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Design of a Digital Communication System
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INTRODUCTION
The power of digital signal processing can probably be best appreciated in
the enormous progresses which have been made in the field of telecom-
munications. These progresses stem from three main properties of digital
processing:
• The flexibility and power of discrete-time processing techniques,
which allow for the low-cost deployment of sophisticated and, more
importantly, adaptive equalization and filtering modules.
• The ease of integration between low-level digital processing and high-
level information-theoretical techniques which counteract transmis-
sion errors.
• The regenerability of a digital signal: in the necessary amplification
of analog signals after transmission, the noise floor is amplified as
well, thereby limiting the processing gain. Digital signals, on the other
hand, can be exactly regenerated under reasonable SNR conditions
(Fig. 1.10).
The Communication Channel
A telecommunication system works by exploiting the propagation of elec-
tromagnetic waves in a medium. In the case of radio transmission, the
medium is the electromagnetic spectrum; in the case of land-line communi-
cations such as those in voiceband or ADSL modems, the medium is a cop-
per wire. In all cases, the properties of the medium determine two funda-
mental constraints around which any communication system is designed:
• Bandwith constraint: data transmission systems work best in the fre-
quency range over which the medium behaves linearly; over this pass-
band we can rely on the fact that a signal will be received with only
phase and amplitude distortions, and these are “good” types of dis-
tortion since they amount to a linear filter. Further limitations on the
available bandwidth can be imposed by law or by technical require-
ments and the transmitter must limit its spectral occupancy to the
prescribed frequency region.
The AM Radio Channel
A classic example of a regulated electromagnetic channel is commercial ra-
dio. Bandwidth constraints in the case of the electromagnetic spectrum
are rigorously put in place because the spectrum is a scarce resource which
needs to be shared amongst a multitude of users (commercial radio, ama-
teur radio, cellular telephony, emergency services, military use, etc). Power
constraints on radio emissions are imposed for human safety concerns. The
AM band, for instance, extends from 530 kHz to 1700 kHz; each radio sta-
tion is allotted an 8 kHz frequency slot in this range. Suppose that a speech
signal x (t ), obtained with a microphone, is to be transmitted over a slot ex-
tending from f min = 650 kHz to f max = 658 kHz. Human speech can be
modeled as a bandlimited signal with a frequency support of approximately
12 kHz; speech can, however, be filtered through a lowpass filter with cut-
off frequency 4 kHz with little loss of intelligibility so that its bandwidth can
be made to match the 8 kHz bandwidth of the AM channel.
The Baseband Signal
The upsampling by K operation, used to nar-
row the spectral occupancy of the symbol sequence to the prescribed band-
width, must be followed by a lowpass filter, to remove the multiple copies of
the upsampled spectrum; this is achieved by a lowpass filter which, in dig-
ital communication parlance, is known as the shaper since it determines
the time domain shape of the transmitted symbols. We know from Sec-
tion 11.2.1 that, ideally, we should use a sinc filter to perfectly remove all
repeated copies. Since this is clearly not possible, let us now examine the
properties that a practical discrete-time interpolator should possess in the
context of data communications.
Modem Design: The Receiver
The analog signal s (t ) created at the transmitter is sent over the telephone
channel and arrives at the receiver as a distorted and noise-corrupted signal
ˆ(t ). Again, since we are designing a purely digital communication system,
s
the receiver’s input interface is an A/D converter which, for simplicity, we
assume, is operating at the same frequency Fs as the transmitter’s D/A con-
verter. The receiver tries to undo the impairments introduced by the chan-
nel and to demodulate the received signal; its output is a binary sequence
which, in the absence of decoding errors, is identical to the sequence in-
jected into the transmitter; an abstract view of the receiver is shown in Fig-
ure 12.16.
The Effects of the Channel
If we now abandon the convenient back-to-back scenario, we have to deal
with the impairments introduced by the channel and by the signal process-
ing hardware. The telephone channels affects the received signal in three
fundamental ways:
• it adds noise to the signal so that, even in the best case, the signal-to-
noise ratio of the received signal cannot exceed a maximum limit;
• it distorts the signal, acting as a linear filter;
• it delays the signal, according to the propagation time from transmit-
ter to receiver.