CN107547457A - A kind of approach for blind channel equalization based on Modified particle swarm optimization BP neural network - Google Patents

A kind of approach for blind channel equalization based on Modified particle swarm optimization BP neural network Download PDF

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CN107547457A
CN107547457A CN201710830936.0A CN201710830936A CN107547457A CN 107547457 A CN107547457 A CN 107547457A CN 201710830936 A CN201710830936 A CN 201710830936A CN 107547457 A CN107547457 A CN 107547457A
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廖勇
姚海梅
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Chongqing University
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Abstract

The present invention devises a kind of approach for blind channel equalization for being based on Modified particle swarm optimization (Particle Swarm Optimization, PSO) BP (Back Propagation) neutral net.In the processing of the blind equalization problem based on BP neural network, the determination of BP neural network initial weight and threshold value is theoretically unsound, and the defects of convergence rate is slow, is easily absorbed in local minimum be present, causes Channel blind equalization effect poor.The defects of to overcome BP neural network, Channel blind equalization effect is improved, the present invention proposes a kind of based on the blind balance method for improving PSO BP neural networks.This method overcomes the defects of basic particle group algorithm first, and the parameter of elementary particle group is improved, automatic adjusument inertia weight and Studying factors；Secondly using the initial weight and threshold value for improving the advantages of population ability of searching optimum is strong optimization neural network, recycle BP algorithm more accurately to be searched in this local space, obtain neutral net Best link weights and threshold value；Finally realize based on the blind equalization for improving PSO BP neural networks.

Description

A kind of approach for blind channel equalization based on Modified particle swarm optimization BP neural network
Technical field：
The present invention relates to wireless communication field, more particularly to a kind of fanaticism based on Modified particle swarm optimization BP neural network Trace equalization method.
Background technology：
Blind Equalization Technique carrys out equalization channel merely with the statistical property of reception signal in itself and then eliminates channel distortions to cause Intersymbol interference, improve communication quality, have broad application prospects.With the development of artificial intelligence, with a large scale simultaneously The nonlinear dynamic system neutral net of row disposal ability has become an important field of research to solve blind equalization, and it can To reach the conventional inaccessiable portfolio effect of blind equalization algorithm institute.Both can be balanced using the blind equalization algorithm of neutral net Minimum phase channel, can also balanced non-minimum phase channel, including nonlinear channel.But with BP (Back Propagation) the feedforward neural network blind equalization based on algorithm has the defects of inevitable, is in particular in：
(1) convergence rate is slow.For the portfolio effect reached, the step-length of BP algorithm can not be too big, less learning rate Although being able to ensure that network convergence, the adjustment number that network needs increases, and network convergence is slowed.
(2) easily it is absorbed in local minimum.BP neural network algorithm with gradient descent method by that can ensure that network is received Hold back in a stable value, but this stable value is probably the local minimum of network.
(3) initial weight of network and threshold value, which are chosen, lacks foundation, has randomness.BP algorithm is declined based on gradient Method, different initial weights and threshold value may result in entirely different result, initial weight and threshold value value is improper to draw Play network oscillation or do not restrain.
Particle group optimizing (Particle Swarm Optimization, PSO) algorithm is in nineteen ninety-five by American society's psychology Family Kennedy and U.S. electric engineer Eberhart is proposed, is that one kind is based on migrating during looking for food to flock of birds and assembling mould The Swarm Intelligent Algorithm of plan.The basic thought of algorithm is to find optimal solution by the cooperation in colony and information sharing. Each particle is exactly one in solution space solution in PSO algorithms, it according to the flying experience of oneself and the flying experience of companion come Adjust the state of flight of oneself.The desired positions that each particle is lived through in flight course, are exactly that particle is found most in itself Excellent solution.The desired positions that whole colony is lived through, the optimal solution that exactly whole colony finds at present.The former is called individual pole Value, the latter are called global extremum.Each particle constantly updates oneself by above-mentioned two extreme value, so as to produce group of new generation Body, " quality " degree of particle is evaluated in practical operation by the fitness function value determined by optimization problem.It will be apparent that The behavior of each particle is in population：Current optimal particle is follow, is scanned in solution space.
