CN114826834B - Channel blind equalization method and blind equalizer for high-order quadrature amplitude modulation signals - Google Patents

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, wherein a specific model value R is selected based on the characteristics of a high-order quadrature amplitude modulation signal constellation diagram _i Construction of the R _i Calculating the modulus value and R of the output signal of the equalizer _i Is used for extracting the equalization errors corresponding to the constant modulus value R in the full-scale samples according to the prior probability _i Is denoted omega as the selected sample set _i The method comprises the steps of carrying out a first treatment on the surface of the Then according to classical constant modulus algorithm and omega _i Construction of cost function J under high-order quadrature amplitude modulation channel _MCMA (w); finally, constructing an iteration 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). The invention can effectively restrain human errors and false modulations brought by a classical constant modulus equalization method under a high-order quadrature amplitude modulation channel, and realizes a Newton method optimized channel blind equalizer with rapid convergence.

Description

Channel blind equalization method and blind equalizer for high-order quadrature amplitude modulation signals

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

Currently, a Blind Equalizer (BE) performs channel equalization without the aid of a training sequence, and a practical method can BE provided to reduce signal distortion, and at the same time, it does not use a training sequence, so that bandwidth is not wasted in transmission. More importantly, in a non-cooperative or point-to-multipoint communication scenario, the blind equalization algorithm is the only viable solution to achieve system equalization (c.yu and l.xie, "On recursive blind equalization in sensor networks," IEEE trans.signal process., vol.63, no.3, pp.662-672,2015.) (M.Komatsu, N.Tanabe, and t.furukawa, "Direct blind equalization corresponding to noisy environment using Rayleigh quotient," in proc.2019 IEEE 15th Int.Colloquium Signal Process.Its Appl. (CSPA), penang, malaysia, pp.35-38,2019.).

Since Sato in 1975 an article on this direction (y.sato, "a method of Self-recovering equalization for multilevel amplitude modulation systems," IEEE Trans.Commun., vol.COM-23, no.6, pp.679-682,1975.) a number of blind equalization algorithms have been proposed (n.golard, "Self-recovering equalization and carrier tracking in two-dimensional data communications systems," IEEE Trans.Commun., vol.COM-28, no.11, pp.1867-1875,1980.) (s.j.now and g.e.Hinton, "a soft decision-directed LMS algorithm forblind equalization," IEEE trans.Commun., vol.41, no.2, pp.275-279,1993.). Currently, the most popular blind equalization methods in two-dimensional (2D) modulation methods, such as Quadrature Amplitude Modulation (QAM) and carrier-free amplitude and phase (CAP) modulation, are the Constant Modulus Algorithm (CMA) (n.golard, "Self-recovering equalization and carrier tracking in two-dimensional data communications systems," IEEE Trans.Commun., vol.COM-28, no.11, pp.1867-1875,1980.) and its modified algorithms (j.r.treichler and b.agent, "A new approach to multipath correction of constant modulus signals," IEEE trans.Acust, spech, signal process, vol.assp-31, no.2, pp.459-472,1983.) (y.xiao and j.sun, "RLS CMA blind equalization with adaptive forgetting factor controlled by energy steady state," in proc.2016 9th Int.Congress Image Signal Process, biomed.en.information (CISP-BMEI), dateng, china, pp.935-939,2016. In one aspect, the cost function of the CMA attempts to minimize the difference between the square magnitude of the output and the goldhair dispersion constant, with less local minima and reliable convergence (o.dabeer and e.masry, "Convergence analysis ofthe constant modulus algorithm," IEEE trans.inf.thery, vol.49, no.6, pp.1447-1464,2003.) (r.cusani and a.laurenti, "Convergence analysis of the CMA blind equalizer," IEEE trans.Commun, vol.43, no.2/3/4, pp.1304-1307,1995.). On the other hand, CMA will change its tap value over time and has a complexity similar to LMS, which makes it easy to implement (y.sato, "a method of self-recovering equalization for multilevel amplitude modulation systems," IEEE Trans.Commun., vol.COM-23, no.6, pp.679-682,1975.). Furthermore, according to the above features, CMA can provide good initial conditions for two-stage blind equalization algorithms (c.t.ma, z.ding, and s.f. yau, "a two-stage algorithm for MIMO blind deconvolution of nonstationary colored signals," IEEE trans.signal process, vol.48, no.4, pp.1187-1192,2000.), or double-mode blind equalization algorithms (L.He, M.Amin, C.Reed and r.malkemes, "A hybrid adaptive blind equalization algorithm for QAM signals in wireless communications," IEEE trans.signal process, vol.52, no.7, pp.2058-2069,2004.), either explicitly or implicitly, 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 the 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, "Attractions of saddles and slow convergence in CMA adaptation," Signal process, vol.59, no.3, pp.335-340,1997.). Worse still, to reduce the well-known steady state imbalance and avoid initial instability, the CMA step size is typically set at 10 ^-5 An order of magnitude or less, much less than LMS is typically set to 10 ^-2 Step sizes of orders of magnitude (M.Xiang, Y.Xia, and D.P. Mandic, "Performance analysis of deficient length quaternion least mean square adaptive filters," IEEE Trans. Signal Process., vol.68, pp.65-80,2020.). Thus, 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 a Hessian matrix for calculating the cost function to implement. It should be noted that complex signals are processed, and therefore the Hessian matrix of the constant modulus loss function is always singular (K.K. Delgado and Y.Isukapalli, "Use of the Newton method for blind adaptive equa) lization based on the constant modulus 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 these, it is essential to improve the equation accuracy and convergence speed of CMA.

