CN111064683A - Improved constant modulus equalization algorithm - Google Patents

Improved constant modulus equalization algorithm Download PDF

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CN111064683A
CN111064683A CN201911333821.6A CN201911333821A CN111064683A CN 111064683 A CN111064683 A CN 111064683A CN 201911333821 A CN201911333821 A CN 201911333821A CN 111064683 A CN111064683 A CN 111064683A
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李兵兵
李晨明
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Xidian University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L2025/03592—Adaptation methods
    • H04L2025/03598—Algorithms
    • H04L2025/03611—Iterative algorithms
    • H04L2025/03617—Time recursive algorithms
    • H04L2025/0363—Feature restoration, e.g. constant modulus
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L2025/03592—Adaptation methods
    • H04L2025/03598—Algorithms
    • H04L2025/03675—Blind algorithms using gradient methods

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Abstract

The invention discloses an improved constant modulus equalization algorithm, which comprises S1, establishing an equalization algorithm digital communication model, and simulating the nonlinear characteristic of a channel; s2, in the signal equalization part, the received signal is input into the fixed band-stacking step size mu, the adjustable filter is added into the baseband receiving system by adopting the CMA algorithm to realize the self-adaptive equalization and reduce the ISI, and then the fixed band-stacking step size mu is dynamically controlled by a non-linear function through an MSE function on the basis of the CMA algorithm. In the invention, the fixed band-overlapping step size mu in the CMA equalization algorithm is dynamically controlled by a MSE function through a nonlinear function, so that the convergence speed in the new algorithm is improved by 1500 data points compared with the traditional CMA algorithm, and a momentum factor and a variable step size are added on the basis of the traditional CMA equalization algorithm, so that the switching control error function is 2 × e (k) | 3, the step size can be continuously reduced when the error is small, the steady-state error is reduced, and the intersymbol interference is reduced.

Description

Improved constant modulus equalization algorithm
Technical Field
The invention relates to the technical field of communication, in particular to an improved constant modulus equalization algorithm.
Background
As an indispensable key component in a communication system, the influence of the channel's own characteristics on the performance of the communication system is very direct. Ideally, it is desirable that the electromagnetic wave can propagate in a straight line in space, but in practice, the transmission environment of wireless communication is a very complex environment, and the wireless channel is an open medium, so when the electromagnetic wave carrying useful information propagates therein, the electromagnetic wave is not only interfered by external noise sources and other electromagnetic waves, but also blocked by various obstacles in space and influenced by the geographic environment, for example, the atmosphere causes scattering of the electromagnetic wave, the ionosphere causes reflection and refraction of the electromagnetic wave, and large objects such as mountains, buildings and the like cause reflection of the electromagnetic wave. The reflection, scattering and refraction of these electromagnetic waves will cause the radio signal to finally propagate from the transmitting end to the receiving end along multiple paths, so called multipath propagation, and the lengths of the paths in multipath propagation will cause the final arrival time of each transmitted signal component to be different, which is equivalent to the transmitted signal being spread in the time domain, and if this delay spread exceeds the width of a Symbol in the received signal, it means that the waveform of the previous Symbol is spread into the next Symbol period, forming Inter-Symbol Interference (ISI), for the wireless digital communication system, if there is spread superposition between adjacent Symbol waveforms right at the sampling point, it will cause serious distortion of the sampled signal, thereby causing the decision error of the receiving end, the receiving error rate of the system is increased, so the Inter-Symbol Interference will not only limit the transmission rate of data, but also affects the transmission quality of the signal and threatens the transmission reliability of the communication system greatly. In order to improve the communication quality, the conventional solution is to utilize a channel equalization technique at the receiving end to mitigate the effect of the inter-symbol interference on the system performance, and in a broad sense, the channel equalization refers to any signal processing technique that can be used to combat the inter-symbol interference, and generally, the so-called equalization refers to adding an adjustable filter to the baseband receiving system to make its characteristic opposite to the characteristic of the wireless channel, so as to achieve the purpose of compensating the non-ideal characteristic of the wireless channel and reducing the inter-symbol interference, where the filter that performs the compensation function is a channel equalizer. Since a wireless fading channel has time-varying and random properties in a wireless communication system, it is necessary that a channel equalizer must have the capability of adjusting its parameters at any time to adapt to the time-varying statistical characteristics of the channel, i.e., the capability of adapting. Such a channel equalizer is then also called an adaptive equalizer. Generally, we divide the operation mode of the adaptive equalizer into two types, i.e., a training mode and a tracking mode, and first, in the training mode of the equalizer, a transmitting end needs to transmit a set of known preset training sequences, a receiving end sets tap coefficients of the equalizer according to the received training sequences, a typical training sequence may be a pseudo-random binary signal or a signal sequence with a fixed waveform, the training sequence is followed by the transmission of a user data sequence, at which time, the trained equalizer will continuously track the unknown time-varying channel using an adaptive algorithm during the process of receiving user data, and then adaptively adjusting the parameters of the equalizer according to the change of the channel, thereby finally and correctly recovering the sending sequence, although the influence of the multipath channel is compensated by using a data-assisted adaptive equalization technology, and the receiving reliability of the system is improved.
