enhanced signal detection using hilbert transform for … · 2019-03-17 · volume 8, issue 2,...

International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: [email protected]

Volume 8, Issue 2, February 2019 ISSN 2319 - 4847

Volume 8, Issue 2, February 2019 Page 63

Abstract Enhancing the signal to noise ratio (SNR) is the key objective of many signal processing techniques, and hence there is no exception for atmospheric radar signals too. The narrowband signals of the radar i.e. the backscattered signals from various layers of the atmosphere become frail and freak in the backdrop of atmospheric conditions that prevail during the data acquisition with the progress of the height away from the radar (reference) position. Also, the detectability of the genuine Doppler shift from the received signal becomes difficult from the higher altitudes (beyond 12 Km), as the signal is dominated by noise. DC bias elimination is the key factor using the Hilbert transform is presented herewith. Keywords:DC removal, Hilbert transformation, spectral density, signal model.

1. INTRODUCTION The instrumentation facility MST radar in NARL (National Atmospheric Research Laboratory), Gadanki, India is the state of art facility, in the field of signal processing, that provides research on the atmosphere in the Indian sub-continent not only for the working personnel but also for the user scientists like as academicians, research scholars etc. The target for the atmospheric radars is the air layers, unlike the other radar targets. Therefore, the radar returns areweedy and much dominated by the noise as the height progresses from the base. The computation of the power spectral content is an essential component to find the target velocity whether it is by using parametric or non-parametric methods of estimations.

2. SIGNAL MODEL The speed of the target is much (negligibly) smaller than the velocity of the radar signal (near to the speed of the light), the received signal is considered as a narrowband signal [1],[2].The complex signal model is considered for the received atmospheric radar signal and represented mathematically as in Eq. (1), is the basis for the foregoing discussion:

The complex signal model is not only an essential component for PSD/ESD estimations but also useful to find the direction of the target to determine whether the target is approaching or leaving the radar. The Fourier transform of equation (1) is given by:

The eq. (2) is the basis for computing mean Doppler frequency and thus the speed of the wind.In an ideal case, the in the eq.(1) has a single component which is proportional to the wind speed and produce a spike on the frequency scale. However, the practical case differs this and produce many components in the frequency scale. Finding the genuine Doppler shift under these circumstances become ca olossal task for signal processing engineers the signals acquired beyond 8 Km heights, because the genuine Doppler is much dominated by the noise [3], [4]. The spectral density computation is of two kinds: (a) Energy Spectral Density (ESD) and (b) Power Spectral Density (PSD). The former is

Enhanced signal detection using Hilbert transform for atmospheric radar signals

(A comparative study) S. Leela Lakshmi1, Rajani Kanth. V2

1S. Leela Lakshmi, Assistant Professor (Sr), Dept. of ECE, SKIT, Srikalahasti

2Associate Professor, Dept. of EEE, SKIT, Srikalahasti




applied for deterministic signals and the later for the stochastic signals [5]. The radar return is coupled with noise hence, the PSD has to be computed. While computing the PSD it must be noted that: a. the signal must have oscillatory components only, i.e. the signal is zero mean. Mathematically,

b. and also, the weighted average of the correlation is also zero and is expressed as:

The present work is presented based on these two conditions as they are the essential conditions while computing the spectral density. It is observed that the else while works presented on the MST radar and the existing practice overlooked this fact. Therefore, the computation of the wind velocity components and directions is erroneous, particularly beyond 12 Km even though the wind speeds are little in magnitude. In order to improve the accuracy, the condition described by the equation must be satisfied while computing the PSD.

3. DC BIAS MITIGATION APPROACHES

3.3 Existing approach at NARL (frequency domain technique) The atmospheric radar samples the wind having beam-width, both in horizontal (east, north & south, west)& vertical directions (Zenith-X ‘Zx’ & Zenith-Y ‘Zy’) i.e. six directional components are used for determining the wind direction and radial speed.The Doppler shift is the mean Doppler frequency over the conical shaped narrower beam-width, under ideal conditions a single component of speed prevail irrespective of altitude. The received signal consists of a certain zero velocity component along with noise due to variations in permittivity. The noise is basically Gaussian nature [6], as described in [7] that arise from various conditions during the signal acquisition. This may lead erroneously in computing the wind speed and estimating the wind directions and hence is not desirable. Also, it is fact that at any instant of time the air is not standstill over the layers of the atmosphere. Therefore, the presence of the zero-velocity component of the wind is irrational. It is observed that the presence of the zero-velocity component (zero frequency component) and its dominance increases with the altitude from the reference radar position. The NARL group, approach the following procedure to mitigate the DC bias in the radar return.

i. Sampled the wind speed at different altitudes with a resolution of 150m known as range bin (usually 128/256/512 sampling points).

ii. Compute DFT/spectrum of the radar return {for (i)} of each range bin. iii. Wrap the spectrum by (shifting the center of the frequency scale on to ‘ ’ scale, ‘ ’ indicating the target

reaching the radar, ‘ ‘ indicating away from the radar) as . iv. Compute the average of ‘ ’ points of (iii) for each range binseparately as:

or

v. Replace as in (iii) with equation .

