page_title: Minimum-shift keying
section_title: Gaussian minimum-shift keying
hierarchical_section_title: Minimum-shift keying / Gaussian minimum-shift keying
context_page_description: In digital modulation, minimum-shift keying 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 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 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 δ = 0.5 fₘ 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.
context_section_description: Gaussian minimum-shift keying, or GMSK, is similar to standard minimum-shift keying (MSK); however, the digital data stream is first shaped with a Gaussian filter before being applied to a frequency modulator, and typically has much narrower phase shift angles than most MSK modulation systems.  This has the advantage of reducing sideband power, which in turn reduces out-of-band interference between signal carriers in adjacent frequency channels.
  However, the Gaussian filter increases the modulation memory in the system and causes intersymbol interference, making it more difficult to differentiate between different transmitted data values and requiring more complex channel equalization algorithms such as an adaptive equalizer at the receiver. GMSK has high spectral efficiency, but it needs a higher power level than QPSK, for instance, in order to reliably transmit the same amount of data.
  GMSK is most notably used in the Global System for Mobile Communications (GSM), in the Bluetooth, in the satellite communications, and Automatic Identification System (AIS) for maritime navigation.
caption: Power spectral densities of MSK and GMSK. Note that the decreasing of time-bandwidth 
    
      
        
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   negatively influences bit-error-rate performance due to increasing intersymbol interference.[9]
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