CN114826834A - Channel blind equalization method and blind equalizer for high-order quadrature amplitude modulation signal - Google Patents
Channel blind equalization method and blind equalizer for high-order quadrature amplitude modulation signal Download PDFInfo
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Abstract
The invention belongs to the technical field of channel blind equalization in wireless communication and discloses a channel blind equalization method and a blind equalizer for high-order quadrature amplitude modulation signals i Construction of about R i The prior probability of calculating the modulus of the signal output by the equalizer and R i According to the prior probability, extracting the constant modulus value R in the full-scale sample i Is taken as a selected sample set and is marked as omega i (ii) a Then according to the classical constant modulus algorithm and omega i Construction of cost function J under high-order quadrature amplitude modulation channel MCMA (w); and finally, constructing an iterative formula of a blind equalization method under a high-order quadrature amplitude modulation channel according to a Newton method, and optimizingBlind equalizer and minimization of cost function J MCMA (w) is carried out. The invention can effectively inhibit human errors and misadjustment brought by a classical constant modulus equalization method under a high-order quadrature amplitude modulation channel, and realizes a fast-convergence Newton method optimized channel blind equalizer.
Description
Technical Field
The invention belongs to the technical field of channel blind equalization in wireless communication, and particularly relates to a channel blind equalization method and a blind equalizer for a high-order quadrature amplitude modulation signal.
Background
At present, a Blind Equalizer (BE) can realize channel equalization without the help of a training sequence, and can provide a practical method for reducing signal distortion, and meanwhile, the blind equalizer does not use the training sequence, and bandwidth cannot BE wasted in transmission. More importantly, in non-cooperative or point-to-multipoint communication scenarios, blind equalization algorithms are the only feasible solution to achieve system equalization (c.yu and l.xie, "On rational equalization in sensor networks," IEEE trans. Signal process, vol.63, No.3, pp.662-672,2015.) (m.komatsu, n.tanabe, and t.furukawa, "Direct blue equalization coupled to non-rational equalization using Rayleigh," in proc.2019 IEEE 15th internal color Signal process. ital application (CSPA), Penang, Malaysia, 35-38,2019.).
Since Sato published an article on this direction in 1975 (y.sato, "a method of Self-adapting for multiple amplitude modulation systems," IEEE trans. command, vol. com-23, No.6, pp.679-682,1975.), a number of blind equalization algorithms were proposed (n.godard, "Self-adapting and carrier tracking in two-dimensional communication data systems," IEEE trans. command, vol. com-28, No.11, pp.1867-1875,1980 ") (s.j.non-wlan and g.e.hinton," a soft-adapted LMS-algorithm for adaptation, "IEEE transport-adapted LMS-275, 24-862). By far, the most popular blind equalization methods among two-dimensional (2D) modulation methods, such as Quadrature Amplitude Modulation (QAM) and Carrierless Amplitude and Phase (CAP) modulation, are Constant Modulus Algorithms (CMA) (n.godard, "Self-equalization and carrier tracking in two-dimensional data communication systems," IEEE trans.communication ", vol.com-28, No.11, pp.1867-1875,1980.) and their modified algorithms (j.r.Treichler and b.age," A.new approach to multi-path correlation of control signals, "IEEE.Acouou., Speech, Signal processing, SP.ASSP-31, BM.459-472,1983.) (Y.X.ion and J.acquisition and" CMx. cross. registration and "CMd. cross. registration and cross. 12), and their modified algorithms (J.r.Treichler and B.aging. analysis, S.31, BM.459.3.g. Signal processing, I.12. cross. registration, and data. cross. registration, and data processing). In one aspect, the cost function of CMA attempts to minimize the difference between the squared magnitude of the output and the goral dispersion constant with fewer local minima and reliable Convergence (o.deber and e.mass, "conversion analysis soft term module algorithm," IEEE trans.inf.thoery, vol.49, No.6, pp.1447-1464,2003.) (r.cusani and a.laurenti, "conversion analysis of the CMA blind equalizer," IEEE ns.commun., vol.43, No.2/3/4, pp.1304-1307,1995.). CMA, on the other hand, changes its tap values over time and has LMS-like complexity, which makes it easy to implement (y.sato, "a method of self-recovery equalization for multiple amplification systems," IEEE trans. com., vol. com-23, No.6, pp.679-682,1975.). Furthermore, according to the above features, CMAs may explicitly or implicitly provide good initial states for two-stage blind equalization algorithms (c.t.ma, z.ding, and s.f.yau, "a wo-stage algorithm for MIMO blank cancellation of non-reactive coherent signals," IEEE trans.signal processes, vol.48, No.4, pp.1187-1192,2000 "), or dual-mode blind equalization algorithms (l.he, m.amin, c.reed and r.malkems," a hybrid adaptive blank equalization algorithms for QAM signals wireless communications, "IEEE ns.process, vol.52, No.7, 2058-2069,2004), enabling them to achieve better performance.
The most complex and time consuming task during blind start-up of the receiver is the convergence of the equalizer, which is done by a blind tap update algorithm. Although CMA is known for its LMS-like complexity, its convergence speed is slow. As with classical LMS theory, the choice of step size becomes a trade-off between convergence speed and MSE (s.lambotharan, j.chambers, and c.r.johnson, "transformations of saddles and slow convergence in CMA adaptation," Signal process, vol.59, No.3, pp.335-340,1997.). Worse, to reduceAs is well known for homeostatic imbalance and to avoid initial instability, the step size of the CMA is usually set at 10 -5 Orders of magnitude or less, much smaller than the LMS is typically set to 10 -2 Several orders of magnitude steps (M.Xiang, Y.Xia, and D.P.Mandic, "Performance analysis of specific length dimension mean adaptive filters," IEEE Trans. Signal Process, vol.68, pp.65-80,2020.). Therefore, the convergence speed of CMA is much slower than other LMS type algorithms. In contrast, newton's method has a faster convergence rate. However, newton's method requires the calculation of the Hessian matrix of the cost function to be implemented. It should be noted that complex signals are processed, and therefore the Hessian matrix of constant modulus loss functions is always singular (k.k.delgado and y.isuk ap alli, "Use of the Newton method for applying equilibrium based on the constant module algorithm," IEEE trans.signal process, vol.56, No.8, pp.3983-3995,2008.), which means that fast converging Newton's method can hardly be used in practice without modification. In view of all of this, it is essential to improve the equation accuracy and convergence speed of the CMA.
