Digital Signal Processing Reference
In-Depth Information
For example, the specification of the 802
.
3 Ethernet dll layer expects a ber
better than 1
/
10
8
[Eth05]. It is clear that this performance can simply not be
met by an uncoded wireless link, since this would require an impractically high
signal-to-noise ratio.
1
For this reason, the raw bit stream supplied by the data
link layer to the physical layer (at transmission side) is always extended with
redundant information by encoding the bit stream. Coding and error correction
are commonly regarded upon as a purely digital matter, since it involves some
decision making steps.
However, it does not imply that coding can be seen as a preprocessing step
which is completely independent from the analog back-end. The error correct-
ing capabilities offered by the coding algorithm does not come for free and
strongly depend on the amount of surplus information that is appended to the
original unencoded information stream. It is clear that a coding algorithm with
a higher coding rate
2
will have the best performance in terms of ber.How-
ever, in a bandwidth-limited wireless channel, the extra throughput caused by
coding cannot always be translated to an increased symbol
3
rate. In practice,
there are two possible answers to the increased data rate as a result of the cod-
ing process: (1) reduce the data rate of the unencoded bit stream or (2) adapt
the number of bits that are packed in a single symbol.
Unfortunately, there is no definite algorithm that provides a joint optimum for
the bit rate, coding rate, symbol rate and the modulation depth
4
at once. Find-
ing the (hopefully) optimal parameter settings is rather a process of trial and
error, within boundaries set by implementation constraints in the analog do-
main (Figure 2.1). There are a few things, though, of which the designer of a
wireless system should be fully aware. As a starting point, there is the Shannon
theorem. From the available bandwidth and the expected signal-to-noise ratio,
a good estimation can be obtained for the information capacity of an additive
white Gaussian noise (awgn) channel. If the bit rate of the unencoded data
source is substantially lower than the maximum capacity predicted by Shan-
non, the channel is used below its capabilities. When the data rate provided
by the dll is above the theoretical capacity of the channel, it is obvious that
things are predetermined to go terribly wrong, no matter how ingenious your
combination of channel coding and modulation may be. In practice, the limited
availability of computational resources in the decoder and restrictions imposed
by the modulation scheme in the analog front-end require a certain back-off
from the theoretical capacity of the channel.
2
erfc
E
N
0
. Thus, for a ber better than 1
/
10
8
,E
b
/
N
0
must be larger than 12 dB.
2
Coding rate: the average number of output symbols (bits) used to encode one source symbol (bit).
3
Symbol: a state or transition of phase, frequency and amplitude of the carrier which encodes one or more
binary data bits. The symbol rate and the smoothness of the transition between two symbols determines the
spectral footprint of the signal [Cou97].
4
Modulation depth: defines the number of bits encoded on a single analog symbol.
E.g. bpsk (1 bit/symbol), qpsk (2 bits/symbol), 8-psk (3 bits/symbol), ...
1
For bpsk,P
e
=
