Digital Signal Processing Reference
In-Depth Information
example, each 256-QAM symbol carries eight bits of information,
while a QPSK symbol only carries two bits of information. But if
they both have a common symbol rate, both constellations
require the same bandwidth.
Two issues remain: the sinc impulse response decays very
slowly, and so will take a long filter (many multipliers) to
implement; and although the response of the other symbols does
go to zero at the sampling time when t
T, where N is any
integer, it can be seen visually that if the receiver samples just
a little bit to either side, the adjacent symbols will contribute. This
makes the receiver symbol-detection performance very sensitive
to the sampling timing.
The ideal would be for an impulse response that still goes to
zero at intervals of T, but decay faster and have lower amplitude
lobes, or tails. This way, when sampling a bit to one side of the
ideal sampling point, the lower amplitude tails will make the
unwanted contribution of the neighboring symbols smaller. By
making the impulse response decay faster, we can reduce the
number of taps and therefore multipliers required to implement
the pulse shaping filter.
¼
N
$
17.4 Raised Cosine Filter
There is a type of filter commonly used to meet these
requirements. It is called the “raised cosine filter”, and it has an
adjustable bandwidth, controlled by the “roll off” factor. The
trade-off will be that the bandwidth of the signal will become a bit
wider, and therefore more frequency spectrumwill be required to
transmit the signal.
Table 17.3
Raised cosine
lter frequency rolloff table
excess bandwidth refers to the
percentage of additional bandwidth required
compared to ideal low-pass
Comments
e
Roll off Factor
Label
lter
0.10
A
Requires long impulse response (high multiplier resources),
has small frequency excess bandwidth of 10%
0.25
B
A commonly used roll off factor, excess bandwidth of 25%
0.50
C
A commonly used roll off factor, excess bandwidth of 50%
1.00
D
Excess bandwidth of 100%, never used in practice
