Overlapping Signal Separation in DPX Spectrum Based on EM Algorithm

Overlapping signal separation in spectrum is a difficult problem. We use Gamma Mixture Model to formulate the distribution of signal power in each frequency bin of digital phosphor technology (DPX) spectrum. Then Expectation Maximization (EM) Algorithm is used to solve the model. Simulation results show that when CIR is greater than 2.7dB, parameters’ estimation error rate of this algorithm is less than 1e-5. Introduction The blind signal processing studies how to discover and analyze unknown, unlicensed and malicious signals. It attracts great interests of the spectrum supervision departments around the world. To exploit spectrum efficiently, supervision departments usually divide spectrum into pieces and authorize organizations or individuals to use some specified pieces in specified time and specified places. Thus, supervision departments will receive spectral overlapping signals. Before judging which signal is illegal, they need to separate these overlapping signals. However, it is difficult for traditional methods to separate overlapping signals because traditional methods like spectrum method and time-frequency method mentioned in [1] contain lots of averaging and smoothing calculation. These calculations will decrease the power response of burst signals in spectrum and even regard little signals as noise. Digital Phosphor Technology (DPX) can store the power response during a period of time and display in a pseudo-color way [2]. Compared with traditional methods, DPX only counts the appearance time of signal power. Thus DPX spectrum contains undistorted power information of signals. In this paper, we use Gamma Mixture Model to formulate the distribution of signal power in each frequency bin of DPX spectrum. Expectation Maximization (EM) Algorithm [3] is then adopted to calculate the model parameters which denote the power and the appearance time of signals. Analysis of Received Signals in DPX Spectrum Power Distribution of Received Signals in DPX. DPX counts time-frequency-power information obtained by Short-Time Fourier Transform (STFT) and compresses it into a 2-D histogram whose columns represent the trace of amplitude values and rows for points on the frequency axis. Each grid in the 2-D histogram stores the appearance number of times of signal whose power and frequency correspond to the column and row, respectively [4]. DPX is able to emphasize the signal of interests by pseudo-coloring method. However, there is no automatic method to recognize overlapping signals and separate them in DPX. Fig. 1 DPX Histogram, DPX Display Illustration and DPX Image of Signal 2nd International Workshop on Materials Engineering and Computer Sciences (IWMECS 2015) © 2015. The authors Published by Atlantis Press 464 Assume the received sampled signal is       1 , 0,1,2, S i i r n s n v n n       (1) where,   i s n denotes the i-th signal wave and n is the sample index. Each signal can be narrow-band bursts, wide-band bursts or continued signal.   v n is noise and is usually not white in the broadband spectrum. After the Discrete Fourier Transform (DFT) as (2), the spectrum is divided into multiple narrowband frequency bins.         1 0 1 , , , ,( 0,1, , 1; 0,1,2, ) f i M S i m f s f v f m i H t r tM m e H t H t f M t                    (2) where, 2 / f f M    , 0,1, , 1 f M    is the frequency index, M is the length of DFT and t is the block index of DFT. Let the bandwidth of each frequency bin be smaller than the channel correlation bandwidth. Therefore,   , v f H t  in each bin f  follows the complex Gaussian distribution with zero-mean and 2 f  -variance (the noise power). The measurements of our approach are the average power in frequency f  .     1 2 1 , , r m m