CN117131757B - Construction method and device of low-frequency nonlinear channel equalizer - Google Patents
Construction method and device of low-frequency nonlinear channel equalizer Download PDFInfo
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Abstract
The invention provides a construction method and a device of a low-frequency nonlinear channel equalizer, belonging to the technical field of low-frequency communication, wherein the method comprises the following steps: nonlinear transformation is carried out on the instantaneous error function of the low-frequency nonlinear channel equalizer by utilizing a neural network activation function, and an objective error function is obtained; constructing a target cost function by utilizing a mixed norm algorithm based on the target error function so as to determine an adaptive updating formula of the equalizer weight coefficient; and constructing a target equalizer of the low-frequency nonlinear channel based on the adaptive updating formula. The invention provides a mixed norm algorithm based on a Sigmoid function, which is applied to a low-frequency nonlinear channel equalizer to construct a target equalizer so as to be better suitable for suppressing Alpha stable distribution noise with different pulse intensities in a low-frequency communication system, in particular fractional low-order Alpha stable distribution noise; the system is simple to realize, has strong stability, can well match the existing channel equalizer, and obtains better equalization performance.
Description
Technical Field
The present invention relates to the field of low frequency communications technologies, and in particular, to a method and an apparatus for constructing a low frequency nonlinear channel equalizer.
Background
In a low frequency (operating frequency 3 Hz-3 MHz) communication system, the main source of noise is atmospheric impulse noise caused by global thunderstorm activity from nature, and the noise has instantaneous, impulsive and burstiness properties and shows serious non-gaussian distribution characteristics. Experimental research shows that the atmospheric noise in the low-frequency channel can well accord with the Alpha stable distribution noise model. At present, most of researches on nonlinear channel equalization technology are also adaptive equalization methods based on Gaussian distribution noise distribution, mainly include methods based on a neural network, methods based on a model, and methods of nuclear adaptive equalization, and the like, and equalization performance degradation and even failure of a system can be caused when Gaussian assumption and a method of a second moment theory are applied to a nonlinear communication system under Alpha stable distribution because limited second moment does not exist in Alpha stable distribution.
The existing nonlinear channel equalization method based on Alpha stable distributed noise is insufficient, and two relatively famous methods are mainly available: one is a nonlinear channel equalization method based on Volterra series, because the computational complexity of the algorithm increases exponentially with the increase of the order, a truncated second-order or third-order Volterra equalizer is generally adopted, the structure is relatively complex, and the equalization performance is also greatly compromised; the other is based on a neural network function model and a kernel self-adaptive minimum average p-norm algorithm, and the algorithm introduces the minimum average p-norm algorithm on the basis of the neural network function model and the kernel self-adaptive equalization algorithm, so that the kernel self-adaptive equalization algorithm is suitable for Alpha stable distributed noise. The convergence rate of the algorithm is obviously improved, but the stability of the algorithm is slightly poor under the condition of non-Gaussian noise and Gaussian mixture interference because the algorithm is based on a minimum dispersion coefficient criterion.
Disclosure of Invention
The invention provides a construction method and a construction device of a low-frequency nonlinear channel equalizer, which are used for solving the defects that the low-frequency nonlinear channel equalizer in the prior art is difficult to effectively acquire a low-frequency signal and has poor equalization effect.
In a first aspect, the present invention provides a method for constructing a low frequency nonlinear channel equalizer, including: nonlinear transformation is carried out on the instantaneous error function of the low-frequency nonlinear channel equalizer by utilizing a neural network activation function, and an objective error function is obtained; the instantaneous error function obeys standard Alpha stable distribution; constructing an objective cost function by utilizing a mixed norm algorithm based on the objective error function so as to determine an adaptive updating formula of the equalizer weight coefficient; and constructing a target equalizer of the low-frequency nonlinear channel based on the self-adaptive updating formula.
