An LMS-FNNCMA algorithm for MIMO equalization

Abstract

An LMS-FNNCMA algorithm for MIMO equalization belongs to the field of optical fiber communication technology. Switches A1 and A2 are turned on, and the training input signal is passed through a transverse filter. The weight coefficients are then adjusted using the LMS algorithm to continuously approximate the known desired response d(n). After the learning process is complete, the transverse filter reaches its optimal design. Its weight coefficients are then fixed, and switches B1 and B2 are turned on to filter the working input signal. Then, based on the cost function method, a suitable nonlinear activation function is selected through the neural network coefficients continuously adjusted by the blind equalization algorithm to perform a second filtering operation on the working input signal y(n) after the LMS algorithm filtering, finally obtaining the decision output after passing through the decision unit.

Description

Technical Field

[0001] This invention relates to an LMS-FNNCMA algorithm for MIMO equalization, belonging to the field of optical fiber communication technology. Background Technology

[0002] With the continuous emergence of high-bandwidth services such as 5G mobile communication, big data, and the Internet of Things, optical fiber communication systems are rapidly developing towards ultra-high speed and ultra-large capacity. The application of technologies such as wavelength division multiplexing (WDM) and higher-order modulation has brought the capacity of single-mode optical fiber communication close to the Shannon limit. To further improve the transmission capacity of optical fiber communication systems, space division multiplexing technology based on multi-core, few-mode fibers is highly anticipated. However, in long-distance transmission of multi-core, few-mode fibers, problems such as crosstalk, dispersion, attenuation, and nonlinearity between different modes of the channel make signal demodulation difficult. Equalization technology plays a crucial role in de-crosstalking between modes. Currently, optical equalization algorithms mainly employ adaptive algorithms, such as least mean square (LMS), recursive least squares (RLS), and blind equalization algorithms. The latter is widely used in optical communication because it can equalize the transmission channel using only the information from the received sequence without the aid of a training sequence. Completely eliminating crosstalk between different modes in low-differential-mode delay few-mode fibers is a challenge for MIMO equalization algorithms; furthermore, channel nonlinearity also affects the system. Therefore, new solutions are needed to design and optimize equalization algorithms to achieve higher convergence accuracy and speed, and reduce the bit error rate performance of the system. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention provides an LMS-FNNCMA algorithm for MIMO equalization.

[0004] An LMS-FNNCMA algorithm for MIMO equalization consists of a transversal filter, an adaptive LMS algorithm, a neural network, and a blind equalization algorithm; it includes a test section for the working input signal and contains the following steps:

[0005] First, the data is trained through the test section of the working input signal, and then the data is transmitted through the test section of the working input signal.

[0006] The data training part consists of a transverse filter and weight vector adjustment using an adaptive LMS algorithm.

[0007] The training input signal is filtered by a transverse filter, and the coefficients of the transverse filter are controlled by an adaptive LMS algorithm.

[0008] The error signal of the adaptive LMS algorithm consists of the known desired response d(n) and the estimated response obtained through a transverse filter. The difference determines the outcome.

[0009] The iteration step size is set to 1×10. -3 With 1×10 -4 By using the minimum mean square error criterion, the coefficients of the filter w(n) are continuously adjusted so that the desired response d(n) continuously approximates the estimated response.

[0010] As the iterations continue, the MSE gradually converges and decreases, completing the data training phase.

[0011] MSE, or mean squared error, is a measure of the difference between the estimator and the estimated quantity.

[0012] The testing section for the working input signal consists of a neural network, a blind equalization algorithm, and a decision unit. The working input signal obtained from the training section undergoes a secondary filtering operation through the neural network. The weight coefficients of the neural network are controlled by the blind equalization algorithm. After sufficient iterations, the decision unit makes a decision and outputs the signal. The neural network consists of an input layer, a hidden layer, and an output layer.

[0013] The activation function is defined as

[0014] Among them This represents the mean square error of the blind equalization algorithm.

[0015] R² is a real constant that depends on higher-order statistics of the source sequence.

[0016] Blind equilibrium algorithms construct a cost function,

[0017] in By using the steepest descent method, the weights of the neural network are updated to obtain the optimal coefficients, thereby further reducing the system's bit error rate.