Through the above analysis, the problems and defects of the prior art are as follows: and human errors and misadjustment caused by a classical constant modulus method under a high-order quadrature amplitude modulation channel are inhibited.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a channel blind equalization method and a blind equalizer for a high-order quadrature amplitude modulation signal.
The invention is realized by the method for blind equalization of the channel facing the high-order quadrature amplitude modulation signal, and the method for blind equalization of the channel facing the high-order quadrature amplitude modulation signal firstly selects a specific modulus R based on the constellation diagram characteristic of the high-order quadrature amplitude modulation signal i Construction of about R i The prior probability of calculating the modulus of the signal output by the equalizer and R i According to the prior probability, extracting the constant modulus value R in the full-scale sample i Is taken as a selected sample set and is marked as omega i (ii) a Then according to the classical constant modulus algorithm and omega i Construction ofCost function J under high-order quadrature amplitude modulation channel MCMA (w); and finally, constructing an iterative formula of a blind equalization method under a high-order quadrature amplitude modulation channel according to a Newton method, optimizing a blind equalizer and minimizing a cost function J MCMA (w)。
Further, the channel blind equalization method for the high-order quadrature amplitude modulation signal specifically includes the following steps:
first, sample selection, which means that the mode values of the higher-order qam signal are set to Ω ═ R i I is 1,2, …, I represents the number of specific modulus values, the total number of observation signal samples is recorded as N, and the specific modulus value R of the high-order quadrature amplitude modulation signal is selected first i Then calculated based on R i Prior probability of (d) and equalization error
(N-1, 2, …, N), calculating the sample length N according to the prior probability i And sorting the equalization errors in ascending order, taking the top N i One sample is taken as a selected sample omega i (ii) a The invention makes the transmission signals have the same amplitude by selecting the sample formed by the constant modulus signal, thereby fundamentally avoiding human error and misadjustment;
secondly, constructing a cost function, recording an equalizer as w, and selecting an observation signal sample omega according to a classical constant modulus algorithm i Construction of cost function J under high-order quadrature amplitude modulation channel MCMA (w); the construction of the cost function is beneficial to the performance improvement brought by the optimization scheme of the invention through data comparison in the following process;
thirdly, an iterative formula is constructed, the iterative formula of a blind equalization method under a high-order quadrature amplitude modulation channel is constructed according to a Newton method, a blind equalizer is optimized, and a cost function is minimized; the iterative formula constructed according to the Newton method is helpful for fast convergence to the optimal solution and finding the optimal equalizer.
Further, the selection of the constant modulus sample Ω i A method. The set of modulus values of the high-order quadrature amplitude modulation signal is expressed as Ω ═ R i (I-1, 2, …, I) taking the total of observed signal samplesN, first selecting a specific modulus R of the high-order QAM signal i Then calculated based on R i Prior probability of (d) and equalization error
(N-1, 2, …, N), calculating the sample length N according to the prior probability i And sorting the equalization errors in ascending order, taking the top N i One sample is taken as a selected sample omega i ；
The set of modulus values of the high-order quadrature amplitude modulation signal is expressed as Ω ═ R i Due to the steady state output of the equalizer ═ 1,2, …, I
Is an estimate of the transmitted signal, the output being divided into different subsets according to modulus
The respective channel observation signal vectors x (n) are divided into different subsets:
wherein
Is an ideal equalizer [. C] H Represents the conjugate transpose of the matrix,. represents the absolute value;
keeping in mind that the total number of samples used to search for an optimized equalizer is N, the constant modulus R of the higher order QAM signal is first selected following the following principle i : first, the circle with the selected modulus value should pass through as many points as possible; second, the distance between the selected circle and its neighboring circle should be as large as possible; secondly according to the selected R i Calculate highThe prior probability of the order quadrature amplitude modulation signal is combined with the prior probability and the total amount of the samples to obtain the length of the selected target sample, which is recorded as N i ：
Wherein, P i Is a modulus value R i Q is the order of the high order quadrature amplitude modulation signal,
to have a modulus value R i The prior probability of the transmitted signal of (a),
represents a rounding down operation;
if the blind equalizer converges to the optimal solution, i.e.
Then a mathematical relationship exists
The following inequality holds:
for all x i (n)∈Ω i And
this is true. Obviously, according to the set Ω i Definition of (2), in the ideal case
In addition to this, the present invention is,
and is
Much greater than 0;
based on the above conclusion, the equalizer outputs error
To pair
Sorting in ascending order, then N i Item(s)
Corresponding x (n) form a sample set omega i Is considered to be selected having a modulus value R i A sample set of (a); however, before channel equalization is achieved, the optimal equalizer
Is unknown, and to solve this problem, the kth iteration value w is used k Instead of the former
Then the equalizer output error
Front N of i And taking the sample corresponding to the item as a required sample set.
Further, the method for constructing the cost function is provided. The equalizer is w, and the signal sample omega is selected according to the classical constant modulus algorithm i Construction of cost function J under high-order quadrature amplitude modulation channel MCMA (w)；
s.t.x(n)∈Ω i
Where min represents the minimum, s.t. represents the satisfaction of the above condition, | w H x(n)|-R i For equalizer output error, E [ (| w) H x(n)|-R i ) 2 ]Representing timeAverage, J MCMA (w) represents a cost function, Ω i ＝{x i (1),x i (2),…,x i (N i ) Is corresponding to a constant modulus value R i Is measured.