According to the construction method of the low-frequency nonlinear channel equalizer provided by the invention, after the target equalizer of the low-frequency nonlinear channel is established based on the self-adaptive updating formula, the construction method further comprises the following steps: and constructing a low-frequency nonlinear channel space diversity equalizer model based on the constructed target equalizer of the independent single low-frequency nonlinear channel.
According to the construction method of the low-frequency nonlinear channel equalizer provided by the invention, the instantaneous error function is an S-shaped activation function.
According to the construction method of the low-frequency nonlinear channel equalizer provided by the invention, the transient error function of the low-frequency nonlinear channel equalizer is subjected to nonlinear transformation by utilizing the neural network activation function, and the target error function is obtained, specifically:
Wherein, Representing the target error function, e (k) representing the instantaneous error function, sgm representing the neural network activation function, η being the tilt parameter.
According to the method for constructing the low-frequency nonlinear channel equalizer, the objective cost function is constructed by utilizing a mixed norm algorithm based on the objective error function so as to determine an adaptive updating formula of the equalizer weight coefficient, and the method comprises the following steps: substituting the target error function into a cost function of a mixed norm algorithm to construct the target cost function; and taking the minimum value of the target cost function as a target, and determining an adaptive updating formula of the equalizer weight coefficient by using a steepest descent method.
According to the construction method of the low-frequency nonlinear channel equalizer provided by the invention, the objective cost function is specifically as follows:
wherein lambda (k) E [0,1] is a mixing parameter, E is a statistical mathematical expectation, Is a target error function; the self-adaptive updating formula specifically comprises the following steps:
wherein w (k+1) is the updated equalizer weight coefficient, w (k) is the current equalizer weight coefficient, and is carried forward as a step factor, Is the gradient of the objective cost function.
According to the construction method of the low-frequency nonlinear channel equalizer provided by the invention, the gradient is specifically as follows:
Where sgn denotes a sign function, η is a tilt parameter, exp denotes an exponential function, e (k) denotes an instantaneous error function, and x (k) denotes a signal after the transmitted baseband signal passes through a nonlinear channel.
In a second aspect, the present invention further provides a device for constructing a low-frequency nonlinear channel equalizer, including:
The target error function acquisition module is used for carrying out nonlinear transformation on the instantaneous error function of the low-frequency nonlinear channel equalizer by utilizing the neural network activation function to acquire a target error function; the instantaneous error function obeys standard Alpha stable distribution;
The self-adaptive updating formula determining module is used for constructing a target cost function by utilizing a mixed norm algorithm based on the target error function so as to determine a self-adaptive updating formula of the equalizer weight coefficient;
and the target equalizer construction module is used for constructing a target equalizer of the low-frequency nonlinear channel based on the self-adaptive updating formula.
The construction device of the low-frequency nonlinear channel equalizer provided by the invention further comprises: a space diversity equalizer construction module;
The space diversity equalizer construction module is used for constructing a space diversity equalizer model of the low-frequency nonlinear channel based on the constructed target equalizer of the independent single low-frequency nonlinear channel.
In a third aspect, the present invention provides an equalizer constructed using the method of constructing a low frequency nonlinear channel equalizer as described in any one of the preceding claims.
The invention provides a construction method and a construction device of a low-frequency nonlinear channel equalizer, wherein nonlinear transformation property of a neural network activation function is applied to the low-frequency nonlinear channel equalizer, a mixed norm algorithm (referred to as a Sigmoid-RMN algorithm for short) based on the neural network activation function, namely the Sigmoid function is provided, the Sigmoid-RMN algorithm is applied to the low-frequency nonlinear channel equalizer, a target equalizer is constructed, a low-frequency signal can be effectively acquired, nonlinear channel multipath fading distortion under Alpha stable distribution noise in a low-frequency channel is overcome, poor equalization results are avoided, stable and good equalization performance is obtained, and stability of a low-frequency communication system is improved.
