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Exact symbol error probability of m-psk for multihop transmission with regenerative relays

We determine the exact symbol error probability of M-ary phase shift keying (M-PSK) for multihop communication systems with regenerative relays, where the source terminal transmits data to the destination terminal via a set of intermediate relay stations, which perform hard decisions on the received symbols before forwarding them to their respective successor node. Both, time-invariant additive white Gaussian noise channels as well as frequency-flat fading channels are considered and we derive generic expressions, which might be easily evaluated numerically or even be given in closed-form for various cases.