Further, the iterative formula constructing method constructs an iterative formula of a blind equalization method under a high-order quadrature amplitude modulation channel according to a Newton method, optimizes a blind equalizer and minimizes a cost function;
cost function of construction (| w) H x(n)|-R i ) 2 With a typical quadratic structure, constructing a Newton method of an optimized cost function, and calculating the cost of the optimal cost function MCMA (w) replace the statistical mean with the time mean, replace x (n) e Ω i Is replaced by x i (n) of (a). The cost function is then rewritten as:
wherein N is i Is of constant modulus value R i Length of time-observed signal set:
now, according to J MCMA (w) differentiating w to obtain the following gradient expression:
let the sample matrix be X i ＝[x i (1),x i (2),…,x i (N i )]Normalized output vector of
Gradient of
Is simplified as follows:
further, gradient
Further decomposed into A (w) w-b (w) structure; the matrix A (w) is a positive definite matrix, which is considered to be
Vector b (w) is considered as; according to Newton's method has w k+1 ＝A -1 (w k )b(w k ) (ii) a An iterative formula of the channel blind equalization method under the high-order quadrature amplitude modulation signal based on the Newton method is expressed as follows:
wherein [ ·] T Representing a matrix transposition [ ·] * Denotes complex conjugation [. C] -1 The inverse of the representation matrix is used,
it is a further object of the invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of:
constructing a constant modulus signal set based on the prior probability of the high-order quadrature amplitude modulation signal;
constructing a cost function under a high-order quadrature amplitude modulation channel according to a classical constant modulus algorithm and a selected observation sample;
and constructing a constant modulus method iterative formula of the high-order quadrature amplitude modulation channel according to a Newton method, and optimizing the blind channel equalizer.
It is another object of the present invention to provide a computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
constructing a constant modulus signal set based on the prior probability of the high-order quadrature amplitude modulation signal;
constructing a cost function under a high-order quadrature amplitude modulation channel according to a classical constant modulus algorithm and a selected observation sample;
and constructing a constant modulus method iterative formula of the high-order quadrature amplitude modulation channel according to a Newton method, and optimizing the blind channel equalizer.
Another object of the present invention is to provide a blind equalizer for implementing the method for blind equalization of a channel oriented to a higher-order quadrature amplitude modulated signal, the blind equalizer comprising:
the sample set construction module is used for constructing a constant modulus signal set based on the prior probability of the high-order quadrature amplitude modulation signal;
the cost function generation module is used for constructing a cost function under a high-order quadrature amplitude modulation channel according to a classical constant modulus algorithm and a selected observation sample;
and the blind equalizer optimization module is used for constructing a high-order quadrature amplitude modulation channel constant modulus method iteration formula according to a Newton method and optimizing the channel blind equalizer.
Another object of the present invention is to provide a terminal, which carries the channel blind equalizer for high-order qam signals.
In combination with the technical solutions and the technical problems to be solved, please analyze the advantages and positive effects of the technical solutions to be protected in the present invention from the following aspects:
first, aiming at the technical problems existing in the prior art and the difficulty in solving the problems, the technical problems to be solved by the technical scheme of the present invention are closely combined with results, data and the like in the research and development process, and some creative technical effects are brought after the problems are solved. The specific description is as follows:
firstly, aiming at the problems of human errors and misadjustment caused when CMA is applied to high-order QAM signals, the invention converts the high-order QAM signals into constant modulus signals with specific modulus values by a sample selection technical scheme, so that the transmission signals have the same amplitude theoretically, and the human errors and the misadjustment are fundamentally avoided. The core steps of the technical scheme are that a specific module value is selected from a plurality of constant module values of a high-order QAM signal, the length of a sample is calculated according to the prior probability of the specific module value, the equalization error is calculated according to the specific module value, and the sample set with the number of the sample length is intercepted according to ascending sequence, the equalization error of the sample set is small, and the sample set is obtained under the specific module value, so that the blind equalization is performed on the constant module signal, and the purpose of improving the classical CMA equalization performance is achieved, and in the specific implementation, the changes of MSE, SER and SNR are respectively shown in fig. 4 and fig. 5. From these two figures, it can be seen that the proposed MCMA achieves better balanced performance than CMA and MMA.
Secondly, aiming at the problem of low convergence speed of the gradient descent method, the invention provides a modified Newton method of MCMA by constructing a corresponding Newton method to optimize a blind equalizer: due to the constructed cost function (| w) H x(n)|-R i ) 2 With a typical quadratic structure, a newton-type method with quadratic or asymptotic quadratic convergence speed can BE easily designed to quickly search for the optimal BE.
