Minimum-shift keying

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Modulation techniques
Analog modulation
AM · SSB · FM · PM · QAM · SM
Digital modulation
OOK · FSK · ASK · PSK · QAM MSK · CPM · PPM · TCM · OFDM
Spread spectrum
v • d • e FHSS · DSSS

Minimum-shift keying (MSK) is a type of continuous phase frequency-shift keying.

Similarly to OQPSK, MSK is encoded with bits alternating between quarternary 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.

The resulting signal is represented by the formula

$s(t) = a_{I}(t)\cos{\left(\frac{{\pi}t}{2T}\right)}\cos{(2{\pi}f_{c}t)}+a_{Q}(t)\sin{\left(\frac{{\pi}t}{2T}\right)}\sin{\left(2{\pi}f_{c}t\right)}$

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

$s(t) = \cos[2 \pi f_c t + b_k(t) \frac{\pi t}{2 T} + \phi_k]$

where b_k(t) is +1 when $a I (t) = a Q (t)$ and -1 if they are of opposite signs, and $φ k$ is 0 if $a I (t)$ is 1, and $π$ otherwise. Therefore, the signal is modulated in frequency and phase, and the phase continuously and linearly changes.