The one kind of particle swarm optimization algorithm as global optimization approach, shown in many case histories greatly Advantage.Because particle cluster algorithm concept is simple and clear, without too many parameter setting and adjustment, it is not necessary to which genetic algorithm " is handed over The complex operations such as fork " and " variation ", fast convergence rate and precision height；So particle cluster algorithm just obtains domestic and international crowd from after proposing The extensive concern of more researchers and research.At present, the algorithm has been successfully applied to function optimization, neural metwork training, pattern Many necks such as identification, fuzzy system control, become intelligent optimization and another new study hotspot of progress calculating field.But by In particle cluster algorithm in itself there is also convergence rate it is slow, be easily absorbed in local optimum the defects of, therefore need to make improvements.
, can be by particle cluster algorithm to neutral net because particle cluster algorithm has the advantages of ability of searching optimum is strong Connecting quantity optimizes, and makes up neural network algorithm to network parameter Initialize installation sensitivity and is easily trapped into local minimum The deficiency of point.Meanwhile particle cluster algorithm is easily achieved, is simple in construction, easily combined with other algorithms；Particle cluster algorithm is using simultaneously Row computing, arithmetic speed is fast, and resource utilization is high.After two kinds of algorithms are combined, the convergence essence of neural network algorithm can be improved Degree and generalization ability.
The content of the invention：
Goal of the invention
It is sensitive to network parameter Initialize installation and the defects of be easily trapped into local minizing point in order to solve neutral net, The present invention proposes that improved simplified particle swarm optimization algorithm is combined training neutral net with BP algorithm, is determined by learning training The connection weight and threshold value of neutral net.The dimension of each particle and the weights of network and threshold value are established simultaneously in the algorithm Mapping relations optimize.
A kind of approach for blind channel equalization based on Modified particle swarm optimization BP neural network proposed by the present invention, its feature exist In, including：
S1, according to basic blind equalization principle, determine the structure of BP neural network, including the number of plies of neutral net, input Node layer number, hidden layer node number and output layer node number.
S2, basic particle cluster algorithm is improved.
S3, with modified particle swarm optiziation Optimized BP Neural Network.
S4, the neutral net of Modified particle swarm optimization is used for algorithm for blind channel equalization.
A kind of described algorithm for blind channel equalization algorithm based on Modified particle swarm optimization BP neural network, it is characterised in that institute Stating S1 includes：
Blind equalization principle is：The signal x (n) that emitter is sent is superimposed a noise signal s after a Unknown Channel h (n) (n) y (n) is obtained, y (n) is the input of balanced device, by being equalized device output signal after balanced device equilibriumAgain By being obtained after decision device
According to blind equalization principle, Nonlinear Mapping that three_layer planar waveguide is realized can approach any continuous letter Number network, and it is simple in construction, and operand is relatively small, so in the application of blind equalization, commonly using three-layer network；This hair It is bright using the feedforward neural network with three-decker, output node, using the input of balanced device as neutral net input The input of layer, balanced device export the output as neutral net output layer, if input layer is M, hidden layer node N Individual, output node layer is 1.
A kind of described algorithm for blind channel equalization algorithm based on Modified particle swarm optimization BP neural network, it is characterised in that institute Stating S2 includes：
Basic particle cluster algorithm is described as substantially：In a D dimension space, population is made up of N number of particle, by i-th The positional representation of son is formula
Xi=(xi1,xi2,...,xiD) i=1,2 ..., N
The movement velocity of this particle is expressed as formula
Vi=(vi1,vi2,...,viD) i=1,2 ..., N
Up to the present optimal location that this particle searches in space is then individual extreme value, is represented
For formula
Pibest=(pi1,pi2,...,piD) i=1,2 ..., N
In colony all particle search to optimal location be global extremum, be expressed as formula
Pgbest=(pg1,pg2,...,pgD)
Wherein, subscript g represents global implication；
Then all particles in colony can constantly adjust the position of itself and speed reaches and sought according to following two formula Look for the purpose of optimal solution.
Wherein, vidFor d-th of velocity component of i-th of particle, xidFor d-th of location components of i-th of particle, pidFor The desired positions component that d-th of i-th particle, pgdFor d-th of desired positions component in all particles, t is current iteration time Number, c1And c2To learn the factor, r1And r2For the random number in the range of [0,1]；W is inertia weight, generally linear decrease, i.e. w =wmax-(wmax-wmin)t/Tmax；Wherein, wmaxFor the maximum of inertia weight, wminFor the minimum value of inertia weight, t is current Iterations, TmaxFor maximum iteration.
