Relation between bit and symbol error probabilities for frequency shift keying with limiter-discriminator-integrator detection

In M-ary, Gray coded digital communication, the bit error probability is usually approximated by the symbol error probability divided by the number of bits in a symbol. This approximation is excellent for phase shift keying (PSK) with coherent detection at high-signal-to-noise ratios and Gaussian channel. The exact bit error probability for M-ary frequency shift keying (FSK) with limiter-discriminator-integrator detection in Gaussian, Rayleigh, and Rician channels is computed. The results are compared with the approximation