To facilitate construction of MCMA-related MNMs, the statistical mean is replaced by a time mean, x (n) e Ω i Rewritten as x i (n) of (a). Then the MCMA cost function can be rewritten as:
where N is the length of available samples that can BE used to search for the best BE. In addition, N is added i Is arranged as
Wherein P is i Is provided with a mode R i Q is the order of the QAM signal,
is of modulus R i A priori probability of the transmitted signal. Take a 16-QAM signal as an example, if
Then
According to J MCMA (w) differentiating w to obtain the following gradient expression:
let the sample matrix be X i ＝[x i (1),x i (2),…,x i (N i )]Normalized output vector of
Then the gradient is
Is simplified as follows:
it is apparent that the gradient
Can be further decomposed into A (w) w-b (w) structure. The matrix A (w) is a positive definite matrix, which can be considered as
The vector b (w) can be considered as R i X i y i . According to MNM having w k+1 ＝A -1 (w k )b(w k ). Therefore, the update formula for MNM-based MCMA is expressed as:
wherein
In general, the newton method often appears unstable due to its indeterminate or nearly singular Hessian matrix, and it brings high computational complexity when iteratively calculating the inverse of the Hessian matrix at each step. In contrast, MCMA-MNM employs positive definite matrices
The Hessian matrix is modified so that the MCMA-MNM is stable. More preferably, the matrix X is theoretically i Should follow different w k Remain unchanged because the signal constellation that different samples can recover is predetermined. Thus, it can be calculated in advance
As long as R is obtained i MCMA-MNM only needs to calculate y k,i And R is performed at each iteration step i R i X i y k,i This greatly reduces the computational load of the method. And, the sequence w in the iterative formula k In increments of
Converge to an optimal solution
Secondly, considering the technical scheme as a whole or from the perspective of products, the technical effect and advantages of the technical scheme to be protected by the invention are specifically described as follows:
the invention can effectively inhibit human errors and misadjustment brought by a classical constant modulus method under a high-order quadrature amplitude modulation channel, and realizes a quick-convergence Newton method optimized channel blind equalizer.
Third, as an inventive supplementary proof of the claims of the present invention, there are also presented several important aspects:
the invention solves the problems of artificial errors and misadjustment generated when the high-order QAM signals are equalized by the traditional classical blind equalization algorithm, particularly the problems are caused by the fact that the amplitude of the high-order QAM signals is equal to a plurality of different constants, and for constant modulus signals, the problems can be fundamentally avoided.
Drawings
Fig. 1 is a flowchart of a method for blind equalization of a channel for a high-order qam signal according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of subset division of a 16-QAM constellation according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a constellation output at the k-th iteration of a 16-QAM constellation according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of MSE and SNR of CMA, MMA, DSM, and MCMA for 16-QAM system according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of SER and SNR of CMA, MMA, DSM, and MCMA for 16-QAM system according to an embodiment of the present invention.
Fig. 6 is a diagram illustrating ISI and iteration time for CMA, MMA, DSM, and MCMA for a 16-QAM system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
First, an embodiment is explained. This section is an explanatory embodiment expanding on the claims so as to fully understand how the present invention is embodied by those skilled in the art.
As shown in fig. 1, a method for blind equalization of a channel for a high-order quadrature amplitude modulation signal according to an embodiment of the present invention includes:
s101: constructing a constant modulus signal set based on the prior probability of the high-order quadrature amplitude modulation signal;
s102: constructing a cost function under a high-order quadrature amplitude modulation channel according to a classical constant modulus algorithm and a selected observation sample;
s103: and constructing a constant modulus method iterative formula of the high-order quadrature amplitude modulation channel according to a Newton method, and optimizing the blind channel equalizer.
The channel blind equalization method for the high-order quadrature amplitude modulation signal, provided by the embodiment of the invention, comprises the following steps:
first, sample selection. The set of modulus values of the high-order quadrature amplitude modulation signal is expressed as Ω ═ R i 1,2, …, I, noting that the total number of observed signal samples is N, first selecting a specific modulus value R of the high order quadrature amplitude modulation signal i Then calculated based on R i Prior probability of (d) and equalization error
Calculating the sample length N according to the prior probability i Sorting the equalization errors in ascending order and taking the top N i One sample is taken as a selected sample omega i ；
And secondly, constructing a cost function. Recording the equalizer as w, and selecting an observation signal sample omega according to a classical constant modulus algorithm i Construction of cost function J under high-order quadrature amplitude modulation channel MCMA (w)；
And thirdly, constructing an iterative formula. And (4) constructing an iterative formula of a blind equalization method under a high-order quadrature amplitude modulation channel according to a Newton method, optimizing a blind equalizer and minimizing a cost function.
In the invention, the problem of artificial errors of the algorithm in a high-order QAM system is deduced according to the thought theory of a classical constant modulus algorithm, and a CMA tries to solve the following optimization problems:
wherein
And p is a positive integer, if the implementation is based on an adaptive algorithm with gradient descent, the equalizer taps are updated according to the following equation:
w k+1 ＝w k -μE[(|y(k)| p -R)|y(k)| p-2 y * (k)x(k)]
where μ is the step size that controls the convergence speed and steady state equalizer performance level. For simplicity, the expectation of the gradient is replaced by the value of the instantaneous gradient. Thus, the adaptive equation is rewritten as
w k+1 ＝w k -μ(|y(k)| p -R)|y(k)| p-2 y * (k)x(k)
The cost function j (w) is an expression of the higher order statistics of the implicitly embedded equalizer output y (n). Ideally, the minimization of j (w) keeps the statistics of y (n) consistent with the statistics of the input signal, and equalization is accomplished when the equalization sequence y (n) achieves the same distribution of channel inputs s (n). However, in practice, the statistics of y (n) are estimated using sample data, while the statistics of s (n) are provided by theoretical values, and this inconsistency results in a small error, defined as an artificial error, which can lead to a degradation of the equalization performance. In addition, the random gradient based adaptive method includes large detuning in a high order QAM signal environment. There are in fact the following propositions:
proposition 1: in a high order QAM system, if BE converges to an optimal solution
And completely compensates for channel distortion, that is,
then the instantaneous gradient calculated from the sample data
Not equal to 0 in a noise free environment. Moreover, the instantaneous gradient satisfies the inequality:
obviously, inequality
Is caused by human error. Since the gradient is not equal to 0, even if the optimal solution is reached
W of BE is also continually adjusted, creating additional errors (human error). Instantaneous gradient
Meaning that when BE converges to an optimal solution in its implementation, the CMA will continue to adjust BE, which is called misadjustment, which results in CMA fluctuations in steady state. To overcome these problems, the present invention proposes an MCMA method.
