Maximum-Likelihood Classification for MPSK with Compressive Samplings

This paper focuses on the classification of the MPSK modulations using compressive measurements in additional Gaussian white noise (AWGN). Under the compressive sensing (CS) frame, the compressive maximum-likelihood (CML) classifier provided in this paper tries to recognize the MPSK signals using far fewer samplings than traditional maximum-likelihood (TML) classifier needs. This paper presents the criterion of classification and the classification performance analysis. Finally, several numerical simulations are provided and the results indicate that the CML classifier have a satisfied performance in higher SNR with far lower complexity. It’s an effective approach to promote the real-time property of communication system. Introduction A new framework called compressive sensing for simultaneous sensing and compression has developed recently. A potentially large reduction can be realized in the sampling and computation costs for a communication system under CS framework. Candès, Tao and Donoho present CS in 2006. CS specifies that a signal having a spare representation in one basis can be reconstructed from a small set of projections. The measurement basis is incoherent with the first basis. The CS measurement process is nonadaptive and the reconstruction process is nonlinear. CS has many promising applications in signal acquisition, compression, medical imaging, and sensor networks. In the modern communication system, modulation classification is an important step between the signal receiving and the signal demodulation. Especially in the non-cooperative communication systems, modulation classification plays a more significant role which can identify the modulation type of a modulated signal corrupted by noise. Many methods have been used in the modulation classification, such as spectrum, moments, zero crossings and Bayes decision theory [5] . While the CS literature has focused almost exclusively on problems in signal reconstruction or approximation, this is frequently not necessary. For instance, in many signal processing applications (including most communications and many radar systems), signals are acquired only for the purpose of making a detection or classification decision. Our aim in this paper is to show that the CS framework is useful for a much wider range of statistical inference tasks. Tasks such as classification do not require a reconstruction of the signal, but only require estimates of the relevant sufficient statistics for the problem. The key finding is that in many cases it is possible to directly extract these statistics from a small number of random projections without ever reconstructing the signal. This work expands on the previous work on classification using compressive measurements. The papers on the modulation classification under CS frame is not too many [7] .In this paper, based on the Bayes decision theory, we use the compressive measurements to recognize the modulation type of signals directly. In the framework of CS, modulation classification can process far less data than the conventional approach with the Nyquist sampling rate, so that the speed of modulation classification will be faster and the real-time performance of the communication system can be promoted significantly. International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 2011 Background of Compressive Sensing Sparse representation of signal. If a few entries of a signal are zero or close to zero, this signal is sparse or compressible. Generally, a signal in time domain is always not sparse. However, in some other domains, the signal may be represented sparsely. Consider a finite-length, one-dimensional, discrete-time signal x which can be represented by a vector with elements [ ] x n in N R , 1,2,..., N n = . And a basisΨ consists of vectors i ψ which has N entries , 1,2,...N i = . So the signal x can be expressed in the basisΨ as follows: = x Ψs (1) where s is the N × 1 column vector of weighting coefficients , i i s =< > x ψ . s is the representation of signal x in basisΨ . If the weighting coefficients s has only K entries non-zero, the signal x is K -sparse in basisΨ . Compressive Sensing. Consider a1 M × measurement vector y with M entries [ ] y m , 1,2,...M m = . A M N(M<<N) × measurement matrix Φ can be viewed as 1 2 M [ , ,..., ] φ φ φ , and 1,2,...,M j j φ = , is a1 M × vector. [ ] y j is generated by the inner production of x and j φ , so that y can be written as = = = y Φx ΦΨs Θs (2) whereΘ is a M N × matrix that = Θ ΦΨ . From [1][2], the measurement process is non-adaptive, because the matrixΦ is a fixed matrix which does not depend on signal x . MPSK Classification With Compressive Maximum-Likelihood Classifier MPSK signal model. The modulation of phase-shift keying uses the phase information of a signal during symbols to carry information, so that the signal can be better transmitted in noise environments. This kind of modulated signal can be expressed as: [ ] A cos(2 ) l c c l x n f n π θ θ = + +  (3) K ( 1)K, 0,1,2,... l n l l < ≤ + =