Computation of the Bit Error Rate of Coherent M-ary PSK with Gray Code Bit Mapping

Efficient computation of the bit error rate (BER) for the coherent
M
-ary PSK signals with Gray code bit mapping is considered. A closed-form expression for the exact BER of 8-ary PSK is presented. Tight upper and lower bounds on BER are also obtained for
M
-ary PSK with larger
M
.