Distortion Analysis of Binary FSK

The performance of the binary frequency-shift keying (FSK) data system employing a conventional limiterdiscriminator detector is analyzed. Both additive noise and distortion produced by the transmitter and receiver bandpass filters are taken into account. Performance tradeoffs with respect to transmitter frequency deviation, bandpass filter shape, and bandpass filter bandwidth are investigated. Intersymbol interference caused by distortion is taken into account for each bit sequence by calculating two distortion factors. The first factor is related to the actual baseband signal distortion produced by the bandpass filters. The second factor is related to the power distortion caused by the bandpass filters. It is shown that both factors must be considered in determining the detrimental effect of distortion on system error probability. Three particular bandpass filter shapes are considered. They are the first-, second-, and third-order Butterworth filters. For each of these filter shapes the binary FSK data system is optimized over transmitter frequency deviation and bandpass filter bandwidth. It is found that the third-order Butterworth filter operating at a 3-dB bandwidth of
1.1/T
Hz, where
T
is the bit interval, coupled with a transmitter frequency deviation of
0.36/T
Hz yields the best performance for the binary FSK system with limiterdiscriminator detection. This bandwidth (64 percent of the Carson's rule bandwidth) optimizes a tradeoff between additive noise and distortion effects. This frequency deviation optimizes a tradeoff between the spike and nonspike noise components of the discriminator output. It is shown that the performance of the optimized binary FSKlimiter-discriminator system closely approaches the performance obtained by using an optimum coherent detector on the FSK signal set.