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

706 DIGITAL COMMUNICATIONS UNDER LINEARLY DISTORTIVE CHANNELS
On the other hand, subcarriers with large gains should be assigned more complex constellations
and should carry many more bits in each symbol. This distribution of bits at the transmitter
according to subcarrier conditions is called bit loading. In some cases, a subcarrier gain may be
a little too low to carry n bits per symbol but too wasteful to carry n - I bits per symbol. In such
cases, the transmitter can apply additional power loading to this subcarrier. Therefore, DMT
bit loading and power loading are often complementary at the transmitter. 11• 1 2 Figure 12.14
is a simple block diagram of the highly effective DMT bit-and-power loading.
Cyclic Prefix and Channel Shortening
The principles of OFDM and DMT require that the cyclic prefix be no shorter than the order
of the FIR communication channel response. Although this requirement may be reasonable in
a well-defined environment, for many applications, channel order or delay spread may have
a large variable range. If a long cyclic prefix is always provisioned to target the worst-case
(large) delay spread, then the overall bandwidth efficiency of the OFDM/DMT communication
systems will be very low.
To overcome this problem, it is more desirable to apply an additional time domain equalizer
(TEQ) at the receiver end to shorten the effective channel order. We note that the objective of
this time domain equalizer (TEQ) is not to fully eliminate the ISi as in Sec. 13.3. Instead, the
purpose of TEQ filter GrEQ (z) is to shorten the effective order of the combined response of
channel equalizer such that
L1
GrEQ(z)H(z) ::::::; Lq[k]z - k
k=O
This channel-shortening task is less demanding than full ISi removal. By forcing L1 to be
(approximately) smaller than the original order L, a shorter cyclic prefix can be used to improve
the OFDM/DMT transmission efficiency. The inclusion of a TEQ for channel shortening is
illustrated in Fig. 12.15.
Fi g
ure 1 2. 14
Bit and power
loading in a
DMT (OFDM)
transmission
system with N
subcarriers.
Bit s Bit & power ,__ __
'-- ḻo _a_d1_· n -"-
g ---'
s N [k]
Bit Bit
oadmg
1-------(±)----+
WN
t
:
t
: N
parallel
& power >--
- -
1
s 2 [k J
ti\
utput
bit streams
Bit stream Bit&power .--
--- IH[ l] ,
_
_. loading
s, [k]
· ---,,.-
W1 _ t
Fi g ure 1 2. 15
Time domain
equalizer (TEQ)
for channel
shortening in
DMT (OFDM)
transmission
system with N
subcarriers.
Parallel
to serial
Shortened equivalent channel
FIR channel
Channelshortening
filter
OFDM
receiver