In the invention, the equalization performance of the CMA is improved by selecting a signal set with a constant modulus value and converting high-order signal input into constant modulus signal input.
Set omega in the present invention i The determination of (1): set omega i ＝{x i (1),x i (2),…,x i (N i ) Are not known a priori, and need to be derived from the sample matrix X ═ X (1), X (2), …, X (n)]To find it out. The invention provides a sample selection method based on the following conclusion.
Conclusion 1: if BE converges to the optimal solution, i.e.
Thus having a mathematical relationship
The following inequality:
for all x i (n)∈Ω i And
this is true.
It is clear that according to the set omega i Is ideally defined by
In addition to this, the present invention is,
and is
Much larger than 0. Thus, the inequality holds.
Outputting the error to the equalizer in ascending order according to the inequality
And (6) sorting. It can be safely assumed that for the first N i Error of
The corresponding samples form a set omega i Of the selected sample. However, before channel equalization is achieved, the optimal equalizer
Is unknown. To solve this problem, the k-th iteration value w is used k Instead of the former
Then N is first i Error of
The corresponding sample is considered the selected sample as needed.
Considering a 16-QAM signal, FIG. 3 shows the kth iteration
To output (d). If R is i Is arranged as
Then
According to the above principle, the errors are sorted in ascending order and then output before
The corresponding output (for a 16-QAM signal,
P i q is 16, so
) The error is considered to be the selected output
As shown in FIG. 3, the output of the blue marker (the area between the two green circles) is considered to correspond to
The selected output of (2). The corresponding samples and the sets of these samples are each denoted by x i,k (n)(n＝1,2,…,N i ) And Ω i,k The latter can be seen as a set omega i Alternative(s) to (3).
According to the above set omega i Determination method, modulus of choice R i Is an important parameter.High order QAM has widely varying modulus, and the parameter R is chosen following two rules i . First, as shown in FIG. 3, a circle with a selected modulus (radius) should pass through as many points as possible. Thus, the sample usage is high. Secondly, the distance between the selected circle and its adjacent circle should be as large as possible. The result may be to minimize the number of constellation points for which a wrong decision is made. Typically the distance between adjacent circles is approximately equal, so in practice sample usage is a major consideration.
In the invention, a cost function of MCMA is constructed: the human error and detuning of CMAs is caused by the fact that the amplitude of high order QAM signals is equal to several different constants, using statistical values instead of true values. These problems can be fundamentally avoided if the transmitted signals have the same amplitude, e.g., low order 4-QAM signals. It is inspired by this that the equalization performance of the CMA is improved by converting the high order signal input into a constant modulus signal input. It is generally considered that the equalizer depends on the channel but is independent of the input signal, and if the received data corresponding to a specific modulus can be identified from all the received data and other data can be discarded, the input signal can be regarded as a constant modulus signal, and the equalization performance can be improved by using only selected data. The invention designs a new correction constant modulus method to balance high-order QAM signals by combining the analysis with the classical CMA.
It is obvious that the high order QAM signals can be divided into different subsets according to their modulus, as shown in fig. 2, the 16-QAM constellation points can be divided into three subsets, respectively labeled red, blue and black, the constellation point sets { ± 1 ± 1j }, { ± 1 ± 3j, ± 3 ± 1j } and { ± 3 ± 3j } correspond to the constellation point sets { ± 1 ± 1j }, respectively
And
defined as the set of possible moduli of the signal Ω ═ R i J (I ═ 1,2, …, I). Because of the steady state output of the equalizer
Is an estimate of the transmitted signal, so these outputs can also be divided into different subsets according to their modulus, namely:
relay output
After classification, the regression vectors corresponding to the channel observations x (n) can also be divided into different subsets
Wherein
Is an ideal equalizer. Easily verify belonging to a collection
Satisfies a constant modulus characteristic in a strict sense. Thus, if only the set Ω is used i Of channel observations x (n) to corresponding outputs
To adjust the equalizer, the input signal can be considered a constant modulus signal and human error and misadjustment can be completely avoided.
Finally, according to the above analysis, the CMA cost function can be modified as:
s.t.x(n)∈Ω i
wherein the set Ω i ＝{x i (1),x i (2),…,x i (N i )}，N i Represents the set omega i The cardinality of (c).
Let x (n) be epsilon omega i Is denoted by x i (n) and
according to the statistical gradient algorithm, the proposed update formula corresponding to the MCMA is as follows:
w k+1 ＝w k -μ(|y i (k)|-R i )|y i (k)| -1 y i * (k)x i (k)
MCMA and CMA differ in that: (1) MCMA uses sample x only i (n)(n＝1,2,…,N i ) Wherein x is i (n) is belonging to the set Ω i Sample of (2), N i Is its size; (2) replacing the parameter R in CMA with R in MCMA i (ii) a (3) For CMA, the parameter p is typically set to 2, while MCMA selects the parameter p to be 1.
These differences bring about the following three advantages: first, steady state imbalance is avoided with MCMA. This is because BE converges to the optimal solution
(wherein
). Secondly, because
MCMA can eliminate the resulting human error. Third, MCMA has a typical quadratic structure, which helps to design a fast convergence algorithm to find the best BE.
In the invention, an iterative formula is constructed: an iterative formula of a blind equalization method under a high-order quadrature amplitude modulation channel is constructed according to a Newton method, a blind equalizer is optimized, and a cost function is minimized, and the modified Newton method of MCMA is given by the invention: due to the constructed cost function (| w) H x(n)|-R i ) 2 With a typical quadratic structure, a newton-type method with quadratic or asymptotic quadratic convergence speed can BE easily designed to quickly search for the optimal BE.
