controlled manner. A MLSE must be used to optimally demodulate any signal in the presence of ISI. Whenever the amount of ISI is known, such as with any partial-response signaling scheme, MLSE can be used to determine the exact symbol sequence (in the absence of noise). Since the optimal demodulation of full-response CPM already requires MLSE detection, using partial-response signaling requires little additional complexity, but can afford a comparatively smoother phase trajectory, and thus, even greater spectral efficiency. One extremely popular form of partial-response CPM is GMSK, which is used by GSM in most of the world's 2nd generation cell phones. It is also used in 802.11 FHSS, Bluetooth, and many other proprietary wireless modems. Continuous-phase frequency-shift keying Continuous-phase frequency-shift keying (CPFSK) is a commonly used variation of frequency-shift keying (FSK), which is itself a special case of analog frequency modulation. FSK is a method of modulating digital data onto a sinusoidal carrier wave, encoding the information present in the data to variations in the carrier's instantaneous frequency between one of two frequencies (referred to as the space frequency and mark frequency). In general, a standard FSK signal does not have continuous phase, as the modulated waveform switches instantaneously between two sinusoids with different frequencies. As the name suggests, the phase of a CPFSK is in fact continuous; this attribute is desirable for signals that are to be transmitted over a bandlimited channel, as discontinuities in a signal introduce wideband frequency components. In addition, some classes of amplifiers exhibit nonlinear behavior when driven with nearly discontinuous signals; this could have undesired effects on the shape of the transmitted signal. Theory If a finitely valued digital signal to be transmitted (the message) is m(t), then the corresponding CPFSK signal is where Ac represents the amplitude of the CPFSK signal, fc is the base carrier frequency, and Df is a parameter that controls the frequency deviation of the modulated signal. The integral located inside of the cosine's argument is what gives the CPFSK signal its continuous phase; an integral over any finitely valued function (which m(t) is assumed to be) will not contain any discontinuities. If the message signal is assumed to be causal, then the limits on the integral change to a lower bound of zero and a higher bound of t. Note that this does not mean that m(t) must be continuous; in fact, most ideal digital data waveforms contain