed sensing adaptive channel equalization method according to claim 1, characterized in that: In step (2), the received signal at the kth time on the mth receiving branch is expressed as follows: where x n,k-l represents the transmitted symbol of the nth transmitting branch, h n,m,k (l) represents the lth tap of the subchannel between the nth transmitting branch and the mth receiving branch at time k, n m,k represents additive noise.

3. The sparsity tracking dynamic compressed sensing adaptive channel equalization method according to claim 1, characterized in that: In step (4), based on the received signal and the pilot symbol, the estimation of the kth transmitted symbol of the nth transmit branch output by the full-tap adaptive decision feedback equalizer is as follows: in Represents the received signal vector, and the part beyond the actual received sequence is padded with zeros. is the decision symbol vector, where During the training phase, Using known pilot symbols; w n,k and f n,k The FF equalizer coefficient vector and FB equalizer coefficient vector corresponding to the nth transmitting branch at time k are updated using the sparse adaptive filtering algorithm; the equalizer training process is repeated N times on the pilot signal block. dr After the training, the feedforward FF equalizer is obtained. and FB equalizer The lengths are L w =M(K1+1),L f =NK2-1; and Provides initial equalization vector for data symbol detection.

4. The sparsity tracking dynamic compressed sensing adaptive channel equalization method according to claim 3 is characterized in that: 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 tap support set of the equalizer. The specific implementation method is as follows: First, the candidate support set and coefficient value of the equalizer tap are dynamically updated. The size of the FF and FB equalizer support sets at time k are and Set the initial values ​​to and The proxy signal vectors corresponding to the FF and FB equalizers at time k are The lengths are L w ,L f , set the initial values ​​to zero vector, k time The update equation is: in, is the residual signal, the initial value v n,0 =x n,1 , 0<λ≤1 is the forgetting factor, They represent the received signal vector u at time k-1 respectively k-1 and the decision symbol vector d k-1 conjugation of; based on and the sparsity information at time k and Determine the following support set Where supp(·) represents the operation of obtaining the support set; based on The candidate support set of the equalizer vector at time k is calculated as follows 5. The sparsity tracking dynamic compressed sensing adaptive channel equalization method according to claim 4, 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: Get the candidate support set Afterwards, an adaptive filtering algorithm is used to adaptively filter some taps of the decision feedback equalizer. and The equalizer coefficients at the corresponding positions of the vector are updated, while the coefficients at other positions remain unchanged; define for Middle support set The vector consisting of the corresponding elements on for Middle support set The vector consisting of the corresponding elements on ; The IPNMSER algorithm is used to update the tap coefficients of the partial tap adaptive decision feedback equalizer on the support set as follows in They are The complement of Represents the scale matrix Middle support set The diagonal matrix consisting of the corresponding elements on Depend on Calculated, Represents the scale matrix Middle support set The diagonal matrix consisting of the corresponding elements on Depend on Calculated, I n,k is the error indicator; Next, we obtain a new support set based on the updated equalizer vector and as follows get After that, the symbol estimation is as follows Finally, the equalizer sparsity is updated for symbol estimation at the k+1th moment, and the update equation is as follows: in Indicates rounding up operation. and They represent the sparsity measure of the FF and FB equalizer tap vectors at time k, respectively, and the calculation formula is: Where ζ is a small positive number; repeat step (5) until all data symbols are detected.

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