In particle in flight course, particle state is continually changing, therefore, it is necessary to according to the state of colony to algorithm Parameter do the search capability that adaptive adjustment carrys out the global and local of equilibrium particle group's algorithm, it is contemplated that this problem, this The value of inertia weight and Studying factors is improved in invention.
Inertia weight w improvement：Improved inertia weight w ', with the increase of iterations, the ratio that early stage declines is very fast, Decreased later is slow, and formula is as follows：
W '=a (wmax-wmin)[arccot(t/Tmax)]3+bwmin
Wherein, wmaxFor the maximum of inertia weight, w is typically takenmax=0.9, wminFor the minimum value of inertia weight, typically Take wmin=0.4, t are current iteration number, TmaxFor maximum iteration, T is taken heremax=1500, a and b adjustment curves width Degree, takes a=0.3, b=0.8 here.
The improvement of Studying factors：Improved c1Curve, with the progress of iteration, the ratio that early stage declines is very fast, decreased later Slowly；And improved c2Curve, with the progress of iteration, the ratio that early stage rises is very fast, and the later stage rises slowly, and specific formula is such as Under：
c2=4-c1
Wherein, the amplitude of k adjustment curves, takes k=2 here；c1startFor c1Initial value, take c here1start=2, c1end For c1Final value, take c here1end=1；T is current iteration number, TmaxFor maximum iteration, same Tmax=1500, here Meet c1+c2=4.
A kind of described algorithm for blind channel equalization algorithm based on Modified particle swarm optimization BP neural network, it is characterised in that institute Stating S3 includes：
The step of based on Modified particle swarm optimization BP neural network, is as follows：
Step 1, the structure for determining neutral net and its parameter is set.Neutral net is three_layer planar waveguide, has M Individual input node, N number of hidden layer node and 1 output node；The parameter such as learning efficiency η, target error ε is set, and it is random first One group of weights of beginningization and threshold value；
Step 2, the parameter that population is set, such as the scale M of population, the dimension D of particle, maximum iteration Tmax, position Put the bound [x with speedmax,xmin] and [vmax,vmin], determine fitness function F (n)；
Dimension：The dimension D=input layers of particle to connection weight number+hidden layer to output layer of hidden layer connection weight It is worth the threshold number of threshold number+output layer of number+hidden layer, here D=M × N+N × 1+N+1；
The determination of fitness function：With reference to the attachment structure variable and connection weight variable of particle, neutral net is typically taken Fitness of the mean square error as particle between output and desired output.Herein, the purpose of neutral net blind equalization algorithm To make cost function iteration to minimum value, from the permanent mould blind equalization algorithm of tradition cost function as fitness function
Wherein, J (n) is the cost function of permanent mould blind equalization algorithm,
Step 3, the requirement according to particle position and speed bound, generate the initial position of particle at random within the range Vector sum velocity vector, calculate particle fitness and individual extreme point and the global extremum point of each particle is set；
The determination of individual extreme point and global extremum point：The current location of each particle is set to the optimal position of current individual Put, calculate the adaptive value of current all personal best particles, using all particle personal best particles it is best as global extremum Point；
Step 4, the position according to the more new formula of population position and speed renewal population and speed, wherein inertia are weighed The formula that weight and Studying factors defer to after improving carries out adaptive adjustment respectively；
Step 5, the fitness value for calculating particle after renewal, compare the current fitness value and itself individual extreme value of particle Fitness value, if the fitness value of particle is better than the individual optimal extreme value fitness value of itself in current iteration, retaining should The current location of particle is its individual history desired positions；
Step 6, compare the current adaptive value of all particles of colony and global history is preferably adapted to be worth, if current adaptive value is more Excellent, then the current location for retaining particle is the global history desired positions of population；
Step 7, judge whether to meet end condition, end condition has generally reached maximum iteration or adaptive value Error reaches the adaptive value limits of error of setting；
If step 8, meeting end condition, stop iteration, output global optimum particle is BP neural network initial weight And threshold value, otherwise return to step 4 continue search for；
Step 9, with BP algorithm continue to be trained neutral net；
Step 10, calculating network training error；
Whether step 11, error in judgement reach target error, if not having, continue to be trained with BP algorithm, otherwise terminate algorithm.
