CN111654455B - Underwater sound channel equalization method based on breadth-enhanced firework algorithm - Google Patents

Underwater sound channel equalization method based on breadth-enhanced firework algorithm Download PDF

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CN111654455B
CN111654455B CN202010483899.2A CN202010483899A CN111654455B CN 111654455 B CN111654455 B CN 111654455B CN 202010483899 A CN202010483899 A CN 202010483899A CN 111654455 B CN111654455 B CN 111654455B
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fireworks
firework
population
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breadth
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CN111654455A (en
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王景景
姜宁
童刚
徐凌伟
杨星海
施威
李海涛
郭瑛
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Qingdao University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0238—Channel estimation using blind estimation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B13/00—Transmission systems characterised by the medium used for transmission, not provided for in groups H04B3/00 - H04B11/00
    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
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Abstract

The invention discloses an underwater sound channel equalization method based on an breadth-enhanced firework algorithm, which comprises the steps of firstly providing the breadth-enhanced firework algorithm, initializing a population by adopting a good point set theory in a new algorithm, and improving the randomness and uniformity of individual population; the next generation population selection method based on the breadth-first strategy and the goodness-first strategy is provided, so that the position information of other fireworks with good adaptability is utilized, the population diversity is ensured, and the convergence speed is accelerated; by means of Gaussian disturbance on the selected fireworks, population diversity is further increased, the ability of an algorithm to jump out of a local extreme value is increased, and the situation that the selected fireworks fall into local optimum is avoided; and secondly, taking the mean square error between the equalized signal and the ideal noiseless signal as a fitness function of the breadth-enhanced firework algorithm, further optimizing the initial tap coefficient of the CMA, and finally obtaining a blind equalization signal under the optimal initial tap coefficient. By utilizing the method and the device, the underwater acoustic channel transmission signal with strong robustness and good balance can be finally obtained.

Description

Underwater sound channel equalization method based on breadth-enhanced firework algorithm
Technical Field
The invention belongs to the field of underwater sound channel equalization, and particularly relates to an underwater sound channel equalization method based on an breadth-enhanced firework algorithm.
Background
Intersymbol interference is very serious in a complex marine environment, and great difficulty is brought to underwater acoustic communication. The multipath interference of the underwater acoustic channel can be overcome by adopting the channel equalization technology. The channel equalization technique recovers the original signal as much as possible by compensating for the loss of the transmission signal in terms of amplitude, frequency, phase, etc. during the channel transmission. The traditional equalization technology needs to continuously send training sequences to track channel changes, and although the reliability of data transmission can be improved, a large amount of repeated training reduces the communication efficiency. The blind equalization technique does not need to send training sequences between transmission data, only needs to obtain some statistical characteristics of the sending sequences, and can recover the sending signals according to the observation data received by the receiving end. The most classical Constant Modulus Algorithm (CMA) of blind equalization is simple in calculation and good in robustness, but has a slow convergence rate and a large steady-state error.
In order to make up for the defects of the traditional blind equalization algorithm, the intelligent optimization algorithm based on the meta-heuristic method is introduced into the optimization of the blind equalization algorithm, and comprises a gray wolf optimization algorithm, an artificial fish swarm algorithm, an artificial bee swarm algorithm and the like. These optimization algorithms still have a great room for improvement in convergence speed and search accuracy. Moreover, the performance of the equalizer can be optimized only to a certain extent through the improvements, and the problems of low convergence speed and large steady-state error are not fundamentally solved.
Disclosure of Invention
The invention provides an underwater sound channel equalization method based on an breadth-enhanced firework algorithm, which is used for overcoming the defects of the prior art.
The invention firstly provides a breadth-enhanced firework algorithm (BEFWA), and the new algorithm adopts a good point set theory to initialize a population, so that the randomness and uniformity of individual population are improved; the next generation population selection method based on the breadth-first strategy and the goodness-first strategy is provided, so that the position information of other fireworks with good adaptability is utilized, the population diversity is ensured, and the convergence speed is accelerated; by means of Gaussian disturbance on the selected fireworks, population diversity is further increased, the ability of an algorithm to jump out of a local extreme value is increased, and the situation that the selected fireworks fall into local optimum is avoided. And secondly, taking the mean square error between the equalized signal and the ideal noiseless signal as a fitness function of the breadth-enhanced firework algorithm, further optimizing the initial tap coefficient of the CMA, and finally obtaining a blind equalization signal under the optimal initial tap coefficient.
