Time-delay estimation iti radar Let xa (t) be the transmitted signal and ya(t) be the received signal in a radar system, where
and is additive random noise. The signals xa(t) and ya(t) are sampled in the receiver, according to the sampling, theorem, and are processed digitally to deter-mine the time delay and hence the distance of the object. The resulting discrete-time signals are
(a) Explain how we can measure the delay D by computing the cross-correlation rxx (l).
(b) Let x(n) be the 13-point Barker sequence
Write a program that generates the sequence y (n) , 0 ≤ n ≤ 199 for a = 0.9 and D = 20. Plot the signals x(n), y(n), 0 ≤ n ≤ 199.
(c) Compute and plot the cross-correlation Use the plot to estimate the value of the delay D.
(d) Repeat parts (b) and (c) for
(e) Repeat parts (b) and (c) for the signal sequence
which is obtained from the four-stage feedback shift register shown in Fig. P2.65. Note that x(n) is just one period of the periodic sequence obtained from the feedback shift register.
(f) Repeat parts (b) and (c) for a sequence of period N = 27 — 1, which is obtained from a seven-stage feedback shift register. Table 2.2 gives the stages connected to the modulo-2 adder for (maximal-length) shift-register sequences of length
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