A kind of described algorithm for blind channel equalization algorithm based on Modified particle swarm optimization BP neural network, it is characterised in that institute Stating S4 includes：
In the algorithm for blind channel equalization based on Modified particle swarm optimization BP neural network, by BP neural network and Blind Equalization Technique With reference to BP neural network is used as balanced device, cost function is minimized to adjust god by improving the continuous iteration of particle cluster algorithm Initial weight and threshold value through network, recycle BP algorithm more accurately to be searched in this local space, obtain nerve net Network Best link weights and threshold value, so as to realize compensation and tracking to unknown linearly or nonlinearly channel, reach blind equalization Purpose.
Beneficial effects of the present invention are:
First, in order to overcome the defects of basic particle group algorithm is easily trapped into Local Minimum, late convergence is slow, this hair It is bright that basic particle group algorithm is improved using two strategies of inertia weight and Studying factors adaptive change；Then use and change The particle cluster algorithm entered finds the preferable weights of network and threshold value, reduces the possibility that BP neural network is absorbed in local minimum Property, improve the learning performance and constringency performance of whole network；Finally, there is good nonlinear fitting energy using BP neural network This feature of power, the BP neural network of Modified particle swarm optimization is used to improve portfolio effect in algorithm for blind channel equalization.
Advantages of the present invention will be set forth below in the following description, and partly will become apparent from the description below.
Brief description of the drawings
Figure 1B P neural network structure schematic diagrames；
The improved inertia weight w curvilinear motion figures of Fig. 2；
The improved Studying factors c of Fig. 31Curvilinear motion figure；
The improved Studying factors c of Fig. 42Curvilinear motion figure；
The improved PSO-BP neural network algorithms flow charts of Fig. 5；
Fig. 6 is based on the algorithm for blind channel equalization schematic diagram for improving PSO-BP neutral nets.
Specific embodiment
Embodiments of the invention are described below in detail, the example of the embodiment is shown in the drawings
1st, the structure of BP neural network is determined
Blind Equalization Technique need not be by training sequence, and the unknown signaling sent just with emitter carrys out equalization channel spy Property, make the output signal of balanced device as far as possible close to transmission signal.This adaptive technique first need not carry out blind discrimination to channel, Directly input signal can be recovered using balanced device, effectively compensate for the non-ideal characteristic of channel, overcome intersymbol interference, Reduce the bit error rate and improve communication quality.Blind Equalization Technique principle is as follows：
The signal x (n) that emitter is sent is superimposed a noise signal s (n) after a Unknown Channel h (n) and is equalized device Input y (n), y (n) after balanced device equilibrium by being equalized device output signalAgain by being obtained after decision device
According to Blind Equalization Technique principle, Nonlinear Mapping that three_layer planar waveguide is realized can approach any company Continuous Function Network, and it is simple in construction, and operand is relatively small, so in the application of blind equalization, commonly using three-layer network； The present invention is using the feedforward neural network with three-decker, the input using the input of balanced device as neural network input layer, Balanced device exports the output as neutral net output layer, it is assumed that input layer has M node, and hidden layer has N number of node, output layer There is 1 node.The connection weight of input layer and hidden layer is wij(i=1,2 ..., M；J=1,2 ..., N), hidden layer with it is defeated The connection weight for going out layer is wj, the threshold value of hidden layer is θj(j=1,2 ..., N), the threshold value of output layer is θo, hidden layer it is defeated It is v (n) to enter for u (n), hidden layer output, and output layer input is z (n), and output layer output isThe activation letter of neutral net Number typically uses sigmoid functions, i.e.,BP neural network structural representation as shown in Figure 1, whole network State equation
vj(n)=f (uj(n))
2nd, basic particle group algorithm is improved
(1) basic particle group algorithm
Particle cluster algorithm is inspired by birds predation, is to be proposed in nineteen ninety-five by Kennedy and Eberhart earliest A kind of Swarm Intelligence Algorithm.Particle swarm optimization algorithm is sought by the common cooperation and information sharing between particle in colony Look for optimal solution.