[0018] J(n) is the cost function.

[0019] f(x) is an activation function, which is a function added to artificial neural networks to help the network learn complex patterns in the data.

[0020] Mean squared error is a measure that reflects the degree of difference between the estimator and the estimated quantity.

[0021] R² is a real constant that depends on higher-order statistics of the source sequence.

[0022] An LMS-FNNCMA algorithm for MIMO equalization includes the following steps: Switches A1 and A2 are turned on, the training input signal is passed through a transverse filter, and the weight coefficients are adjusted using the LMS algorithm to continuously approximate the known desired response d(n). After the learning process is completed, the value of the transverse filter reaches its optimal design. Its weight coefficients are then fixed. Switches B1 and B2 are turned on to filter the working input signal. Then, based on the cost function method, a suitable nonlinear activation function is selected using the neural network coefficients continuously adjusted by the blind equalization algorithm to perform a secondary filtering operation on the working input signal y(n) after the LMS algorithm filtering, finally obtaining the decision output after passing through the decision unit.

[0023] The technical advantages of this invention are as follows: The LMS pre-equalization algorithm is used to update the filter coefficients, improving the convergence speed. The algorithm incorporates a neural network, and by setting the nonlinear activation function of the neural network, it can compensate for nonlinear factors appearing in the channel, resulting in better equalization of the system, higher convergence accuracy and speed, and reduced system bit error rate performance. Compared with traditional LMS and CMA algorithms, it has superior characteristics such as faster convergence speed and higher convergence accuracy. Improvements to the adaptive LMS algorithm and blind equalization algorithm further enhance the convergence speed and accuracy, enabling descrambling of crosstalk between all modes and improving system reliability. Attached Figure Description

[0024] When considered in conjunction with the accompanying drawings, the invention will become more fully and better understood by referring to the following detailed description, and many of its accompanying advantages will become readily apparent. However, the accompanying drawings, which are provided to further illustrate the invention and form part of this invention, are used to explain the invention and do not constitute an undue limitation thereof, as shown in the figures:

[0025] Figure 1 This invention presents a system framework for the LMS-FNNCMA algorithm for MIMO equalization.

[0026] Figure 2 This invention presents a neural network system framework for the LMS-FNNCMA algorithm used for MIMO equalization.

[0027] Figure 3 The convergence graph shows the LMS-FNNCMA algorithm for MIMO equalization proposed in Embodiments 1 and 2 of this invention.

[0028] Figure 4 This is a comparison diagram of the LMS-FNNCMA algorithm for MIMO equalization proposed in this invention with the traditional LMS algorithm and the CMA algorithm.

[0029] Figure 5 This is a transmission error characteristic diagram of an LMS-FNNCMA algorithm system for MIMO equalization proposed in this invention. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] Obviously, many modifications and variations made by those skilled in the art based on the spirit of this invention fall within the scope of protection of this invention.

[0032] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when an element or component is referred to as “connected” to another element or component, it may be directly connected to the other element or component, or there may be intermediate elements or components. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0033] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art.

[0034] To facilitate understanding of the embodiments, further explanations and descriptions will be provided below, and the various embodiments do not constitute a limitation of the present invention.

[0035] Example 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown, an LMS-FNNCMA algorithm for MIMO equalization consists of four parts: a transverse filter, an adaptive LMS algorithm, a neural network, and a blind equalization algorithm.

[0036] The algorithm is divided into a training part for training input signals and a testing part for working input signals.

[0037] The algorithm first undergoes data training using the training input signal, and then transmits data using the testing input signal.

[0038] The algorithm training section consists of a transverse filter and weight vector adjustments for the adaptive LMS algorithm. The training input signal is filtered through the transverse filter, and the coefficients of the transverse filter are controlled by the adaptive LMS algorithm. The error signal of the adaptive LMS algorithm is composed of the known desired response d(n) and the estimated response obtained through the transverse filter. The difference is determined by the iteration step size, which is set to 1×10. -3 With 1×10 -4 By using the minimum mean square error criterion, the coefficients of the filter w(n) are continuously adjusted so that the desired response d(n) continuously approximates the estimated response. like Figure 3 As shown, with continuous iteration, the MSE continuously converges and decreases to complete the data training part.

