New analytical probability of error expressions for classes of orthogonal signals in Rayleigh fading

New exact expressions for the symbol-error rate and bit-error rate of coherent 3-ary and 4-ary orthogonal and transorthogonal signaling in slowly fading Rayleigh channels are derived. New exact error probability expressions for coherent 6-ary and 8-ary biorthogonal signaling in slow Rayleigh fading are also presented. The use of these exact expressions as accurate approximations for the error rates of M-ary orthogonal, biorthogonal, and transorthogonal signaling with arbitrary M is illustrated. Index Terms--Biorthogonal signals, bit-error rate (BER), M-ary orthogonal frequency-shift keying (FSK), orthogonal signals, Rayleigh fading, symbol-error rate (SER), transorthogonal signals.