However, this equalization technique based on training sequence also inevitably faces many drawbacks, on one hand, transmitting training sequence causes waste of resources, firstly, training sequence does not contain any useful information, so that transmission of training sequence will cause waste of valuable spectrum resources, and secondly, while transmitting user data, it also needs to periodically transmit training sequence regularly, so that transmission efficiency of system is reduced, especially for some severely faded or fast time-varying wireless channels, the transmitting end must frequently train equalizer to ensure its characteristic to track changes of upper channel in real time, otherwise, it will not be able to correctly recover transmitted signal, in view of the above mentioned problems, another new equalization technique different from the traditional data-aided channel equalization technique, called Blind equalization technique (Blind Eq μ equalization, BE), the channel equalizer using the blind equalization technique does not need to rely on the assistance of a training sequence, and uses its own prior information to realize channel equalization according to the received signal, compared with the adaptive data-assisted equalization technique, the blind equalization technique can significantly improve the transmission efficiency of the system, improve the spectrum utilization, and is the only equalization scheme that can BE used by the receiving end in the non-cooperative communication system.
Disclosure of Invention
The invention aims to: the improved constant modulus equalization algorithm is provided for solving the problems of low convergence speed and large steady-state error of the Constant Modulus Algorithm (CMA) equalization algorithm.
In order to achieve the purpose, the invention adopts the following technical scheme:
an improved constant modulus equalization algorithm comprising:
s1, establishing an equalization algorithm digital communication model and simulating the nonlinear characteristic of a channel;
s2, in the signal equalization part, the received signal is input into the fixed band-stacking step size mu, the adjustable filter is added into the baseband receiving system by adopting the CMA algorithm to realize the self-adaptive equalization and reduce the ISI, then the fixed band-stacking step size mu is dynamically controlled by a non-linear function through an MSE function on the basis of the CMA algorithm, the convergence speed is accelerated, and the steady-state error is further reduced.
As a further description of the above technical solution:
the implementation balance of the CMA algorithm in the S2 specifically comprises the following steps:
received signal of the system:
Figure BDA0002330402380000031
where s (k) is the transmitted signal, h (k) is the impulse response of the wireless multipath channel, n (k) is the channel noise, and the constant LnIs the channel order;
the received signal is taken as the input signal of the blind equalizer, and the output signal of the blind equalizer can be expressed as
Figure BDA0002330402380000041
Wherein w ═ w (0), w (1), …, w (L)e-1)]TIs of order LeThe weight vector of the blind equalizer;
in general, the weight vectors of blind equalizers are iterated using a stochastic gradient descent method
wk+1＝wk-μ˙▽J
＝wk-μ˙e*(k)x(k)
Wherein mu is an iteration step size, and e (k) is an error term of a blind equalization algorithm, and the error term is obtained by carrying out nonlinear transformation on an output signal y (k) of the blind equalizer through a zero memory nonlinear estimator because the blind equalization algorithm does not have a training sequence;
the CMA constructs a cost function using only amplitude information, without considering phase information of the received signal:
JCMA＝E{(|y(k)|p-Rp)2}
wherein the content of the first and second substances,
Rp＝E[|s(k)|2p]/E[|s(k)|p]
it can be seen that RpIs a normal number only related to the statistical characteristics of the system transmission signal, where p is a positive integer, and is usually selected to be 2 in consideration of the trade-off between implementation complexity and algorithm performance;
by adopting the steepest gradient descent method, the weight vector updating formula of the CMA can be obtained as follows:
w＝w-μ˙▽J
＝w-μ(|y(k)|-R)|y(k)|y(k)x(k)
therefore, the error term of the CMA blind equalization algorithm is:
e(k)＝(|y(k)|-R)|y(k)|y(k)。
as a further description of the above technical solution:
in said S2, the fixed band-overlapping step size mu is dynamically controlled by a non-linear function using an MSE function based on the CMA algorithm, the MSE meaning MSE (k) ═ E { E (k)*e(k)}；
e(k)＝|y(k)|2-R2
The nonlinear function is:
y(k)＝1/(1+exp(-a*((|e(k)|)-b)))；
wherein a and b are parameters.
