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

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The signal component of a coherent PSK system is defined by s(t) Ack sin(2πfct) + Ac √1 – k2 cos (2πfct) 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 Eb/N0 required to realize a probability of error equal to 10–4

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

(1 - k2) No Es erfc P.

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