Through the above analysis, the problems and defects existing in the prior art are as follows: human errors and false modulations caused by a classical constant-mode method under a high-order quadrature amplitude modulation channel are restrained.

Disclosure of Invention

Aiming at the problems existing 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 in such a way that a channel blind equalization method facing to high-order quadrature amplitude modulation signals is realized, firstly, a specific module value R is selected based on the characteristics of a high-order quadrature amplitude modulation signal constellation diagram _i Construction of the R _i Calculating the modulus value and R of the output signal of the equalizer _i Is used for extracting the equalization errors corresponding to the constant modulus value R in the full-scale samples according to the prior probability _i Is denoted omega as the selected sample set _i The method comprises the steps of carrying out a first treatment on the surface of the Then according to classical constant modulus algorithm and omega _i Construction of cost function J under high-order quadrature amplitude modulation channel _MCMA (w); finally, constructing an iteration 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 comprises the following steps:

first, sample selection, recording the set of modulus values of the high-order quadrature amplitude modulation signal as Ω= { R _i I=1, 2, …, I), I representing the number of specific model values, noting the total number of observation signal samples as N, first selecting a high order quadrature amplitude modulation signal specific model value R _i Then calculate based on R _i Prior probability and equalization error of (c)(n=1, 2, …, N), the sample length N is calculated from the prior probability _i And the equalization errors are ordered according to ascending order, wherein the first N is taken _i As selected samples Ω _i The method comprises the steps of carrying out a first treatment on the surface of the The invention ensures that the transmission signals have the same amplitude by selecting the samples formed by the constant module value signals, thereby fundamentally avoiding human errors and misadjustment;

step two, 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 improvement of the performance brought by embodying the optimization scheme of the invention through data comparison in the follow-up process;

thirdly, constructing an iteration 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; the iterative formula constructed according to the Newton method is helpful for quickly converging to the optimal solution and finding the optimal equalizer.

Further, the constant modulus sample Ω is selected _i The method. Note that the set of modulus values of the higher-order quadrature amplitude modulation signal is Ω= { R _i First, a specific model value R of the high-order quadrature amplitude modulation signal is selected, wherein (i=1, 2, …, I) is recorded that the total number of the observation signal samples is N _i Then calculate based on R _i Prior probability and equalization error of (c)(n=1, 2, …, N), the sample length N is calculated from the prior probability _i And the equalization errors are ordered according to ascending order, wherein the first N is taken _i As selected samples Ω _i ；

Note that the set of modulus values of the higher-order quadrature amplitude modulation signal is Ω= { R _i I=1, 2, …, I) due to the steady state output of the equalizerIs an estimated value of the transmission signal, the output is divided into different subsets according to the modulus value +. >

The corresponding channel observation signal vectors x (n) are divided into different subsets:

wherein the method comprises the steps ofIs an ideal equalizer, [] ^H Representing the conjugate transpose of the matrix, representing taking the absolute value;

the total number of samples recorded for searching the optimized equalizer is N, and the constant modulus value R of the high-order quadrature amplitude modulation signal is first selected according to the following principle _i : first, a circle with a selected modulus should pass through as many points as possible; second, the distance between the selected circle and its adjacent circle should be as large as possible; second 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 sample quantity to obtain the length of the selected target sample, and marking the length as N _i ：

Wherein P is _i Is a modulus R _i Is the order of the high-order quadrature amplitude modulated signal,has a modulus of R _i Is>Representing a downward rounding operation;

if the blind equalizer converges to the optimal solution, i.eThere is a mathematical relationship->Thus, the following inequality holds:

for all x _i (n)∈Ω _i Andthis is true. Obviously, according to the set Ω _i Definition of (3), in an ideal caseFurthermore, the->And->Far greater than 0;

from the above conclusion, the equalizer output errorFor->Ordered in ascending order, then top N _i Item->Corresponding x (n) sample set Ω _i Is considered to be selected to have a modulus R _i Is a sample of (a)A present collection; however, before achieving channel equalization, an optimal equalizer +.>Is unknown, to solve this problem, the kth iteration value w is used _k Replace->Equalizer output error is then added>Is N the first of (2) _i The sample corresponding to the item is taken as the required sample set.

