Time-delay estimation iti radar Let xa (t) be the transmitted signal and ya(t) be the re...

Time-delay estimation iti radar Let x_a (t) be the transmitted signal and y_a(t) be the received signal in a radar system, where

and is additive random noise. The signals x_a(t) and y_a(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 r_xx (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