CN115913842A - Efficient channel equalization method for direct sequence spread spectrum underwater acoustic communication - Google Patents
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Abstract
The invention discloses an efficient channel equalization method for direct sequence spread spectrum underwater acoustic communication. Aiming at a direct sequence spread spectrum underwater acoustic communication system, the problems of slow convergence, high complexity and high pilot frequency overhead of adaptive channel equalization are mainly solved. The method comprises the following implementation steps: firstly, determining related parameters of a hypothesis feedback equalizer; secondly, training the coefficient of the equalizer by adopting a proportional adjustment type adaptive filtering algorithm and a data reuse technology based on the pilot frequency symbol; thirdly, filtering unimportant equalizer coefficients based on a threshold method to obtain partial coefficient structure equalizers; and finally, estimating the data symbols by adopting a partial coefficient structure equalizer. The method fully utilizes the inherent sparse characteristic of the underwater acoustic channel equalization system, effectively solves the problems of high equalization complexity, low tracking speed and the like of the direct sequence spread spectrum underwater acoustic communication channel, and has higher practical application value.
Description
Technical Field
The invention belongs to the technical field of underwater acoustic communication, and particularly relates to a high-efficiency channel equalization method for direct sequence spread spectrum underwater acoustic communication.
Background
The Direct Sequence Spread Spectrum (DSSS) communication technology reduces the system operating signal-to-noise ratio requirement by spreading the transmitted signal energy over a wide frequency Spectrum, improves the concealment of communication, and has received wide attention in the field of underwater acoustic communication. The complexity of the underwater acoustic communication channel makes implementing reliable direct sequence spread spectrum underwater communication still face many challenges, and receiver algorithm design is still the focus of current research.
Currently, conventional direct sequence spread spectrum underwater acoustic communication receiver techniques include classical RAKE reception techniques, time Reversal (TR) techniques, and combinations thereof.
The performance of the RAKE reception technique depends on accurate tracking of channel state, which is difficult to guarantee under fast-changing underwater acoustic channel condition, and on the length of the spreading sequence, which may cause non-negligible inter-path interference if the sequence length is insufficient, and also may affect the performance. The basic idea of the time reversal technology is to focus multi-path signals into single-path signals to achieve the purpose of eliminating path interference, but the performance of the time reversal technology depends on the acquisition precision of channel state information and the number of receiving array elements, and the inter-path interference cannot be completely eliminated generally, so that the time reversal technology can only be applied to specific scenes.
In addition to the above-mentioned schemes, the Equalization-based reception technique is also concerned, and considering that direct sequence spread spectrum communication generally works under a low signal-to-noise ratio condition, and an error propagation phenomenon easily occurs by using a conventional decision Feedback Equalization technique, a Hypothesis Feedback Equalization (HFE) technique is proposed in the literature, so that the problem of error propagation is effectively solved. However, the equalization-based reception scheme is more complex than RAKE reception and time reversal reception, and especially the use of hypothesis feedback equalization further increases the amount of computation and is therefore less used in practical systems for a long time.
Disclosure of Invention
The technical problem is as follows: aiming at the problems of high complexity and low convergence of the existing direct sequence spread spectrum underwater acoustic communication self-adaptive hypothesis feedback equalization scheme, the invention provides an efficient channel equalization method for direct sequence spread spectrum underwater acoustic communication by utilizing the sparsity of an equalizer, so that the equalization complexity is effectively reduced while the convergence speed is improved.
The technical scheme is as follows: a high-efficiency channel equalization method for direct sequence spread spectrum underwater acoustic communication specifically comprises the following steps:
(1) Obtaining a chip-level received data sequence y (K), K =1,2, …, K, where the first K is p * L corresponding pilot symbols, L being the length of the spreading code;
(2) Determining the length of a full coefficient hypothesis feedback equalizer, including the length L of a forward equalizer w w And length L of backward equalizer f f Modulating the symbol constellation size Q;
(3) Determining proportion regulation type sparse self-adaptive filtering algorithm and data reuse times N dr And a partial coefficient hypothesis feedback equalizer coefficient selection threshold lambda w And λ f ；
(4) Training coefficients of a hypothesis feedback equalizer by adopting a self-adaptive filtering algorithm and a data reuse technology based on pilot frequency data;
(5) Based on the full coefficient hypothesis feedback equalizer obtained in the training stage, determining a reserved partial coefficient by applying a threshold, discarding the rest coefficients with small contribution, and obtaining a partial coefficient self-adaptive hypothesis feedback equalizer;
(6) And based on a part of coefficient self-adaptive hypothesis feedback equalizer, carrying out chip level equalization on the data symbols, and carrying out de-spread operation on the chip level equalized symbols to obtain final symbol estimation.
