form recognition
3.2.1 Morphologically processed Choi-Williams distribution based waveform recognition
In [175], a supervised radar waveform classification system based on time- frequency distribution images has been proposed. The estimated Choi- Williams distribution is considered as a 2D-image and processed using mor- phological image processing operations, dilation and erosion, to extract a binary feature image. The extracted binary feature image is fed to a super- vised MLP classifier which performs the final classification. The continuous wave waveforms are classified to 5 classes: binary phase shift keying (BPSK), LFM, Frank codes, P4 codes, and polytime modulation T1. In the simula- tions, the proposed classification system achieved over 90 % overall correct classification rate at SNR of roughly 0 dB.
3.2.2 Pseudo Wigner-Ville distribution based estimation and classification of FM signals
In [176], a frequency modulation (FM) waveform classification algorithm based on the estimated instantaneous frequency has been proposed. The instantaneous frequency is estimated from the PWVD using the peak loca- tion for each time instant. Three different FM waveform models are defined and considered: LFM, sinusoidal FM, and “S”-shaped FM. The model pa- rameters of each possible class are estimated using a statistical model for the estimated instantaneous frequency. Finally, a statistical hypothesis test based on the mean-square errors of the intercepted radar pulse and the es- timated models is employed for classifying among the three different FM
waveform classes. The proposed method achieved over 90 % overall correct classification rate at SNR of -4 dB in the examples.
3.2.3 Short-time Fourier transform based waveform recogni- tion
In [177], a channelized waveform recognition system based on the short time Fourier transform (STFT) has been proposed. The proposed algorithm obtains multiple time-frequency representations by averaging the estimated STFT using different integration lengths, hence providing better adaptation to signals with different lengths. The waveform classifier is a hierarchical classifier using threshold tests based on features extracted from the time- frequency distribution based instantaneous frequency estimate. Features extracted are the magnitude and error of a fitted linear model, as well as the maximum first-order difference of the instantaneous frequency. The proposed classifier is able to classify signals to four classes: LFM, phase shift keying (PSK), frequency shift keying (FSK), and non-modulated.
The classification performance of the proposed recognition system is an- alyzed using both simulated and real-world measured signals. Due to the channelized structure the classification performance varies heavily for dif- ferent waveforms. In general, the performance for PSK and FSK signals occupying several channels is very poor because the filtering destroys the modulation information carried in the phase [177]. For the other waveforms considered as well as for the PSK and FSK signals when the signal band- width is small enough, 90 % correct classification rate is attained between SNRs of -5 dB and 8 dB depending on the waveform.
3.2.4 Atomic decomposition-based waveform recognition
In [178, 179], atomic decomposition (AD)-based complex radar signal detec- tion and classification has been proposed. AD represents the intercepted signal by the expansion of atoms, i.e., the basis functions forming a dic- tionary. In [178, 179], the employed dictionary of atoms is composed of chirplets. Fig. 3.2 presents the block diagram of the intercept receiver pro- posed in [178]. First, the analytic signal is obtained using the Hilbert trans- form. The analytic signal is then decomposed to atoms, after which the atoms are clustered. The purpose of the clustering stage is to group atoms coming from the same signal to the same cluster. Hence, the clustering stage enables classification of simultaneous signals. After the atoms have been assigned to different clusters, the signals corresponding to the clus- ters are reconstructed. The instantaneous frequencies are estimated from the reconstructed signals. The modulation recognition is based on features extracted from the estimate of each instantaneous frequency. Features ex- tracted are the magnitude and error of a fitted linear model, as well as the
transform Hilbert
AD Clustering estimation of inst. freq.Reconstruction and Modulationrecognition
Figure 3.2: Block diagram of an atomic decomposition-based intercept re- ceiver [178].
ratio of the error and squared magnitude, and the maximum deviation of the instantaneous frequency and the variance of a median-filtered instanta- neous frequency. The modulation classifier is a hierarchical classifier based on threshold tests. Similarly as the STFT based classifier of [177], the pro- posed classifier is able to classify signals to four classes: LFM, PSK, FSK, and non-modulated.
The classification performance is tested using three test signals obtained from real radar and communication systems. The test signals are LFM, BPSK, and 2-FSK signals, respectively. Over 90 % correct classification rate is obtained for the BPSK signal (Barker-13 pulse) at SNR of -2 dB, and for the 2-FSK signal at SNR of 4 dB. For the LFM signal the correct classification rate is 100 % conditioned on detection for all tested SNRs.
In [179], the detection and estimation stage is improved by using the expectation maximization (EM) algorithm and an information theoretic cri- terion in addition to the AD. That is, the initial representation provided by the AD is improved using the EM algorithm that iteratively finds the ML estimate. Information theoretic criterion is then employed for the model order selection, i.e., for the detection of the number of signals. The authors employ their own information theoretic criterion that depends directly on the false alarm rate parameter. The improved method employing the EM algorithm and information theoretic criterion obtains a sparser representa- tion, i.e. fewer atoms, than the original algorithm and hence has a more desirable performance in practical applications. However, its influence to waveform classification performance has not been studied in [179].