Minimum-shift keying

In digital modulation, minimum-shift keying (MSK) is a type of continuous-phase frequency-shift keying that was developed in the late 1950s and 1960s. Similar to OQPSK, MSK is encoded with bits alternating between quadature 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

$s(t)\; =\; a\_\{I\}(t)\backslash cos\{\backslash left(\backslash frac\{\{\backslash pi\}t\}\{2T\}\backslash right)\}\backslash cos\{(2\{\backslash pi\}f\_\{c\}t)\}-a\_\{Q\}(t)\backslash sin\{\backslash left(\backslash frac\{\{\backslash pi\}t\}\{2T\}\backslash right)\}\backslash sin\{\backslash left(2\{\backslash pi\}f\_\{c\}t\backslash right)\}$

where $a\_\{I\}(t)$ and $a\_\{Q\}(t)$ 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,

$s(t)\; =\; \backslash cos[2\; \backslash pi\; f\_c\; t\; +\; b\_k(t)\; \backslash frac\{\backslash pi\; t\}\{2\; T\}\; +\; \backslash phi\_k]$

where b_k(t) is +1 when $a\_\{I\}(t)\; =\; a\_\{Q\}(t)$ and -1 if they are of opposite signs, and $\backslash phi\_k$ is 0 if $a\_\{I\}(t)$ is 1, and $\backslash pi$ otherwise. Therefore, the signal is modulated in frequency and phase, and the phase changes continuously and linearly.

Gaussian minimum-shift keying

GMSK is most notably used in the Global System for Mobile Communications (GSM).

See also

References

Category:Quantized radio modulation modes