In the step (4), an improved proportional normalization least mean square adaptive algorithm is adopted to train the full coefficient hypothesis feedback equalizer based on the pilot frequency data. Since the training utilizes pilot symbols, the decision feedback symbol vector is completely known, and therefore only one equalizer needs to be trained, i.e., assuming that the feedback equalizer degenerates to a conventional decision feedback equalizer. For the convenience of discussion, we do not distinguish which transmitted symbol a certain chip-level symbol belongs to, and the forward part and reverse part of the equalizer are updated according to the formula
Wherein y (k) = [ y (k + L) w -1),...,y(k)] t For the received signal vector, d (k) = [ d (k-1),. D, d (k-L) f )] t For the chip-level decision symbol vector,
estimating an error for a symbol at the chip level, representing a conjugate, and->
For chip level equalization of symbols, μ is the update step size and δ is a small positive number, preventing division from being meaningless. />
For phase estimation, it can be obtained by phase-locked loop (PLL) techniques, i.e.
Wherein
K f1 And K f2 Are PLL parameters. G w (k) And G f (k) Is a diagonal matrix whose diagonal elements are respectively
Wherein w l (k) And f l (k) The l-th elements of w (k) and f (k), respectivelyThe content of the element is as follows,
epsilon is a small positive number, and | alpha | is less than or equal to 1. The above training process repeats N dr Next, a final full coefficient equalizer vector is obtained>
And &>
In the step (5), based on the threshold lambda w And λ f Obtaining a partial coefficient index set as follows: first, two null sets Λ are defined w And Λ f Then, the following operations are performed: for 1. Ltoreq. L. Ltoreq.L w If, if
Then Λ w ＝Λ w U.l; likewise for 1. Ltoreq. L. Ltoreq.L f If->
Then Λ f ＝Λ f U.l, the finally obtained partial coefficient index set is
And &>
L 'are the sizes thereof' w And L' f . Based on Λ w And Λ f Obtaining a partial coefficient equalizer vector pick>
And &>
/>
In step (6), a block diagram of the hypothesis feedback equalizer for estimating the data symbols is shown in fig. 3. As can be seen, to obtain an estimate of the ith symbol in the nth symbol period, the equalizer has Q parallel branches, the ith branch corresponding to the ith hypothesis H for the nth symbol i :s(n)＝a i Wherein a is i Is the ith symbol of the constellation diagram. The initialization values of the forward and backward equalizers of each branch are set to the partial coefficient equalizer w obtained in step 5 s And f s After that, each time equalization of one symbol is completed, they are reset to the equalizer corresponding to the best hypothesis branch. In hypothesis H i Under the condition, the following chip level equalization symbols are obtained
Wherein w s,i (n, l) and f s,i (n, l) are the forward and reverse equalizer vectors for the ith symbol in the nth symbol period,
for a corresponding phase estimate, is>
Is H i A chip decision vector under conditions. When the balance of all L code element symbols in the nth symbol is finished, the code element balance symbols obtained under different hypotheses are despread, and the hypothesis H i The corresponding despread symbol is estimated to be->
Wherein->
Is a spreading code. Finally, based on the despread symbol estimate, the best decision index->
And then obtains the final symbol estimate as->
Has the beneficial effects that: the invention utilizes the inherent sparse characteristic of the underwater acoustic channel equalizer, reduces the effective tap number of the equalizer, improves the convergence speed of the equalizer and saves the pilot frequency symbol expenditure on one hand, and reduces the calculation complexity on the other hand.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a block diagram of a direct sequence spread spectrum underwater acoustic communication system;
FIG. 3 is a block diagram of an adaptive hypothesis feedback equalizer;
FIG. 4 is a channel impulse response estimated based on experimental data;
fig. 5 is an equalized symbol constellation obtained under the condition that the signal-to-noise ratio is about 4.5dB, wherein (a) and (b) are a chip symbol constellation and a symbol constellation, respectively, obtained by the full coefficient hypothesis feedback equalizer, and (c) and (d) are a chip symbol constellation and a symbol constellation, respectively, obtained by the partial coefficient hypothesis feedback equalizer of the present invention.
FIG. 6 is a plot of the symbol mean square error of a full coefficient and partial coefficient equalizer in comparison;
fig. 7 is a graph comparing Symbol Error Rates (SER) of 17 receive channels using full coefficient and partial coefficient hypothesis feedback equalizers under the experimental conditions.
Detailed Description
The invention is further explained below with reference to the drawings.