To facilitate construction of MCMA-related MNMs, the statistical mean is replaced by a time mean, x (n) e Ω i Rewritten as x i (n) of (a). Then the MCMA cost function can be rewritten as:
where N is the length of available samples that can BE used to search for the best BE. In addition, N is i Is arranged as
Wherein P is i Is provided with a die R i Q is the order of the QAM signal,
is of modulus R i A priori probability of the transmitted signal. Take a 16-QAM signal as an example, if
Then
According to J MCMA (w) differentiating w to obtain the following gradient expression:
let the sample matrix be X i ＝[x i (1),x i (2),…,x i (N i )]Normalized output vector of
Then the gradient is
Is simplified as follows:
it is apparent that the gradient
Can be further decomposed into A (w) w-b (w) structure. The matrix A (w) is a positive definite matrix, which can be considered as
The vector b (w) can be considered as R i X i y i . According to MNM having w k+1 ＝A -1 (w k )b(w k ). Therefore, the update formula for MNM-based MCMA is expressed as:
wherein
In general, the newton method often appears unstable due to its indeterminate or nearly singular Hessian matrix, and it brings high computational complexity when iteratively calculating the inverse of the Hessian matrix at each step. In contrast, MCMA-MNM employs a positive definite matrix
The Hessian matrix is modified so that the MCMA-MNM is stable. More preferably, the matrix X is theoretically i Should follow different w k Remain unchanged because the signal constellation that different samples can recover is predetermined. Thus, it can be calculated in advance
As long as R is obtained i MCMA-MNM only needs to calculate y k,i And R is performed at each iteration step i R i X i y k,i Operation, this is largeThe calculation amount of the method is greatly reduced. And, the sequence w in the iterative formula k In increments of steps
Converge to an optimal solution
From the above analysis, the achievable MCMA-MNM is:
wherein X i,k ＝[x i,k (1),x i,k (2),…,x i,k (N i )]，
Notably, the sample matrix X i,k And R i,k More or less may change with iteration. Therefore, R needs to be updated in each iteration i,k And R unchanged from theoretical analysis i In contrast, this results in a significant increase in the amount of calculation. However, X i Is predetermined and is independent of BE. This indicates that X i,k And X i,k+1 The variation between is small, especially when BE is close to the convergence value. Thus, the Hessian matrix (correlation matrix) R i,k+1 It can be quickly calculated by the following formula:
wherein
Because of the aggregation
And
medium element is little, and R is updated based on the above formula i,k Only a very small amount of calculations is required, thereby significantly reducing the amount of calculations for the proposed MCMA-MNM.
The invention provides a channel blind equalizer facing to a high-order quadrature amplitude modulation signal, which comprises:
the sample set construction module is used for constructing a constant modulus signal set based on the prior probability of the high-order quadrature amplitude modulation signal;
the cost function generation module is used for constructing a cost function under a high-order quadrature amplitude modulation channel according to a classical constant modulus algorithm and a selected observation sample;
and the blind equalizer optimization module is used for constructing a high-order quadrature amplitude modulation channel constant modulus method iteration formula according to a Newton method and optimizing the channel blind equalizer.
And II, application embodiment. In order to prove the creativity and the technical value of the technical scheme of the invention, the part is the application example of the technical scheme of the claims on specific products or related technologies.
Embodiment one, point-to-multipoint communication
In point-to-multipoint communication, it is difficult to provide a training sequence, for digital television system, if a certain television receiver is failed temporarily, it must be equalized again, so that it can interrupt communication with other television receivers, and the blind equalization technical scheme provided by the invention is aimed at overcoming intersymbol interference in channel transmission, and the blind equalizer does not need to know the exact characteristics of channel, and also does not need to know channel input sequence, and is different from general channel equalizer, at the same time, it also does not need a training sequence to obtain related channel characteristics, so that in digital television broadcasting, the blind equalization technique has extensive application prospect, and the scheme provided by the invention can raise the performance of blind equalizer, and has significant meaning in its embodiment.
Example two, non-cooperative communication
In non-cooperative communication, a transmission channel is generally a wireless channel, and is affected by various factors such as multipath and preferential loan, and a signal received by a receiving end has serious intersymbol interference (ISI), so that the error rate of communication is high, and moreover. The statistical characteristics and channel characteristics of the transmitting end signal are unknown, and the receiving end cannot or is difficult to acquire the training sequence, so that the problem of intersymbol interference needs to be solved by using a blind equalization technology. In addition, burst non-cooperative reception means that each frame of data segment received in communication has only tens to hundreds of elements, and since the amount of data is small, the triggering of non-cooperative reception requires a fast convergence rate of a blind equalizer. The blind equalization technical scheme provided by the invention optimizes the blind equalizer by applying a Newton method, so that the blind equalization performance is improved.
Third embodiment, blind demodulation system
The blind demodulation receiver can not obtain the signal parameters of the modulation mode, the symbol rate, the carrier frequency, the start-stop position and the like of the transmitted signal from the transmitter, does not have frame structure information and a training sequence, can extract related parameters, and can only estimate by utilizing the characteristics of the received signal. In addition, multipath and Doppler spread effects in short-wave communication cause serious intersymbol interference of received signals. In addition, in modern military communication, a burst communication mode is often adopted for anti-reconnaissance, and a signal received by an interception system has the characteristic of short duration, and sometimes, the signal has data of even one or two hundred symbols. Short-wave sensing reception is a third-party reception that may receive different burst waveforms transmitted by multiple transmission sources, with the carrier frequency of each burst waveform typically being different. Based on the blind equalization scheme, the blind equalization scheme provided by the invention is used for a blind demodulation system so as to eliminate intersymbol interference, compensate the influence of short wave channel response on signals and improve the blind demodulation performance.
And thirdly, evidence of relevant effects of the embodiment. The embodiment of the invention achieves some positive effects in the process of research and development or use, and has great advantages compared with the prior art, and the following contents are described by combining data, diagrams and the like in the test process.
