A method for reducing bit error rate based on improved PMSER algorithm

Abstract

The present invention relates to a method for reducing the bit error rate based on an improved PMSER algorithm, comprising the following steps: S1, constructing an equalizer feedback channel model and defining the error of the signal; S2, using a Gaussian function to approximate the L0 norm and substituting it into the model to obtain the expression form of the L0 norm after function approximation; S3, introducing the L0 norm approximated by the Gaussian function into the algorithm to obtain the corresponding iterative formula and recording the number of iterations; S4, simplifying the iterative formula by the Taylor formula expansion method; S5, selecting sparse matrix elements through the constraint of the L0 norm to obtain new sparse matrix elements; S6, substituting the obtained updated iterative formula and new sparse matrix elements into the model to calculate the bit error rate of underwater acoustic channel transmission. Compared with the prior art, the present invention has the advantages of faster convergence speed, better effect of reducing the bit error rate, etc.

Description

Technical Field

[0001] The invention relates to the field of underwater acoustic channels, and in particular to a method for reducing a bit error rate based on an improved PMSER algorithm. Background Art

[0002] Underwater acoustic communication technology was born in the middle of the 20th century. Analog communication was its main system. Later, it gradually transitioned to underwater acoustic digital communication and introduced modern radio communication system into underwater acoustic communication. In the 21st century, the game between major powers in the international community is becoming more and more intense. Underwater acoustic communication (UAC) technology plays an increasingly important role in the marine military field of various countries. Not only in the military field, but also in the exploration of marine resources and the study of complex underwater environments, underwater acoustic communication technology is indispensable. Under the combined effect of these factors, underwater acoustic communication technology has achieved faster and faster development.

[0003] The underwater acoustic channel is highly selective, with multipath delay spreads of tens or hundreds of milliseconds, resulting in severe frequency selective signal distortion. In particular, at the low propagation speed of 1500m / s, multipath propagation leads to long-term delay characteristics and severe inter-symbol interference (ISI) in the underwater acoustic channel. The superposition of received signals from different delay paths leads to extremely severe inter-symbol crosstalk. In order to eliminate the impact of severe multipath effects, an equalization module is used. The zero-forcing algorithm has been proven to be a linear equalization algorithm that can minimize peak distortion. Zero-forcing equalization is very simple to use, but it will cause the disadvantage of noise amplification. It is not actually used much under the condition of large background noise in the underwater acoustic environment. The equalizer based on maximum likelihood symbol detection (MLSD) and maximum likelihood sequence estimation (MLSE) is basically not used in underwater communications due to its high computational complexity. The adaptive decision feedback equalizer (DFE) is currently the most commonly used equalizer in underwater communications.

[0004] DFE (Adaptive Decision Feedback Equalizer), applied to underwater acoustic channels, has been proven to be more effective than traditional linear adaptive equalizers. It is designed based on the minimum mean square error (MMSE) principle. However, the minimum mean square error does not necessarily achieve the minimum bit error rate (MSER) ​​performance. In order to achieve better performance, the MSER standard has been used to design DFE. In order to better reduce the bit error rate (SER) of the channel, the PMSER algorithm is proposed based on the MSER criterion to achieve a lower SER effect. However, the convergence speed of this algorithm is slow.

[0005] Therefore, how to achieve rapid convergence of the PMSER algorithm and reduce the bit error rate of underwater acoustic channel transmission has become a technical problem that needs to be solved. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for reducing the bit error rate based on an improved PMSER algorithm.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A method for reducing bit error rate based on an improved PMSER algorithm, the method comprising the following steps:

[0009] Step S1, constructing an equalizer feedback channel model and defining a signal error;

[0010] Step S2, using a Gaussian function to approximate the L0 norm, and bringing it into the equalizer feedback channel model constructed in step S1 to obtain an expression form of the L0 norm after function approximation;

[0011] Step S3, introducing the L0 norm obtained by approximating the Gaussian function obtained in step S2 into the improved PMSER algorithm to obtain a corresponding iterative formula, and recording the number of iterations;

[0012] Step S4, deriving and simplifying the iterative formula obtained in step S3 by Taylor formula expansion method to obtain a related update iterative formula;

[0013] Step S5, selecting sparse matrix elements through the constraint of L0 norm to obtain new sparse matrix elements;

[0014] Step S6, bringing the obtained update iteration formula and the new sparse matrix elements into the equalizer feedback channel model constructed in step S1 to calculate the underwater acoustic channel transmission bit error rate.

