Digital Signal Processing Reference
In-Depth Information
Note:
Critical transmission media are linearly distorting channels, i.e. the medium
causes a change in the amplitude- and phase spectrum of the signal. Physical
reasons are frequency-dependent absorption, dispersion (sinusoidal oscillations of
different frequencies propagate at different speeds), and multipath propagation
caused by reflection at obstacles. The latter indirectly has the same effects.
DMT procedures are used in:
•
Speech band modem technology (300 - 3400 Hz)
•
Fast digital transmission via metallic wire pairs. Examples are HDSL
(High Speed Digital Subscriber Line) and ADSL (Asymmetric Digital
Subscriber Line).
•
Radio transmission via channels with multipath propagation (mobile
communication or mobile telephony) including DAB (Digital Audio
Broadcasting).
DMT transmits multilevel PSK and QAM using many equidistant carrier frequencies.
This is shown in Illustration 270. It presents a DMT system for a particularly straightfor-
ward case (4-PSK). A very simple mapper distributes the bit stream on two channels
(serial parallel conversion). One channel represents the real part, the other the imaginary
part. The effect is that the symbolic length (bit duration) doubles.
In principle, this is what a demultiplexer does. It conducts a serial parallel conversion by
splitting the two input channels into, for example, 1000 parallel channels. Thus the
symbolic duration is additionally increased by the factor 1000. A precondition is that the
2 times 1000 output signals are synchronous. Therefore the demultiplexer needs to buffer
the 2 times 1000 channels and output them simultaneously. In addition, the output signals
need to be bipolar.
After pre-filtering to reduce the bandwidth of the rectangular sequences each real-part bit
pattern is multiplied with a cosine-shaped carrier, and the imaginary bit pattern with a
sinusoidal carrier of a given frequency f
k
(0 < k < 1001). The situation is quite simple
because with PSK the amplitudes of all carrier oscillations are always the same.
Cosine and sine-part of one carrier oscillation are added - depending on the 2-bit pattern
- to form a carrier oscillation with the phase shifts 45, 135, 225 and 315 degrees. The
output signal s
DMT
of the adder contains a total of 1000 carrier frequencies the phases of
which change in line with the rate of symbolic duration between these four values. This
is shown in Illustration 270, bottom.
This process needs to be reversed in the receiver by “projecting” the received signal into
the (three-dimensional) signal space. Illustration 267 shows that certain ranges
surrounding the signal points of the undistorted signal should not be exceeded. But errors
can still be identified by means of an effective channel coding so long as they do not occur
too often.
The complexity of a DMT system appears hardly imaginable. 1000 carrier frequencies
and more, multipliers, pre-filters, a highly complex demultiplexer etc. We tend, however,