Further, the cost function constructing method. The equalizer is w, and according to classical constant modulus algorithm and selected observation signal sample omega _i Construction of cost function J under high-order quadrature amplitude modulation channel _MCMA (w)；

s.t.x(n)∈Ω _i

Wherein min represents minimization, s.t. represents meeting the above condition, |w ^H x(n)|-R _i For equalizer output error, E [ (|w) ^H x(n)|-R _i ) ² ]Represents 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 R _i Is a set of observation signals of (a).

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;

the cost function (|w) of the construction ^H x(n)|-R _i ) ² Newton's method with typical quadratic structure, constructing optimized cost function, will J _MCMA The statistical average in (w) is replaced by a time average, x (n) ∈Ω _i Replaced by x _i (n). The cost function is then rewritten as:

wherein N is _i Is a constant modulus value R _i Length of time observation 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 isGradient->Is simplified as follows:

further, gradientFurther decomposed into a (w) w-b (w) structures; matrix A (w) is a positive definite matrix, considered +.>Vector b (w) is considered to be; according to Newton's method, w is _k+1 ＝A ^-1 (w _k )b(w _k ) The method comprises the steps of carrying out a first treatment on the surface of the Based on NewtonThe iterative formula of the channel blind equalization method under the high-order quadrature amplitude modulation signal of the method is expressed as follows:

wherein [ (S)] ^T Representing matrix transposition, [. Cndot.] ^* Representing complex conjugate [ ·] ^-1 The matrix inversion is represented by a matrix inversion,

it is a further object of the present 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 module value 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-mode method iteration formula of the high-order quadrature amplitude modulation channel according to the Newton method, and optimizing the channel blind equalizer.

Another object of the present invention is 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 module value 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-mode method iteration formula of the high-order quadrature amplitude modulation channel according to the Newton method, and optimizing the channel blind equalizer.

Another object of the present invention is to provide a blind equalizer for implementing the channel blind equalization method for high order quadrature amplitude modulation signals, the blind equalizer comprising:

the sample set construction module is used for constructing a constant module value 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 constant-mode method iteration formula of the high-order quadrature amplitude modulation channel according to the Newton method and optimizing the channel blind equalizer.

Another object of the present invention is to provide a terminal that carries the channel blind equalizer for a high-order quadrature amplitude modulation signal.

In combination with the above technical solution and the technical problems to be solved, please analyze the following aspects to provide the following advantages and positive effects:

first, aiming at the technical problems in the prior art and the difficulty in solving the problems, the technical problems solved by the technical proposal of the invention are analyzed in detail and deeply by tightly combining the technical proposal to be protected, the results and data in the research and development process, and the like, and some technical effects brought after the problems are solved have creative technical effects. The specific description is as follows:

firstly, aiming at the problems of human error and misregulation caused by the application of CMA to high-order QAM signals, the invention converts the high-order QAM signals into constant-mode signals with specific mode values through a sample selection technical scheme, so that transmission signals have the same amplitude in theory, thereby fundamentally avoiding human error and misregulation. The technical scheme comprises the core steps of selecting a specific one of a plurality of constant modulus values of a high-order QAM signal, calculating a sample length according to the prior probability of the specific modulus value, calculating equalization errors according to the specific modulus value, and sequencing according to ascending order, so as to intercept a sample set with the number of the sample lengths, wherein the equalization errors of the sample set are smaller, and the sample set is obtained under the specific modulus value, so that blind equalization is equivalent to constant modulus signals, thereby achieving the aim of improving classical CMA equalization performance, and in specific implementation, the changes of MSE and SER and SNR are respectively shown in fig. 4 and 5. From these two figures, it can be seen that the proposed MCMA achieves better balance performance than CMA and MMA.

Secondly, aiming at the problem of low convergence speed of the gradient descent method, the invention optimizes the blind equalizer by constructing a corresponding Newton method, and provides a modified Newton method of the MCMA: due to the constructed cost function (|w) ^H x(n)|-R _i ) ² With a typical quadratic structure, newton-type methods with quadratic or asymptotic quadratic convergence speed can BE easily designed to quickly search for optimal BE.