[0015] Furthermore, the equalizer feedback channel model in step S1 is specifically expressed as:

[0016]

[0017] Among them, m(k) represents the decision feedback result, w k represents the feedforward filter coefficient, b k represents the feedback filter coefficient, represents the signal sent in the past, y(k) represents the received signal, and k represents the number of signals.

[0018] Furthermore, the y(k) is specifically expressed as:

[0019]

[0020] Among them, r(k) represents the input signal, h(l) represents the time-invariant signal, n(k) represents Gaussian white noise, and l represents the step size.

[0021] Furthermore, the error of the signal in step S1 is specifically defined as:

[0022] e k =m k -r k (D)

[0023] Among them, e k represents the signal error, m(k) represents the decision feedback result, r(k) represents the input signal, D represents the equalizer delay, and k represents the number of signals.

[0024] Furthermore, the expression of the L0 norm in step S2 is:

[0025]

[0026] Among them, w k-1 represents the feedforward filter coefficient, l represents the step size, β represents the numerical coefficient, and k represents the number of signals.

[0027] Furthermore, the iterative formula in step S3 includes an iterative formula of a feedback filter and an iterative formula of a feedforward filter.

[0028] Furthermore, the iterative formula of the feedforward filter is:

[0029]

[0030] Among them, G f,k represents the sparse matrix of the feedforward filter, μ represents the influence of all scalars on the iterative formula, e k represents the error of the signal, r(k) represents the input signal, w k-1 and w k represents the feedforward filter coefficient, y(k) represents the received signal, and k represents the number of signals;

[0031] The iterative formula of the feedback filter is:

[0032]

[0033] Among them, G b,k represents the sparse matrix of the feedback filter, b k and b k-1 Represents the feedback filter coefficient.

[0034] Further, the updated iterative formula in step S4 includes an updated iterative formula of the feedforward filter and an updated iterative formula of the feedback filter;

[0035] The iterative formula of the updated feedforward filter is:

[0036]

[0037] The iterative formula of the updated feedback filter is:

[0038]

[0039] Here, β represents a numerical coefficient.

[0040] Furthermore, the new sparse matrix elements in step S5 include G f,k The elements of the sparse matrix and G b,k The elements of the sparse matrix; G f,k The elements of a sparse matrix are represented as:

[0041]

[0042] Among them, f , k represents the step size function of the feedforward filter, α represents the numerical coefficient of the allocated step size, N f Indicates the number of feedforward carriers;

[0043] The G b,k The elements of a sparse matrix are represented as:

[0044]

[0045] Among them, b,k represents the step size function of the feedback filter, N b Indicates the number of feedback carriers.

[0046] Furthermore, the method for obtaining new sparse matrix elements in step S5 is a Lagrangian relaxation method.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. The number of iterations required for the improved PMSER algorithm to achieve a bit error rate of 0.01 is 1450, while the number of iterations required for the existing MSER algorithm to achieve a bit error rate of 0.01 is 1700. The present invention has better convergence, can effectively reduce the bit error rate of underwater acoustic channel transmission, and achieve better signal transmission effect.

[0049] 1. In order to improve the convergence speed of the PMSER algorithm, the present invention uses the L0 norm in the sparse matrix selection of the PMSER algorithm to achieve better sparsity.

[0050] 2. In order to solve the problem that it is difficult to obtain an approximate solution of the L0 norm, the present invention selects a Gaussian function to achieve an effect of approximating the L0 norm, thereby making the PMSER algorithm converge faster and having better performance in reducing the bit error rate of underwater acoustic channel transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a schematic diagram of the process of the present invention;

[0052] Figure 2 Schematic diagram of the algorithm model of the present invention. DETAILED DESCRIPTION

[0053] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0054] Example 1

[0055] In order to reduce the bit error rate of underwater acoustic channel transmission, it is necessary to solve the problem of slow convergence speed of PMSER algorithm. The present invention uses L0 norm to improve the sparsity of the algorithm. The principle of optimal sparsity of L0 norm is: according to the theory of compressed sensing, the norm of a vector can be regarded as a unit sphere with a constantly changing radius. The number of intersections between the unit sphere and the spatial straight line on the coordinate axis is the sparsity. The higher the sparsity, the stronger the sparsity. As the radius of the unit sphere increases and is 1, it is the L1 norm. At this time, there is only one intersection with the spatial straight line on the coordinate axis, and the sparsity is 1; when the radius is greater than 1, the number of intersections with the spatial straight line on the coordinate axis is 0, and the sparsity is 0; from an ideal state, when the radius is 0, it is the L0 norm. At this time, the unit sphere coincides with the two coordinate axes, and has two intersections with the spatial straight line on the coordinate axis, and the sparsity is 2. It can be concluded that the sparsity of L0 norm is the best. However, since it is difficult to obtain an approximate solution for the L0 norm, the present invention selects a Gaussian function to approximate the L0 norm to achieve a faster convergence effect and reduce the bit error rate of underwater acoustic channel transmission.