In order to realize the purpose of the invention, the invention is realized by adopting the following specific technical scheme:
an underwater sound channel equalization method based on an extent-enhanced firework algorithm comprises the following steps:
s1: collecting and processing underwater acoustic signal data;
s2: generating an initial firework population by using a good point set method, wherein each individual in the population is an initial tap coefficient vector of an equalizer;
s3: establishing a fitness function, specifically taking the mean square error between the equalized signal and the ideal noiseless signal as the fitness function of the breadth-enhanced firework algorithm;
s4: calculating the fitness value of each individual by using the initial tap coefficient vector obtained in the step S2 and the fitness function established in the step S3;
s5: updating the position information of the fireworks based on the fitness value obtained in the step S4;
s6: selecting the next-generation fireworks from the fireworks position information obtained in S5 by applying a breadth-first selection strategy or a goodness-first selection strategy;
s7: performing Gaussian disturbance on the next-generation fireworks selected in the step S6;
s8: repeating the steps S3-S7 until the optimal initial tap coefficient under the condition of the minimum mean square error is obtained;
s9: and based on the optimal initial tap coefficient, processing the underwater sound signal data obtained in the step S1 by using a blind equalizer (CMA), and finally outputting a blind equalization signal.
The initial firework population should be distributed in the solution space as uniformly as possible, and particularly when the multivariate problem is solved, only the most representative individuals in the solution space are used as the initial population, so that the characteristics of the global space can be better reflected. If the excellence of the initial firework population is ensured, the convergence speed of the algorithm is greatly improved. Therefore, aiming at the defect of random initialization of the traditional firework algorithm, the initial firework population is generated by adopting the theory of the optimal point set.
The S2 is specifically:
setting the initial population of fireworks as X ═ X1,x2,…,xn) Wherein X isi(i-1, 2, …, n) is the initial position vector of the ith firework, n is the number of individuals in the firework, and the initial firework population is generated by using the optimal point set；
Firstly, solving the minimum prime number p according to the constraint condition (p-3)/2> -size, wherein the size represents the size of the firework population; substituting the obtained p into the following formula:
R(i)＝2×cos(2×pi×i/p)
obtaining R, wherein R is a one-dimensional vector with the length being the size of the firework population,
secondly, multiplying the decimal part of R with SN correspondingly, wherein SN is a one-dimensional vector from 1 to size; by the formula:
nest＝minV+(maxV-minV)×R
obtaining nest, wherein maxV and minV are the upper and lower boundaries of the firework population individuals;
and finally, disordering nest, assigning values to each dimension of the population, and finishing the initialization of the firework population.
The step S3 is specifically as follows:
taking an error function of the normal mode blind equalization technology as a fitness function of the breadth-enhanced firework algorithm, wherein the function is as follows:
Figure BDA0002518432560000031
wherein z (k) is a desired signal without noise, a (k) is a reconstructed signal after equalization, and N is a signal length; the cost function of the CMA is a function of the initial weight vector w, so w can be regarded as the position of fireworks in the breadth-enhanced firework algorithm, and the optimal value can be obtained by minimizing the fitness function; n signals are sequentially received by each generation of the evolution of the breadth-enhanced firework algorithm, the firework population individuals are brought into the fitness function to calculate the mean square error, namely the fitness value of each individual, and the optimal initial weight vector w is obtained under the condition of obtaining the minimum mean square error.
The firework algorithm firstly reserves the optimal fireworks in the next generation of population selection mode, and then selects a part of fireworks farthest from other fireworks as a new generation of population. In the candidate set, if the individual density is high, i.e. when there are many other candidates around the individual, the probability that the individual is selected will be reduced. Although the overall diversity is ensured by the selection mode of the firework algorithm, better fireworks are not selected at the first time, and heuristic information in the optimization problem solving process is not considered. Namely, the traditional firework algorithm shows poor local searching capability. Therefore, aiming at the defects of the traditional firework algorithm selection mode, the invention adopts a breadth-first selection strategy or a goodness-first selection strategy to select the next generation fireworks.
