B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

PROBLEMS
Problems 73 1
12.1-1 In a QAM transmission of symbol rate 1/T = 1 MHz, assume that p(t) is a raised-cosine pulse
with roll-off factor of 0.5. The carrier frequency in use is 2.4 GHz.
(a) Derive the resulting baseband pulse part q(t) when the multipath channel impulse response
is given by
0.958(t) - 0.38 (t - T /2)
(b) Show whether the eye is open for QPSK transmission in part (a) when the channel outputs
are sampled at t = kT.
12.2-1 Consider the signal transmission model of Prob. 12.1-1.
(a) Determine the matched filter for the equivalent baseband pulse resulting from the multipath
channel.
(b) Determine the equivalent discrete time linear system transfer function H (z) between the
QAM input symbols and the matched filter output sampled at t = kT.
12.2-2 In a digital QAM system, the received baseband pulse shape is q(t) = t, ( 2 ). The channel
noise (before the matched filter) is AWGN with spectrum of N /2.
(a) Find the power spectral density of the noise w(t) at the matched filter output.
(b) Determine the mean and the variance of the sampled noise w[kT] at the matched filter
output.
(c) Show whether the noise samples w[kT] are independent.
12.3-1 In a BPSK baseband system, the discrete time channel is specified by
H(z) = 1 + 0.6z - 1
The received signal samples are
z[k] = H(z)sk + w[k]
The BPSK signal is sk = ±1 with equal probability. The discrete channel noise w[k] is additive
white Gaussian with zero mean and variance /1/ /2 such that the Eb/ N = 18.
(a) Find the probability of error if z[k] is directly sent into a BPSK decision device.
(b) Find the probability of error if z[k] first passes through a zero-forcing equalizer before a
BPSK decision device.
12.3-2 Repeat Prob. 12.3-2 if the discrete channel
H(z) = 1 + 0.9z - 1
12.3-3 Compare the BER results of Probs. 12.3-1 and 12.3-2. Observe the different depth of the channel
spectral nulls and explain their BER difference based on the different the noise amplification
effect.