[0056] like Figure 1 As shown, a method for reducing bit error rate based on an improved PMSER algorithm comprises the following steps:

[0057] Step S1, constructing an equalizer feedback channel model, defining the error of the signal, and achieving the minimum bit error rate by minimizing the error;

[0058] Step S2, using a Gaussian function to approximate the L0 norm, and bringing it into the model constructed in step S1 to obtain an expression of the L0 norm after function approximation;

[0059] Step S3, using the improved PMSER algorithm to reduce the bit error rate while introducing the selection of sparse matrix to improve the convergence speed, introducing the L0 norm obtained by the Gaussian function approximation obtained in step S2 into the algorithm to obtain the corresponding iterative formula, and recording the number of iterations;

[0060] Step S4: The iterative formula has a very high complexity. In order to reduce the computational complexity of the formula and facilitate the calculation, the iterative formula in step S3 is derived and simplified using the Taylor formula expansion method to obtain the relevant update iterative formula;

[0061] Step S5, selecting sparse matrix elements through the constraint of L0 norm to obtain new sparse matrix elements;

[0062] Step S6, bringing the obtained update iteration formula and new sparse matrix elements into the model constructed in step S1 to calculate the bit error rate of underwater acoustic channel transmission.

[0063] S1. Build the model:

[0064] The equalizer feedback model is constructed and expressed as:

[0065]

[0066] m(k) is the decision feedback result, w k is the feedforward filter coefficient, b k is the feedback filter coefficient, is the signal sent in the past, y(k) represents the received signal, and k represents the number of signals;

[0067] Among them, y(k) is specifically expressed as:

[0068]

[0069] r(k) represents the input signal, h(l) represents the time-invariant signal, n(k) represents Gaussian white noise, and l represents the step size; the error of the signal is defined as:

[0070] e k =m k -r k (D)

[0071] e k is the signal error, D represents the equalizer delay;

[0072] The object of the present invention is to obtain k , thereby minimizing the symbol error rate.

[0073] S2, approximation to L0 norm:

[0074] The Gaussian function is converted into an L0 norm and introduced into the equalizer feedback model to be expressed as:

[0075]

[0076] Here, β represents a numerical coefficient.

[0077] S3. Construct iterative formula:

[0078] The sparsity of the equalizer is studied, and a sparse matrix based on the L0 norm is introduced into the PMSER algorithm to obtain the iterative formula of the feedforward filter:

[0079]

[0080] Among them, G f,k represents the sparse matrix of the feedforward filter, and μ represents the influence of all scalars on the iterative formula.

[0081] Simplifying the formula, we can get:

[0082]

[0083] S4, iterative formula simplification:

[0084] The last term in the iterative formula has a very high computational complexity. In order to facilitate the calculation of the formula, it is necessary to reduce the computational complexity of the formula. The present invention uses the Taylor first-order expansion of the exponential function to expand the last term to achieve the purpose of reducing the complexity of the formula. The update iterative formula is obtained by expanding the Taylor first-order formula:

[0085]

[0086] Since the exponential function is greater than zero, the iterative formula for Taylor's first-order formula expansion will be discussed in two cases;

[0087] Case 1: The following formula is obtained:

[0088]

[0089] Case 2: The following formula is obtained:

[0090]

[0091] Construct a new function f that makes the formula expression more concise β (x)

[0092]

[0093] Substituting it into the iterative formula and simplifying it, we get the following formula:

[0094]

[0095] S5. Sparse matrix element selection:

[0096] The update of the iterative formula requires the determination of the elements of the sparse matrix. In order to avoid the problem of too long step length, a smaller step length is allocated while considering sparsity to achieve the purpose of improving the convergence speed. When calculating the step length, use ||w k-1 ||0 instead of ||w k-1 ||1, by using the Lagrangian relaxation method, we get G f,k Elements of a sparse matrix:

[0097]

[0098] Among them, f,k represents the step size function of the feedforward filter, α represents the numerical coefficient of the assigned step size, N f Indicates the number of feedforward carriers;

[0099] The update iteration formula of the feedback filter and the elements of the sparse matrix are calculated using the method described, which are:

[0100]

[0101]

[0102] Among them, G b,k represents the sparse matrix of the feedback filter, ζ b,k represents the step size function of the feedback filter, N b Indicates the number of feedback carriers.

