• Gaussian Minimum Shift Keying is a more complicated version of Minimum Shift Keying (MSK)
  • Which is a more complicated version of Frequency Shift Keying (FSK)…
  • Which is a more complicated version of Binary Frequency Shift Keying (BFSK)

BFSK

• Bits of 0 and 1 are converted to -1 and 1 and rewritten as frequencies:

• Even uglier… we can write it as:

  

• Resultingly, we get:

  

• Note that the 1s refer to high frequency sections and the 0s refer to low frequency sections

• Also, each of the corresponding sections are discontinuous

Minimum Frequency Spacing

• In order to transmit signals, we want each of the frequencies to be as “different as possible
• This is represented by orthogonality

• If we do a ton of math, we get that for BFSK, the peak frequency deviation should be

• Using this value, we can plug back into equation for BFSK and get an equation with minimal tone spacing

  

Continuous Phase FSK

• From this minimal tone spacing equation, there are a few more steps to get to MSK
• Step 1: For each bit, the phase can be written as