Original particle cluster algorithm is described as substantially：In a D dimension space, population is made up of N number of particle, by i-th The positional representation of son is formula
Xi=(xi1,xi2,...,xiD) i=1,2 ..., N
The movement velocity of this particle is expressed as formula
Vi=(vi1,vi2,...,viD) i=1,2 ..., N
Up to the present optimal location that this particle searches in space is then individual extreme value, is expressed as formula
Pibest=(pi1,pi2,...,piD) i=1,2 ..., N
In colony all particle search to optimal location be global extremum, be expressed as formula
Pgbest=(pg1,pg2,...,pgD)
Wherein, subscript g represents global implication；
Then all particles in colony can constantly adjust the position of itself and speed reaches and sought according to following two formula Look for the purpose of optimal solution；
Wherein, vidFor d-th of velocity component of i-th of particle, xidFor d-th of location components of i-th of particle, pidFor The desired positions component that d-th of i-th particle, pgdFor d-th of desired positions component in all particles, t is current iteration time Number, c1And c2To learn the factor, r1And r2For the random number in the range of [0,1].
In order to efficiently control and adjust the flying speed of particle, Shi and Eberhart are proposed in speed formula In add inertia weight w concept, i.e. standard PSO algorithms, the iterative formula of its speed and position is
Inertia weight w in PSO algorithm is linear decrease, and formula is
Wherein, wmaxFor the maximum of inertia weight, wminFor the minimum value of inertia weight, t is current iteration number, Tmax For maximum iteration.
(2) inertia weight and Studying factors are improved
1) to the improvement of inertia weight
Choosing linear decline trend to inertia weight in traditional PS O algorithms reduces, but particle is during motion With larger speed, into current population, optimal position is flown, when near particle flight to global optimum position, due to this The flying speed of particle still quickly, so be likely to miss globe optimum, so that convergence precision reduces.In grain In the optimized algorithm running of subgroup, it is intended that initial period all particles of particle group optimizing can be in bigger search space Interior global search, and the ending phase particle of algorithm has probably determined optimal position, as long as small around its position The searching of scope, now to strengthen Local Search.Therefore the parameter of algorithm should be done adaptively according to the state of colony Adjustment come equilibrium particle group's algorithm global and local search capability.In view of this problem, inertia is weighed in the present invention The value of weight is improved：Improved inertia weight w ', with the increase of iterations, the ratio that early stage declines is very fast, the later stage Decline slowly, as shown in Figure 2, corresponding calculation formula is as follows for improved inertia weight w ' curvilinear motions figure：
W '=a (wmax-wmin)[arccot(t/Tmax)]3+bwmin
Wherein, wmaxFor the maximum of inertia weight, w is typically takenmax=0.9, wminFor the minimum value of inertia weight, typically Take wmin=0.4, t are current iteration number, TmaxFor maximum iteration, T is taken heremax=1500, a and b adjustment curves width Degree, takes a=0.3, b=0.8 here.
2) to the improvement of Studying factors
Studying factors c1、c2Parameter represents in particle search experience in itself and all particles searching for best particle respectively Influence degree of the rope experience to current flight speed.In general, in the optimization method based on population, we always want to individual Body in the starting stage of algorithm, have big " itself cognition " partly with small " group cognition " part, so that algorithm is whole Individual optimizing space carries out global search, is unlikely to be absorbed in local minimum too early；And in the algorithm later stage, Ying You little " itself recognizes Know " partly with big " group cognition " part, so that algorithmic statement is in globally optimal solution, improve algorithm the convergence speed and essence Degree.Therefore, we can dynamic regularized learning algorithm factor c during evolution1、c2Value, and most people takes Studying factors For constant, we will be improved to Studying factors in the present invention.
Improved c1Curve, with the progress of iteration, the ratio that early stage declines is very fast, and decreased later is slow；And improved c2It is bent Line, with the progress of iteration, the ratio that early stage rises is very fast, and the later stage rises slow, improved Studying factors c1And c2Curvilinear motion figure Respectively as shown in accompanying drawing 3 and accompanying drawing 4, corresponding calculation formula is as follows：
c2=4-c1
Wherein, the amplitude of k adjustment curves, k=2, c are taken here1startFor c1Initial value, take c here1start=2, c1end For c1Final value, take c here1end=1, and meet c1+c2=4.T is current iteration number, TmaxFor maximum iteration, take Tmax=1500.
