Week 4 Update

2. Outline More on Pulse Doppler Radar Finding Doppler Frequency Shift Determination of Moving/Stationary Objects on A-Scope and PPI Use of Single and Double Delay Line Cancellers Blind Speeds Received Signals from Precipitation Signal Sampling and Power Spectrum Doppler Spectrum Mean Doppler Velocity and Doppler Spectrum Variance Radar Noise

3. MTI vs. Pulse Doppler Radars Both distinguish moving objects from stationary objects by looking at the Doppler Frequency shift. MTI (moving target indication) radars Typically operate with ambiguous velocity measurements (blind speeds), but with unambiguous range measurements Pulsed Doppler Radars PRF usually high enough to operate with unambiguous Doppler measurements but with ambiguous range measurements

5. Finding Doppler Frequency Shift

6. Determining Moving Objects From A-scope A-scope is a display of echo amplitude vs. time Superposition of echoes can be helpful in separating moving objects from stationary object �Butterfly Effect�

7. Determination of Moving Objects on PPI PPI (plan position indicator) Angle vs. Range display Different method must be utilized on PPI � Delay line canceller

8. Single Delay Line Canceller

9. Frequency Response of Single Delay Line Canceller

10. Frequency Response of Single Delay Line Canceller Response is zero when

11. Frequency Response of Delay Line Cancellers

12. Frequency Response of Delay Line Cancellers Avoid blind speeds by making first blind speed greater than maximum radial velocity Increase wavelength of signal propagated Increase PRF Low radar frequencies (large wavelength) require larger antenna size High PRF results in Range Ambiguity! Example: First blind speed 600 knots Range (without ambiguity) = 130 nautical miles at 300 MHz or 13 nautical miles at 30 MHz Trade off between range and velocity ambiguities One solution is �Staggered PRF MTI�

13. Received signal from Precipitation Received signal due to point scatter is a scaled replica of the transmitted wave from but shifted by the Doppler shift Received signal Sr(t) can be expressed as: where lambda is the wavelength, Pt is the Power transmitted, G is the gain, and S is the back scattering matrix It may be rewritten as : Where A is the Amplitude times

14. Received signal from Precipitation Functional dependence of r on t results in theta varying with time. Thus the phase of the scattered wave from particle changes with it�s movement relative to the radar and the time rate of change of theta is related to the Doppler frequency shift

15. Received signal from Precipitation Precipitation is composed of a large number of hydrometeors over a large range with widely different scattering amplitudes and moving with different velocities The received voltage increment from this shell follows the other from discussed earlier. The lower and upper limits can be extended from zero to infinity so that the general form of the of the receieved voltage from and arbitrary transmitted waveform is given by:

16. Mean Power of the Received Signal One key measurement is the mean power corresponding to the received voltage, Vr(t) which can be related to the back scatter cross section per unit volume of the precipitation.

17. Signal Sampling and Power Spectrum Conversion from continuous time to discrete samples Power Spectrum Density (PSD) Describes power as a function of frequency Fourier transform of the autocorrelation function, if it can be treated as a stationary process.

18. Doppler Spectrum Backscattered power received as a function of Doppler frequency, or velocity Describes the echo of a contributing region of signal Function given as S(f), S(V), or S(?); Doppler Spectrum Spread Large difference of size means large spread Turbulence Air motion across beam

19. Average Power Average Power can be given in terms of Doppler velocity or frequency

20. Mean Doppler Velocity and Doppler Spectrum Variance A more convenient measure of the Doppler spectrum spread can be given by the variance, s2 Found from mean Doppler velocity

21. Radar Noise Thermal Noise Thermal excitation of electrons in electrical components Always exists in any electrical system Totally random, but has a normal distribution Coherent Averaging or Stacking Quantization Noise Quantization noise due to rounding errors Dithering Coherent Noise Coherent radar systems use a master oscillator to derive frequencies and timing signals Leakage from these signals into the receiver causes noise 0/p Phase Modulation