To facilitate construction of MCMA-related MNMs, the statistical average is replaced with a time average, x (n) ∈Ω _i Rewritten as x _i (n). The MCMA cost function can be rewritten as:

where N is the length of the available samples that can BE used to search for the best BE. In addition, N is _i Is arranged asWherein P is _i Is provided with a die R _i Is the order of the QAM signal, +.>Is provided with a modulus R _i Is used for the transmission of the signal. Taking the 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 isGradient +.>Is simplified as follows:

it is evident that the gradientCan be further decomposed into a (w) w-b (w) structures. Matrix A (w) is a positive definite matrix and can be considered as +.>Vector b (w) can be considered as R _i X _i y _i . According to MNM has w _k+1 ＝A ^-1 (w _k )b(w _k ). Thus, the updated formula for MNM-based MCMA is expressed as:

wherein the method comprises the steps of

In general, newton's method often appears unstable due to its indefinite or nearly singular Hessian matrix, and newton's method brings high computational complexity when iteratively computing the inverse matrix of the Hessian matrix at each step. In contrast, MCMA-MNM employs a positive definite matrixThe Hessian matrix is modified so that the MCMA-MNM is stable. Preferably, the matrix X is theoretically _i Should follow different w _k Remains unchanged because the signal constellation that different samples can recover is predetermined. Therefore, +.>As long as R is obtained _i The 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 In operation, this greatly reduces the computational effort of the method. And, the sequence w in the iterative formula _k By a step amount +.>Is converged to the optimal solution->

Secondly, the technical scheme is regarded as a whole or from the perspective of products, and the technical scheme to be protected has the following technical effects and advantages:

the invention can effectively restrain human errors and false modulations brought by a classical constant-mode method under a high-order quadrature amplitude modulation channel, and realizes a Newton method optimized channel blind equalizer with rapid convergence.

Thirdly, as inventive supplementary evidence of the claims of the present invention, the following important aspects are also presented:

the invention solves the problems of human error and misregulation generated by the classical blind equalization algorithm in the equalization of the high-order QAM signals, particularly because the amplitude of the high-order QAM signals is equal to a plurality of different constants, and can fundamentally avoid the problems for constant-mode signals.

Drawings

Fig. 1 is a flowchart of a channel blind equalization method for a high-order quadrature amplitude modulation 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 constellation diagram of the kth iteration output of the 16-QAM constellation provided by an embodiment of the present invention.

Fig. 4 is a schematic diagram of MSE versus SNR for CMA, MMA, DSM, MCMA of a 16-QAM system according to an embodiment of the present invention.

Fig. 5 is a diagram of SER versus SNR for CMA, MMA, DSM, MCMA of a 16-QAM system according to an embodiment of the present invention.

Fig. 6 is a schematic diagram of ISI versus iteration time for CMA, MMA, DSM, MCMA of a 16-QAM system provided by an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

1. The embodiments are explained. In order to fully understand how the invention may be embodied by those skilled in the art, this section is an illustrative embodiment in which the claims are presented for purposes of illustration.

As shown in fig. 1, the channel blind equalization method for a high-order quadrature amplitude modulation signal provided by the embodiment of the invention includes:

s101: constructing a constant module value 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-mode method iteration formula of the high-order quadrature amplitude modulation channel according to the Newton method, and optimizing the channel blind 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. Note that the set of modulus values of the higher-order quadrature amplitude modulation signal is Ω= { R _i First, a specific model value R of the high-order quadrature amplitude modulation signal is selected, wherein (i=1, 2, …, I) is recorded that the total number of the observation signal samples is N _i Then calculate based on R _i Prior probability and equalization error of (c)Calculating the sample length N according to the prior probability _i And the equalization errors are ordered according to ascending order, and the first N is taken _i As selected samples Ω _i ；

And secondly, constructing a cost function. The equalizer is recorded as w, and the observed 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)；

Thirdly, constructing an iteration formula. And constructing an iteration formula of a blind equalization method under a high-order quadrature amplitude modulation channel according to the Newton method, optimizing the blind equalizer and minimizing a cost function.

According to the invention, the artificial error problem of the algorithm in the high-order QAM system is deduced according to the classical constant modulus algorithm thought theory, and the CMA tries to solve the following optimization problems:

wherein the method comprises the steps ofAnd p is a positive integer, if the implementation is based on an adaptive algorithm implemented by 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 desire for gradients 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 for higher order statistics of the implicitly embedded equalizer output y (n). Theoretically, the minimization of J (w) keeps the statistics of y (n) consistent with those of the input signal, and equalization is accomplished when the equalization sequence y (n) achieves the same distribution of channel inputs s (n). In practice, however, the statistics of y (n) are estimated using sample data, while the statistics of s (n) are provided by theoretical values, and this inconsistency leads to a small error, which is defined as an artificial error, which can lead to reduced equalization performance. In addition, the adaptive method based on random gradient contains larger offset in the high-order QAM signal environment. In fact, the following propositions are present:

proposition 1: in a high order QAM system, if BE converges to an optimal solutionAnd completely compensates for channel distortion, i.e.,

then the instantaneous gradient calculated from the sample dataAnd not equal to 0 in a noise-free environment. Moreover, the instantaneous gradient satisfies the inequality:

obviously, does not Equation(s)Is generated by human error. Since the gradient is not equal to 0, even if the optimal solution is reached>The w of BE is also continuously adjusted, thereby generating additional errors (human errors). Instantaneous gradientMeaning that when the BE converges to an optimal solution in its implementation, the CMA will continue to adjust the BE, which is called detuning, 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 a high-order signal input into a constant modulus signal input.