The step S5 includes:
s5-1: evaluating individual fitness and generating explosion spark
The firework algorithm firstly generates N fireworks randomly in a feasible region omega, and records the adaptability value of each firework, wherein the fireworks with small adaptability values have small explosion range, generate more sparks, have large explosion range and generate less sparks. The fireworks explosion generates new explosion sparks, the number of the generated sparks and the explosion radius are respectively as follows:
Figure BDA0002518432560000032
Figure BDA0002518432560000033
wherein Y ismaxAnd YminRespectively representing the maximum value and the minimum value of population fitness, SiFor the number of sparks generated, AiThe radius of explosion is used, A and M are constants and are respectively used for adjusting the radius of explosion and the number of sparks, and epsilon is a minimum constant and is used for avoiding zero operation;
s5-2: generating variant sparks and applying mapping rules to off-boundary fireworks
In order to ensure the population diversity, Gaussian variation sparks are introduced into the algorithm, the global search capability of the algorithm is enhanced, the generated explosion sparks are subjected to Gaussian variation by randomly selecting k dimensions, and the process is shown as the following formula
Figure BDA0002518432560000034
Wherein randn (0,1) is a Gaussian variation function.
The firework algorithm is close to the boundary of the feasible region by adopting a random initialization method, so some explosion sparks and variant sparks exceed the range of omega of the feasible region, and are mapped into the range of the feasible region by adopting a certain mapping rule, and the mapping formula is as follows
Figure BDA0002518432560000041
Wherein
Figure BDA0002518432560000042
And
Figure BDA0002518432560000043
each represents the upper and lower boundaries of a k-dimensional boundary, and U (0,1) represents a random number distributed in a (0,1) interval.
The step S6 is specifically as follows:
selecting the next generation fireworks by adopting a breadth-first selection strategy:
sequencing all fireworks according to the size of the fitness value, firstly reserving an optimal firework, calculating the Euclidean distance between all fireworks and the optimal firework, and recording the Euclidean distance as dist (x, y) which is expressed as:
Figure BDA0002518432560000044
wherein xiAnd yiRepresenting each dimension of a position vector; sorting is carried out according to the distance between every two fireworks, and N/2-1 points (sparse areas) far away from the fireworks and N/2 points (dense areas) near to the fireworks are selected. Therefore, the global search range is ensured, the leadership capability of points with good adaptability is enhanced, the local search capability of fireworks with better adaptability is enhanced, a global optimal value is possibly found, and the iteration times are reduced.
The step S6 is specifically as follows:
selecting the next generation fireworks by adopting a goodness preference strategy:
and sequencing all fireworks according to the size of the fitness value, and selecting and reserving the optimal individuals and the suboptimal individuals. And calculating Euclidean distances between all fireworks and the fireworks, and recording the Euclidean distances as dist (x, y) and expressing the Euclidean distances as follows:
Figure BDA0002518432560000045
and arranging all fireworks in an ascending order according to the distance from the optimal fireworks, and selecting the first N/2-1 fireworks for reservation. And then, arranging all fireworks in a descending order according to the distance from the second optimal fireworks, and selecting the first N/2-1 fireworks for reservation. Therefore, the position information of other excellent fireworks in the population is fully utilized, and the diversity of the population is ensured.
The two selection strategies both play a role in balancing global search capability and local development capability, improve search precision on the basis of ensuring global search capability, and obviously improve convergence speed of the algorithm and stability of the algorithm.
The step S7 is detailed as follows
In order to further improve the diversity of the firework population and avoid the algorithm from falling into a local optimal value, Gaussian disturbance is respectively carried out on the selected next-generation fireworks: the Gaussian disturbance intensity is 1+ randn (1, D), where D is xiGenerating a 1 x D matrix meeting normal distribution, taking a dot product with the selected firework position vector, and selecting a constant 1 as a balance factor to avoid the firework position vector becoming smaller after disturbance. And performing Gaussian disturbance on the fireworks with poor fitness to obtain some better elite solutions, wherein the global optimum value may appear near the fireworks with poor fitness, and the global optimum value may be found by adding the Gaussian disturbance. The method has the advantages that Gaussian disturbance is carried out on the fireworks with good adaptability, the leadership capability of the fireworks with good adaptability is enhanced, the fireworks are closer to the trend of optimal position search, the global optimal value is found more quickly, and the convergence speed is accelerated.
