Page 224 - Fundamentals of Radar Signal Processing

for one CPI of data?

12. There is sometimes a concern as to whether a target will stay in the same

range bin while during the time it takes to collect a CPI of data. Sometimes
this is an issue, but often it is not. Using the PRF and number of pulses in
the CPI from the previous problem, what is the total duration of the CPI in
seconds? Consider a target moving at 100 m/s (about 224 mph). How far
does the target move during one CPI, and how does that compare to the
range bin size? What is the minimum target velocity in m/s such that the
target would move more than one range bin in range during the CPI?

13. Suppose N samples of time-domain data are collected at a sampling rate of

F samples per second. The K-point DFT of the data is computed.
s
Depending on the relative values of K and N, zero padding or data turning
is used as required. Develop a formula for the spacing of the DFT bins in
hertz.

14. Consider a sequence of 20 slow-time data samples collected at a PRF of 2
kHz. If a 1000-point DFT of this sequence is computed, what is the spacing
between DFT frequency samples in hertz?

15. Derive a condition on the DFT size K similar to that of Eq. (3.21) for a
maximum straddle loss of 1 dB. The result will depend on the value of M.
Instead of solving the appropriate equations numerically, use the first two

terms of the Taylor series for sin(x) to get a closed-form result. Figure 3.15
can be used as an approximate check on the result for the case M = 100.

16. Consider a search radar at 1 GHz (L band) with a rotating D = 10 m dish
antenna. Suppose the beamwidth is θ = 2º. What is the antenna parameter k
3
in Eq. (3.31)? What is the Nyquist sampling rate in degrees for this
antenna? If the antenna rotates at a rate of one revolution every 6 seconds,
what is the PRF required to achieve this angular sampling rate?

17. Compute the relative power ratio P in the image component of the output of
r
an I/Q receiver when there is a simultaneous mismatch of 0.1 dB in gain

and 1º in phase. Express the answer in dB. Use Fig. 3.19 to check the
answer.
18. Consider a digital I/Q architecture similar to Rader’s. Starting with the

original signal spectrum of Fig. 3.21a, assume that the signal is
demodulated from the original center frequency F to an IF of β Hz. What
0
will be the minimum required sampling rate F of the real-valued data?
s
Assuming this value for F and also that the sampling rate is reduced to the
s
minimum possible without aliasing in the last step, sketch the complete set

of spectra from the original analog spectrum X(F) to the final discrete time
spectrum Y(ω), similar to Fig. 3.21. Also show the required frequency
response H(ω) of the digital filter, assuming the upper sideband is the one