In the present invention, the omega is gathered _i Is determined by: aggregation omega _i ＝{x _i (1),x _i (2),…,x _i (N _i ) Is not known in advance, and it is necessary to first extract the sample matrix x= [ X (1), X (2), …, X (n)]Finding it. The invention provides a sample selection method based on the following conclusion.

Conclusion 1: if BE converges to an optimal solution, i.eThus having a mathematical relationshipThe following inequality:

for all x _i (n)∈Ω _i Andthis is true.

It is apparent that according to the set Ω _i Definition of (1), in the ideal case ofIn addition, in the case of the optical fiber,and->Much greater than 0. Thus, the inequality holds.

According to the inequality, the error is output to the equalizer in ascending orderAnd sequencing. Then it can be safely assumed that for the first N _i Error->The corresponding sample is a composition set omega _i Is selected from the group consisting of a sample of the sample. However, before achieving channel equalization, an optimal equalizer +.>Is unknown. To solve this problem, the kth iteration value w is used _k Replace->Then top N _i Error->The corresponding sample is considered the desired selected sample.

Considering a 16-QAM signal, FIG. 3 shows the kth iterationIs provided. If R is _i Set to->Then->According to the principle, the errors are ordered in ascending order, and then the pre +.>Corresponding outputs (for 16-QAM signal, < >>P _i = 8,Q =16, so->) The error is considered to be the selected outputAs shown in FIG. 3, the output of the blue mark (the area between the two green circles) is considered to correspond to +.>Is selected from the group consisting of a plurality of outputs. The corresponding samples and the sets of samples are each represented by x _i,k (n)(n＝1,2,…,N _i ) And omega _i,k The latter can be regarded as the set Ω, representing _i Is an alternative to (a).

According to the above set Ω _i Determination method, selected modulus R _i Is an important parameter. Higher order QAM has widely varying moduli, and the parameter R is selected 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 relatively high. Second, the distance between the selected circle and its adjacent circle should be as large as possible. As a result, the number of constellation points for erroneous decisions can be minimized. Typically the distance between adjacent circles is approximately equal, so in practice the sample usage is mainly considered.

The cost function of MCMA is constructed in the present invention: the artifacts and misadjustments of CMA are caused by the amplitude of the higher order QAM signal being 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., a low-order 4-QAM signal. In this way, the equalization performance of CMA is improved by converting the higher order signal input to a constant modulus signal input. It is generally considered that an equalizer depends on a channel but is independent of an input signal, and if received data corresponding to a specific modulus can be identified from all received data and other data can be discarded, the input signal can be regarded as a constant modulus signal, and 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 classical CMA.

It is apparent that higher order QAM signals can be divided into different subsets according to their modulus, as shown in fig. 2, 16-QAM constellation points can be divided into three subsets, labeled red, blue and black, respectively, and constellation point sets { ±1±1j }, { ±1±3j, ±3±1j } and { ±3±3j } correspond respectively And->Is defined as Ω= { R _i I=1, 2, …, I). Because of steady state output of equalizer->Is an estimate of the transmitted signal, so these outputs can also be divided into different subsets according to their modulus, namely:

relay outputAfter classification of the corresponding channel observations x (n) regression vectors are alsoCan be divided into different subsets

Wherein the method comprises the steps ofIs an ideal equalizer. Easily verify that it belongs to the collection->The output of (2) satisfies the constant modulus characteristic in the strict sense. Thus, if only the data belonging to the set Ω is used _i Output +.corresponding to channel observation x (n)>To adjust the equalizer, the input signal can be considered as a constant modulus signal and human error and offset can be completely avoided.

Finally, from the above analysis, the CMA cost function can be modified as:

s.t.x(n)∈Ω _i

wherein, the aggregate Ω _i ＝{x _i (1),x _i (2),…,x _i (N _i )}，N _i Representing a collection Ω _i Is a base of (c).

Let x (n) be ∈Ω _i Represented as x _i (n) parallel instructionAccording to a 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: (1) MCMA uses only samplesThe X is _i (n)(n＝1,2,…,N _i ) Wherein x is _i (n) is a member of the group Ω _i N, N _i Is its size; (2) Replacing parameter R in CMA with R in MCMA _i The method comprises the steps of carrying out a first treatment on the surface of the (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 disturbances are avoided with MCMA. This is because when BE converges to the optimal solution(wherein->). Second, becauseMCMA can eliminate the human error generated. 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: according to an iteration formula of a blind equalization method under a Newton method construction high-order quadrature amplitude modulation channel, optimizing a blind equalizer and minimizing a cost function, the invention provides a modified Newton method of MCMA: due to the constructed cost function (|w) ^H x(n)|-R _i ) ² With a typical quadratic structure, newton-type methods with quadratic or asymptotic quadratic convergence speed can BE easily designed to quickly search for optimal BE.