Starting stage, w ', c1It is larger, c2Smaller, now particle relies primarily on experience, expands search space, on a large scale Search, avoid population Assembling Behavior.With the progress of optimization process, w ', c1It is gradually reduced and c2It is gradually increased, between particle Influence each other, use for reference the position of optimal particle, increase local search ability.
3rd, BP neural network is optimized with improved population
Based on Modified particle swarm optimization BP neural network flow chart as shown in Figure 5, step is as follows：
Step 1, start；
Step 2, the structure for determining neutral net and its parameter is set.Neutral net is three_layer planar waveguide, has M Individual input node, N number of hidden layer node and 1 output node；The parameter such as learning efficiency η, target error ε is set, and it is random first One group of weights of beginningization and threshold value；
Step 3, the parameter that population is set, such as the scale M of population, the dimension D of particle, maximum iteration Tmax, position Put the bound [x with speedmax,xmin] and [vmax,vmin], determine fitness function F (n)；
Dimension：The dimension D=input layers of particle to connection weight number+hidden layer to output layer of hidden layer connection weight It is worth the threshold number of threshold number+output layer of number+hidden layer, here D=M × N+N × 1+N+1；
The determination of fitness function：With reference to the attachment structure variable and connection weight variable of particle, neutral net is typically taken Fitness of the mean square error as particle between output and desired output.Herein, the purpose of neutral net blind equalization algorithm To make cost function iteration to minimum value, from the permanent mould blind equalization algorithm of tradition cost function as fitness function
Wherein, J (n) is the cost function of permanent mould blind equalization algorithm,
Step 4, the requirement according to particle position and speed bound, generate the initial position of particle at random within the range Vector sum velocity vector, calculate particle fitness and individual extreme point and the global extremum point of each particle is set；
The determination of individual extreme point and global extremum point：The current location of each particle is set to the optimal position of current individual Put, calculate the adaptive value of current all personal best particles, using all particle personal best particles it is best as global extremum Point；
Step 5, the position according to the more new formula of population position and speed renewal population and speed, wherein inertia are weighed The formula that weight and Studying factors defer to after improving carries out adaptive adjustment respectively；
Step 6, the fitness value for calculating particle after renewal, compare the current fitness value and itself individual extreme value of particle, If the fitness value of particle is better than the fitness value of the individual optimal extreme value of itself in current iteration, retain working as the particle Anteposition is set to its individual history desired positions；Compare the current adaptive value of all particles of colony and global history is preferably adapted to be worth, if Current adaptive value is more excellent, then the current location for retaining particle is the global history desired positions of population；
Step 7, judge whether to meet end condition, end condition has generally reached maximum iteration or adaptive value Error reaches the adaptive value limits of error of setting；
If step 8, meeting end condition, stop iteration, output global optimum particle is BP neural network initial weight And threshold value, otherwise return to step 4 continue search for；
Step 9, with BP algorithm neutral net is trained；
Step 10, calculating network training error；
If step 11, error are not reaching to target error, return to step 9, continue to be trained with BP algorithm；
If step 12, error have reached target error, terminate algorithm.
4th, the BP neural network of Modified particle swarm optimization is used in algorithm for blind channel equalization, its theory structure block diagram such as accompanying drawing 6 It is shown.Wherein, x (n) is the signal that emitter is sent, and h (n) is the shock response of Unknown Channel, and s (n) is noise signal, y (n) For the receiving sequence of balanced device,Exported for balanced device,By being obtained after decision deviceBased on improvement population In the algorithm for blind channel equalization of Optimized BP Neural Network, BP neural network is combined with Blind Equalization Technique, BP neural network is used as equal Weighing apparatus, cost function is minimized to adjust the initial weight of neutral net and threshold value by improving the continuous iteration of particle cluster algorithm, Recycle BP algorithm more accurately to be searched in this local space, obtain neutral net Best link weights and threshold value, from And the compensation and tracking to unknown linearly or nonlinearly channel are realized, reach the purpose of blind equalization.