Compared with the prior art, the invention has the following advantages and technical effects:
the method optimizes the initial weight of the CMA by utilizing the characteristics of strong global search capability and high convergence speed of the breadth-enhanced firework algorithm, effectively overcomes the influence of the initial weight in the CMA on the performance of the whole algorithm, improves the convergence speed of the traditional CMA algorithm, reduces steady-state errors and improves the balance effect. By utilizing the method and the device, the underwater acoustic channel transmission signal with strong robustness and good balance can be finally obtained.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 shows four optimization algorithms at f1(x)Testing a convergence performance curve graph on the function;
FIG. 3 shows four optimization algorithms at f2(x)Testing a convergence performance curve graph on the function;
FIG. 4 shows four optimization algorithms at f3(x)Testing a convergence performance curve graph on the function;
FIG. 5 shows four optimization algorithms at f4(x)Testing a convergence performance curve graph on the function;
FIG. 6 shows four optimization algorithms at f5(x)Testing a convergence performance curve graph on the function;
FIG. 7 shows four optimization algorithms at f6(x)Testing a convergence performance curve graph on the function;
FIG. 8 shows four optimization algorithms at f7(x)Testing a convergence performance curve graph on the function;
FIG. 9 shows four optimization algorithms at f8(x)Testing a convergence performance curve graph on the function;
FIG. 10 is a constellation comparison before and after CMA equalization;
FIG. 11 is a constellation comparison diagram before and after BEFWA-CMA equalization;
FIG. 12 is a plot of mean square error before and after equalization BEFWA-CMA, FWA-CMA, ABC-CMA and GWO-CMA at a signal-to-noise ratio of 5 dB;
FIG. 13 is a plot of mean square error before and after equalization BEFWA-CMA, FWA-CMA, ABC-CMA and GWO-CMA at a signal-to-noise ratio of 10 dB;
FIG. 14 is a plot of mean square error before and after equalization BEFWA-CMA, FWA-CMA, ABC-CMA and GWO-CMA at a signal-to-noise ratio of 15 dB;
FIG. 15 is a plot of mean square error before and after equalization for BEFWA-CMA, FWA-CMA, ABC-CMA and GWO-CMA at a signal-to-noise ratio of 20 dB.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and examples.
Example 1:
after collecting and processing underwater acoustic signal data, referring to fig. 1, an underwater acoustic channel equalization method based on an breadth-enhanced firework algorithm comprises the following steps:
s1: all relevant parameters in the algorithm are set, an initial firework population is generated by using a good point set method, and each individual in the population is an initial tap coefficient vector of the equalizer. The method comprises the following specific steps:
setting the initial population of fireworks as X ═ X1,x2,…,xn) Wherein X isiAnd (i-1, 2, …, n) is the initial position vector of the ith firework, n is the number of individuals in the fireworks, and the initial firework population is generated by using the good point set.
First, the smallest prime number p is found from the constraint condition (p-3)/2> -size, where size represents the firework population size. Substituting the obtained p into the following formula:
R(i)＝2×cos(2×pi×i/p)
obtaining R, wherein R is a one-dimensional vector with the length being the size of the firework population,
secondly, multiplying the decimal part of R with SN correspondingly, wherein SN is a one-dimensional vector from 1 to size; by the formula:
nest＝minV+(maxV-minV)×R
obtaining nest, wherein maxV and minV are the upper and lower boundaries of the firework population individuals;
and finally, disordering nest, assigning values to each dimension of the population, and finishing the initialization of the firework population.
S2: establishing a fitness function, specifically taking the mean square error between the equalized signal and the ideal noiseless signal as the fitness function of the breadth-enhanced firework algorithm: taking an error function of the normal mode blind equalization technology as a fitness function of the breadth-enhanced firework algorithm, wherein the function is as follows:
Figure BDA0002518432560000061
wherein z (k) is a desired signal without noise, a (k) is a reconstructed signal after equalization, and N is a signal length; the cost function of the CMA is a function of the initial weight vector w, so w can be regarded as the position of fireworks in the breadth-enhanced firework algorithm, and the optimal value can be obtained by minimizing the fitness function; n signals are sequentially received by each generation of the evolution of the breadth-enhanced firework algorithm, the firework population individuals are brought into the fitness function to calculate the mean square error, namely the fitness value of each individual, and the optimal initial weight vector w is obtained under the condition of obtaining the minimum mean square error.
S3: calculating the fitness value of each individual by using the initial tap coefficient vector obtained in the step S1 and the fitness function established in the step S2;
s4: evaluating individual fitness, generating explosion sparks and variant sparks and applying a mapping rule to fireworks beyond the boundary. The method comprises the following specific steps:
s4-1: evaluating individual fitness and generating explosion spark
The firework algorithm firstly generates N fireworks randomly in a feasible region omega, and records the adaptability value of each firework, wherein the fireworks with small adaptability values have small explosion range, generate more sparks, have large explosion range and generate less sparks. The fireworks explosion generates new explosion sparks, the number of the generated sparks and the explosion radius are respectively
Figure BDA0002518432560000071
Figure BDA0002518432560000072
Wherein Y ismaxAnd YminRespectively representing the maximum value and the minimum value of population fitness, SiFor the number of sparks generated, AiThe explosion radius, A and M are constants for adjusting the explosion radius and the spark number respectively, and epsilon is a minimum constant for avoiding zero operation.
