Constant modulus blind equalization method based on chaotic mapping and Gaussian perturbation

Abstract

The invention provides a constant modulus blind equalization method based on chaotic mapping and Gaussian perturbation, which comprises the following steps of: 1, estimating a receiving signal of a receiving end of a channel simulator to obtain a constant value; initializing related parameters; 2, entering a particle swarm optimization (PSO) main cycle; step 3, according to the chaos Sine mapping and the upper and lower limits of the inertia weight, obtaining the inertia weight and the learning factor of the current iteration number; 4, calculating fitness values of the particles; 5, updating the speed and the position of the particle; step 6, repeating the steps 2-5 until a termination condition is met; and step 7, obtaining a global optimal fitness value and a global optimal position after a termination condition is satisfied, and calculating an output signal according to an equalizer constructed at the global optimal position at the moment. According to the method, a logarithmic function is introduced to construct a nonlinear asynchronous learning factor which is different from a constant learning factor in an original algorithm, so that the global development capability and the local search capability of the algorithm are balanced.

Description

Technical Field

[0001] The invention belongs to the field of wireless communications, and in particular relates to a constant modulus blind equalization method based on chaotic mapping and Gaussian disturbance. Background Art

[0002] Multi-channel communication systems have several independent and complete transceiver channels. The RF front end of each channel is composed of analog devices such as intermediate frequency filters, broadband couplers, high-frequency amplifiers, detectors, analog mixers, analog / digital converters, etc. Due to the manufacturing process of each device in the transceiver and the thermal effect caused by the device itself, the amplitude and phase of the channel frequency response will inevitably be inconsistent, that is, channel mismatch. At the same time, during the signal processing process, the errors caused by modulation and demodulation, the quantization error caused by the A / D converter, the error caused by the finite word length effect, the aperture jitter error caused by the sampling pulse, etc., will cause changes in the amplitude and phase during multi-channel sampling. In addition, the frequency response of the channel will also change with the influence of time, temperature, and environment. Channel mismatch will seriously affect the calculation results of the baseband backend, and the core goal of channel equalization technology is to correct the amplitude and phase of the channel so that each channel is consistent, so channel equalization technology is an indispensable component in the communication system.

[0003] In traditional equalizer design, the receiver usually needs to know certain characteristics of the transmitted signal or training sequence in advance to estimate the channel characteristics and perform equalization. However, in some special applications, such as channel emulators, the use of training sequences will increase bandwidth overhead, reduce the effective data transmission rate of the communication system, affect the authenticity of channel simulation, and interfere with the simulation process. Blind equalization algorithms do not require training sequences, directly extract information from the received signal and restore the original signal, thereby improving system efficiency and not interfering with the simulation process.

[0004] The most commonly used blind equalization algorithm is the Constant Modulus Algorithm (CMA), but the CMA algorithm cannot recover the phase, and uses the traditional gradient descent method to find the optimal solution of the filter coefficient, which has a slow convergence speed and low convergence accuracy. Therefore, the existing scheme has been modified on the basis of CMA, and a modified constant modulus algorithm (MCMAPSO) based on the particle swarm algorithm has been proposed. In view of the defect that the phase cannot be recovered, the cost function of the algorithm is redesigned to make the optimization weights of the real and imaginary cost functions the same to minimize the phase error. In view of the problems of slow convergence speed and low convergence accuracy, the particle swarm algorithm (PSO) is used to find the optimal solution of the filter coefficient, which improves the convergence speed and steady-state error.

[0005] However, this algorithm still has some shortcomings. The MCMAPSO algorithm uses the PSO algorithm in the optimization part. The algorithm is sensitive to parameters. Improper selection of initial parameters will lead to failure to find the optimal solution. The PSO algorithm uses a constant inertia weight, the steady-state error of the algorithm is not high, and the algorithm is easy to fall into the local optimal solution. The constant individual and social learning factors will lead to an imbalance in the local and global search capabilities of the algorithm. Summary of the invention

[0006] Purpose of the invention: The technical problem to be solved by the present invention is to provide a constant modulus blind equalization method based on chaotic mapping and Gaussian perturbation in view of the shortcomings of the prior art, comprising the following steps:

[0007] Step 1, estimating the received signal of the receiving end of the channel simulator to obtain a constant value; initializing relevant parameters, wherein the relevant parameters include the initial position, initial velocity and population size of the particles;

[0008] Step 2: Enter the main loop of the particle swarm optimization (PSO) algorithm.

