Anomalous Union Bound Behavior for MFSK Signaling on Inverse Linear Channels

Application of the union bound to MFSK signaling on certain channels where probability of bit error varies in an inverse linear fashion with
E_{b}/N_{0}
can lead to the erroneous conclusion that performance degrades with increasing alphabet size. The anomaly is shown for the worst-case partial band Gaussian interference channel and the Rayleigh fading channel.