Wei Su

Distributed Maximum Likelihood Classification of Linear Modulations Over Nonidentical Flat Block-Fading Gaussian Channels

In this paper, we consider distributed maximum likelihood (ML) classification of digital amplitude-phase modulated signals using multiple sensors that observe the same sequence of unknown symbol transmissions over nonidentical flat blockfading Gaussian noise channels. A variant of the expectation-maximization (EM) algorithm is employed to obtain the ML estimates of the unknown channel parameters and compute the global log-likelihood of the observations received by all the sensors in a distributed manner by means of an average consensus filter. This procedure is repeated for all candidate modulation formats in the reference library, and a classification decision, which is available at any of the sensors in the network, is declared in favor of the modulation with the highest log-likelihood score. The proposed scheme improves the classification accuracy by exploiting the signal-to-noise ratio (SNR) diversity in the network while restricting the communication to a small neighborhood of each sensor. Numerical examples show that the proposed distributed EM-based classifier can achieve the same classification performance as that of a centralized classifier, which has all the sensor measurements, for a wide range of SNR values.

Asynchronous Linear Modulation Classification With Multiple Sensors via Generalized EM Algorithm

In this paper, we consider the problem of automatic modulation classification with multiple sensors in the presence of unknown time offset, phase offset and received signal amplitude. We develop a novel hybrid maximum likelihood (HML) classification scheme based on a generalized expectation maximization (GEM) algorithm. GEM is capable of finding ML estimates numerically that are extremely hard to obtain otherwise. Assuming a good initialization technique is available for GEM, we show that the classification performance (in terms of the probability of error) can be greatly improved with multiple sensors compared to that with a single sensor, especially when the signal-to-noise ratio (SNR) is low. We further demonstrate the superior performance of our approach when simulated annealing (SA) with uniform as well as nonuniform grids is employed for initialization of GEM in low SNR regions. The proposed GEM based approach employs only a small number of samples (in the order of hundreds) at a given sensor node to perform both time and phase synchronization, signal power estimation, followed by modulation classification. We provide simulation results to show the efficiency and effectiveness of the proposed algorithm.

A novel approach to dictionary construction for automatic modulation classification

Abstract In almost all the work carried out in the area of automatic modulation classification (AMC), the dictionary of all possible modulations that can occur is assumed to be fixed and given. In this paper, we consider the problem of discovering the unknown digital amplitude-phase modulations when the dictionary is not given. A deconvolution based framework is proposed to estimate the distribution of the transmitted symbols, which completely characterizes the underlying signal constellation. The method involves computation of the empirical characteristic function (ECF) from the received signal samples, and employing constrained least squares (CLS) filtering in the frequency domain to reveal the unknown symbol set. The decoding of the received signals can then be carried out based on the estimate of the signal constellation. The proposed method can be implemented efficiently using fast Fourier transform (FFT) algorithms. In addition, we show that the distribution estimate of the transmitted symbols can be refined if the signal constellation is known to satisfy certain symmetry and independence properties.

Asynchronous hybrid maximum likelihood classification of linear modulations

In this paper, we consider the problem of linear modulation classification in the presence of unknown time offset, phase offset and received signal amplitude. We develop a novel hybrid maximum likelihood (HML) approach based on a Generalized Expectation Maximization (GEM) algorithm [1]. Our approach is applicable to all QAM and PSK modulations, and it does not require any assumptions on the received signal-to-noise ratio (SNR). The GEM algorithm provides a tractable procedure to obtain maximum likelihood (ML) estimates which are extremely hard to obtain otherwise. Moreover, our approach employs only a small number of samples (in the order of hundreds) to perform both time and phase synchronization, signal power estimation, followed by modulation classification. The proposed approach also enables maximum a posteriori (MAP) decoding of the unknown constellation symbol sequence as a by-product of the GEM algorithm. We provide simulation results that show that the proposed approach provides excellent classification performance.

Multisensor Modulation Classification (MMC): Implementation Considerations -- USRP Case Study

This paper provides hardware implementation considerations for previously developed algorithms designed to improve the classification of the modulation of weak radio signals utilizing multiple sensors. The case study presented focuses on a likelihood-based approach in a centralized data fusion framework. Data sets from multiple sensors are fused to obtain a more accurate modulation classification as previously demonstrated in simulations. The algorithms are implemented on a hardware test bed that consists of the laboratory grade software defined radio platforms. The performance is examined in realistic environments and compared with results obtained via simulations. The test bed results indicate that the predicted performance improvements are difficult to achieve in practice and the algorithms need to be tailored to account for hardware features and signal propagation effects. Differences between results obtained in simulations and in hardware implementation are discussed and adjustments are made to achieve consistent improvement necessary for refinement of the solution toward military applications.

Distributed asynchronous modulation classification based on hybrid maximum likelihood approach

In this paper, we consider the problem of automatic modulation classification (AMC) with multiple sensors. A distributed hybrid maximum likelihood (HML) based algorithm in the presence of unknown time offset, phase offset and channel gain is presented. The proposed distributed algorithm that employs the generalized expectation maximization (GEM) algorithm is robust to initialization of unknown parameters, computationally efficient and require much less communication overhead compared to performing GEM in a centralized setting. Simulation and experimental results depict the efficacy of the proposed algorithm.

Modulation Discovery Over Arbitrary Additive Noise Channels Based on the Richardson-Lucy Algorithm

We address the problem of discovering unknown digital amplitude-phase modulations over block-fading additive noise channels. The proposed method uses the iterative Richardson-Lucy algorithm to determine the distribution of the transmitted symbols, which completely characterizes the underlying signal constellation. The decoding of the received signals can then be carried out based on the estimate of the signal constellation. An important application of the proposed method is to construct a modulation dictionary in an offline manner prior to performing any type of real time classification, thereby improving the performance of the automatic modulation classification algorithms proposed in the literature.

Detection of Single Versus Multiple Antenna Transmission Systems Using Pilot Data

In this paper, we consider the problem of classifying the transmission system when it is not known a priori whether the transmission is via a single antenna or multiple antennas. The receiver is assumed to be employed with a known number of antennas. In a data frame transmitted by most multiple input multiple output (MIMO) systems, some pilot or training data are inserted for symbol timing synchronization and estimation of the channel. Our goal is to perform MIMO transmit antenna classification using this pilot data. More specifically, the problem of determining the transmission system is cast as a multiple hypothesis testing problem where the number of hypotheses is equal to the maximum number of transmit antennas. Under the assumption of receiver having the exact knowledge of pilot data used for timing synchronization and channel estimation, we consider maximum likelihood (ML) and correlation test statistics to classify the MIMO transmit system. When only probabilistic knowledge of pilot data is available at the receiver, a hybrid ML-based test statistic is constructed using the expectation-maximization algorithm. The performance of the proposed algorithms is illustrated via simulations and comparative merits of different techniques in terms of the computational complexity and performance are discussed.