In digital modulation, minimum-shift keying (MSK) is a type of continuous-phase frequency-shift keying Similar to OQPSK, MSK is encoded with bits alternating between quadrature components, with the Q component delayed by half the symbol period.

However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half sinusoid. This results in a constant-modulus 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.

Mathematical representation:

The resulting signal is represented by the formula

where aI(t) and aQ(t) encode the even and odd information respectively with a sequence of square pulses of duration 2T. Using the trigonometric identity, this can be rewritten in a form where the phase and frequency modulation are more obvious,

where bk(t) is +1 when aI(t) = aQ(t) and -1 if they are of opposite signs, and φk is 0 if aI(t) is 1, and π otherwise. Therefore, the signal is modulated in frequency and phase, and the phase changes continuously and linearly.

Reason for Minimum Shift Keying, MSK

It is found that binary data consisting of sharp transitions between "one" and "zero" states and vice versa potentially creates signals that have sidebands extending out a long way from the carrier, and this creates problems for many radio communications systems. as any sidebands outside the allowed bandwidth cause interference to adjacent channels and any radio communications links that may be using them.