Consider a communication system with QPSK modulation. Based on the received signal, the receiver can make any of the three decisions: ‘Correct’, ‘Error’, and ‘Erasure’. The receiver will make a decision of ‘Erasure’ if the received signal falls in the shaded region as shown in the figure below.

Note that making a decision ‘Erasure’ is not an error. If ‘Erasure’ is decided, the receiver will make a retransmission request to the transmitter.

(i) Calculate the value of the constant C in terms of energy per bit Eb.
(ii) Derive the expression of the probability of error Ps1 when symbol S1 is transmitted.
(iii) Derive the expression of the average probability of symbol error PS.

-2c-c -20 -C --C +-2C fc