[0039] The testing section for the working input signal consists of a neural network, a blind equalization algorithm, and a decision unit. The working input signal obtained from the training section undergoes a secondary filtering operation through the neural network. The weight coefficients of the neural network are controlled by the blind equalization algorithm. After sufficient iterations, the signal is output by the decision unit.

[0040] like Figure 2 As shown, a neural network consists of an input layer, a hidden layer, and an output layer.

[0041] The activation function is defined as in Among them This represents the mean square error of the blind equalization algorithm.

[0042] Blind equilibrium algorithms construct a cost function,

[0043] in By using the steepest descent method, the weights of the neural network are updated to obtain the optimal coefficients, thereby further reducing the system's bit error rate.

[0044] like Figure 4 The diagram shows a comparison of the three algorithms. Through training on the data shown in the illustration, it can be found that the CMA algorithm has better convergence compared to the one without a training set.

[0045] Compared to the LMS algorithm, the use of a neural network for further filtering after training further improves the convergence accuracy, resulting in better processing capabilities and performance for channels with high time-varying interference. After processing 20,000 data points, the MSE of the LMS-FNNCMA algorithm decreased to 0.016, while LMS and CMA achieved MSEs of 0.12 and 0.062, respectively.

[0046] like Figure 5The figure shows the bit error rate characteristics after processing with the LMS-FNNCMA algorithm under two different sets of working signals. At an optical signal-to-noise ratio of 20dB, the bit error rate is lower than 1×10⁻⁶. 3 This ensures that the needs of communication transmission are met.

[0047] Example 2: As Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown, an LMS-FNNCMA algorithm for MIMO equalization includes a transverse filter, an adaptive LMS algorithm, a neural network, and a blind equalization algorithm. It is divided into a training part for training input signals and a testing part for working input signals. The neural network consists of an input layer, hidden layers, and an output layer.

[0048] Blind equalization algorithm: It can equalize the channel characteristics by relying solely on the prior information of the received sequence itself without the aid of training sequence, so that the output sequence approximates the transmitted sequence as closely as possible.

[0049] MIMO: Multiple Input Multiple Output technology refers to the input and output of multiple fiber optic mode signals.

[0050] LMS-FNNCMA algorithm: Least Mean Square Feedforward Neural Network Blind Algorithm. It introduces a neural network and a blind equalization algorithm to perform secondary processing of the data after training the Least Mean Square algorithm, thereby improving the accuracy of the algorithm.

[0051] Adaptive LMS algorithm: The least mean square algorithm is an improvement on the steepest descent algorithm. This algorithm does not require known statistical characteristics of the input signal and the desired signal, and has the best stability and wide application.

[0052] An LMS-FNNCMA algorithm for MIMO equalization includes the following steps: first, data training is performed using the training part of the training input signal, and then data transmission is performed using the test part of the working input signal.

[0053] The data training part of the training input signal includes the transverse filter and the weight vector adjustment of the adaptive LMS algorithm. The training input signal is first filtered by the transverse filter.

[0054] Obtain training error output The coefficients of the transverse filter are then adjusted by the adaptive LMS algorithm using the formula w1(n+1)=w1(n)+μ*u(n)e*(n), where μ is the iteration step size, ranging from 0 to 1; after sufficient iterations, the data training part is completed.

[0055] w1(n+1) represents the filter coefficients after one iteration.

[0056] n represents the data being transmitted.

[0057] w1(n) are the filter coefficients.

[0058] u(n) is the training input signal.

[0059] e * (n) represents the conjugate of the error signal.

[0060] The testing section for the working input signal includes neural networks, blind equalization algorithms, and decision devices.

[0061] The working input signal obtained from the training part is subjected to a secondary filtering operation through the neural network. The neural network equalization structure is divided into an input layer, a hidden layer, and an output layer.

[0062] For a channel with N modes, the input consists of N data taps, which are filtered by the FILTER1 filter.

[0063] N is a positive integer representing the number of channels in the mode.

[0064] The filter includes N 2 The number of filters in each group is the same as the number of input layers.

[0065] The filtered data enters the hidden layer, forming N. 2 EOUTU is a data point.