[0009] Step 3: According to the chaotic Sine map and the upper and lower limits of the inertia weight, the inertia weight of the current iteration number is obtained; according to the logarithmic function and the upper and lower limits of the learning factor, the learning factor of the current iteration number is obtained;

[0010] Step 4, the received signal is passed through the equalizer to obtain the output signal, and the fitness value of the particle is calculated according to the output signal and the constant value obtained in step 1;

[0011] Step 5, evaluate whether the fitness value of the particle decreases. If the fitness value decreases, update the individual and global optimal fitness values, and update the particle speed and position; if the fitness value does not decrease, do not update the individual and global optimal fitness values, and update the particle speed and position;

[0012] Step 6, repeat steps 2 to 5 until the termination condition is met;

[0013] Step 7, after the termination condition is met, the global optimal fitness value and the global optimal position are obtained, and the output signal is calculated based on the equalizer constructed according to the global optimal position at this time.

[0014] In step 1, the equalizer receives the signal To estimate, use The real part of and the imaginary part Get constant values The real part of and the imaginary part :

[0015] (1)

[0016] in, For hope, is a constant, usually taken .

[0017] In step 3, the inertia weight is calculated using the following formula:

[0018] (2)

[0019] in is the current iteration number; is the maximum number of iterations; For the The inertia weight at the iteration; , are the upper and lower limits of the inertia weight respectively; For the The chaotic Sine map at the iteration; the initial value of the chaotic Sine map , rand represents a random number, is a constant.

[0020] In step 3, the learning factor includes individual learning factor and social learning factors , the calculation formula is:

[0021] (3)

[0022] in , Represents individual learning factors The upper and lower limits of , Social learning factors The upper and lower limits of ; e is a natural constant.

[0023] In step 4, the fitness value of the particle is calculated using the following formula: , first use the real part of the output signal and the real part of a constant value Calculate the real part of the fitness value ; Use the imaginary part of the output signal and the imaginary part of a constant value Calculate the imaginary part of the fitness value :

[0024] (4)

[0025] In step 5, the particle velocity and position are updated using the following formula:

[0026] (5)

[0027] (6)

[0028] in, , , , for A random number; Represents particles In the The speed at the iteration; Represents particles In the The optimal position at the iteration Indicates The global optimal position at the iteration; Represents particles In the The position at the iteration; Represents particles In the The Gaussian perturbation generated at the iteration is represents the mean, is the variance; is the constructed Gaussian function.

[0029] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the described method.

[0030] The present invention also provides a storage medium storing a computer program or instruction. When the computer program or instruction is run on a computer, the steps of the method described are executed.

[0031] The beneficial effects of the present invention are as follows: (1) The algorithm performance is less sensitive to the parameters set in the initial stage of the PSO algorithm. (2) The algorithm steady-state error is reduced by using nonlinear random incremental inertia weights as opposed to constant weights. (3) A Gaussian perturbation term is added to the individual cognition part of the particle velocity update formula, so that the algorithm has the ability to jump out of the local optimal solution and restore the original signal. (4) The introduction of a logarithmic function to construct a nonlinear asynchronous learning factor is different from the constant learning factor in the original algorithm, thereby balancing the global development capability and local search capability of the algorithm. (5) After verification, the optimal effect that can be achieved is: the fitness of the algorithm is reduced by 0.011 after stabilization; when the symbol error rate reaches 10 -3 At the same time, the signal-to-noise ratio is the smallest; the mean square error is reduced by 1.77dB; and the inter-symbol interference is reduced by 0.64dB. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A block diagram of the method of the present invention.

[0033] Figure 2 The figure is a flow chart of the method of the present invention.

[0034] Figure 3 Constellation diagram of the MCMAPSO algorithm.

[0035] Figure 4 The constellation diagram of the embodiment of the present invention is

[0036] Figure 5 Schematic diagram of fitness curve comparison between the embodiment of the present invention and the MCMAPSO algorithm.

[0037] Figure 6 The figure is a schematic diagram comparing symbol error rate curves of the embodiment of the present invention and CMA, MCMA and MCMAPSO algorithms.