To verify the effectiveness of the proposed method, the proposed MCMA was compared to the conventional CMA (p ═ 2), MMA, CNA and DMS by criteria of Symbol Error Rate (SER), MSE and ISI. MSE is defined as
MSE＝E[|Cy(k)-s(k-τ)| 2 ]
Wherein the content of the first and second substances,
and, ISI is defined as
Wherein
Is the combined impulse response of the channel and the equalizer, and
in an embodiment, QAM signals on a complex-valued frequency selective channel with gaussian noise are considered. Assumed order of
Has a channel impulse response of h ═ 0.250+ j0.201,0.153+ j0.171,0.100+ j0.097,0.073+ j0.062,0.041+ j0.063] T Corresponding to channel gains in dB [ -9.8758, -12.7860, -17.1200, -20.3749, -22.4795]. In addition, a six tap equalizer is used and a central single spike initialization is used. The 16-QAM case for the high order modulation scheme was analyzed. The set Ω is defined as
The examples simulate various performances of CMA, MMA, DSM, and MCMA in a 16-QAM system. The step sizes of CMA and MMA were set to 5X 10, respectively -5 And 8X 10 -4 For DMS, the step size associated with the CMLF is set to 5 × 10 -5 The step size associated with the CME is set to 5 × 10 -3 Parameter R of MCMA i Is arranged as
In the following simulations, except the simulation related to the MSE sample number, the sample number N of the other simulations is 1500.
Fig. 4 and 5 show the changes in MSE and SER and SNR, respectively. From these two figures, it can be seen that the proposed MCMA achieves better balanced performance than CMA and MMA. Furthermore, the MSE and SER of the proposed method are even lower than DMS, which is difficult to achieve. The preferred balance of performance of the proposed method is due to the following two reasons. 1) MCMA can effectively suppress human error and steady state disturbances. 2) Since the proposed algorithm uses a large number of samples simultaneously, excessive errors of the adaptive method due to the use of only one sample per iteration are avoided.
For a 16-QAM system, given SNR 28dB and N1500, the convergence performance of CMA, MMA, DSM, MCMA in terms of ISI is shown in fig. 6. As can be seen from the figure, the proposed MCMA method converges much faster than the other three methods. The reason why the proposed algorithm converges fast is as follows: 1) the method effectively inhibits human errors and steady state maladjustment, and can stably converge without fluctuation. 2) The comparison shows that the iterative approximation of the proposed method is equivalent to computing a large number of samples by an adaptive algorithm. 3) The proposed method uses a structured MNM, so its convergence speed is faster. On the other hand, the proposed method can also converge to a much lower steady-state ISI than CMA and MMA and have a similar steady-state ISI as DMS.
In summary, the improved constant modulus method equalizer for blind equalization of the above embodiments shows that the classical CMA has the problem of human error and maladjustment, and the MCMA effectively solves the problem caused by human error and maladjustment. The example results show that the MCMA proposed by the present invention has better equalization performance than other existing methods. Thereby meeting the use requirements and being worth being popularized and used.
It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The above description is only for the purpose of illustrating the embodiments of the present invention, and the scope of the present invention should not be limited thereto, and any modifications, equivalents and improvements made by those skilled in the art within the technical scope of the present invention as disclosed in the present invention should be covered by the scope of the present invention.
Claims (10)
1. A channel blind equalization method facing high-order quadrature amplitude modulation signals is characterized in that the channel blind equalization method facing the high-order quadrature amplitude modulation signals is firstly to select a specific modulus R based on the constellation diagram characteristics of the high-order quadrature amplitude modulation signals i Construction of about R i The prior probability of calculating the modulus of the signal output by the equalizer and R i According to the prior probability, extracting the constant modulus value R in the full-scale sample i Is taken as a selected sample set and is marked as omega i (ii) a Then according to the classical constant modulus algorithm and omega i Construction of cost function J under high-order quadrature amplitude modulation channel MCMA (w); and finally, constructing an iterative formula of a blind equalization method under a high-order quadrature amplitude modulation channel according to a Newton method, optimizing a blind equalizer and minimizing a cost function J MCMA (w)。
2. The method for blind equalization of a channel oriented to a higher order qam signal as claimed in claim 1, wherein the method for blind equalization of a channel oriented to a higher order qam signal comprises the following steps:
first, sample selection, which means that the mode values of the higher-order qam signal are set to Ω ═ R i I is 1,2, …, I represents the number of specific modulus values, the total number of observation signal samples is recorded as N, and the specific modulus value R of the high-order quadrature amplitude modulation signal is selected first i Then calculated based on R i Prior probability of (d) and equalization error
(N-1, 2, …, N), calculating the sample length N according to the prior probability i And sorting the equalization errors in ascending order, taking the top N i One sample is taken as a selected sample omega i ；
Secondly, constructing a cost function, recording an equalizer as w, and selecting an observation signal sample omega according to a classical constant modulus algorithm i Construction of cost function J under high-order quadrature amplitude modulation channel MCMA (w)；
And thirdly, constructing an iterative formula, constructing the iterative formula of the blind equalization method under the high-order orthogonal amplitude modulation channel according to a Newton method, optimizing the blind equalizer and minimizing a cost function.