[0103] S6. Substitute the formula into the bit error rate calculation

[0104] The update iterative formula and sparse matrix elements of the obtained feedforward filter, as well as the update iterative formula and sparse matrix elements of the feedback filter are introduced into the equalizer feedback channel model, and the bit error rate of the underwater acoustic channel transmission is calculated when the number of iterations is 3000 under the condition of a signal-to-noise ratio of 17dB, and the result is 0.0028. The bit error rate of the underwater acoustic channel transmission of the existing MSER algorithm is calculated when it is iterated 3000 times under the same conditions, and the result is 0.025. Under the same conditions and the same number of iterations, the performance of the method of the present invention in reducing the bit error rate of underwater acoustic channel transmission is better than that of the existing method. And as the signal-to-noise ratio increases, the performance advantage of the method of the present invention becomes more obvious.

[0105] Example 2

[0106] The difference between this embodiment and embodiment 1 is that, in this embodiment, the bit error rate of underwater acoustic channel transmission is fixed to 0.01, and the number of iterations required for the method of the present invention and the existing method to achieve the bit error rate under the condition of a signal-to-noise ratio of 17 dB is calculated respectively.

[0107] Calculation shows that the method of the present invention requires 1450 iterations to achieve an underwater acoustic channel transmission bit error rate of 0.01; the existing method requires 1700 iterations to achieve an underwater acoustic channel transmission bit error rate of 0.01. The method of the present invention has better convergence and is more effective in reducing the underwater acoustic channel transmission bit error rate.

[0108] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for reducing bit error rate based on an improved PMSER algorithm, characterized in that: The method comprises the following steps: Step S1, constructing an equalizer feedback channel model and defining a signal error; The equalizer feedback channel model is specifically expressed as: Among them, m k represents the decision feedback result, w k represents the feedforward filter coefficient, b k Represents the feedback filter coefficient, y k Indicates receiving signal, represents the signal sent in the past, and k represents the number of signals; The received signal y k Specifically expressed as: Among them, r k represents the input signal, h l represents a time-invariant signal, n k represents Gaussian white noise, l represents the step size; The error of the signal is specifically defined as: e k =m k -r k (D) Among them, e k Represents the signal error, m k Represents the decision feedback result, r k represents the input signal, and D represents the equalizer delay; Step S2, using a Gaussian function to approximate the L0 norm, bringing it into the equalizer feedback channel model constructed in step S1 to obtain the expression of the L0 norm after function approximation, specifically: Among them, w k-1 represents the feedforward filter coefficient, l represents the step size, and β represents the numerical coefficient; Step S3, introducing the L0 norm obtained by approximating the Gaussian function obtained in step S2 into the improved PMSER algorithm to obtain a corresponding iterative formula, and recording the number of iterations; The iterative formula includes an iterative formula of a feedback filter and an iterative formula of a feedforward filter; The iterative formula of the feedforward filter is: Among them, μ represents the influence of all scalars on the iterative formula, G f,k A sparse matrix representing a feedforward filter; The iterative formula of the feedback filter is: Among them, G b,k A sparse matrix representing the feedback filter; Step S4, deriving and simplifying the iterative formula obtained in step S3 by Taylor formula expansion method to obtain a related update iterative formula; The updated iterative formula includes an updated iterative formula of a feedforward filter and an updated iterative formula of a feedback filter; The iterative formula of the updated feedforward filter is: The iterative formula of the updated feedback filter is: Step S5, selecting sparse matrix elements through the constraint of L0 norm to obtain new sparse matrix elements; Step S6, bringing the obtained update iteration formula and the new sparse matrix elements into the equalizer feedback channel model constructed in step S1 to calculate the underwater acoustic channel transmission bit error rate.

2. The method for reducing bit error rate based on the improved PMSER algorithm according to claim 1, characterized in that: The new sparse matrix elements in step S5 include G f,k The elements of the sparse matrix and G b,k The elements of the sparse matrix; the G f,k The elements of a sparse matrix are represented as: Among them, f,k represents the step size function of the feedforward filter, α represents the numerical coefficient of the assigned step size, N f Indicates the number of feedforward carriers; The G b,k The elements of a sparse matrix are represented as: Among them, b,k represents the step size function of the feedback filter, N b Indicates the number of feedback carriers.

3. The method for reducing bit error rate based on the improved PMSER algorithm according to claim 1, characterized in that: The method for obtaining new sparse matrix elements in step S5 is the Lagrangian relaxation method.

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