The Effect of β in Kaiser Window on the SNR of MST Radar Signals

INTRODUCTION

Harmonic analysis with the Discrete Fourier Transform (DFT) plays a central role in radar signal processing. The significance of using data weighting windows with the DFT (Harris, 1978; Kay, 1988; Marple, 1987) plays an important role in resolving the frequency components of the signal buried under the noise. Since the use of an in-appropriate window can lead to corruption of the principal spectral parameters it is instructive to consider the criteria by which the choice of data weighting window to be used is made (Hooper, 1999). This paper presents the effect of β in Kaiser window on the SNR of radar returns and proposed an optimum value of β with which data may be weighted using Kaiser window.

The Data Weighting Windows
Windowing
It is well known (Harris, 1978; Kay, 1988; Marple, 1987) that the application of FFT to a finite length data gives rise to leakage and picket fence effects. Weighting the data with suitable windows can reduce these effects. However the use of the data windows other than the rectangular window affects the bias, variance and frequency resolution of the spectral estimates (Kay, 1988; Marple, 1987). In general, the variance of the estimate increases with the use of a window. An estimate is to be consistent if the bias and the variance both tend to zero as the number of observations is increased. Thus, the problem associated with the spectral estimation of a finite length data by the FFT techniques is the problem of establishing efficient data windows or data smoothing schemes.

Data windows are used to weight time series of the in-phase and quadrature components of the radar return samples prior to applying the DFT. The observed Doppler spectra therefore represent convolutions of the Fourier transforms of the original signals with those of the data weighting windows, projected onto the discrete (angular) frequencies (Harris, 1978).

Spectral Leakage
For signal frequencies, observed through the rectangular window, which do not correspond exactly to one of the sampling frequencies, the pattern is shifted such that non-zero values are projected onto all sampling frequencies. This phenomenon of spreading signal power from the nominal frequency across the entire width of the observed spectrum is known as spectral leakage (Harris, 1978).

The radar returns considered to be composed of a quasi-monotonic (atmospheric) signal superimposed on a background of white noise. As might be expected, since the signal does not correspond exactly to one of the sampling frequencies, the forms of the signal portions of the spectra follow those of the envelopes of the side lobe maxima. Spectral leakage from the signal therefore exceeds noise level, evaluated by the method (Hildebrand and Sekhon, 1974) and a corresponding underestimate of signal-to-noise ratio.

The Kaiser Window
It is a relatively simple approximation of the prolate spheroidal functions. For discrete time the Kaiser window is expressed as (Alan and Schafer, 1988; Kay, 1988):

(1)

Where:

In contrast to the other windows, the Kaiser window has two parameters: The length of the sequence N and a shape parameter β. As the length of the window is fixed to 512 data points here, the shape parameter β can be varied. As the parameter β increases the side lobe level of the frequency response decreases (Alan and Schafer, 1988). In this paper we have investigated the effect of β on the SNR of MST radar data. The results are presented in Fig. 1a-f and 2a-f.

Kaiser-Window Applied to Atmospheric Radar Signals
Wind profile detection of a MST Radar signal meant the measurement of Dopplers of the signal due to scattering of the atmospheric elements. Atmospheric Radar signal meant the signal received by the Radar due to the back scattering property of the atmospheric layers, stratified or turbulent. The back-scattered signal from the atmospheric layers is very small in terms of power with which it was emitted. The received back-scattered signals otherwise called as Radar returns are associated with Gaussian noise. The noise dominates the signal as the distance between the Radar and the target increases and this leads to a decrease in Signal to Noise ratio. This makes the detection of the signal difficult. Doppler profile information is obtained from the power spectrum using Fast Fourier Transform. Frequency characteristics of the back-scattered signals of the Radar s are analyzed with power spectrum, which specifies the spectral characteristics of a signal in frequency domain.

Fig. 1:	Average SNR for the MST Radar data collected from NARL, Gadanki, India on 8th July 2002

The specifications of the data are shown in Table 1. The SNR analysis is performed on MST Radar data corresponds to the lower stratosphere obtained from the NARL, Gadanki, India, on 8th July 2002. The Radar was operated in Zenith X, Zenith Y, North, South, West and East with an angle of 10° from the vertical, direction. The data obtained from the six directions are used to carry on the analysis. The complete implementation of the scheme using C ++ and Matlab, to study the effect of β on the SNR of the radar returns can be put as follows.

Table 1:	Specifications of the MST Radar, India data on which the analysis is performed
E10y = East West polarization with off-zenith angle of 100; W10y = East West polarization with off-zenith angle of 100; N10x = North South polarization with off-zenith angle of 100; S10x = North South polarization with off-zenith angle of 100