In digital modulation
, minimum-shift keying (MSK) is a type of continuous-phase frequency-shift keying
that was developed in the late 1950s by Collins Radio
employees Melvin L. Doelz and Earl T. Heald. Similar to OQPSK
, MSK is encoded with bits alternating between quadrature component
s, with the Q component delayed by half the symbol
However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half sinusoid
This results in a constant-modulus signal (constant envelope signal), which reduces problems caused by non-linear distortion. In addition to being viewed as related to OQPSK, MSK can also be viewed as a continuous-phase frequency-shift keyed (CPFSK
) signal with a frequency separation of one-half the bit rate.
In MSK the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. Thus, the maximum frequency deviation is where ''fm
'' is the maximum modulating frequency. As a result, the modulation index ''m''
is 0.5. This is the smallest FSK modulation index
that can be chosen such that the waveforms for 0 and 1 are orthogonal
. A variant of MSK called Gaussian minimum-shift keying
(GMSK) is used in the GSM mobile phone
The resulting signal is represented by the formula:
encode the even and odd information respectively with a sequence of square pulses of duration ''2T''.
has its pulse edges on