Digital Transmission Techniques III: Modulation - Signals, Processes, and Systems - page 405

Digital Quadrature Amplitude Modulation (QAM)
The utilization of bandwidth has been doubled thanks to QPSK and this points the way to
a possible further drastic increase in utilization: instead of four discrete states possibly 16,
i.e. 4 < 4 states arranged in a grid, 64 (= 8 < 8) or even 256 (=16 < 16).

How can such grids be generated in the GAUSSian numerical plane? This is demonstrated
in Illustration 265. The schematic circuit diagram shows a mapper which generates two
signals with four different amplitude levels each from the incoming serial bit stream. The
black box of the DASY Lab circuit reveals that this mapper has a rather complex structure.
First, a serial parallel transducer or demultiplexer generates a 4-channel sequence of bit
patterns from the serial bit stream. Its pulse frequency is lower than that of the serial bit
stream by the factor 4.

Accordingly, this “4-bit-signal” can take on 2 4 = 16 different states instantaneously. Thus
the relevant signal space needs to consist of 16 different discrete states. The mapper now
allocates a 4-step signal to each of the 4-bit-patterns on two outputs, one for the I-signal,
the other one for the Q-signal. The 16-QAM-signal with a total of 4 <

4 = 16 signal states

arranged in a grid is created by adding the I- and the Q- components.

From a mathematical point of view one can say that the mapper
depicts a 4-bit-pattern on 16 points in the signal space.

The most important result is in the frequency domain. The bandwidth decreases by the
factor 4 as is demonstrated by comparing the zero distance of the Si-shaped spectra with
the serial bit stream and the 16-QAM-signal.

Illustration 266 shows the signal space, an eye diagram and a detail of a signal to be able
to check the regularities:

• The signal space shows 10 (there are a total of 16) different signal states which were
taken up within a short period of time. In addition, it shows which transitions to other
states took place.

• The eye diagram is very complex due to the numerous possible signal states. The
diagrams shown here are different from conventional eye diagrams in signalling
technology in that a periodical triangular oscillation with a rising and a falling ramp
is used instead of a periodic sawtooth with a rising ramp. In contrast to an oscillo-
scope, the backshift of the sawtooth cannot be suppressed. This is why the symmetry
of the eye diagrams is slightly different.

• The detail of the signal permits a better examination of the relation between I-signal,
Q-signal and 16-QAM-signal. The vertical line shows very clearly that the sum of a
sine and cosine can result in a sinusoidal signal with a different phase position and
amplitude.