Experiments were carried out according to the block diagram of the underwater acoustic communication system shown in fig. 2, with the number of sending hydrophones N t 1, number of received hydrophones N r Carrier frequency f of 17 c At 5.5kHz, QPSK modulation is used and the spreading code is an m-sequence of length L = 7. Each transmitted data block comprises 1300 symbols, wherein the number of pilot symbols K p 276, number of data symbols K d Is 1024, the symbol period T s Is 2.7ms. Receiving end sampling rate f s Is 64kHz. Based on experimental numberAccording to the estimated impulse response of the underwater acoustic channel as shown in fig. 4, it can be seen that the underwater acoustic channel in the experimental environment has a significant 2-path and the chip-level channel length is about 200.
Firstly, an improved proportional normalization least mean square adaptive filtering algorithm is adopted to carry out full coefficient equalizer training, and parameters in a training stage are set as follows: α = -0.5, μ =0.1, e =1, δ =0.00001, partial coefficient equalizer amplitude threshold λ w And λ f All are 0.0067, and the parameters of the second-order phase-locked loop are as follows: k f1 ＝0.007，K f2 ＝K f1 /10. Setting the full coefficient forward equalizer length L according to the channel length w 400, inverse equalizer length L f Is 200. Number of data reuse N dr Is 8. Applying a threshold to the trained full coefficient equalizer to obtain a partial coefficient equalizer with respective lengths L 'of forward equalizer and backward equalizer' w =85 and L' f =188, whereby the partial coefficient equalizer and full coefficient equalizer complexity ratio can be calculated as
Therefore, partial coefficient equalization can save nearly 43% of the calculation amount.
Data symbols are equalized by adopting full coefficient hypothesis feedback equalization and partial coefficient hypothesis feedback equalization respectively, in the data symbol equalization stage, the parameters of the self-adaptive equalizer are set to be mu =0.15 and epsilon =0.1, and the parameters of the phase-locked loop are set to be K f1 ＝0.006，K f2 ＝K f1 And/10, the rest parameters are the same as the training stage.
FIG. 5 shows a chip-level and symbol-level equalized symbol constellation diagram for two equalization methods, with a received data chip-level signal-to-noise ratio of about 4.5dB dr And =4. The graph (a) and the graph (c) are full coefficient and partial coefficient hypothesis feedback equalization chip-level equalization symbol constellations respectively, and the graph (b) and the graph (d) are full coefficient and partial coefficient hypothesis feedback equalizer symbol-level constellations respectively. From the constellation diagramThe performance of both balances is comparable.
Fig. 6 is a diagram of the equalized symbol mean square error comparison of two equalizers, and it can be seen that partial coefficient equalization achieves a lower mean square error when the data reuse number is greater than 3.
Fig. 7 is a graph comparing Symbol Error Rates (SER) over 17 receive channels for two equalizers. It can be seen that the partial coefficient equalization scheme has overall performance comparable to the full coefficient equalization scheme, with additional performance gain on individual channels.
In conclusion, the invention can reduce the computation complexity while ensuring good balance performance.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention
The scope of the invention is defined by the following claims.
Claims (4)
1. A method for efficient channel equalization for direct sequence spread spectrum underwater acoustic communications, comprising the steps of:
(1) Obtaining a chip-level received data sequence y (K), K =1,2, …, K, where the first K is p * L corresponding pilot symbols, L being the length of the spreading code;
(2) Determining the length of a full coefficient hypothesis feedback equalizer, including the length L of a forward equalizer w w And length L of backward equalizer f f Modulating the symbol constellation size Q;
(3) Determining proportion regulation type sparse self-adaptive filtering algorithm and data reuse times N dr And a partial coefficient hypothesis feedback equalizer coefficient selection threshold lambda w And λ f ；
(4) Training coefficients of a hypothesis feedback equalizer by adopting a self-adaptive filtering algorithm and a data reuse technology based on pilot frequency data;
(5) Based on the full coefficient hypothesis feedback equalizer obtained in the training stage, determining a reserved partial coefficient by applying a threshold, and discarding the other coefficients with small contribution to obtain a partial coefficient self-adaptive hypothesis feedback equalizer;
(6) And based on a part of coefficient self-adaptive hypothesis feedback equalizer, carrying out chip level equalization on the data symbols, and carrying out de-spread operation on the chip level equalized symbols to obtain final symbol estimation.