To facilitate construction of MCMA-related MNMs, the statistical average is replaced with a time average, x (n) ∈Ω _i Rewritten as x _i (n). The MCMA cost function can be rewritten as:

where N is the length of the available samples that can BE used to search for the best BE. In addition, N is _i Is arranged asWherein P is _i Is provided with a die R _i Is the order of the QAM signal, +.>Is provided with a modulus R _i Is used for the transmission of the signal. Taking the 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 isGradient +.>Is simplified as follows:

it is evident that the gradientCan be further decomposed into a (w) w-b (w) structures. Matrix A (w) is a positive definite matrix and can be considered as +.>(Vector)b (w) can be regarded as R _i X _i y _i . According to MNM has w _k+1 ＝A ^-1 (w _k )b(w _k ). Thus, the updated formula for MNM-based MCMA is expressed as:

wherein the method comprises the steps of

In general, newton's method often appears unstable due to its indefinite or nearly singular Hessian matrix, and newton's method brings high computational complexity when iteratively computing the inverse matrix of the Hessian matrix at each step. In contrast, MCMA-MNM employs a positive definite matrixThe Hessian matrix is modified so that the MCMA-MNM is stable. Preferably, the matrix X is theoretically _i Should follow different w _k Remains unchanged because the signal constellation that different samples can recover is predetermined. Therefore, +.>As long as R is obtained _i The 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 In operation, this greatly reduces the computational effort of the method. And, the sequence w in the iterative formula _k By a step amount +.>Is converged to the optimal solution- >

Based on the above analysis, the MCMA-MNM that can be realized is:

/>

wherein X is _i,k ＝[x _i,k (1),x _i,k (2),…,x _i,k (N _i )]，

Notably, the sample matrix X _i,k And R is _i,k More or less will vary with iteration. Thus, R needs to be updated in each iteration _i,k From R unchanged in theoretical analysis _i This results in a significant increase in the amount of computation compared to that of the previous example. However, X is _i Is predetermined and independent of BE. This indicates X _i,k And X _i,k+1 The variation between is small, especially when BE approaches the convergence value. Thus, hessian matrix (correlation matrix) R _i,k+1 The fast calculation can be performed by the following formula:

wherein the method comprises the steps ofBecause of the collection->And->Few elements, R is updated based on the above formula _i,k Only a very small amount of calculation is required, thereby greatly reducing the amount of calculation of the proposed MCMA-MNM.

The invention provides a channel blind equalizer facing to high-order quadrature amplitude modulation signals, which comprises:

the sample set construction module is used for constructing a constant module value 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 constant-mode method iteration formula of the high-order quadrature amplitude modulation channel according to the Newton method and optimizing the channel blind equalizer.

2. Application example. In order to prove the inventive and technical value of the technical solution of the present invention, this section is an application example on specific products or related technologies of the claim technical solution.

Embodiment one, point-to-multipoint communication

In point-to-multipoint communication, it is difficult to provide a training sequence, for a digital television system, if a certain television receiver is to resume operation after temporary failure, the television receiver must be re-equalized, which may interrupt communication with other television receivers.

Second embodiment, non-cooperative communication

In non-cooperative communication, a transmission channel is generally a wireless channel, and is affected by various factors such as multipath, preferential loan, etc., and a signal received by a receiving end has serious inter-symbol interference (ISI), which results in high error rate of communication. The statistical characteristics and the channel characteristics of the signal at the transmitting end are unknown, and the receiving end cannot or hardly acquire the training sequence, so that the problem of inter-code crosstalk is solved by using a blind equalization technology. In addition, burst non-cooperative reception means that there are only tens to hundreds of elements per frame of data received in communication, and because the amount of data is small, the blind equalizer must have a fast convergence speed to trigger non-cooperative reception. The blind equalization technical scheme provided by the invention applies Newton method to optimize the blind equalizer so as to improve the blind equalization performance.

Embodiment III, blind demodulation System

The blind demodulation receiver cannot acquire signal parameters such as a modulation mode, a symbol rate, a carrier frequency, a start-stop position and the like of a transmitted signal from a transmitting party, and does not have frame structure information and a training sequence, so that the relevant parameters can be extracted, and only the characteristics of a received signal can be used for estimation. Also, multipath, doppler spread effects in short wave communications cause severe intersymbol interference in the received signal. In addition, in modern military communication, in order to resist reconnaissance, a burst communication mode is often adopted, so that signals received by a interception system have the characteristic of short duration, and sometimes even only one hundred symbols of data are needed. Short wave interception reception is used as third party reception, and the received short wave interception reception can be different burst waveforms sent by a plurality of transmitting sources, and the carrier frequencies of the burst waveforms are usually different. Based on the method, the blind equalization scheme provided by the invention is used for a blind demodulation system to eliminate intersymbol interference, compensate the influence of a short wave channel response on signals and improve the blind demodulation performance.

