Fundamentals of Wireless Communication Engineering Technologies

Exercise Solutions

Chapter 1

1.1 and . Therefore, expanding the cosine and sine functions and collecting terms, we equate the coefficients of the complex exponentials, and we have c₀=a₀ and

1.2 It is very similar to the autocorrelation function of the random binary waveform.

1.3 . By the indepedence of x(t) from the sinusoid, we can regroup terms and write

and the result follows.

1.4 We simply take the Fourier transform of R_yy(t), given by (1.97), and by the “modulation” property in Table 1.2, S_y(f) is just S_x(f) shifted/translated by the carrier frequency.

1.5 Let y(t) be the output of the matched filter. Then y(T) is the output of the sampling operation following the matched filter. We have

Thus,

and this is exactly the correlation receiver.

Chapter 2

2.1 Cylindrical: , , and . Spherical: ...