[0038] Figure 7 It is a schematic diagram comparing the mean square error curves of the embodiment of the present invention and the CMA, MCMA, and MCMAPSO algorithms.

[0039] Figure 8 It is a schematic diagram comparing the inter-symbol interference curves of the embodiment of the present invention and the CMA, MCMA, and MCMAPSO algorithms. DETAILED DESCRIPTION

[0040] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0041] like Figure 1 As shown, this embodiment provides a constant modulus blind equalization method (Chaotic Asynchronous Gaussian Particle Equalizer, referred to as CAG-PE) based on chaotic mapping and Gaussian perturbation, wherein is the input signal, For the transmission channel, For noise, is the received signal of the equalizer, is the weight vector of the equalizer, is the equalized signal. In order to avoid using a training sequence, this type of blind equalizer estimates the received signal of the equalizer and obtains a constant value and , calculated using formula (1), For hope, is a constant, usually taken :

[0042] (1)

[0043] The CAG-PE algorithm is used to adjust the equalizer weight vector Make adjustments.

[0044] The basic steps of implementing the technical solution of this embodiment are as follows: Figure 2 As shown:

[0045] Step 1, estimating the received signal at the receiving end of the channel simulator to obtain a constant value; initializing relevant parameters, which include the initial position, initial velocity and population size of the particles.

[0046] Step 2: Enter the PSO main loop. Step 3: Get the inertia weight of the current iteration number based on the chaotic Sine map and the upper and lower limits of the inertia weight. Get the learning factor of the current iteration number based on the logarithmic function and the upper and lower limits of the learning factor.

[0047] The chaotic Sine map has good ergodicity and increases the randomness of the algorithm. Therefore, the chaotic Sine map is introduced to construct a nonlinear random increasing inertia weight. The constructed inertia weight is formula (2):

[0048] (2)

[0049] in is the current iteration number; is the maximum number of iterations; For the The inertia weight at the iteration; , are the upper and lower limits of the inertia weight respectively; For the The chaotic Sine map at the iteration; the initial value of the chaotic Sine map , rand represents a random number, is a constant.

[0050] In the early stage of the algorithm, particles should focus on individual experience, and in the later stage of the algorithm, they should focus on group experience. The logarithmic function is introduced to construct a nonlinear asynchronous learning factor to balance the global development ability and local search ability of the algorithm. The constructed individual learning factor and social learning factor are formula (3):

[0051] (3)

[0052] in , Represents individual learning factors The upper and lower limits of , Social learning factors The upper and lower limits of ; e is a natural constant.

[0053] Step 4: After the received signal passes through the equalizer, the output signal is obtained. The fitness value of the particle is calculated based on the output signal and the constant value obtained in step 1. The filter is constructed using the current particle position, and the current output signal is obtained through the MCMA algorithm. The fitness is calculated using formula (4). The fitness of the real part and the imaginary part of the output signal are calculated separately and then added.

[0054] (4)

[0055] Step 5: Evaluate whether the fitness value of the particle decreases. If the fitness value decreases, update the individual and global optimal fitness values, and update the particle speed and position, that is, formula (5) and (6). A Gaussian perturbation term is added to the individual cognition part of the particle speed update formula, so that the algorithm has the ability to jump out of the local optimal solution; if the fitness value does not decrease, do not update the individual and global optimal fitness values, and directly update the particle speed and position.

[0056] (5)

[0057] (6)

[0058] in, , , , for A random number; Represents particles In the The speed at the iteration; Represents particles In the The optimal position at the iteration Indicates The global optimal position at the iteration; Represents particles In the The position at the iteration; Represents particles In the The Gaussian perturbation generated at the iteration is represents the mean, is the variance; is the constructed Gaussian function.

[0059] Step 6: Repeat steps 2 to 5 until the termination condition is met.

[0060] Step 7, after the termination condition is met, the global optimal fitness value and the global optimal position are obtained, and the output signal is calculated based on the equalizer constructed according to the global optimal position at this time. The output signal obtained at this time is basically close to the original signal.

[0061] The complexity comparison of the constant modulus algorithm (CMA), modified constant modulus algorithm (MCMA), modified constant modulus algorithm based on particle swarm optimization (MCMAPSO) and chaotic asynchronous Gaussian particle equalizer (CAG-PE) algorithm is shown in Table 1, where the signal length is , the filter order is , the maximum number of iterations in the particle swarm algorithm is , the number of particles is , the particle dimensions are .

