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Sec. 5–11 Minimum-Shift Keying and GMSK 383
Another form of MSK is Gaussian-filtered MSK (GMSK). For GMSK, the data
(rectangular-shaped pulses) are filtered by a filter having a Gaussian-shaped frequency
response characteristic before the data are frequency modulated onto the carrier. The transfer
function of the Gausian low-pass filter is
H(f) = e -[(f>B)2 ( ln 2>2)]
(5–116)
where B is the 3-dB bandwidth of the filter. This filter reduces the spectral sidelobes on the
transmitted MSK signal. The PSD for GMSK is difficult to evaluate analytically, but can
be obtained via computer simulation [Muroto, 1981]. The result is shown in
Fig. 5–35 for the case when the 3-dB bandwidth is 0.3 of the bit rate (i.e., BT b = 0.3). For
smaller values of BT b , the spectral sidelobes are reduced further, but the ISI increases.
BT b = 0.3 gives a good compromise for relatively low sidelobes and tolerable ISI that is
below the noise floor for cellular telephone applications. For BT b = 0.3, GMSK has lower
spectral sidelobes than those for MSK, QPSK, or OQPSK (with rectangular-shaped data
pulses). In addition, GMSK has a constant envelope, since it is a form of FM.
Consequently, GMSK can be amplified without distortion by high-efficiency Class C
amplifiers. GMSK and MSK can also be detected either coherently or incoherently.
(See Sec. 7–5.) As discussed in Chapter 8, GMSK with BT b = 0.3 is the modulation format
used in GSM cellular telephone systems.
Other digital modulation techniques, such as tamed frequency modulation (TFM),
have even better spectral characteristics than MSK [DeJager and Dekker, 1978; Pettit, 1982;
Taub and Schilling, 1986], and the optimum pulse shape for minimum spectral occupancy of
FSK-type signals has been found [Campanella, LoFaso, and Mamola, 1984].
MSK signals can be generated by using any one of several methods, as illustrated in
Fig. 5–36. Figure 5–36a shows the generation of FFSK (which is equivalent to Type I
MSK with differential encoding of the input data). Here, a simple FM-type modulator
having a peak deviation of ∆F = 1(4T b ) = (14)R is used. Figure 5–36b shows an MSK
Type I modulator that is a realization of Eq. (5–112). This is called the parallel method of
generating MSK, since parallel in-phase (I) and quadrature-phase (Q) channels are used.
Figure 5–36c shows the serial method of generating MSK. In this approach, BPSK is first
generated at a carrier frequency of f 2 = f c - ∆F, and the bandpass is filtered about f 1 = f c +
∆F to produce an MSK signal with a carrier frequency of f c . (See Prob. 5–83 to demonstrate
that this technique is correct.) More properties of MSK are given in Leib and
Pasupathy [1993].
Sections 5–9, 5–10, and 5–11, on digital bandpass signaling techniques, are summarized
in Table 5–9. The spectral efficiencies of various types of digital signals are shown for
the case when rectangular-shaped data pulses are used and for two different bandwidth
criteria—the null-to-null bandwidth and the 30-dB bandwidth. A larger value of h indicates a
better spectral efficiency. Of course, as shown in Table 5–8, raised cosine-rolloff filtering of
the rectangular pulses could be used to reduce the bandwidth and increase h. Alternatively,
Gaussian filtering could be used, but it introduces some ISI.
When designing a communication system, one is concerned with the cost and the error
performance, as well as the spectral occupancy of the signal. The topic of error performance
is covered in Chapter 7.