Furthermore, the invention utilizes the nonlinear transformation property of the neural network function Sigmoid to transform the instantaneous error function in the channel equalizer, and the instantaneous error function obtained after transformation can be better suitable for inhibiting the Alpha stable distribution noise with different pulse intensities in a low-frequency communication system, in particular to fractional low-order Alpha stable distribution noise.
Furthermore, the method utilizes the obtained objective cost function and the self-adaptive iteration formula to calculate the quantity is small, the iteration speed is high, and the stability is strong.
Furthermore, the invention is based on the existing self-adaptive equalizer and utilizes the target equalizer of the low-frequency nonlinear channel constructed by the self-adaptive iterative formula, thereby having simple realization, strong operability and strong matching performance with the existing low-frequency channel self-adaptive equalizer.
Furthermore, the invention constructs the space diversity equalizer by utilizing the space diversity receiving technology of the target equalizer, and compared with each independent equalizer, the space diversity equalizer based on the algorithm can improve the convergence speed of the channel equalizer to a certain extent, and obtain better equalization performance.
Drawings
In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of a method for constructing a low-frequency nonlinear channel equalizer according to the present invention;
fig. 2 is a functional block diagram of an adaptive equalizer for a low frequency nonlinear channel provided by the present invention;
fig. 3 is a schematic block diagram of a decision feedback equalizer for a low frequency nonlinear channel provided by the present invention;
fig. 4 is a functional block diagram of a Sigmoid-RMN space diversity equalizer provided by the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that in the description of embodiments of the present invention, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The terms "first," "second," and the like in this specification are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged, as appropriate, such that embodiments of the present application may be implemented in sequences other than those illustrated or described herein, and that the objects identified by "first," "second," etc. are generally of a type, and are not limited to the number of objects, such as the first object may be one or more.
The method and apparatus for constructing a low frequency nonlinear channel equalizer according to the embodiments of the present invention are described below with reference to fig. 1 to 4.
Fig. 1 is a flow chart of a method for constructing a low frequency nonlinear channel equalizer according to the present invention, as shown in fig. 1, including but not limited to the following steps:
Step 101: and carrying out nonlinear transformation on the instantaneous error function of the low-frequency nonlinear channel equalizer by using a neural network activation function to obtain an objective error function. The transient error function obeys a standard Alpha stable distribution.
Specifically, the step needs to analyze and calculate to obtain the fractional low-order statistical moment of Alpha stable distribution noise in the low-frequency communication system. Alpha stable noise (Alpha-stable noise) distribution is an ideal mathematical model of non-Gaussian impulse noise and can be well fit to the non-Gaussian noise.
Fig. 2 is a schematic block diagram of an adaptive equalizer for a low-frequency nonlinear channel according to the present invention, as shown in fig. 2, where s (k) is a baseband symbol sequence that is independently and uniformly distributed, and the present invention mainly uses minimum shift keying MSK signals.
X (k) represents a signal after the transmitted baseband signal passes through the nonlinear channel (Non-LINEAR CHANNEL), that is, the input signal vector x (k) of the equalizer, which may be expressed as x (k) = [ x 0(k),x1(k),…,xN-1(k)]T), the input signal vector x (k) is simultaneously input into the unknown system (Unknow system) and the adaptive filter (ADAPTIVE FILTER), w (k) = [ w 0(k),w1(k),…,wN-1(k)]T ] is a weight coefficient vector of the equalizer, and then the output signal value of the equalizer is y (k) = x (k) Twopt, where w opt is an optimal weight coefficient vector. The desired signal is d (k) =y (k) +n (k), the system noise n (k) is sαs distributed noise, k represents the kth iteration, and the output instantaneous error is e (k) =d (k) -w (k) T x (k).
