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

Problems 733
12.7-3 Consider an FIR channel with impulse response
h[0] = 1.0, h[l] = -0.5, h[2] = 0.3
The channel noise is additive white Gaussian with spectrum N /2. Design an OFDM system
with N = 16 by (a) specifying the length of the cyclic prefix; (b) determining the N subchannel
gains; (c) deriving the bit error rate of each subchannels for BPSK modulations; (d) finding the
average bit error rate of the entire OFDM system.
12.7-4 Consider an FIR channel of order up to L. First, we apply the usual IDFT on the source data
vector via
Next, instead of applying a cyclic prefix as in Eq. (12.64b), we insert a string of L zeros in front
of every N data before transmission as in
SJ
0
(N + L) x 1
0
This zero-padded data vector is transmitted normally over the FIR channel {h[k ]). At the receiver
end, we stack up the received symbols {z[n]) into
z[N] 0
z[N - l]
Y= z[L]
+
0
z[N + L]
z[lJ z[N + 1]
Prove that
z = (wN)Y =
[ll[N]
H[N - 1]
H[+ J
This illustrates the equivalence between zero padding and cyclic prefix in OFDM.
12.7-5 Show that in AWGN channels, cyclic OFDM and zero-padded OFDM achieve identical SNRs
for the same channel input power.