563489578934

Sec. 5–10 Multilevel Modulated Bandpass Signaling 371
Example 5–11 QAM SIGNALING
Using Eq. (5–94), evaluate and plot a QAM signal. Let x(t) be a 4-level stair-step signal with step
levels of -3, -1, 1, 3, and step widths of 1 sec. Let y(t) be a 4-level stair-step signal with the same
step levels, but having step widths of 4 sec. Plot the QAM signal constellation. Plot x(t), y(t), and
the QAM signal over the interval 0 6 t 6 16 sec. See Example5_11.m for the solution.
The waveforms of I and Q components are represented by
x(t) = an
x n h 1 at - n D b
(5–96)
and
y(t) = an
y n h 1 at - n D b
(5–97)
where D = R and (x n , y n ) denotes one of the permitted (x i , y i ) values during the symbol time
that is centered on t = nT s = nD s. (It takes T s s to send each symbol.) h 1 (t) is the pulse shape
that is used for each symbol. If the bandwidth of the QAM signal is not to be restricted, the
pulse shape will be rectangular and of T s s duration. Some examples of QAM modem standards
are shown in Tables 5–6 and 5–7. These modems are used to provide dial-up connections
from a PC to an ISP (internet service provider).
In some applications, the timing between the x(t) and y(t) components is offset by
T s 2 = 1(2D) s. That is, x(t) would be described by Eq. (5–96), and the offset would be
described by
y(t) = an
y n h 1 at - n D - 1
2D b
(5–98)
One popular type of offset signaling is offset QPSK (OQPSK), which is identical to offset
QAM when M = 4. A special case of OQPSK when h 1 (t) has a sinusoidal type of pulse shape
is called minimum-shift keying (MSK). This type of signaling will be studied in a later section.
Furthermore, a QPSK signal is said to be unbalanced if the x(t) and y(t) components have
unequal powers or unequal data rates (or both).
OQPSK and p/4 QPSK
Offset quadrature phase-shift keying (OQPSK) is M = 4 PSK in which the allowed data transition
times for the I and Q components are offset by a 2 symbol (i.e., by 1 bit) interval. The
1
technique is described by Eqs. (5–96) and (5–98), where the offset is 1(2D). This offset
provides an advantage when nonrectangular (i.e., filtered) data pulses are used, because the
offset greatly reduces the AM on the OQPSK signal compared with the AM on the
corresponding QPSK signal. The AM is reduced because a maximum phase transition of only