As a further description of the above technical solution:
in the above function, y approaches 0 when e (k) is 0; the approaching speed is influenced by parameters a and b, so a threshold | e (n) | is set, when the error is less than the threshold, the switching control error function is 2| e (k) | ^3, when the error is very small, the iteration step length can be continuously reduced, the precision is improved, as the average error is replaced by the instantaneous error, the control function has fluctuation, the solution is that a window with the length of L is used for averaging e (n), namely L data are added to average, so the new tap coefficient iteration formula is provided:
when | e (n) | > η
W(n+1)＝W(n)-(1/(1+exp(-a(|e(n)|-c))))y(k)e(n)X*(n)+αD(W(n)-W(n-1))
When | e (n) | > η
W(k+1)＝W(k)-(2*|e(k)|3)y(k)e(k)X*(k)+αD(W(k)-W(k-1))
Wherein e (k) ═ y (k) does not warp2-R2,
Figure BDA0002330402380000051
To output a signal, Y*(n) is the conjugate of the vector of the filter input signal, W (n) is the tap vector of the filter, η is the threshold for error function switching, αD(W (n) -W (n-1)) is an additional momentum term, αDIs a coefficient of momentum.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. in the invention, through a newly proposed tap coefficient iteration formula, the fixed iterative band step length mu in the CMA equalization algorithm is dynamically controlled by a MSE function through a nonlinear function, so that the convergence rate in the new algorithm is improved by 1500 data points compared with the traditional CMA algorithm.
2. In the invention, momentum factors and variable step lengths are added on the basis of the traditional CMA (constant matrix adaptive equalizer) equalization algorithm, so that the switching control error function is 2 × e (k) | ^3, the step length can be continuously reduced when the error is very small, the steady-state error is reduced, and the intersymbol crosstalk is reduced.
Drawings
Fig. 1 is a block diagram of a digital communication system of an improved constant modulus equalization algorithm proposed by the present invention;
FIG. 2 is a block diagram of an equivalent baseband system of an improved constant modulus equalization algorithm proposed by the present invention;
FIG. 3 is a non-linear functional relationship diagram of an improved constant modulus equalization algorithm proposed by the present invention;
FIG. 4 is a comparison graph of a conventional CMA algorithm and an improved algorithm of an improved constant modulus equalization algorithm proposed by the present invention;
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
Referring to fig. 1, an improved constant modulus equalization algorithm includes:
s1, establishing an equalization algorithm digital communication model and simulating the nonlinear characteristic of a channel;
s2, in the signal equalization part, the received signal is input into a fixed band-stacking step length mu, an adjustable filter is added into the baseband receiving system by adopting a CMA algorithm to realize self-adaptive equalization and reduce ISI, then the fixed band-stacking step length mu is dynamically controlled by a MSE function through a nonlinear function on the basis of the CMA algorithm, the convergence speed is accelerated, and the steady-state error is further reduced;
the CMA algorithm implementation balance in S2 specifically includes:
received signal of the system:
x(k)＝h(k)s(k)+n(k)
＝h(l)s(k-l)+n(k)
wherein, s (k) is a sending signal, h (k) is an impulse response of a wireless multipath channel, n (k) is channel noise, and a constant is a channel order;
taking the received signal as the input signal of the blind equalizer, the output signal of the blind equalizer can be expressed as y (k) ═ w (l) x (k-l)
＝wx(k)
Wherein w ═ w (0), w (1), …, w (L-1) is the weight vector of the blind equalizer of order L;
