Page 323 - Satellite Communications, Fourth Edition

Digital Signals 303

shown in Fig. 9.1, the DSBSC spectrum extends to twice the highest fre-
quency in the baseband spectrum. For BPSK modulation the latter is
given by Eq. (10.11) with R sym replaced with R :
b
B 2B (1 )R b (10.15)
IF
Thus, for BPSK with a rolloff factor of unity, the IF bandwidth in
hertz is equal to twice the bit rate in bits per second.
As shown in the previous section, QPSK is equivalent to the sum of
two orthogonal BPSK carriers, each modulated at a rate R b /2, and there-
fore, the symbol rate is R sym R /2. The spectra of the two BPSK mod-
b
ulated waves overlap exactly, but interference is avoided at the receiver
because of the coherent detection using quadrature carriers. Equation
(10.15) is modified for QPSK to

B (1 )R sym
IF
1 (10.16)
R b
2
An important characteristic of any digital modulation scheme is the
ratio of data bit rate to transmission bandwidth. The units for this ratio
are usually quoted as bits per second per hertz (a dimensionless ratio
in fact because it is equivalent to bits per cycle). Note that it is the data
bit rate R and not the symbol rate R sym which is used.
b
For BPSK, Eq. (10.15) gives an R /B IF ratio of 1/(1 ), and for
b
QPSK, Eq. (10.16) gives an R /B IF ratio of 2/(1 ). Thus QPSK is
b
twice as efficient as BPSK in this respect. However, more complex
equipment is required to generate and detect the QSPK modulated
signal.

10.6.4 Bit error rate for PSK modulation
Referring back to Fig. 10.13, the noise at the input to the receiver can
cause errors in the detected signal. The noise voltage, which adds to
the signal, fluctuates randomly between positive and negative values,
and thus the sampled value of signal plus noise may have the oppo-
site polarity to that of the signal alone. This would constitute an error
in the received pulse. The noise can be represented by a source at the
front of the receiver, shown in Fig. 10.13 (this is discussed in detail
in Chap. 12). It is seen that the noise is filtered by the receiver input
filter. Thus the receive filter, in addition to contributing to minimiz-
ing the ISI, must minimize noise while maximizing the received
signal. In short, it must maximize the received signal-to-noise ratio.
In practice for satellite links (or radio links), this usually can be