阅读说明：本技术 一种mpsk信号的cma盲均衡变步长优化方法 (CMA blind equalization variable step length optimization method of MPSK signal ) 是由 江虹 辜馨月 伍春 蒋亮亮 杨浩 于 2018-06-07 设计创作，主要内容包括：一种MPSK信号的CMA盲均衡变步长优化方法,属于数字通信信号处理领域,其特征在于通过盲均衡收敛误差来控制盲均衡算法收敛步长,优化后的CMA盲均衡算法步长由反比例函数与指数函数协同控制,利用分式性质,使均衡算法步长在算法前期减小迅速,加快了收敛速度,算法后期算法步长变化缓慢,减小了剩余误差。与传统固定步长的CMA算法相比,优化后的CMA盲均衡算法具有收敛速度快,剩余误差小等优良特性。(a CMA blind equalization variable-step optimization method of MPSK signals belongs to the field of digital communication signal processing and is characterized in that blind equalization algorithm convergence step is controlled through blind equalization convergence errors, the optimized CMA blind equalization algorithm step is cooperatively controlled by an inverse proportion function and an exponential function, and the step of the equalization algorithm is rapidly reduced in the early stage of the algorithm by utilizing the fractional property, so that the convergence speed is increased, the algorithm step is slowly changed in the later stage of the algorithm, and the residual errors are reduced. Compared with the traditional CMA algorithm with fixed step length, the optimized CMA blind equalization algorithm has the excellent characteristics of high convergence rate, small residual error and the like.)

1. a CMA blind equalization variable step length optimization method of MPSK signals is characterized in that:

(1) taking the algorithm residual error as an independent variable of an inverse proportion function, and cooperatively controlling the change of the algorithm step length by using monotonicity of an inverse proportion function interval and the monotonicity of an exponential function;

(2) When the fraction value is a positive number, the characteristics of reduction of the numerator, increase of the denominator and reduction of the fraction value are utilized, so that the step length is rapidly changed in the early stage of the algorithm, the convergence speed of the algorithm is improved, the later stage tends to be stable, and the convergence precision of the algorithm is improved;

(3) the step size is calculated by:

In the formula:nIn the form of a node of time,μ(n) In order to be the step size of the algorithm,αIs a step factor, is used to control the step range,βis a real number slightly less than 1 and,γIs greater than 1 and less than 1αreal number of (2) for limitingIs made smaller thanβ ⁿ the value of (a) is,Cis a real number slightly larger than 0 and,e(n) Is the residual error.

2. The CMA blind equalization variable step size optimization method of the MPSK signal according to claim 1, wherein:

residual error in early stage of algorithme(n) Greater, over timengradually increasing, exponential functionβ ⁿ Gradually decrease in value of (A) to (B)e(n) The arguments, which are inverse proportional functions, as the algorithm converges gradually,e(n) Gradually decreases so that 1-e(n) Gradually increase in value of (A) to prevent occurrence ofe(n) 0 1-e(n) In the meaningless case, a real number slightly larger than 0 is added to the denominator of the inverse proportional functionC(ii) a The exponential function and the inverse proportion function act together, so that the step length is converged quickly in the early stage of the algorithm, and the convergence speed of the CMA blind equalization algorithm is improved.

3. a CMA blind equalization variable step size optimization method for MPSK signals according to claim 1 and claim 2, characterized in that:

In the expression of the step length calculated by the optimization method, an exponential function is taken as a fraction numerator part, an inverse proportion function is taken as a denominator part, and the time is increasednGradually increasing, the fraction value rapidly decreasing, but whene(n) After the algorithm is stable, the numerical value changes of the inverse proportion function and the exponential function are smooth, so that the step length of the optimized CMA blind equalization algorithm at the later stage does not have too large jump, the residual error after equalization is reduced, and the convergence precision of the algorithm is improved.

Technical Field

the method is mainly used for optimizing the situation that the effect of the CMA blind equalization algorithm with fixed step length at the demodulation end of the digital communication system is not ideal. The method relates to the monotonic characteristic of an exponential function, the monotonic characteristic of an inverse proportional function and the fractal property. The method aims to improve the contradiction between convergence precision and convergence speed in the traditional CMA algorithm so as to obtain better convergence performance, and belongs to the field of communication signal processing.

Background

In wireless communication systems, errors may result from intersymbol interference due to channel fading, time variation, non-linearity, multipath propagation, and the like. To reduce the effect of intersymbol interference on the performance of communication demodulation, the channel must be properly corrected, i.e., channel equalized. The training-based adaptive equalization technique occupies extra communication bandwidth, and needs to retransmit the training sequence when the channel changes, which requires the system to add a feedback channel, resulting in increased system complexity. The blind equalization technology overcomes the defect of self-adaptive equalization based on training, and can equalize the channel under the condition of not sending a training sequence. Among the blind equalization algorithms, the CMA algorithm is widely applied to various communication systems due to small calculation amount, low complexity and good convergence. However, the traditional CMA blind equalization algorithm adopts a fixed step length, which results in a large residual error after equalization and a slow convergence rate. To solve the contradiction between the convergence speed and the convergence accuracy, an effective method is to replace the fixed step size with the variable step size.