S4-2: generating variant sparks and applying mapping rules to off-boundary fireworks
In order to ensure the population diversity, Gaussian variation sparks are introduced into the algorithm, the global search capability of the algorithm is enhanced, the generated explosion sparks are subjected to Gaussian variation by randomly selecting k dimensions, and the process is shown as the following formula
Figure BDA0002518432560000073
Wherein randn (0,1) is a Gaussian variation function.
The firework algorithm is close to the boundary of the feasible region by adopting a random initialization method, so some explosion sparks and variant sparks exceed the range of omega of the feasible region, and are mapped into the range of the feasible region by adopting a certain mapping rule, and the mapping formula is as follows
Figure BDA0002518432560000074
Wherein
Figure BDA0002518432560000075
And
Figure BDA0002518432560000076
each represents the upper and lower boundaries of a k-dimensional boundary, and U (0,1) represents a random number distributed in a (0,1) interval.
S5: applying improved selection strategy to obtain next-generation firework population
Selecting next-generation fireworks by adopting breadth-first selection strategy
Sequencing all fireworks according to the size of the fitness value, firstly reserving an optimal firework, calculating the Euclidean distance between all fireworks and the optimal firework, and recording the Euclidean distance as dist (x, y) which is expressed as:
Figure BDA0002518432560000077
wherein xiAnd yiRepresenting each dimension of the position vector. Sorting is carried out according to the distance between every two fireworks, and N/2-1 points (sparse areas) far away from the fireworks and N/2 points (dense areas) near to the fireworks are selected. Therefore, the global search range is ensured, the leadership capability of points with good adaptability is enhanced, the local search capability of fireworks with better adaptability is enhanced, a global optimal value is possibly found, and the iteration times are reduced.
Or selecting the next generation fireworks by adopting a goodness preference strategy
And sequencing all fireworks according to the size of the fitness value, and selecting and reserving the optimal individuals and the suboptimal individuals. And calculating Euclidean distances between all fireworks and the fireworks, and recording the Euclidean distances as dist (x, y) and expressing the Euclidean distances as follows:
Figure BDA0002518432560000081
and arranging all fireworks in an ascending order according to the distance from the optimal fireworks, and selecting the first N/2-1 fireworks for reservation. And then, arranging all fireworks in a descending order according to the distance from the second optimal fireworks, and selecting the first N/2-1 fireworks for reservation. Therefore, the position information of other excellent fireworks in the population is fully utilized, and the diversity of the population is ensured.
S6 Gaussian disturbance on the selected fireworks according to a certain strategy
In order to further improve the diversity of the firework population and avoid the algorithm from falling into a local optimal value, Gaussian disturbance is respectively carried out on the selected fireworks. The Gaussian disturbance intensity is 1+ randn (1, D), where D is xiGenerating a 1 x D matrix satisfying normal distribution, taking dot product with the selected firework position vector, and selecting constant 1 as balance factor to avoid disturbanceThe firework position vector becomes smaller after the movement. And performing Gaussian disturbance on the fireworks with poor fitness to obtain some better elite solutions, wherein the global optimum value may appear near the fireworks with poor fitness, and the global optimum value may be found by adding the Gaussian disturbance. The method has the advantages that Gaussian disturbance is carried out on the fireworks with good adaptability, the leadership capability of the fireworks with good adaptability is enhanced, the fireworks are closer to the trend of optimal position search, the global optimal value is found more quickly, and the convergence speed is accelerated.
The breadth-enhanced firework algorithm pseudo code is as follows:
Figure BDA0002518432560000082
Figure BDA0002518432560000091
s7: and optimizing the initial weight vector by using the breadth-enhanced firework algorithm to obtain a blind equalization signal under the optimal initial tap coefficient.
The method comprises the following specific steps:
a fitness function is determined and the quality of the reconstructed signal can be used to evaluate the performance of the equalization algorithm. The method minimizes the mean square error of the original signal and the equalized signal through the breadth-enhanced firework algorithm, and determines the initial weight vector w.
