B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

524 PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS
Figure 10. 1 1
(a) The minimum
of the sine
function and
(b) the MSK
spectrum.
(a)
J-
(b)
This is because abrupt phase changes at the bit transition instants when we are switching
frequencies would significantly increase the signal bandwidth. FSK schemes maintaining phase
continuity are known as continuous phase FSK (CPFSK), of which MSK is one special case.
These schemes have rapid spectral roll-off and better spectral efficiency.
To maintain phase continuity in CPFSK ( or MSK), the phase at every bit transition is made
to depend on the past data sequence. Consider, for example, the data sequence 1001 . .. starting
at t = 0. The first pulse corresponding to the first bit 1 is cos [w e + (llw/2)]t over the interval
0 to T b seconds. At t = T b , this pulse ends with a phase [w e + (llw/2)]T b . The next pulse,
corresponding to the second data bit 0, is cos [w e - (llw/2)]t. To maintain phase continuity
at the transition instant, this pulse is given additional phase (w e + llw )T b . We achieve this
continuity at each transition instant kT b .
MSK being an orthogonal scheme, its error probability is given by
(10.41b)
Although this performance appears inferior to that of the optimum case in Eq. (10.41a), closer
examination tells a different story. Indeed, this result is true only ifMSK is coherently detected
as ordinary FSK using an observation interval of T b . However, recall that MSK is CPFSK,
where the phase of each pulse is dependent on the past data sequence. Hence, better performance
may be obtained by observing the received waveform over a period longer than T b • Indeed,
it can be shown that if an MSK signal is detected over an observation interval of 2T b , then the
performance of MSK is identical to that of optimum PSK, that is,
(10.41c)