digital communication

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digital communication

The above transmitter consists of two coherent QPSK transmitters. The average energy in the upper arm is 2 Joules while it is 8 Joules for the lower arm. The two outputs are added to formulate the output waveforms Si(t). The output of each QPSK transmitter is defined as:

𝑆𝑖(𝑡)=√2𝐸𝑇cos(2𝜋𝑓𝑐𝑡−(𝑖−1)𝜋2) 0≤𝑡≤𝑇

i = 1,2,3,4. fcT = integer.

Where, E is the symbol energy and T is the symbol duration time.

a) Sketch the signal space for each arm, then find the signal space for the possible output waveforms and define the DBs and DRs.

b) Calculate the average energy per symbol.

c) Evaluate the minimum average probability of error Pav[e] if the noise is assumed to be AWGN with zero mean and two-sided PSD=No/2=1W/Hz.

d) Suggest a receiver for this system

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Consider the M-ary signal given by