Taking an error function of the normal mode blind equalization technology as a fitness function of the breadth-enhanced firework algorithm, wherein the function is as follows:
Figure BDA0002518432560000092
where z (k) is a desired signal without noise, a (k) is a reconstructed signal after equalization, and N is a signal length. The cost function of CMA is a function of the initial weight vector w, so w can be seen as the location of the fireworks in the breadth-enhanced firework algorithm, and the optimal value can be obtained by minimizing the fitness function. N signals are sequentially received by each generation of the evolution of the breadth-enhanced firework algorithm, the firework population individuals are brought into the fitness function to calculate the mean square error, namely the fitness value of each individual, and the optimal initial weight vector w is obtained under the condition of obtaining the minimum mean square error.
And finally, processing the underwater sound signal data obtained in the step S1 by using a blind equalizer (CMA) based on the optimal initial tap coefficient, and finally outputting a blind equalization signal.
Example 2:
in order to verify the effectiveness of the breadth-enhanced firework algorithm, the embodiment of the invention performs simulation comparison on the provided breadth-enhanced firework algorithm and three classical algorithms such as a traditional firework algorithm, an artificial bee colony algorithm and a gray wolf optimization algorithm based on eight standard test functions, and compares experimental results to show the performance of the algorithm. A large number of simulation verification results show that the convergence performance obtained by respectively selecting the two selection strategies is approximately the same. Therefore, for simplicity, the breadth-first strategy of strategy 1 is used in the simulations below. The computer configuration used was: intel i5-4570 processor, Windows 10 operating system, 8G memory, MATLAB R2015 b. Table 1 shows the parameter settings for the four algorithms in the experiment.
Table 1 simulation experiment parameter set-up
Figure BDA0002518432560000093
Figure BDA0002518432560000101
The 8 typical benchmark test functions adopted in the experiment are all from a global optimization test function library, and the expressions of the eight test functions are as follows:
Figure BDA0002518432560000102
Figure BDA0002518432560000103
Figure BDA0002518432560000104
f4(x)＝(1.5-x1+x1x2)2+(2.25-x1+x1x2 2)2+(2.625-x1+x1x2 3)2
f5(x)＝(x1+2x2-7)2+(2x1+x2-5)2
Figure BDA0002518432560000105
f7(x)＝-cos(x1)cos(x2)exp(-(x1-π)2-(x2-π)2)
Figure BDA0002518432560000106
the properties of the eight standard test functions are shown in table 2.
TABLE 2 basic characteristics of the functions
Figure BDA0002518432560000107
Figure BDA0002518432560000111
Wherein f is3(x) And f8(x) Is a multi-peak function, and the rest are unimodal functions. f. of2(x) And f3(x) The dimension is set to d 30, f6(x) The dimension is set to d 10, f8(x) The dimension is set to d 2.
In order to visually reflect the iterative comparison of various algorithms, fig. 2 to 9 show the convergence curves of different optimization algorithms with the increase of the number of iterations based on eight reference functions.
TABLE 3 minimum number of iterations required for convergence of eight algorithms under different test functions
Testing functions BEFWA FWA ABC GWO
f1(x) 17 252 153 104
f2(x) 19 128 125 125
f3(x) 41 186 100 205
f4(x) 16 52 108 77
f5(x) 15 40 45 48
f6(x) 5 17 20 28
f7(x) 12 42 20 Non-convergence
f8(x) 8 22 Non-convergence 40
As can be seen from fig. 2 to 9, the extent-enhanced firework algorithm has better performance than other algorithms. Compared with BEFWA, the fitness function curve of other optimization algorithms has larger fluctuation and even has the situation of increasing errors, so the BEFWA algorithm is the best in the stability of the algorithm. As can be seen from table 3, the minimum iteration times required for convergence of the breadth-enhanced firework algorithm under different test functions are all the minimum, and compared with the artificial bee colony algorithm with the shortest iteration time, the iteration times of the BEFWA are reduced by more than 50%, so that the BEFWA algorithm converges fastest. In general, the breadth-enhanced firework algorithm obtains better performance than other algorithms in terms of convergence speed and algorithm stability, and particularly, the convergence speed is improved by more than 50%.
Table 4 gives the run times of the BEFWA, FWA, ABC and GWO algorithms for eight different test functions, each algorithm running 50 times independently for averaging. The parameter settings are as above. From the temporal data in table 4, BEFWA and FWA have little difference in temporal complexity, and FWA is not much different from ABC when the variable dimension is low, and both are better than GWO. When the variable dimensions are many, the running time of BEFWA is slightly longer than that of the artificial bee colony algorithm. The results show that the time complexity is acceptable.