3. The method for blind equalization of a channel for higher order qam signals according to claim 2, wherein the selecting constant modulus samples Ω i The method records the mode value of the high-order quadrature amplitude modulation signal as a set of omega ═ R i The total number of observation signal samples is recorded as N, and a specific modulus value R of the high-order quadrature amplitude modulation signal is selected firstly i Then calculated based on R i Prior probability of (d) and equalization error
(N-1, 2, …, N), calculating the sample length N according to the prior probability i And arranging the equalization errors in ascending orderSequence, taking the first N i One sample is taken as a selected sample omega i ；
The set of modulus values of the high-order quadrature amplitude modulation signal is expressed as Ω ═ R i Due to the steady state output of the equalizer ═ 1,2, …, I
Is an estimate of the transmitted signal, the output being divided into different subsets according to modulus
The respective channel observation signal vectors x (n) are divided into different subsets:
wherein
Is an ideal equalizer [. C] H Representing the conjugate transpose of the matrix, | · | represents the absolute value;
keeping in mind that the total number of samples used to search for an optimized equalizer is N, the constant modulus R of the higher order QAM signal is first selected following the following principle i : first, the circle with the selected modulus value should pass through as many points as possible; second, the distance between the selected circle and its neighboring circle should be as large as possible; secondly according to the selected R i Calculating the prior probability of the high-order quadrature amplitude modulation signal, combining the prior probability and the total amount of the samples to obtain the length of the selected target sample, and recording as N i ：
Wherein, P i Is a modulus value R i Q is the order of the high order quadrature amplitude modulation signal,
to have a modulus value R i The prior probability of the transmitted signal of (a),
represents a rounding down operation;
if the blind equalizer converges to the optimal solution, i.e.
Then a mathematical relationship exists
The following inequality holds:
for all x i (n)∈Ω i And
if true; obviously, according to the set Ω i Definition of (2), in the ideal case
In addition to this, the present invention is,
and is
Much greater than 0;
based on the above conclusion, the equalizer outputs error
To pair
Sorting in ascending order, then N i Item(s)
Corresponding x (n) form a sample set omega i Is considered to be selected having a modulus value R i A sample set of (a); however, before channel equalization is achieved, the optimal equalizer
Is unknown, and to solve this problem, the kth iteration value w is used k Instead of the former
Then the equalizer output error
Front N of i And taking the sample corresponding to the item as a required sample set.
4. The method for blind equalization of a channel for higher order qam signals according to claim 2, wherein the method for constructing a cost function is w, based on a classical constant modulus algorithm and the selected observed signal sample Ω i Construction of cost function J under high-order quadrature amplitude modulation channel MCMA (w)；
s.t.x(n)∈Ω i
Where min represents the minimum, s.t. represents the satisfaction of the above condition, | w H x(n)|-R i For equalizer output error，E[(|w H x(n)|-R i ) 2 ]Represents the time average, J MCMA (w) represents a cost function, Ω i ＝{x i (1),x i (2),…,x i (N i ) Is corresponding to a constant modulus value R i Is measured.
5. The method for blind equalization of channel oriented to higher order qam signals according to claim 2, wherein the method for constructing an iterative formula is to construct an iterative formula of the blind equalization method under the higher order qam channel according to newton's method, optimize the blind equalizer and minimize the cost function;
cost function of construction (| w) H x(n)|-R i ) 2 With a typical quadratic structure, constructing a Newton method of an optimized cost function, and calculating the cost of the optimal cost function MCMA (w) replace the statistical mean with the time mean, replace x (n) e Ω i Is replaced by x i (n), then rewriting the cost function as:
wherein N is i Is of constant modulus value R i Length of time-observed signal set:
now, according to J MCMA (w) differentiating w to obtain the following gradient expression:
let the sample matrix be X i ＝[x i (1),x i (2),…,x i (N i )]Normalized output vector of
Gradient of
Is simplified as follows:
6. the method of claim 5 wherein the gradient is applied to the channel blind equalization of higher order QAM signals
Further decomposed into A (w) w-b (w) structure; the matrix A (w) is a positive definite matrix, which is considered to be
Vector b (w) is considered as; according to Newton's method has w k+1 ＝A -1 (w k )b(w k ) (ii) a An iteration formula of a channel blind equalization method under a high-order quadrature amplitude modulation signal based on a Newton method is expressed as follows:
wherein [ ·] T Representing a matrix transposition [ ·] * Denotes complex conjugation [. C] -1 The inverse of the representation matrix is used,
7. a computer device, characterized in that the computer device comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of:
constructing a constant modulus signal set based on the prior probability of the high-order quadrature amplitude modulation signal;
constructing a cost function under a high-order quadrature amplitude modulation channel according to a classical constant modulus algorithm and a selected observation sample;
and constructing a constant modulus method iterative formula of the high-order quadrature amplitude modulation channel according to a Newton method, and optimizing the blind channel equalizer.
8. A computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
constructing a constant modulus signal set based on the prior probability of the high-order quadrature amplitude modulation signal;
constructing a cost function under a high-order quadrature amplitude modulation channel according to a classical constant modulus algorithm and a selected observation sample;
and constructing a constant modulus method iterative formula of the high-order quadrature amplitude modulation channel according to a Newton method, and optimizing the blind channel equalizer.
9. A blind equalizer for implementing the method for blind equalization of a channel for higher order QAM signals as claimed in any one of claims 1 to 6, wherein said blind equalizer comprises:
the sample set construction module is used for constructing a constant modulus signal set based on the prior probability of the high-order quadrature amplitude modulation signal;
the cost function generation module is used for constructing a cost function under a high-order quadrature amplitude modulation channel according to a classical constant modulus algorithm and a selected observation sample;
and the blind equalizer optimization module is used for constructing a high-order quadrature amplitude modulation channel constant modulus method iteration formula according to a Newton method and optimizing the channel blind equalizer.
10. A terminal characterized in that it carries a channel blind equalizer oriented towards higher order quadrature amplitude modulated signals according to claim 9.
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| CN103401824A (en) * | 2013-07-22 | 2013-11-20 | 西安电子科技大学 | Frequency selectivity MIMO (multiple input multiple output) system space-time blind equalizer method based on MNM (modified Newton method) |
| CN114143152A (en) * | 2021-11-26 | 2022-03-04 | 西安电子科技大学 | Constant modulus blind equalization method based on fractional order correlation entropy and fractional order gradient |
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