Page 325 - Fundamentals of Radar Signal Processing

10°, what will be the actual steering angle (angle of the maximum of E(θ))?

Repeat for θ = 30° and 70°.
0
19. Compute the integrated sidelobe ratios for the Barker codes in Table 4.1.
20. Determine the chip length and pulse length of a biphase-coded waveform

for a pulsed radar to meet the following requirements:

a. Rayleigh range resolution = 0.3 meter.
b. Pulse compression gain > 15 dB.

c. Maximum allowable blind range within first range ambiguity = 50

meters.
d. Less than one-quarter cycle of Doppler phase rotation across the pulse
for Doppler shifts up to 2000 Hz.

One or both parameters may have a range of allowable values. Give the
full range if this is the case.

21. Consider Barker, MPS, and pseudorandom biphase codes. State whether
each code type can meet the requirements of the previous problem. If not,
state the reason; if so, state at least one specific length that will work.

22. Compute explicitly the N = 4 = 2 Frank code. What is the sequence of
2
phases ϕ in the code (expressed as an angle in radians, e.g., 0, π/3, etc.)?
n
Compute the autocorrelation function of the detected code sequence exp

(jϕ ) explicitly by hand. Sketch the magnitude of the autocorrelation
n
function. What is the peak sidelobe level, relative to the peak of the
autocorrelation function, in dB?

23. Repeat the previous problem for an M = 4 P4 code. (Be sure to use the
complex autocorrelation function.)

24. Equation (4.134) expressed the continuous autocorrelation function s (t) of
x
a phase-coded waveform for t = kτ + η as a linear interpolation between
c
the possibly complex discrete autocorrelation values s [k] and s [k + 1] of
A
A
the code sequence s [k]. Show that this linear interpolation of the complex
A
values also linearly interpolates the real and imaginary parts of s [k] and
A
s [k + 1], but that the magnitude of the interpolated value is not the linear
A
interpolation of the magnitudes of s [k] and s [k + 1].
A
A
25. Some waveform/matched filter pairs are more sensitive to Doppler
mismatch (“less Doppler tolerant”) than others. Consider three different
waveforms, all using pulses of length τ seconds: a single simple pulse, a
single LFM pulse with βτ = 1000, and a pulse burst composed of 30 simple
pulses of length τ with a PRI of 10τ seconds. Denote the time of the peak
matched filter output when there is no Doppler shift as t . Suppose a
max
target with a Doppler shift of F = 1/τ Hz is present. The matched filter
D
does not compensate for this Doppler shift. For each waveform, what will