[0066] EOUTI is formed by the function f(·), and then filtered again by the FILTER2 filter to obtain EOUTV.

[0067] EOUTU: Input signal for the hidden layer.

[0068] EOUTI: The input signal EOUTU of the hidden layer is the signal after passing through the nonlinear activation function f(·).

[0069] EOUTV: The hidden layer output signal obtained after the hidden layer EOUTI signal passes through filter FILTER2.

[0070] EOUT: EOUTV is the output layer signal obtained after passing through the nonlinear activation function f(·).

[0071] The output layer EOUT is obtained by activating the function f(·).

[0072] The state equation of a neural network is represented as follows:

[0073]

[0074]

[0075] EOUTIk (n)=f[EOUTU k (n)] (3)

[0076]

[0077] EOUT m (n)=f[EOUTV m (n)] (5)

[0078] Where k (between 0 and N) 2 (Integers between -1 and 1) represent the (k+1)th value of the filtered INPUT.

[0079] The variable i is an integer between 0 and Ntaps-1, where Ntaps represents the number of taps, and the variable j (j = 0, 1, ..., N-1) represents the number of channels.

[0080] N is the total number of channels.

[0081] FILTER1 represents the connection weights between the input layer and the hidden layer, while FILTER2 represents the connection weights between the hidden layer and the output layer.

[0082] J(n) represents the defined cost function.

[0083] This represents the data after the signal passes through the neural network.

[0084] X(n) is the working input signal.

[0085] Input signals to the INPUT input layer.

[0086] f(·) is a nonlinear activation function.

[0087] EOUTU: Input signal for the hidden layer.

[0088] EOUTI: The input signal EOUTU of the hidden layer is the signal after passing through the nonlinear activation function f(·).

[0089] EOUTV: The hidden layer output signal obtained after the hidden layer EOUTI signal passes through filter FILTER2.

[0090] EOUT: EOUTV is the output layer signal obtained after passing through the nonlinear activation function f(·).

[0091] Based on the theory of the CMA algorithm, the following weight iteration formula is obtained:

[0092]

[0093] p(n) = (|EOUT) m(n)|-R2)q k (n) (7)

[0094] q k (n)=f[Re{EOUTV k (n)}]f′[Re{EOUTV k (n)}]+jf[Im{EOUTV k (n)}]f′[Im{EOUTV k (n)}] (8)

[0095]

[0096]

[0097] Here, p, q, and h have no actual physical meaning; they only represent intermediate quantities for solving the formula.

[0098] Where μ1=μ2=α|EOUT m (n)| is the iteration step size, and α is a constant.

[0099] In formulas (6) to (10), the range of k is Channel×m≤k≤Channel×m+Channel-1.

[0100] The error signal of the adaptive LMS algorithm consists of the known desired response d(n) and the estimated response obtained through a transverse filter. The difference Decide.

[0101] The desired response is continuously approximated using the minimum mean square error criterion. A neural network consists of an input layer, hidden layers, and an output layer.

[0102] The activation function is defined as in Among them This represents the mean square error of the blind equalization algorithm.

[0103] Blind equilibrium algorithms construct a cost function,

[0104] in By using the steepest descent method, the weights of the neural network are updated to obtain the optimal coefficients, thereby further reducing the system's bit error rate.

[0105] As described above, embodiments of the present invention have been explained in detail. However, many modifications are possible without departing substantially from the inventive points and effects of the present invention, which will be apparent to those skilled in the art. Therefore, all such modifications are also included within the scope of protection of the present invention.