FIG. 3 is a schematic block diagram of a decision feedback equalizer for a low frequency nonlinear channel according to the present invention, as shown in FIG. 3, if the system noise n (k) is S.alpha.S. distributed noise, the second moment of the instantaneous error e (k) is when alpha <2If α <1, the first moment e|e (k) | of the instantaneous error E (k) is not limited. The transient error function e (k) obeys the standard Alpha stable distribution, and the expression is shown in the formula (1):
e(k)＝d(k)-w(k)Tx(k)＝y(k)+n(k)-w(k)Tx(k)
＝[w(k)-wopt(k)]Tx(k)+n(k)＝v(k)Tx(k)+n(k) (1)
The transient error function e (t) is subjected to nonlinear transformation by using a neural network activation function, a Sigmoid function (namely an S-shaped activation function with nonlinear transformation property), and the expression is shown in a formula (2):
Wherein, Representing the target error function, e (k) representing the instantaneous error function, sgm representing the neural network activation function, η being the tilt parameter for adjusting the attenuation scale for different e (k).
And (3) bringing the formula (1) into the formula (2), wherein the target error function after Sigmoid transformation has limited first-order statistical moment and second-order statistical moment.
Step 102: and constructing an objective cost function by utilizing a mixed norm algorithm based on the objective error function so as to determine an adaptive updating formula of the equalizer weight coefficient.
The mixed norm (RMN) algorithm is an adaptive filtering algorithm based on the stable distribution of fraction low-order Alpha, the algorithm essentially combines the error second-order norm and the first-order norm convexly, and the p-norm algorithm of the subsequent research can be regarded as an extension and expansion of the algorithm, which has a remarkable effect of suppressing non-gaussian.
According to the self-adaptive iterative updating formula, the weight coefficient of the equalizer is determined according to the first moment quantity and the second moment quantity of the Alpha stable distribution noise obtained through calculation.
Step 103: and constructing a target equalizer of the low-frequency nonlinear channel based on the self-adaptive updating formula.
Specifically, the equalizer weight coefficient may be determined based on an adaptive update formula, and the output signal y (k) =x (k) T w (k) of the equalizer may be taken into the adaptive equalizer model (i.e., the target equalizer) of the nonlinear channel based on the mixed norm algorithm (Sigmoid-RMN algorithm) of the neural network Sigmoid function.
Based on the foregoing embodiment, the method for constructing a low-frequency nonlinear channel equalizer according to the present invention further includes, after establishing a target equalizer for a low-frequency nonlinear channel based on the adaptive update formula:
Step 104: and constructing a space diversity equalizer model of the low-frequency nonlinear channel based on the constructed target equalizer of the independent single low-frequency nonlinear channel.
Specifically, a model of an adaptive equalizer based on a neural network Sigmoid function low-frequency nonlinear channel is adopted, and a spatial diversity equalizer of the model algorithm is obtained by utilizing a spatial diversity receiving technology to analyze and research a model of a diversity equalization system.
Fig. 4 is a schematic block diagram of a Sigmoid-RMN space diversity equalizer provided by the present invention, such as the Sigmoid-RMN space diversity equalizer shown in fig. 4. And (3) performing equal gain combination on output signals received by the target equalizer of each nonlinear channel by adopting a space diversity receiving technology to obtain a model total output signal y (k) =y 1(k)+y2(k)+...+yk (k) of the nonlinear channel adaptive equalizer based on the neural network algorithm.
Based on the foregoing embodiments, as an optional embodiment, the method for constructing a low-frequency nonlinear channel equalizer according to the present invention constructs a target cost function by using a mixed norm algorithm based on the target error function, so as to determine an adaptive update formula of an equalizer weight coefficient, where the adaptive update formula includes: substituting the target error function into a cost function of a mixed norm algorithm to construct the target cost function; and taking the minimum value of the target cost function as a target, and determining an adaptive updating formula of the equalizer weight coefficient by using a steepest descent method.
The objective cost function specifically comprises the following steps:
wherein lambda (k) E [0,1] is a mixing parameter, E is a statistical mathematical expectation, As a function of the target error.