2. The method for efficient channel equalization for direct sequence spread spectrum underwater acoustic communication according to claim 1, characterized by: in step (4), the forward part and reverse part of the equalizer are updated according to the formula
Wherein y (k) = [ y (k + L) w -1),K,y(k)] t For receiving the signal vector, d (K) = [ d (K-1), K, d (K-L) f )] t For the chip-level decision symbol vector,
estimating an error for a symbol at the chip level, representing a conjugate, and->
For chip level equalized symbols, μ is the update step size, δ is a positive number;
Wherein
K f1 And K f2 Is a PLL parameter; g w (k) And G f (k) Is a diagonal matrix whose diagonal elements are respectively
Wherein, w l (k) And f l (k) The l-th elements of w (k) and f (k),
epsilon is a positive number, and | alpha | is less than or equal to 1; the above training process repeats N dr Next, a final full coefficient equalizer vector is obtained>
And &>
3. The method for efficient channel equalization for direct sequence spread spectrum underwater acoustic communication according to claim 1, characterized by: in step (5), based on the threshold lambda w And λ f Obtaining a partial coefficient index set as follows: first, two null sets Λ are defined w And Λ f Then, the following operations are performed: for 1. Ltoreq. L. Ltoreq.L w If it is determined that
Then Λ w ＝Λ w U is not greater than l; likewise for 1. Ltoreq. L. Ltoreq.L f If->
Then Λ f ＝Λ f U.l, the finally obtained partial coefficient index set is
And &>
L 'are the sizes thereof' w And L' f (ii) a Based on Λ w And Λ f Obtaining a partial coefficient equalizer vector pick>
And &>
4. The method for efficient channel equalization for direct sequence spread spectrum underwater acoustic communication according to claim 1, characterized by: in step (6), to obtain the estimate of the ith symbol in the nth symbol period, the equalizer has Q parallel branches, and the ith branch corresponds to the ith hypothesis H of the nth symbol i :s(n)＝a i Wherein a is i Is the ith symbol of the constellation diagram; the initialization value of each branch forward and backward equalizer is set as a partial coefficient equalizer w s And f s After that, every time the equalization of one symbol is completed, they are reset to the equalizer corresponding to the best hypothesis branch; in hypothesis H i Under the condition, the following chip level equalization symbols are obtained
Wherein w s,i (n, l) and f s,i (n, l) is the nth symbolThe forward and reverse equalizer vectors corresponding to the ith symbol in the cycle,
for a corresponding phase estimate, based on the phase value of the reference signal>
Is H i A chip decision vector under conditions; when the balance of all L code element symbols in the nth symbol is finished, the code element balance symbols obtained under different hypotheses are despread, and the hypothesis H i The corresponding despread symbol is estimated to be->
Wherein->
Is a spreading code; finally, based on the despread symbol estimate, the best decision index->
And then obtains the final symbol estimate as->
/>
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105323203A (en) * | 2015-11-12 | 2016-02-10 | 哈尔滨工程大学 | Anti-multipath underwater acoustic communication based on orthogonal carrier sweep expansion technology |
| CN107359899A (en) * | 2017-06-24 | 2017-11-17 | 苏州桑泰海洋仪器研发有限责任公司 | OFDM spread-spectrum underwater sound communication is without pilot tone judgment feedback channel estimation method under the conditions of condition of sparse channel |
| US20190068294A1 (en) * | 2017-08-25 | 2019-02-28 | Yahong Rosa Zheng | Turbo receivers for multiple-input multiple-output underwater acoustic communications |
| CN109474304A (en) * | 2018-11-29 | 2019-03-15 | 中国海洋大学 | Adaptive multi-standard underwater sound communication system and method |
| CN114389754A (en) * | 2021-12-28 | 2022-04-22 | 大连理工大学 | Frequency domain self-adaptive Turbo equalization method based on FBNLMS algorithm |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105323203A (en) * | 2015-11-12 | 2016-02-10 | 哈尔滨工程大学 | Anti-multipath underwater acoustic communication based on orthogonal carrier sweep expansion technology |
| CN107359899A (en) * | 2017-06-24 | 2017-11-17 | 苏州桑泰海洋仪器研发有限责任公司 | OFDM spread-spectrum underwater sound communication is without pilot tone judgment feedback channel estimation method under the conditions of condition of sparse channel |
| US20190068294A1 (en) * | 2017-08-25 | 2019-02-28 | Yahong Rosa Zheng | Turbo receivers for multiple-input multiple-output underwater acoustic communications |
| CN109474304A (en) * | 2018-11-29 | 2019-03-15 | 中国海洋大学 | Adaptive multi-standard underwater sound communication system and method |
| CN114389754A (en) * | 2021-12-28 | 2022-04-22 | 大连理工大学 | Frequency domain self-adaptive Turbo equalization method based on FBNLMS algorithm |
Non-Patent Citations (1)
| Title |
|---|
| 韩晶;黄建国;申晓红;汪玉;: "一种用于多码扩频水声通信的假设反馈均衡算法", 西北工业大学学报, no. 06, 30 December 2006 (2006-12-30) * |
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