Recommended Readings:

Baseband Modulation: Glover and Grant, Sec. 6.4; Sklar, Sec. 2.8

Performance Analysis, matched-filter receiver: G&G Secs. 6.2, 8.3; Sklar Secs. 3.1-3.2

Problem 1: Baseband Binary Communication

Consider a binary communication system with bit rate 1/T in which equi-probable databits 0 and 1 are, respectively, encoded by the following pulse shapes:

Suppose that the communication channel is an AWGN one with two-sided spectral density N0 / 2 with no other distortions.

a)    Plot s0 (t)  and s 1 (t) .

b)   What is the bandwidth efficiency of this modulation technique?

c)    Find the energy associated with the above pulse shapes. What is the average energy per bit, Eb ?

d)   Find the inner product between s0 (t)  and s 1 (t) .

e)    Draw s0 (t)  and s 1 (t)  as vectors in a plane. Specify the length of each vector as well as the angle between the two vectors.

f)    Obtain and draw the correlation receiver for this signaling.

g)    Find the bit error rate for this system and write it in terms of Eb / N0 .

Problem 2: Baseband Binary Communication

Consider a binary communications system with bit rate 1/T = 1 Mbps, in which equi-probable data bits 0 and 1 are, respectively, encoded by the following pulse shapes:

where  and zero elsewhere. We use an AWGN channel with two-sided spectral density N0 / 2  to transmit the data.