[0062] Table 1

[0063] According to the complexity analysis, due to the introduction of particle swarm algorithm, the complexity of MCMAPSO and CAG-PE algorithm is significantly increased compared with that of CMA and MCMA algorithm. Compared with MCMAPSO algorithm, the complexity of CAG-PE algorithm is only increased by 1.0% due to the addition of nonlinear increasing inertia weight and nonlinear asynchronous learning factor. ; Gaussian perturbation is added to the particle velocity update part, and the complexity only increases Therefore, among the four algorithms, the complexity of the CAG-PE algorithm is higher, and it increases with the number of particles, particle dimensions, and the number of iterations.

[0064] In a specific embodiment, a constant modulus blind equalization method based on chaotic mapping and Gaussian perturbation is provided, comprising the following steps:

[0065] Step 1: Initialize relevant parameters. The original signal is a 4QAM signal, the signal-to-noise ratio is 25dB, and the channel parameters are ;

[0066] Where j represents the imaginary part of the complex number;

[0067] In formula (1) , the length of the equalizer is 21, the total number of particles is 35, the maximum number of iterations is 500, the upper and lower limits of all particles are 2 and -2, and the particle dimension is 42;

[0068] Step 2: Enter the PSO main loop;

[0069] Step 3: According to the chaotic Sine map and the upper and lower limits of the inertia weight, the inertia weight of the current iteration number is obtained. According to the logarithmic function and the upper and lower limits of the learning factor, the learning factor of the current iteration number is obtained.

[0070] The nonlinear random increasing inertia weight is constructed using formula (2), where .

[0071] The nonlinear asynchronous learning factor is constructed using formula (3), where .

[0072] Step 4: After the received signal passes through the equalizer, the output signal is obtained. The fitness value of the particle is calculated based on the output signal and the constant value obtained in step 1. The filter is constructed using the current particle position. The current output signal is obtained through the MCMA algorithm. The fitness is calculated using formula (4);

[0073] Step 5: Evaluate whether the fitness value of the particle decreases. If the fitness value decreases, update the individual and global optimal fitness values, and update the particle speed and position. A Gaussian perturbation term is added to the individual cognition part of the particle speed update formula, so that the algorithm has the ability to jump out of the local optimal solution, and use formulas (5) and (6) to update the particle speed and position; if the fitness value does not decrease, do not update the individual and global optimal fitness values, and update the particle speed and position. In formula (5), .

[0074] Step 6: Repeat steps 2 to 5 until the termination condition is met, that is, the maximum number of iterations is reached.

[0075] Step 7, after the termination condition is met, the global optimal fitness value and the global optimal position are obtained, and the output signal is calculated based on the equalizer constructed according to the global optimal position at this time. The output signal obtained at this time is basically close to the original signal.

[0076] The constellation diagram of this embodiment is compared with that of the MCMAPSO algorithm. Figure 3 , Figure 4 It can be seen that this embodiment can recover the 4QAM signal, and compared with the MCMAPSO algorithm, the constellation diagram is more compact, the error is smaller, and the equalization effect is better.

[0077] The fitness curve of this embodiment is compared with that of the MCMAPSO algorithm. Figure 5Although the convergence speed of the embodiment is slower than that of the MCMAPSO algorithm, the fitness value is slightly lower than that of the MCMAPSO algorithm after reaching stability. The fitness value of the MCMAPSO algorithm after stabilization is about 0.09, and the fitness value of the embodiment is about 0.079.

[0078] The symbol error rate curve of this embodiment is compared with that of CMA, MCMA, and MCMAPSO algorithms. Figure 6 As shown. When the symbol error rate reaches the order of magnitude, the signal-to-noise ratio of the CMA algorithm is about 30dB; the signal-to-noise ratio of the MCMA algorithm is about 26dB; the signal-to-noise ratio of the MCMAPSO algorithm is about 18dB; and the signal-to-noise ratio of the CAG-PE algorithm is about 16dB. When the same symbol error rate is achieved, the signal-to-noise ratio of the CAG-PE algorithm is the smallest, and the algorithm equalization effect is better. In order to facilitate the comparison of the mean square error and inter-symbol interference of this embodiment with CMA, MCMA, and MCMAPSO, the number of iterations of MCMAPSO and the embodiment is increased to 10,000 times.