It is observed, the existing procedure, from the equations ( ) & ( ) reveals that the DC bias effect is reduced but its effect is not nullified. In contrast, the existing moving average technique doesn’t remove the DC bias present in the signal completely. Therefore, according to Todd K. Moon, et.al [5], ref. to Eq. (3) and (4) the spectrum computation yields erroneous results and hence the wind speed too particularly the direction may be erroneous at higher altitude is observed.

3.4 DC bias elimination using Hilbert – Transform approach (proposed time-domain technique) The Hilbert transform of function is given by:




The equation can be written in the convolution form as:

Accordingly, If , then

The result is due to the fact that is an odd function and . Similarly, . If is a finite duration function, then the equation takes the form:

If , then the equation ( ), yields to ZERO, as .This implies that the Hilbert transform eliminates the mean value/DC quantity present in the given signal.

Figure 1The time-domain form of the received signal (__) showing a shift in the vertical axis indicating the presence

of DC and the processed signal using Hilbert-transform (__) free from the DC component.

Fig.1 depicts the performance of the Hilbert transform approach is illustrated on the received signal at 12 Km altitude. This approach exhibit displays impressive results beyond eight kilometers.It is also true from the practical conditions that the wind possesses certain velocity over the layers of the atmosphere. It is important to know that the application of Hilbert transformation doesn’t affect the noise component from the signal that arises due to various reasons such as variations in refractive index, instrument noise, etc.

Figure 2 The spectrum of the received signal (__) showing a shift in the vertical axis indicating the dominance of DC component of Fig.1 and the processed signal using Hilbert-transform (__) free from the DC component.

The fig 2. represents the spectrum of the fig.1, showing the dominance of the DC component over genuine dopplerand removal of the DC component using the Hilbert-transformation. Therefore, the method in Sec. 3.2 is superior to the existing practice as explained in Sec. 3.1.




4. CONCLUSION In view of [5], the techniques described in [2] and [6] are based on the existing practice as described in Sec. 3.2, the present approach (proposed) satisfy the conditions (a) and (b) noted in Sec. (2) and hence the object of the work is achieved for enhanced signal detection of the atmospheric radars operate in VHF band using the time-domain approach: the Hilbert transformation.

Acknowledgments The authors sincere acknowledge the working scientists of National Atmospheric Research Laboratory (NARL), ISRO, Gadanki, Chittoor (dist.), A.P., India for providing the time-series data from archives and conducting an exclusive experiment for the research work.

References [1] M.I Skolnik, “Radar Hand Book”, Mc Graw-Hill, Boston, 1990. [2] Lakshmi S.L., et.al, “Doppler Profile Estimation in VHF Radars using Wavelets”, In Proceedings of the IEEE –

International Conference on Signal and Image Processing, pp 243-249, 2010. [3] HildebandSekhon, “Objective Determination of Noise Level in Doppler Spectra”, Journal of Applied Metrology,

Vol. 13.pp 808-812, 1974. [4] Moran K.P, et.al, “Signal Processing Techniques in the ARM-8mm Cloud Radars, in Proc. Ninth ARM Science

Team Meeting, San Antonio, Texas, 1999. [5] Todd K. Moon, et.al, “Mathematical Methods and Algorithms for Signal Processing”, Upper Saddle River,

NJ,Prentice Hall 2000, pp12-16, 50-51, 59, 819-832. [6] Anandan V.K., et.al., “Multi-SpectralAnalysis of Atmospheric Radar Signals”, J.Ann. Geophysciae, Vol. 22, pp.

3995-4004, © ECS, - Springer-Verlag, 2004. [7] W.K. Hocking, “Strengths and Limitations of MST radar measurements of middle - atmosphere winds”, J.Ann.

Geopysciae, Vol. 15, pp. 1111-1122, © ECS, - Springer-Verlag, 1997. AUTHORS

S. Leela Lakshmi received the B.,Tech, in Electronics and Communication Engineering and M.Tech in Atmospheric Science from Sri Venkateswara University, Tirupati from 1996. And 2001 respectively. Later, worked as Assistant Professor in various institutions. Received Ph.D. from the Sri Venkateswara University in the year 2014. Area of interests is signal processing including wavelets, image processing, radars, etc. Published over twenty-five papers in reputed national, international journals and conferences.

Rajani Kanth. V received B.Tech, M.Tech,andPh.D. from the Sri Venkateswara University, Tirupati from 1998, 2003 and 2015 respectively. Published several research papers in reputed journals and delivered expert lectures in various institutions to impart research in the field of signal processing applications in radar signals & power distribution system. Conducted various conference & technical symposiums at the national level. Also, attended conferences in national & international level. Conducted international workshop on audio signal processing, Field of interests is control systems, fuzzy systems, artificial neural network, wavelets, etc.Also, a life member of the Indian Mathematical Society. Also, having experience as an academician over a couple of decades.

enhanced signal detection using hilbert transform for … · 2019-03-17 · volume 8, issue 2,...

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