Where the desired signal d (k) is symmetrically distributed, d 0 is a positive number, and f D (x) is a probability density function of the desired response d (k). In particular case, when d (k) is a gaussian distribution function of zero mean, unit variance, formula (4) becomes:
where erfc () is the residual error function, To expect the response, d (k) is the variance of the gaussian element.
To minimize the objective cost function J (k), its gradient to the conjugate of the equalizer tap coefficients is calculated and the instantaneous gradient is substituted for the true gradient, i.e., the gradient of the objective cost function is:
Where sgn denotes a sign function, η is a slope parameter, exp denotes an exponential function, e (k) denotes an instantaneous error function, and x (k) denotes a signal after the transmitted baseband signal passes through a nonlinear channel (Non-LINEAR CHANNEL).
The adaptive updating formula of the equalizer weight coefficient can be obtained by using the steepest descent method:
Substituting the formula (6) into the formula (7) to obtain an adaptive iteration update formula:
Based on the content of the above embodiments, as an alternative embodiment, a procedure for constructing a target equalizer for a low frequency nonlinear channel based on the adaptive update formula will be described below.
Let the initialization w (0) =0, where 0 is the all-zero column vector, and iterate by applying equation (8):
Wherein: μ is a step factor for controlling the convergence speed. And
Σ n 2 and σ x 2 represent the variance of the input noise and the input signal variance, respectively, and N is the length of the adaptive equalizer.
Substituting the formula (9) into the equalizer output signal y (k) =x (k) T w (k) to obtain the nonlinear channel adaptive equalizer based on the mixed norm algorithm (Sigmoid-RMN algorithm) of the neural network Sigmoid function.
The invention applies the nonlinear transformation property of the neural network activation function to the nonlinear equalizer of the low-frequency channel, and provides a mixed norm algorithm (Sigmoid-RMN algorithm for short) based on the neural network activation function, namely the Sigmoid function.
In one aspect, the present invention further provides a device for constructing a low-frequency nonlinear channel equalizer, including: the system comprises a target error function acquisition module, an adaptive update formula determination module and a target equalizer construction module.
The target error function acquisition module is used for carrying out nonlinear transformation on the instantaneous error function of the low-frequency nonlinear channel equalizer by utilizing the neural network activation function to acquire a target error function; the instantaneous error function obeys standard Alpha stable distribution;
The self-adaptive updating formula determining module is used for constructing a target cost function by utilizing a mixed norm algorithm based on the target error function so as to determine a self-adaptive updating formula of the equalizer weight coefficient;
and the target equalizer construction module is used for constructing a target equalizer of the low-frequency nonlinear channel based on the self-adaptive updating formula.
Optionally, the construction device of the low-frequency nonlinear channel equalizer provided by the invention further comprises: a space diversity equalizer construction module; and constructing a space diversity equalizer model of the low-frequency nonlinear channel based on the constructed target equalizer of the independent single low-frequency nonlinear channel.
I.e. based on the equalizer model of the constructed single independent Sigmoid-RMN algorithm, a spatial diversity equalizer model is constructed.
It should be noted that, when the apparatus for constructing a low-frequency nonlinear channel equalizer according to the embodiment of the present invention specifically operates, the method for constructing a low-frequency nonlinear channel equalizer described in any one of the embodiments above may be executed, which is not described in detail in this embodiment.
