The signal component of a coherent PSK system is defined by s(t) A c k sin(2f c t) + Ac 1 k 2 cos

The signal component of a coherent PSK system is defined by s(t) A_ck sin(2πf_ct) + Ac √1 – k² cos (2πf_ct) where 0 < t < Tb, and the plus sign corresponds to symbol 1 and the minus sign corresponds to symbol 0. The first term represents a carrier component included for the purpose of synchronizing the receiver to the transmitter.

(a) Draw a signal-space diagram for the scheme described here; what observations can you make about this diagram?

(b) Show that, in the presence of additive white Gaussian noise of zero mean and power spectral density N0/2, the average probability of error is where

(c) Suppose that 10 percent of the transmitted signal power is allocated to the carrier component. Determine the E_b/N₀ required to realize a probability of error equal to 10^–4. 

(d) Compare this value of E_b/N₀ with that required for a conventional PSK system with the same probability of error.

(1 - k2) No Es erfc P.