Claims (5)

  1. A kind of 1. approach for blind channel equalization based on Modified particle swarm optimization BP neural network, it is characterised in that including：
    S1, according to basic blind equalization principle, determine the structure of BP neural network, including the number of plies of neutral net, input layer section Point number, hidden layer node number and output layer node number；
    S2, basic particle cluster algorithm is improved；
    S3, with modified particle swarm optiziation Optimized BP Neural Network；
    S4, the neutral net of Modified particle swarm optimization is used for algorithm for blind channel equalization.
  2. 2. a kind of algorithm for blind channel equalization algorithm based on Modified particle swarm optimization BP neural network according to claim 1, its It is characterised by, the S1 includes：
    Blind equalization principle is：The signal x (n) that emitter is sent is superimposed a noise signal s (n) after a Unknown Channel h (n) and obtained To y (n), y (n) is the input of balanced device, by being equalized device output signal after balanced device equilibriumPass through again Obtained after decision device
    According to blind equalization principle, Nonlinear Mapping that three_layer planar waveguide is realized can approach any continuous function net Network, and it is simple in construction, and operand is relatively small, so in the application of blind equalization, commonly using three-layer network；The present invention adopts With the feedforward neural network with three-decker, output node, using the input of balanced device as neural network input layer Input, balanced device export output as neutral net output layer, if input layer is M, hidden layer node be it is N number of, it is defeated Go out node layer for 1.
  3. 3. a kind of algorithm for blind channel equalization algorithm based on Modified particle swarm optimization BP neural network according to claim 1, its It is characterised by, the S2 includes：
    Basic particle cluster algorithm is described as substantially：In a D dimension space, population is made up of N number of particle, by i-th particle Positional representation is formula
    Xi=(xi1,xi2,...,xiD) i=1,2 ..., N
    The movement velocity of this particle is expressed as formula
    Vi=(vi1,vi2,...,viD) i=1,2 ..., N
    Up to the present optimal location that this particle searches in space is then individual extreme value, is expressed as formula
    Pibest=(pi1,pi2,...,piD) i=1,2 ..., N
    In colony all particle search to optimal location be global extremum, be expressed as formula
    Pgbest=(pg1,pg2,...,pgD)
    Wherein, subscript g represents global implication；
    Then all particles in colony can reach searching most according to following two formula constantly to adjust the position of itself and speed The purpose of excellent solution.
    <mrow> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>wv</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mrow> <mi>g</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>+</mo> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow>
    Wherein, vidFor d-th of velocity component of i-th of particle, xidFor d-th of location components of i-th of particle, pidFor i-th The desired positions component that d-th of particle, pgdFor d-th of desired positions component in all particles, t is current iteration number, c1 And c2To learn the factor, r1And r2For the random number in the range of [0,1]；W is inertia weight, generally linear decrease, i.e. w= wmax-(wmax-wmin)t/Tmax；Wherein, wmaxFor the maximum of inertia weight, wminFor the minimum value of inertia weight, t changes to be current Generation number, TmaxFor maximum iteration；
    In particle in flight course, particle state is continually changing, therefore, it is necessary to according to the state of colony to the ginseng of algorithm Number does the search capability that adaptive adjustment carrys out the global and local of equilibrium particle group's algorithm, it is contemplated that this problem, the present invention In the values of inertia weight and Studying factors is improved；
    Inertia weight w improvement：Improved inertia weight w ', with the increase of iterations, the ratio that early stage declines is very fast, the later stage Decline slowly, formula is as follows：
    W '=a (wmax-wmin)[arccot(t/Tmax)]3+bwmin
    Wherein, wmaxFor the maximum of inertia weight, w is typically takenmax=0.9, wminFor the minimum value of inertia weight, w is typically takenmin =0.4, t are current iteration number, TmaxFor maximum iteration, T is taken heremax=1500, a and b adjustment curves amplitude, this In take a=0.3, b=0.8；
    The improvement of Studying factors：Improved c1Curve, with the progress of iteration, the ratio that early stage declines is very fast, and decreased later is slow； And improved c2Curve, with the progress of iteration, the ratio that early stage rises is very fast, and the later stage rises slowly, and specific formula is as follows：
    <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mi>k</mi> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mrow> <mn>1</mn> <mi>s</mi> <mi>t</mi> <mi>a</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>c</mi> <mrow> <mn>1</mn> <mi>e</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>/</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>0.5</mn> </msup> </mrow> </mfrac> </mrow>
    c2=4-c1
    Wherein, the amplitude of k adjustment curves, takes k=2 here；c1startFor c1Initial value, take c here1start=2, c1endFor c1 Final value, take c here1end=1；T is current iteration number, TmaxFor maximum iteration, same Tmax=1500, meet here c1+c2=4.