in general, the weight vectors of blind equalizers are iterated using a stochastic gradient descent method
w＝w-μ˙▽J
＝w-μ˙e(k)x(k)
Wherein mu is an iteration step size, and e (k) is an error term of a blind equalization algorithm, and the error term is obtained by carrying out nonlinear transformation on an output signal y (k) of the blind equalizer through a zero memory nonlinear estimator because the blind equalization algorithm does not have a training sequence;
the CMA constructs a cost function using only amplitude information, without considering phase information of the received signal:
J＝E{(|y(k)|-R)}
wherein R isp＝E[|s(k)|2p]/E[|s(k)|p]
It can be seen that R is a normal number related only to the statistical properties of the system transmission signal, where p is a positive integer, and p is usually chosen to be 2 in consideration of the trade-off between implementation complexity and algorithm performance;
by adopting the steepest gradient descent method, the weight vector updating formula of the CMA can be obtained as follows:
w＝w-μ˙▽J
＝w-μ(|y(k)|-R)|y(k)|y(k)x(k)
therefore, the error term of the CMA blind equalization algorithm is:
e(k)＝(|y(k)|-R)|y(k)|y(k)；
w＝w-μ˙▽J
＝w-μ(|y(k)|-R)|y(k)|y(k)x(k)
therefore, the error term of the CMA blind equalization algorithm is:
e(k)＝(|y(k)|-R)|y(k)|y(k)。
example 2
The difference from example 1 is:
in S2, the fixed band-overlapping step size mu is dynamically controlled by a MSE function through a nonlinear function on the basis of the CMA algorithm, wherein MSE means thatMSE(k)＝E{e(k)*e(k)}；
e(k)＝|y(k)|2-R2
The nonlinear function is:
y(k)＝1/(1+exp(-a*((|e(k)|)-b)))；
wherein a and b are parameters;
in the above function, y approaches 0 when e (k) is 0; the approaching speed is influenced by parameters a and b, so a threshold | e (n) | is set, when the error is less than the threshold, the switching control error function is 2| e (k) | ^3, when the error is very small, the iteration step length can be continuously reduced, the precision is improved, as the average error is replaced by the instantaneous error, the control function has fluctuation, the solution is that a window with the length of L is used for averaging e (n), namely L data are added to average, so the new tap coefficient iteration formula is provided:
when | e (n) | > η
W(n+1)＝W(n)-(1/(1+exp(-a(|e(n)|-c))))y(k)e(n)X*(n)+αD(W(n)-W(n-1))
When | e (n) | > η
W(k+1)＝W(k)-(2*|e(k)|3)y(k)e(k)X*(k)+αD(W(k)-W(k-1))
Wherein e (k) ═ y (k) does not warp2-R2，
Figure BDA0002330402380000091
To output a signal, Y*(n) is the conjugate of the vector of the filter input signal, W (n) is the tap vector of the filter, η is the threshold for error function switching, αD(W (n) -W (n-1)) is an additional momentum term, αDAs the coefficient of momentum, the simulation parameters in fig. 4: the transmission signal is QPSK signal with length N of 10000, variance of 1, SNR of 30DB, and channel W [ -0.005-0.004j 0.009-0.003 j-0.0024-0.104 j 0.854+0.52 j-0.218 +0.2731j 0.049-0.074 j-0.016 +0.02j]The filter tap length is 11, the center tap is initialized, the fixed step size in the CMA algorithm is 0.003, the improved algorithm is η -0.09, αDIs 0.4.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (4)

1. An improved constant modulus equalization algorithm, comprising:
s1, establishing an equalization algorithm digital communication model and simulating the nonlinear characteristic of a channel;
s2, in the signal equalization part, the received signal is input into the fixed band-stacking step size mu, the adjustable filter is added into the baseband receiving system by adopting the CMA algorithm to realize the self-adaptive equalization and reduce the ISI, then the fixed band-stacking step size mu is dynamically controlled by a non-linear function through an MSE function on the basis of the CMA algorithm, the convergence speed is accelerated, and the steady-state error is further reduced.