Claims

1. An LMS-FNNCMA algorithm for MIMO equalization, consisting of a transversal filter, an adaptive LMS algorithm, a neural network and a blind equalization algorithm; comprising a test section of the working input signal and a test section of the working input signal, characterized in that, It includes the following steps: First, the data is trained using the test section of the working input signal; then, the data is transmitted using the test section of the working input signal. The data training part consists of a transverse filter and weight vector adjustment using an adaptive LMS algorithm. The training input signal is filtered by a transverse filter, and the coefficients of the transverse filter are controlled by an adaptive LMS algorithm. The error signal for the adaptive LMS algorithm is determined by the difference between the known desired response d(n) and the estimated response (n) obtained by the transversal filter The iteration step is set to 1 x 10 -3 and 1 x 10 -4 The coefficients of the filter w(n) are adjusted continuously by the least mean square error criterion so that the desired response d(n) continuously approximates the estimated response (n). As iterations continue, the MSE gradually converges and decreases to complete the data training phase. The testing section for the working input signal consists of a neural network, a blind equalization algorithm, and a decision unit. The working input signal obtained from the training section undergoes a secondary filtering operation through the neural network. The weight coefficients of the neural network are controlled by the blind equalization algorithm. After sufficient iterations, the decision unit makes a decision and outputs the signal. The neural network consists of an input layer, hidden layers, and an output layer. The activation function is defined as , of which The mean square error of the blind equalization algorithm. Blind equilibrium algorithms construct a cost function, in By using the steepest descent method, the weights of the neural network are updated to obtain the optimal coefficients, thereby further reducing the system's bit error rate.

2. The LMS-FNNCMA algorithm for MIMO equalization according to claim 1, characterized in that, Data training involves the following steps: Obtain training error output The coefficients of the transverse filter are then calculated using the formula... Adjusted by the adaptive LMS algorithm, where The iteration step size ranges from 0 to 1; after sufficient iterations, the data training part is complete. For a channel with N modes, the input consists of N data taps, which are filtered by a FILTER1 filter. The filter includes N 2 groups, the number of filters in each group being consistent with the number of input layers, The filtered data enters the hidden layer to form N 2 data points EOUTU, Through the function f( EOUTI is generated, and then filtered again by the FILTER2 filter to obtain EOUTV. EOUTU: Input signal of the hidden layer EOUTI: The signal obtained after the input signal EOUTU of the hidden layer passes through the nonlinear activation function f(·). EOUTV: The hidden layer output signal obtained after the hidden layer EOUTI signal passes through filter FILTER2. EOUT: The output layer signal obtained by passing EOUTV through the nonlinear activation function f(·). By activation function f( The output layer output EOUT is obtained. The state equation of a neural network is represented as follows: where k is an integer between 0 and N 2 -1, represents the (k+1)th value of the filtered INPUT, The variable i is an integer between 0 and Ntaps-1, where Ntaps represents the number of taps, and the variable j, j=0,1, N-1 represents the number of channels. N is the total number of channels. FILTER1 represents the connection weights between the input layer and the hidden layer, while FILTER2 represents the connection weights between the hidden layer and the output layer. J(n) represents the defined cost function. This represents the data after the signal passes through the neural network. X(n) is the working input signal. Input signal to the INPUT input layer f(·) is a nonlinear activation function. EOUTU: Input signal of the hidden layer EOUTI: The signal obtained after the input signal EOUTU of the hidden layer passes through the nonlinear activation function f(·). EOUTV: The hidden layer output signal obtained after the hidden layer EOUTI signal passes through filter FILTER2. EOUT: The output layer signal obtained by passing EOUTV through the nonlinear activation function f(·). Based on the theory of the CMA algorithm, the following weight iteration formula is obtained: in The iteration step size, It is a constant. In formulas (6) to (10), the range of values ​​for k is: , The error signal of the adaptive LMS algorithm consists of the known desired response d(n) and the estimated response obtained through a transverse filter. The difference of (n) Decide, By using the minimum mean square error criterion, the desired response is continuously approximated. A neural network consists of an input layer, hidden layers, and an output layer. The activation function is defined as , of which This represents the mean square error of the blind equalization algorithm.

3. The LMS-FNNCMA algorithm for MIMO equalization according to claim 2, characterized in that, The process includes the following steps: Turn on switches A1 and A2, pass the training input signal through a transverse filter, and then adjust the weight coefficients using the LMS algorithm to continuously approximate the known desired response d(n). After completing the learning process, the transverse filter reaches its optimal design. Fix its weight coefficients, turn on switches B1 and B2, and filter the working input signal. Then, based on the cost function method, through the neural network coefficients continuously adjusted by the blind equalization algorithm, select a suitable nonlinear activation function to perform a secondary filtering operation on the working input signal y(n) after filtering by the LMS algorithm, finally obtaining the decision output after passing through the decision unit.

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