(Solved): Question 6 (a) A ground based pulsed primary radar system is capable of detecting the range and bea ...

Question 6 (a) A ground based pulsed primary radar system is capable of detecting the range and bearing of long range ballistic objects is shown in Figure Q6(a). (i) Apply an appropriate method to find the minimum operational pulse repetitive frequency and the pulse duration for the radar installation. Use an illustration to show the time waveform of the pattern of transmitted and received pulses if a target appears at a slant range of $2,500\mathrm{km}$. (ii) The radar system of part (i) has a transmitter power of $5\mathrm{MW}$ and an antenna gain of $40\mathrm{dB}$. Determine the system signal-to-noise ratio variation in $\mathrm{dB}$ with slant range in Log Scale using MatLAB. Show with the aid of MatLAB, how the signal-to-noise ratio changes with variation in the slant range. Assume that the ambient temperature is $300\mathrm{K}$. Read off the approximate signal-to-noise ratios from the plot for slant ranges at $10\mathrm{km}$ and $6000\mathrm{km}$ respectively, after you have tagged these co-ordinates on the MatLAB plot. (b) The pulse Doppler capability of the radar system detected that the ballistic missile was approaching the ground radar station radially at a closure speed of $3000\mathrm{kts}$. If the pulsed radar system operates with a transmission frequency of $400\mathrm{MHz}$, appraise the Doppler Shift of the approaching missile in $\mathrm{Hz}$ with Matlab. Describe how you are able to find the missile's closure speed by extracting the relevant numerical data from the the spectral plots of the transmitted pulse and the received target echo.