Aiming at the variable step length, scholars at home and abroad propose a plurality of methods, which mainly comprise:

(1) The Yaoyusan is characterized in that the Yaoyusan is in a text of 'variable step size blind equalization algorithm based on hyperbolic tangent function' published in 'Chinese New communication', the residual error is taken as the hyperbolic tangent function independent variable, the value of a module value of the function is zero when the independent variable is zero, the module value is gradually increased along with the increase of the independent variable, and finally the step size is defined by the property of approaching to 1;

(2) Zhang yu in "improved CMA blind equalization algorithm based on error peaks", published by "university of vinpock industry," university of china, "the text defines the step size as a constant multiplied by an exponential function with the base of a natural constant e. Wherein, the constant is used for limiting the value range of the step length, and the residual error is used as the index part of the exponential function to control the real-time change of the step length;

(3) in the text Improved algorithm for blind channel equalization by PS Tang et al, International Computer Conference on Wavelet Active Media Technology & Information Processing, the residual error is used as an argument of a non-linear function for controlling the step size to change in real time.

although the above documents use different methods, the step length is controlled by the residual error to change in real time, so that the algorithm is ensured to use a larger step length when the residual error is larger, and a smaller step length when the residual error is smaller, thereby improving the convergence performance of the CMA algorithm. However, the method in the document (1) has a slow convergence rate, and the methods in the documents (2) and (3) have a large step change near the zero point, so that the step size at the later stage of the algorithm is large, and a small steady-state error cannot be obtained.

Aiming at the problems existing in the optimization method, the invention provides a CMA blind equalization variable-step optimization method of MPSK signals, aiming at improving the convergence precision of the algorithm with lower time overhead.

Disclosure of Invention

in order to solve the contradiction between the convergence speed and the convergence precision of the traditional CMA algorithm, the invention provides a CMA blind equalization variable step length optimization method of MPSK signals. On the basis of the traditional CMA algorithm, the method defines the expression of the step length of the algorithm by utilizing the monotonicity of the interval of an inverse proportional function, the monotonicity of an exponential function and the related properties of a fraction, replaces the fixed step length with the variable step length, and improves the convergence performance of the algorithm.

The invention specifically realizes the following steps:

(1) Constant initialization: the order of the equalizer, the tap weight vector and the constants involved in calculating the step length by the optimization method are initialized. Input signal through equalizerx(n) Calculating constant modulus constant of CMA algorithmR ₂ Is calculated as:

(2) Calculating an error functione(n): using input signals at the present momentx(n) Output after passing through equalizery(n) And constant modulus constantR ₂ Calculating the error of the current timee(n) The calculation formula is:

(3) Calculating step sizeμ(n): by error of the current timee(n) Calculating the step length of the current timeμ(n) The calculation formula is:

In the formula (I), the compound is shown in the specification,nin the form of a time series of,CIs a real number slightly greater than 0.αThe step size factor is generally 0.01, and the function of the step size factor is to limit the step size range.βA real number slightly less than 1.γis a real number greater than 1 and has an upper value of 1-αFor limiting the divisionis made smaller than the exponential functionβ ⁿ The value of (c).e(n) For algorithm residual error, over time seriesnGradually decreasing in value. From the monotonicity of the inverse proportional function interval, 1/(. sup.)e(n)|+C) And gradually increases. The inverse proportional function and the exponential functionβ ⁿ the real-time variation of the step size is controlled together. As can be seen from the monotonicity of the exponential function,β ⁿ Is as followsnThe increase of (a) is gradually reduced, in combination with the fractal nature,The value of (c) is decreased. The inverse proportion function and the exponential function act together, so that the algorithm uses a larger step length in the early stage, the convergence speed is improved, and a smaller step length is used in the later stage, and the convergence precision is improved;

(4) Update equalizer weight vector: calculating the weight vector W (n +1) of the equalizer at the next time by using the weight vector W (n) of the equalizer at the current time, the output y (n) of the equalizer, the step size mu (n) and the residual error e (n), and the calculation formula is as follows:

In the formula (I), the compound is shown in the specification,X ^* (n) For equalizer input signalsx(n) Complex conjugation of (a);

(5) Obtaining an equalized signal: through the above steps, the channel has been properly corrected, and the signal with multipath fading passes through the improved blind equalizer, i.e. the equalized signal is output.

compared with the prior art, the invention has the innovation points that:

Combining the inverse proportional function and the exponential function to jointly control the step length. The step length can quickly track the residual error in the early stage of the algorithm by utilizing the fractional property, the convergence speed is accelerated, the change near the zero point is small in the later stage, and the residual error is reduced, so that the convergence performance of the CMA algorithm can be improved.

the invention at least comprises the following beneficial effects:

(1) the algorithm uses larger step length in the early stage, so that the time overhead is reduced, and the convergence speed is improved;

(2) and a small step length is used in the later stage of the algorithm, so that the residual error is reduced, and the convergence precision is improved.

drawings

fig. 1 is a schematic block diagram of blind equalization.