3. Evidence of the effect of the examples. The embodiment of the invention has a great advantage in the research and development or use process, and has the following description in combination with data, charts and the like of the test process.

To verify the effectiveness of the proposed method, the proposed MCMA is compared with the conventional CMA (p=2), MMA, CNA and DMS by standards of Symbol Error Rate (SER), MSE and ISI. MSE is defined as

MSE＝E[|Cy(k)-s(k-τ)| ² ]

Wherein,and ISI is defined as

Wherein the method comprises the steps ofIs the combined impulse response of the channel and equalizer, and

embodiments contemplate QAM signals on complex-valued frequency selective channels with gaussian noise. The number of hypothesis ordersThe channel impulse response of (a) is 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]. Furthermore, a six tap equalizer is used and a central single spike initialization is used. The 16-QAM case for the higher order modulation scheme was analyzed. Set Ω is defined as +.>

The examples simulate various performances of CMA, MMA, DSM, MCMA in a 16-QAM system. The steps of CMA and MMA were set to 5X 10, respectively ^-5 And 8X 10 ^-4 For DMS, the step size associated with CMLF is set to 5×10 ^-5 The step size associated with CME is set to 5×10 ^-3 Parameter R of MCMA _i Is arranged asIn the following simulations, the number of samples n=1500 was taken in addition to the simulation related to the number of MSE samples.

Fig. 4 and 5 show the variation of MSE and SER with SNR, respectively. From these two figures, it can be seen that the proposed MCMA achieves better balance performance than CMA and MMA. Furthermore, both MSE and SER of the proposed method are even lower than DMS, which is difficult to achieve. The preferred balance of the proposed method is due to two reasons. 1) MCMA is effective in suppressing human error and steady state disturbances. 2) Since the proposed algorithm uses a large number of samples at the same time, excessive errors in the adaptive method due to the fact that only one sample is used per iteration are avoided.

For a 16-QAM system, given snr=28 db, n=1500, and convergence performance of cma, MMA, DSM, MCMA in terms of ISI is shown in fig. 6. As can be seen from this figure, the proposed MCMA method converges much faster than the other three methods. The reason for the fast convergence speed of the proposed algorithm is as follows: 1) The method effectively inhibits human errors and steady state disturbance, and can stably converge without fluctuation. 2) Comparison shows that the iterative approximation of the proposed method is equivalent to calculating a large number of samples by an adaptive algorithm. 3) The proposed method uses a structured MNM and therefore 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 steady state ISI similar to DMS.

In summary, the improved constant-mode equalizer for blind equalization in the above embodiments shows that the classical CMA has the problems of human error and imbalance, and the MCMA effectively solves the problems caused by human error and imbalance. The results of the examples show that the MCMA provided by the invention has better balance performance than other existing methods. Thereby meeting the use requirement and being worth being popularized and used.

It should be noted that the embodiments of the present invention can be realized in 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 special purpose design hardware. Those of ordinary skill 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 as provided on a carrier medium such as a magnetic disk, CD or DVD-ROM, a programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present invention and its modules may be implemented by hardware circuitry, such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., as well as software executed by various types of processors, or by a combination of the above hardware circuitry and software, such as firmware.

The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.

Claims (5)

1. A channel blind equalization method facing high-order quadrature amplitude modulation signals is characterized in that the channel blind equalization method facing high-order quadrature amplitude modulation signals is characterized in that firstly, a specific model value R is selected based on the characteristics of a high-order quadrature amplitude modulation signal constellation diagram _i Construction of the R _i Calculating the modulus value and R of the output signal of the equalizer _i Is used for extracting the equalization errors corresponding to the constant modulus value R in the full-scale samples according to the prior probability _i Is denoted omega as the selected sample set _i The method comprises the steps of carrying out a first treatment on the surface of the Then according to classical constant modulus algorithm and omega _i Construction of cost function J under high-order quadrature amplitude modulation channel _MCMA (w); finally, constructing an iteration 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)；

The channel blind equalization method for the high-order quadrature amplitude modulation signal specifically comprises the following steps:

First, sample selection, recording the set of modulus values of the high-order quadrature amplitude modulation signal as Ω= { R _i I=1, 2, …, I), I representing the number of specific model values, noting the total number of observation signal samples as N, first selecting a high order quadrature amplitude modulation signal specific model value R _i Then calculate based on R _i Prior probability and equalization error of (c) Calculating corresponding R according to prior probability _i Is of sample length N _i And the equalization errors are ordered according to ascending order, wherein the first N is taken _i As selected samples Ω _i ；