  4. 4. a kind of algorithm for blind channel equalization algorithm based on Modified particle swarm optimization BP neural network according to claim 1, its It is characterised by, the S3 includes：
    The step of based on Modified particle swarm optimization BP neural network, is as follows：
    Step 1, the structure for determining neutral net and its parameter is set；Neutral net is three_layer planar waveguide, has M individual defeated Ingress, N number of hidden layer node and 1 output node；The parameter such as learning efficiency η, target error ε, and random initializtion are set One group of weights and threshold value；
    Step 2, the parameter that population is set, such as the scale M of population, the dimension D of particle, maximum iteration Tmax, position and Bound [the x of speedmax,xmin] and [vmax,vmin], determine fitness function F (n)；
    Dimension：The connection weight of the dimension D=input layers of particle to connection weight number+hidden layer to output layer of hidden layer is individual The threshold number of threshold number+output layer of number+hidden layer, here D=M × N+N × 1+N+1；
    The determination of fitness function：With reference to the attachment structure variable and connection weight variable of particle, typically neutral net is taken to export Fitness of the mean square error as particle between desired output；Herein, the purpose of neutral net blind equalization algorithm is to make Cost function iteration to minimum value, from the permanent mould blind equalization algorithm of tradition cost function as fitness function
    <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>J</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mrow> <mo>&amp;lsqb;</mo> <mo>|</mo> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mi>R</mi> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow>
    Wherein, J (n) is the cost function of permanent mould blind equalization algorithm,
    Step 3, the requirement according to particle position and speed bound, the initial position of generation particle is vectorial at random within the range With initial velocity vector, calculate particle fitness and individual extreme point and the global extremum point of each particle is set；
    The determination of individual extreme point and global extremum point：The current location of each particle is set to current individual optimal location, counted Calculate the adaptive value of current all personal best particles, using all particle personal best particles it is best as global extremum point；
    Step 4, according to the more new formula of population position and speed update population position and speed, wherein inertia weight and The formula that Studying factors defer to after improving carries out adaptive adjustment respectively；
    Step 5, the fitness value for calculating particle after renewal, compare the current fitness value of particle and the adaptation of itself individual extreme value Angle value, if the fitness value of particle is better than the fitness value of itself individual extreme value in current iteration, retain working as the particle Anteposition is set to its individual history desired positions；
    Step 6, compare the current adaptive value of all particles of colony and global history is preferably adapted to angle value, if current adaptive value is more excellent, The current location for then retaining particle is the global history desired positions of population；
    Step 7, judge whether to meet end condition, end condition has generally reached maximum iteration or adaptive value error Reach the adaptive value limits of error of setting；
    If step 8, meeting end condition, stop iteration, output global optimum particle is BP neural network initial weight and threshold Value, otherwise return to step 4 continues search for；
    Step 9, with BP algorithm continue to be trained neutral net；
    Step 10, calculating network training error；
    Whether step 11, error in judgement reach target error, if not having, continue to be trained with BP algorithm, otherwise terminate algorithm.
  5. 5. a kind of algorithm for blind channel equalization algorithm based on Modified particle swarm optimization BP neural network according to claim 1, its It is characterised by, the S4 includes：
    In the algorithm for blind channel equalization based on Modified particle swarm optimization BP neural network, by BP neural network and Blind Equalization Technique knot Close, BP neural network is used as balanced device, minimize cost function by improving the continuous iteration of particle cluster algorithm to adjust first The initial weight and threshold value of neutral net, recycle BP algorithm more accurately to be searched in this local space, obtain nerve Network Best link weights and threshold value, so as to realize compensation and tracking to unknown linearly or nonlinearly channel, reach blind equalization Purpose.
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