TABLE 4 comparison of the running times of the four algorithms
Testing functions BEFWA FWA ABC GWO
f1(x) 1.2402 1.2431 1.3012 1.8432
f2(x) 1.7078 1.7269 1.4431 2.3951
f3(x) 2.1493 2.2437 1.8735 3.3754
f4(x) 1.1653 1.1675 1.1946 1.4315
f5(x) 3.1254 3.2124 4.2154 3.5121
f6(x) 12.4358 13.4612 13.5421 12.3561
f7(x) 7.2453 7.2542 7.1246 7.6545
f8(x) 10.5645 10.6568 10.4857 11.6541
In order to verify the equalization performance based on the invention, a CMA algorithm is selected as a comparison object, the equalizer weight length in a simulation experiment is set to be 13, the weight vector w is [0000001000000], and the sample number N is 10000. The population size of BEFWA-CMA is 100, the iteration number is 500, the number of variant sparks is 5, the number of explosions is 6, the explosion radius is 5, and the Gaussian disturbance intensity is 0.1. The channel adopts a minimum phase underwater sound channel, the impulse response of the channel is c [ -0.3122, -0.1040,0.8908,0.3134], in a zero pole diagram of the channel, 3 zeros are all in a unit circle, and the amplitude and the phase of the channel are seriously distorted. In the simulation experiment, a 16QAM transmitting signal is adopted, and Gaussian white noise is adopted as channel noise.
Fig. 10 and 11 show the constellation comparison before and after CMA equalization and BEFWA-CMA equalization at a signal-to-noise ratio of 20dB, respectively. It can be seen that the output constellation of BEFWA-CMA is more compact and clear, indicating better equalization.
FIGS. 12-15 are pre-and post-equalization mean square error plots for BEFWA-CMA, FWA-CMA, ABC-CMA and GWO-CMA at signal-to-noise ratios of 5dB, 10dB, 15dB and 20dB, respectively. Each algorithm was run independently 50 times to average, with the other parameter settings as above. Wherein BEFWA-CMA basically converges in the 21 st generation, FWA-CMA, ABC-CMA and GWO-CMA basically converge in the 28 th generation, and the convergence rate is improved by 25%. And the other three algorithm curves have larger fluctuation range, which indicates that the stability of the algorithm is poor. Meanwhile, in the whole view, along with the improvement of the signal-to-noise ratio, the mean square error of the algorithm in convergence is also reduced, and the BEFWA-CMA is improved in convergence speed and stability compared with other three algorithms. Therefore, BEFWA-CMA not only improves the convergence speed of the algorithm and enhances the stability of the algorithm, but also reduces the mean square error before and after equalization and improves the equalization effect.
The above-mentioned embodiments are only preferred embodiments of the present invention, and the scope of the present invention is not limited thereby, and all changes, modifications, additions and substitutions that are made within the form and spirit of the principles of the present invention are covered thereby.

Claims (7)

1. An underwater sound channel equalization method based on an breadth-enhanced firework algorithm is characterized by comprising the following steps:
s1: collecting and processing underwater acoustic signal data;
s2: generating an initial firework population by using a good point set method, wherein each individual in the population is an initial tap coefficient vector of an equalizer;
s3: establishing a fitness function, specifically taking the mean square error between the equalized signal and the ideal noiseless signal as the fitness function of the breadth-enhanced firework algorithm;
s4: calculating the fitness value of each individual by using the initial tap coefficient vector obtained in the step S2 and the fitness function established in the step S3;
s5: updating the position information of the fireworks based on the fitness value obtained in the step S4;
s6: selecting the next-generation fireworks from the fireworks position information obtained in S5 by applying a breadth-first selection strategy or a goodness-first selection strategy;
s7: performing Gaussian disturbance on the next-generation fireworks selected in the step S6;
s8: repeating the steps S3-S7 until the optimal initial tap coefficient under the condition of the minimum mean square error is obtained;
s9: and based on the optimal initial tap coefficient, processing the underwater sound signal data obtained in the step S1 by using a blind equalizer (CMA), and finally outputting a blind equalization signal.
2. The method for underwater acoustic channel equalization according to claim 1, wherein the S2 specifically is:
setting the initial population of fireworks as X ═ X1，x2，...，xn) Wherein X isi(i 1, 2., n) is the initial position vector of the ith firework, n is the number of individuals in the firework, and the firework is produced by using the optimal point setGenerating an initial firework population;
firstly, solving the minimum prime number p according to a constraint condition (p-3)/2 ═ size, wherein the size represents the size of the firework population; substituting the obtained p into the following formula:
R(i)＝2×cos(2×pi×i/p)
obtaining R, wherein R is a one-dimensional vector with the length being the size of the firework population,
secondly, multiplying the decimal part of R with SN correspondingly, wherein SN is a one-dimensional vector from 1 to size; by the formula:
nest＝minV+(maxV-minV)×R
obtaining nest, wherein maxV and minV are the upper and lower boundaries of the firework population individuals;
and finally, disordering nest, assigning values to each dimension of the population, and finishing the initialization of the firework population.