Step two, 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)；

Thirdly, constructing an iteration 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;

the constant modulus sample omega is selected _i Method, note that the set of modulus values of the higher-order quadrature amplitude modulation signal is Ω= { R _i First, a specific model value R of the high-order quadrature amplitude modulation signal is selected, wherein (i=1, 2, …, I) is recorded that the total number of the observation signal samples is N _i Then calculate based on R _i Prior probability and equalization error of (c)Calculating the sample length N according to the prior probability _i And the equalization errors are ordered according to ascending order, wherein the first N is taken _i As selected samples Ω _i ；

Note that the set of modulus values of the higher-order quadrature amplitude modulation signal is Ω= { R _i I=1, 2, …, I) due to the steady state output of the equalizerIs an estimated value of the transmission signal, the output is divided into different subsets according to the modulus value +.>

The corresponding channel observation signal vectors x (n) are divided into different subsets:

wherein the method comprises the steps ofIs an ideal equalizer, [] ^H Representing the conjugate transpose of the matrix, and taking the absolute value;

the total number of samples recorded for searching the optimized equalizer is N, and the constant modulus value R of the high-order quadrature amplitude modulation signal is first selected according to the following principle _i : first, a circle with a radius of the selected modulus should pass through as many constellation points as possible; second, the distance between the selected circle and its adjacent circle should be as large as possible; second 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 sample quantity to obtain the length of the selected target sample, and marking the length as N _i ：

Wherein P is _i Is of the modulus of R _i Is the order of the high-order quadrature amplitude modulated signal,has a modulus of R _i Is>Representing a downward rounding operation;

If the blind equalizer converges to the optimal solution, i.eThere is a mathematical relationship->Thus, the following inequality holds:

for all x _i (n)∈Ω _i Andestablishment; obviously, according to the set Ω _i Definition of (3), in an ideal caseFurthermore, the->And->Far greater than 0;

from the above conclusion, the equalizer output errorFor->Ordered in ascending order, then top N _i Item->Corresponding x (n) sample set Ω _i Is considered to be selected to have a modulus R _i Is a sample set of (1); however, before achieving channel equalization, an optimal equalizer +.>Is unknown, to solve this problem, the kth iteration value w is used _k Replace->Equalizer output error is then added>Is N the first of (2) _i Taking the sample corresponding to the item as a required sample set;

the cost function constructing method includes that an equalizer is w, and according to a classical constant modulus algorithm and a selected observation signal sample omega _i Construction of cost function J under high-order quadrature amplitude modulation channel _MCMA (w)；

s.t.x(n)∈Ω _i

Wherein min represents minimization, s.t. represents meeting the above condition, |w ^H x(n)|-R _i For equalizer output error, E [ (|w) ^H x(n)|-R _i ) ² ]Represents 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 R _i A set of observation signals of (a);

the method for constructing the iterative formula is used for 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;

The cost function (|w) of the construction ^H x(n)|-R _i ) ² Newton's method with typical quadratic structure, constructing optimized cost function, will J _MCMA The statistical average in (w) is replaced by a time average, x (n) ∈Ω _i Replaced by x _i (n) then rewrites the cost function as:

wherein N is _i Is a constant modulus value R _i Length of time observation signal set:

pair J _MCMA (w) differentiating with respect to 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 isGradient->Is simplified as follows:

gradient ofFurther decomposed into a (w) w-b (w) structures; matrix A (w) is a positive definite matrix, known asVector b (w) is considered R _i X _i y _i The method comprises the steps of carrying out a first treatment on the surface of the According to Newton's method, w is _k+1 ＝A _-1 (w _k )b(w _k ) The method comprises the steps of carrying out a first treatment on the surface of the The iterative formula of the channel blind equalization method under the high-order quadrature amplitude modulation signal based on Newton method is expressed as follows:

wherein [ (S)] ^T Representing matrix transposition, [. Cndot.] ^* Representing complex conjugate [ ·] ^-1 The matrix inversion is represented by a matrix inversion,

2. a computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the high order quadrature amplitude modulation signal oriented channel blind equalization method of claim 1.

3. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the channel blind equalization method for high order quadrature amplitude modulated signals of claim 1.

4. A blind equalizer for implementing the high order quadrature amplitude modulated signal oriented channel blind equalization method of claim 1, said blind equalizer comprising:

the sample set construction module is used for constructing a constant module value 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 constant-mode method iteration formula of the high-order quadrature amplitude modulation channel according to the Newton method and optimizing the channel blind equalizer.

5. A terminal carrying the channel blind equalizer for high-order quadrature amplitude modulation signals of claim 4.