Assignment:
Consider a QPSK digital modulation system over an AWGN channel as a quaternary channel with an the transmitted symbols and ˆan the detected symbol, as described.
a) Assuming that the transmitted symbols are iid with equally likely values, express the entropies H(ˆa), H(ˆa|a), H(a|ˆa) and the mutual information I(a,ˆa), as functions of the ratio Es/N0. Find their values for (Es/N0)dB = 0 dB, 10 dB, 20 dB.
b) Calculate the capacity of the quaternary channel when the symbol period is T = 1 ms, and the transmit pulse is hTx(t) = A sinc(t/T ), with amplitude A = 2 mV, while the noise PSD is N0/2 = 10-10 V2/Hz.