EXTRACTION OF POLYPHASE RADAR MODULATION PARAMETERS USING A WIGNER-VILLE DISTRIBUTION – RADON TRANSFORM T. O. Gulum , P. E. Pace and R. Cristi Department of Electrical and Computer Engineering Naval Postgraduate School Monterey, CA 93943 pepace@nps.edu Abstract - Often used in low probability of intercept continuous waveform (CW) emitters, polyphase modulations can have extremely long code lengths (large processing gain), good sidelobe performance and robust Doppler tolerance. This paper presents an efficient algorithm to autonomously extract the polyphase radar modulation parameters from an intercepted waveform using a Wigner-Ville Radon transform. Results show that our method results in a small relative error in the extracted parameters for signal-to-noise ratios as low as – 6 dB. Index Terms— Wigner-Ville distribution, Modulation parameters, Radon transform. 1. INTRODUCTION Polyphase modulation of a continuous wave (CW) carrier frequency is becoming increasingly important in low probability of intercept wideband emitter design [1]. Non-cooperative intercept receivers looking for these emitters must detect the modulation across a broad spectrum in the presence of noise and multi-path. The intercept receiver can increase its processing gain by implementing time-frequency (T-F) signal processing such as the pseudo Wigner-Ville distribution (PWVD). The T-F output images can provide details about the polyphase CW modulation parameters that are unavailable using power spectral density techniques. The need for human interpretation of the T-F results however limits the extraction of the waveform parameters to non-real time electronic intelligence receivers. Autonomous parameter extraction of the LPI emitter modulations can eliminate the need for a human operator and enable near real-time coherent handling of the threat emitters being intercepted. Parameter extraction followed by correlation with existing emitters in a database (identification) can then aid in signal tracking and coherent response management. This paper investigates an algorithm to efficiently extract the polyphase radar modulation parameters (bandwidth B, cycles of the carrier per subcode cpp, code length , code period T and carrier frequency c N c f ) using a Wigner- Ville distribution – Radon transform. We show that the Radon transform is particularly useful for this time- frequency signal processing task since the majority of polyphase modulations are developed by approximating a linear frequency modulation waveform. We evaluate the sensitivity of the algorithm using the five polyphase modulations Frank, P1, P2, P3, and P4 for signal-to-noise ratios (SNRs) of 0 dB and dB. To illustrate the algorithm, a Frank code is used with subcodes, a carrier frequency of Hz and an analog-to-digital converter (ADC) sampling frequency of 6  c N 1495 c f  s f  7 kHz with SNR = 0 dB. The Frank code is a polyphase code with each sub-code phase defined as , 2 ( 1)( 1) ij i j M S I    1, 2, i M  ! 2 36 c N M   cpp  / 1495 Hz c B f cpp   T  c f B (1) where with total sub-codes. The number of carrier frequency cycles within a subcode is 1, giving a transmitted bandwidth and a code period of 24.1 ms [1]. 2. PWVD–RADON TRANSFORM ALGORITHM A block diagram of the autonomous PWVD – Radon transform algorithm is shown in Figure 1. The first step is to compute the Wigner-Ville distribution. The carrier frequency is then extracted by finding the location of the maximum intensity level within the PWVD image. In order to extract the code length T and bandwidth , the Radon transform is computed from the T-F PWVD image. The Radon transform is the projection of the image intensity along a radial line oriented at a specific angle. It transforms the 2-D image with line- trends into a domain of the possible line parameters U and , where T U is the smallest distance from the origin and is its angle with the x-axis. In this form, a line is defined as T cos sin x y U T T   (, ) fxy ( , ) ( cos sin , sin cos ) R f s s ds UT U T TU T T f f    ｳ [2]. Using this, the Radon transform of a 2-D image is (2) 1505 U.S. Government Work Not Protected by U.S. Copyright ICASSP 2008