FIG. 2 is a flow chart of the algorithm of the present invention.

Detailed description of the invention

In the drawings, fig. 1 is a schematic block diagram of blind equalization according to the present invention, and a specific implementation process thereof is shown by a flowchart in fig. 2. In order to further explain the contents, effects and innovative points of the invention, the technical details thereof are further described in detail below.

Firstly, the input signal of the blind equalizer is a quasi-baseband signal after the receiver is roughly demodulated, and the input signal is divided into two paths of signals of an I path and a Q path. Order of the blind equalizer isNthe tap weight vector isW(n) The input signal isx(n) The output signal isy(n) Wherein the input signal isx(n) Including multipath and noise. Using memoryless non-linear estimatorsgoutput signal of (a) pair blind equalizery(n) Performing nonlinear transformation to obtain estimated value of transmitting end signalz(n). Error signale(n) Weighting vector of blind equalizer by optimized CMA algorithmW(n) And (6) adjusting. The blind equalizer needs to be initialized and the CMA calculation needs to be calculated at the beginning of the algorithmConstant modulus constant in methodR ₂ . According to the priori knowledge, when the blind equalizer orderNWhen the weight vector is not less than 11, a better equalization effect can be obtained, and the equalizer weight vector can be initialized to beW(n) = 0,0,0,0,1,0,0,0,0,0 }. Constant modulus constant in algorithmR ₂ can be derived from an input signalx(n) Calculated by the following formula:

Secondly, input signals are inputx(n) By blind equalizers, byx(n) AndW(n) Can calculate the output value of the equalizer at the current momenty(n) The calculation formula is as follows:

Output signal of blind equalizery(n) Pass threshold decision devicegcan calculate the estimated value of the transmitting end signalz(n). And error functione(n) For transmit end signal estimationz(n) And equalizer output signaly(n) A difference of (i.e.e(n)= z(n)- y(n)=g(y(n))-y(n). Wherein the content of the first and second substances,g(. is) a memoryless nonlinear function in the CMA algorithm, through whichy(n) Performing a non-linear transformation, expressed asg(·) = g(y(n)) = y(n)/|y(n)|·{|y(n)|+R ₂ |y(n)|-|y(n)|³}. Thereby, the error of the current timee(n) The calculation formula of (2) is as follows:

Under the condition that the error of the current moment is known, the variable step length is calculated according to the error characteristic, and the calculation formula is as follows:

in the formula (I), the compound is shown in the specification,αThe step size factor is generally 0.01, and is used for limiting the value range of the step size.nIn the form of a time series of,βIs a real number slightly less than 1 and,γA real number greater than 1, with an upper value of 1-αFor limiting the divisionIs made smaller than the exponential functionβ ⁿ The value of (c).e(n) In order to be an error in the algorithm,β ⁿ Ande(n) The step size is controlled to change in real time together. To prevent frome(n) A 1 is present when it is 0e(n) In the meaningless case, a real number slightly larger than 0 is addedC. At the beginning of the algorithm, time seriesnSmall value and residual errore(n) Is greater, when the step size is largerμ(n) Is mainly composed ofβ ⁿ And (5) controlling. Due to the fact thatβ ⁿ With followingnThe error is increased and monotonically decreased, so that the algorithm uses a large step length when the residual error is large, and the convergence speed of the algorithm is improved. Node over timenThe size of the mixture is increased, and the mixture is,β ⁿ ande(n) Gradually decreases. According to the property of monotonic decrease between the intervals of the inverse proportional function, 1/(. visually)e(n)|+C) The size of the mixture is gradually increased, and the mixture is gradually increased,The numerator of (2) is decreased, the denominator is increased, the fraction value is decreased, and the step length is rapidly decreased at this time. At the later stage of the algorithm,β ⁿ Ande(n) The reduction trend of (2) tends to be gentle, and the reduction trend of the fractional value also tends to be gentle. At the same time, the user can select the desired position,β ⁿ The reduction trend of the fractional value and the reduction trend of the fractional value are mutually restricted, so that the step length is not greatly changed near the zero point, the residual error is reduced, and the convergence rate of the algorithm is improved.

After the step length of the current moment is calculated, a new weight of the equalizer can be calculated according to a weight iteration formula of the equalizer of the CMA algorithm, wherein the calculation formula is as follows:

In the formula (I), the compound is shown in the specification,X ^* (n) For equalizer input signal at present timex(n) The complex conjugate of (a) and (b),μ(n) Is the step size at the present time instant,e(n) As an error at the present time, the error is,W(n) Is the equalizer weight vector at the current time.

Finally, the input signal is inputx(n) The equalized signal can be obtained by the improved blind equalizer.