On the one hand, the invention also provides an equalizer which is constructed by applying the construction method of the low-frequency nonlinear channel equalizer as described in any one of the above.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A method for constructing a low frequency nonlinear channel equalizer, comprising:
Nonlinear transformation is carried out on the instantaneous error function of the low-frequency nonlinear channel equalizer by utilizing a neural network activation function, and an objective error function is obtained; the instantaneous error function obeys standard Alpha stable distribution; the target error function specifically comprises the following steps:
Wherein, Representing a target error function, e (k) representing an instantaneous error function, sgm representing a neural network activation function, η being a tilt parameter;
constructing an objective cost function by utilizing a mixed norm algorithm based on the objective error function so as to determine an adaptive updating formula of the equalizer weight coefficient;
constructing a target equalizer of the low-frequency nonlinear channel based on the self-adaptive updating formula;
Constructing an objective cost function by utilizing a mixed norm algorithm based on the objective error function to determine an adaptive update formula of the equalizer weight coefficient, wherein the adaptive update formula comprises the following steps:
substituting the target error function into a cost function of a mixed norm algorithm to construct the target cost function;
Taking the minimum value of the target cost function as a target, and determining an adaptive updating formula of the equalizer weight coefficient by using a steepest descent method;
the objective cost function specifically comprises the following steps:
wherein lambda (k) E [0,1] is a mixing parameter, E is a statistical mathematical expectation, Is a target error function;
The self-adaptive updating formula specifically comprises the following steps:
Wherein w (k+1) is the updated equalizer weight, w (k) is the current equalizer weight, μ is the step size factor, Gradient as objective cost function;
The gradient is specifically as follows:
Where sgn denotes a sign function, η is a tilt parameter, exp denotes an exponential function, e (k) denotes an instantaneous error function, and x (k) denotes a signal after the transmitted baseband signal passes through a nonlinear channel.
2. The method for constructing a low frequency nonlinear channel equalizer as claimed in claim 1, further comprising, after establishing a target equalizer for a low frequency nonlinear channel based on the adaptive update formula:
and constructing a space diversity equalizer model of the low-frequency nonlinear channel based on the constructed target equalizer of the independent single low-frequency nonlinear channel.
3. The method of constructing a low frequency nonlinear channel equalizer in accordance with claim 1, wherein said instantaneous error function is an S-type activation function.
4. A device for constructing a low frequency nonlinear channel equalizer, comprising:
The target error function acquisition module is used for carrying out nonlinear transformation on the instantaneous error function of the low-frequency nonlinear channel equalizer by utilizing the neural network activation function to acquire a target error function; the instantaneous error function obeys standard Alpha stable distribution; the target error function specifically comprises the following steps:
Wherein, Representing a target error function, e (k) representing an instantaneous error function, sgm representing a neural network activation function, η being a tilt parameter;
The self-adaptive updating formula determining module is used for constructing a target cost function by utilizing a mixed norm algorithm based on the target error function so as to determine a self-adaptive updating formula of the equalizer weight coefficient;
The target equalizer construction module is used for constructing a target equalizer of the low-frequency nonlinear channel based on the self-adaptive updating formula;
Constructing an objective cost function by utilizing a mixed norm algorithm based on the objective error function to determine an adaptive update formula of the equalizer weight coefficient, wherein the adaptive update formula comprises the following steps:
substituting the target error function into a cost function of a mixed norm algorithm to construct the target cost function;
Taking the minimum value of the target cost function as a target, and determining an adaptive updating formula of the equalizer weight coefficient by using a steepest descent method;
the objective cost function specifically comprises the following steps:
wherein lambda (k) E [0,1] is a mixing parameter, E is a statistical mathematical expectation, Is a target error function;
The self-adaptive updating formula specifically comprises the following steps:
Wherein w (k+1) is the updated equalizer weight, w (k) is the current equalizer weight, μ is the step size factor, Gradient as objective cost function;
The gradient is specifically as follows:
Where sgn denotes a sign function, η is a tilt parameter, exp denotes an exponential function, e (k) denotes an instantaneous error function, and x (k) denotes a signal after the transmitted baseband signal passes through a nonlinear channel.
5. The apparatus for constructing a low frequency nonlinear channel equalizer in accordance with claim 4, further comprising: a space diversity equalizer construction module;
The space diversity equalizer construction module is used for constructing a space diversity equalizer model of the low-frequency nonlinear channel based on the constructed target equalizer of the independent single low-frequency nonlinear channel.
6. An equalizer constructed by applying the construction method of the low frequency nonlinear channel equalizer as claimed in any one of claims 1 to 3.
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