基于字典学习的不完整信号星座图分类算法

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"不完整信号分类算法通过字典学习实现对缺失星座点的星座图的识别，采用正交匹配追踪(OMP)方法获取稀疏表示，并利用顺序广义K均值(SGK)方法更新字典集。" 在无线通信领域，自动识别接收到的信号的调制类型是一项关键任务，它是信号检测与解调之间的桥梁。通常，调制识别有两种主要方法：基于似然比(Likelihood-Based, LB)的方法和基于特征(Feature-Based, FB)的方法。然而，当信号不完整或观测数据有限时，这两种传统方法的性能会显著下降。针对这一问题，本文提出了一种基于字典学习的不完整信号分类算法。该算法旨在有效处理缺失星座点的星座图，即那些由于信道衰落、噪声或其他干扰因素导致的不完整信号。字典学习是一种机器学习技术，它能从数据中学习一组基向量，这些基向量可以用来近似表示原始信号，尤其是在信号稀疏的情况下。在本文的方法中，首先应用正交匹配追踪(Orthogonal Matching Pursuit, OMP)算法来获取不完整信号的稀疏表示。OMP是一种压缩感知技术，它通过迭代寻找信号中贡献最大的几个元素，从而构建一个接近原信号的稀疏表示。这样的稀疏表示有助于减少噪声和不完整数据的影响，提高识别准确性。接下来，为了进一步优化字典以适应不完整信号，采用了顺序广义K均值(Sequential Generalized K-means, SGK)方法更新字典集。K均值算法是一种常见的聚类方法，而SGK是其扩展，它允许在每次迭代中动态调整类别数量，以更好地适应数据的分布变化。在不完整信号的场景下，SGK能有效地捕捉不同调制类型的特征，从而改进分类性能。实验结果证明了所提出的基于字典学习的不完整信号分类算法的有效性，尤其是在处理少量观测数据和不完整信号时，相比传统的LB和FB方法，该方法能显著提升调制类型识别的准确性和鲁棒性。这对于现代无线通信系统中的实时信号处理和解析具有重要的实用价值。

Modulation Recognition for Incomplete signals

through Dictionary Learning

Guangcheng Lu, Kezhong Zhang, Sai Huang, Yifan Zhang, Zhiyong Feng

Wireless Technology Innovation Institute(WTI),

Beijing University of Posts and Telecommunications,

Beijing, P.R.China, 100876

Email: {luguangcheng, zhangkz, huangsai, zhangyf, fengzy}@bupt.edu.cn

Abstract—The automatic recognition of modulation type for

a detected signal is a signiﬁcant task in wireless communica-

tion, which is the intermediate step between signal detection

and demodulation. There are two general methods adopted in

modulation recognition, i.e., likelihood-based (LB) method and

feature-based (FB) method. Both LB and FB approach do not

perform well when the signals are incomplete and received from

a very limited number of observations. Therefore, we adopt a

method based on dictionary learning to identify the modulation

type of incomplete signals. The orthogonal matching pursuit

(OMP) method is used to obtain the sparse representation and

the sequential generalization of K-means (SGK) method is used

to update the dictionary set. The experimental result shows that

the recognition accuracy of our method is much higher, compared

with the method based on higher-order cumulant.

Index Terms—Incomplete signals, modulation recognition, dic-

tionary learning

I. INTRODUCTION

The automatic recognition of modulation type for a detected

signal is a signiﬁcant task in wireless communication, which

is the intermediate step between signal detection and demod-

ulation. The goal of modulation recognition is to estimate

the modulation types and other parameters of the transmitted

signals by observing the received data samples, which would

be useful for further signal analyzing and processing.

There are two general classes of method [1] : likelihood-

based (LB) method [2][3] and feature-based (FB) method

[4][5]. The former is based on the likelihood function of

the received signal and makes the decision by comparing the

likelihood ratio against a threshold. A solution offered by the

LB methods is optimal in the Bayesian sense, viz., it minimizes

the probability of false classiﬁcation. The optimal solution

suffers from computational complexity, which often gives rise

to suboptimal classiﬁers. In the FB approach, on the other

hand, several features are usually employed and a decision

is made based on their observed values. In most cases, FB

approach relies on deﬁning and extracting a set of features

that, intuitively, look as an optimum set. The main methods

of the LB and FB method are illustrated in Table. I.

However, both LB and FB approach do not perform well

when the signals are incomplete and received from a very

limited number of observations. The LB approach is valid

when the number of modulation candidates is ﬁnite and is

based on composite hypotheses testing [6]. Therefore, incom-

TABLE I

LB METHODS AND FB METHODS

LB methods

average likelihood ratio test

generalized likelihood ratio test

hybrid likelihood ratio test

FB methods

entropy

fuzzy logic

a moment matrix technique

constellation shape

plete signal with no prior knowledge available is difﬁcult to

identify through the LB method. On the other hand, the FB

approach adopts the pattern recognition method to classify

the modulation type. However, features of incomplete signals

are not similar to the complete signals, especially in the

blind environment. Dictionary learning based which is the

combination of LB and FB approach performs well in the

modulation recognition of incomplete signals.

In recent years, there has been a growing interest in the

study of the sparse representation of signals [7]. Using an

overcomplete dictionary that contains prototype signal-atoms,

signals are described by sparse linear combinations of these

atoms. Let D denotes the dictionary set and x is the coefﬁcient

vectors. There are two steps of dictionary learning, i.e. sparse

representation and dictionary update. In the ﬁrst step, D is

kept constant and search the sparse representation x. After

the sparse representation x is obtained. The dictionary set D

should learn from the statements of received signals.

Previous literature adopted two main methods to obtain

sparse representation. Gersho et. al [8] and Krishnamurthy

et. al [9] adopt the clustering based method that the distances

between received signals and dictionary atoms are compared.

This method is widely used in the vector quantization (VQ)

achieved by clustering algorithms. Since each signal is rep-

resented by only one atom, the sparse approximation step

becomes trivial. Therefore, clustering based method cannot

separate the aliasing signals and is not used in our method. An-

other method is greedy algorithms such as the matching pursuit

(MP) proposed by Mallat et.al in [10] and the orthogonal MP

(OMP) proposed by Tropp et.al in [11]. Due to orthogonal,

the OMP update step will only consider each variable once,

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