[0079] The mean square error curve of this embodiment is compared with that of CMA, MCMA, and MCMAPSO algorithms. Figure 7 As shown. After stabilization, the mean square error of the CMA algorithm is the highest, about 1.3788dB, and the mean square errors of the MCMA algorithm and the MCMAPSO algorithm are almost the same, about -7.22dB, but the convergence speed of the MCMAPSO algorithm is significantly higher than that of the MCMA algorithm. The mean square error of the embodiment is the lowest, about -8.99dB. This shows that the proposed algorithm has a lower steady-state error.

[0080] The inter-symbol interference curves of this embodiment and CMA, MCMA, and MCMAPSO algorithms are compared. Figure 8 As shown. When convergence is reached, the inter-code interference of the CMA algorithm is about -16.19dB, and the inter-code interference of the MCMA algorithm is about -17.07dB. And the fluctuations of the inter-code interference of CMA and MCMA are relatively large. The inter-code interference of the MCMAPSO algorithm and the embodiment is more stable, the inter-code interference of MCMAPSO is -23.04dB, and the inter-code interference of the embodiment is -23.68dB. The inter-code interference of the embodiment after convergence is more stable and lower, and the convergence effect is better.

[0081] The present invention provides a method for constant modulus blind equalization based on chaotic mapping and Gaussian perturbation. There are many methods and ways to implement the technical solution. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A constant modulus blind equalization method based on chaotic mapping and Gaussian perturbation, characterized in that: The following steps are involved: Step 1, estimating a received signal at a receiving end of a channel emulator to obtain a constant value; Initializing relevant parameters, including initial position, initial velocity and population size of particles; Step 2, enter the particle swarm algorithm PSO main loop; Step 3: According to the chaotic Sine map and the upper and lower limits of the inertia weight, the inertia weight of the current iteration number is obtained; according to the logarithmic function and the upper and lower limits of the learning factor, the learning factor of the current iteration number is obtained; Step 4, the received signal is passed through the equalizer to obtain the output signal, and the fitness value of the particle is calculated according to the output signal and the constant value obtained in step 1; Step 5, evaluate whether the fitness value of the particle decreases. If the fitness value decreases, update the individual and global optimal fitness values, and update the particle speed and position; if the fitness value does not decrease, do not update the individual and global optimal fitness values, and update the particle speed and position; Step 6, repeat steps 2 to 5 until the termination condition is met; Step 7, after the termination condition is met, the global optimal fitness value and the global optimal position are obtained, and the output signal is calculated based on the equalizer constructed according to the global optimal position at this time.

2. The method according to claim 1, characterized in that In step 1, the equalizer receives the signal To estimate, use The real part of and the imaginary part Get constant values The real part of and the imaginary part : （1）， in, For hope, is a constant.

3. The method according to claim 2, characterized in that In step 3, the inertia weight is calculated using the following formula: （2）， in is the current iteration number; is the maximum number of iterations; For the The inertia weight at the iteration; , are the upper and lower limits of the inertia weight respectively; For the The chaotic Sine map at the iteration; the initial value of the chaotic Sine map , rand represents a random number, is a constant.

4. The method according to claim 3, characterized in that In step 3, the learning factor includes individual learning factor and social learning factors , the calculation formula is: （3）， in , Represents individual learning factors The upper and lower limits of , Social learning factors The upper and lower limits of ; e is a natural constant.

5. The method according to claim 4, characterized in that In step 4, the fitness value of the particle is calculated using the following formula: , first use the real part of the output signal and the real part of a constant value Calculate the real part of the fitness value ; Use the imaginary part of the output signal and the imaginary part of a constant value Calculate the imaginary part of the fitness value : （4）。 6. The method according to claim 5, characterized in that In step 5, the particle velocity and position are updated using the following formula: （5）， （6）， in, , , , for A random number; Represents particles In the The speed at the iteration; Represents particles In the The optimal position at the iteration Indicates The global optimal position at the iteration; Represents particles In the The position at the iteration; Represents particles In the The Gaussian perturbation generated at the iteration is represents the mean, is the variance; is the constructed Gaussian function.

7. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 6.

8. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 6 are executed.

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