3. The method for underwater acoustic channel equalization according to claim 1, wherein the step S3 is as follows:
taking an error function of the normal mode blind equalization technology as a fitness function of the breadth-enhanced firework algorithm, wherein the function is as follows:
Figure FDA0002975442620000011
wherein z (k) is a desired signal without noise, a (k) is a reconstructed signal after equalization, and N is a signal length; the cost function of the CMA is a function of an initial weight vector w, so that w can be regarded as the position of fireworks in the breadth-enhanced firework algorithm, and an optimal value can be obtained by minimizing the fitness function; n signals are sequentially received by each generation of the evolution of the breadth-enhanced firework algorithm, the firework population individuals are brought into the fitness function to calculate the mean square error, namely the fitness value of each individual, and the optimal initial weight vector w is obtained under the condition of obtaining the minimum mean square error.
4. The method for underwater acoustic channel equalization according to claim 1, wherein the S5 specifically is:
s5-1 individual fitness evaluation and explosion spark generation
The firework algorithm comprises the steps that firstly, N fireworks are randomly generated in a feasible region Q, and the adaptability value of each firework is recorded, wherein the fireworks with small adaptability values have a small explosion range, generate more sparks, have a large explosion range and generate less sparks; the fireworks explosion generates new explosion sparks, the number of the generated sparks and the explosion radius are respectively as follows:
Figure FDA0002975442620000021
Figure FDA0002975442620000022
wherein Y ismaxAnd YminRespectively representing the maximum value and the minimum value of population fitness, SiFor the number of sparks generated, AiThe radius of explosion is used, A and M are constants and are respectively used for adjusting the radius of explosion and the number of sparks, and epsilon is a minimum constant and is used for avoiding zero operation;
s5-2 generating variant sparks and applying mapping rules to fireworks beyond boundaries
Introducing Gaussian variation sparks in the algorithm, randomly selecting k dimensions from the generated explosion sparks to perform Gaussian variation, wherein the process is shown in the following formula
Figure FDA0002975442620000023
Wherein randn (0,1) is a Gaussian variation function;
certain mapping rules are adopted to map the domain into a feasible domain range, and the mapping formula is as follows
Figure FDA0002975442620000024
Wherein
Figure FDA0002975442620000025
And
Figure FDA0002975442620000026
each represents the upper and lower boundaries of a k-dimensional boundary, and U (0,1) represents a random number distributed in a (0,1) interval.
5. The method for underwater acoustic channel equalization according to claim 1, wherein the step S6 is as follows:
selecting the next generation fireworks by adopting a breadth-first selection strategy:
sequencing all fireworks according to the size of the fitness value, firstly reserving an optimal firework, calculating the Euclidean distance between all fireworks and the optimal firework, and recording the Euclidean distance as dist (x, y) which is expressed as:
Figure FDA0002975442620000027
wherein xiAnd yiRepresenting each dimension of a position vector; sorting according to the distance between every two fireworks, and selecting N/2-1 points far away from the fireworks and N/2 points near to the fireworks.
6. The method for underwater acoustic channel equalization according to claim 1, wherein the step S6 is as follows:
selecting the next generation fireworks by adopting a goodness preference strategy:
sequencing all fireworks according to the size of the fitness value, selecting and reserving the optimal individual and the suboptimal individual, calculating the Euclidean distance between all fireworks and the optimal individual, and recording the Euclidean distance as dist (x, y) which is expressed as:
Figure FDA0002975442620000031
arranging all fireworks in an ascending order according to the distance from the optimal fireworks, and selecting the first N/2-1 fireworks for reservation; and then, arranging all fireworks in a descending order according to the distance from the second optimal fireworks, and selecting the first N/2-1 fireworks for reservation.
7. The method for underwater acoustic channel equalization according to claim 1, wherein the step S7 specifically includes: and (3) carrying out Gaussian disturbance: the Gaussian disturbance intensity is 1+ randn (1, D), where D is xiGenerating a 1 x D matrix meeting normal distribution, taking a dot product with the selected firework position vector, and selecting a constant 1 as a balance factor to avoid the firework position vector becoming smaller after disturbance.
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