2. The improved constant modulus equalization algorithm according to claim 1, wherein the CMA algorithm in S2 realizes equalization specifically as follows:
received signal of the system:
Figure FDA0002330402370000011
where s (k) is the transmitted signal, h (k) is the impulse response of the wireless multipath channel, n (k) is the channel noise, and the constant LnIs the channel order;
the received signal is taken as the input signal of the blind equalizer, and the output signal of the blind equalizer can be expressed as
Figure FDA0002330402370000012
Wherein w ═ w (0), w (1), …, w (L)e-1)]TIs of order LeThe weight vector of the blind equalizer;
in general, the weight vectors of blind equalizers are iterated using a stochastic gradient descent method
wk+1＝wk-μ·▽J
＝wk-μ·e*(k)x(k)
Wherein mu is an iteration step size, and e (k) is an error term of a blind equalization algorithm, and the error term is obtained by carrying out nonlinear transformation on an output signal y (k) of the blind equalizer through a zero memory nonlinear estimator because the blind equalization algorithm does not have a training sequence;
the CMA constructs a cost function using only amplitude information, without considering phase information of the received signal:
JCMA＝E{(|y(k)|p-Rp)2}
wherein the content of the first and second substances,
Rp＝E[|s(k)|2p]/E[|s(k)|p]
it can be seen that RpIs a normal number only related to the statistical characteristics of the system transmission signal, where p is a positive integer, and is usually selected to be 2 in consideration of the trade-off between implementation complexity and algorithm performance;
by adopting the steepest gradient descent method, the weight vector updating formula of the CMA can be obtained as follows:
w＝w-μ·▽J
＝w-μ(|y(k)|-R)|y(k)|y(k)x(k)
therefore, the error term of the CMA blind equalization algorithm is:
e(k)＝(|y(k)|-R)|y(k)|y(k)。
3. an improved constant modulus equalization algorithm as claimed in claim 2 wherein said fixed stacking step size μ is dynamically controlled by a non-linear function using an MSE function based on CMA algorithm in S2, MSE meaning MSE (k) ═ E (k)*e(k)}；
e(k)＝|y(k)|2-R2
The nonlinear function is:
y(k)＝1/(1+exp(-a*((|e(k)|)-b)))；
wherein a and b are parameters.
4. An improved constant modulus equalization algorithm as claimed in claim 3 wherein said function is characterized by the fact that y approaches 0 when e (k) is 0; the approaching speed is influenced by parameters a and b, so a threshold | e (n) | is set, and when the error is less than the threshold, the switching control error function is 2*The iteration step length can be continuously reduced when the error is very small, the precision is improved, the control function has fluctuation because the average error is replaced by the instantaneous error, the solution is that a window with the length of L is used, the average value is taken for e (n), namely L data are taken and added to be averaged, and the new tap coefficient iteration formula is provided:
when | e (n) | > η
W(n+1)＝W(n)-(1/(1+exp(-a(|e(n)|-c))))y(k)e(n)X*(n)+αD(W(n)-W(n-1))
When | e (n) | > η
W(k+1)＝W(k)-(2*|e(k)|3)y(k)e(k)X*(k)+αD(W(k)-W(k-1))
Wherein e (k) ═ y (k) does not warp2-R2,
Figure FDA0002330402370000031
To output a signal, Y*(n) is the conjugate of the vector of the filter input signal, W (n) is the tap vector of the filter, η is the threshold for error function switching, αD(W (n) -W (n-1)) is an additional momentum term, αDIs a coefficient of momentum.
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CN111800356B (en) * 2020-06-16 2023-01-31 北京银河信通科技有限公司 Parallel variable-step-size CMA (China Mobile alliance) equalization algorithm, device, electronic equipment and storage medium
CN113904898A (en) * 2021-10-09 2022-01-07 中国人民解放军军事科学院国防科技创新研究院 Equalization and carrier synchronization method based on equivalent time sampling
CN114095320A (en) * 2021-11-11 2022-02-25 西安电子科技大学 Channel equalization method based on momentum fractional order multimode blind equalization algorithm
CN114189409A (en) * 2021-12-08 2022-03-15 重庆两江卫星移动通信有限公司 Short burst signal equalization method based on BOOTSTRAP

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