Q1. Determine the signal space representation of the four signals sk(t), k = 1, 2, 3, 4, shown below by using

as basis functions the orthonormal functions o(t) and 2 (t). Plot the signal space diagram, and show

that this signal set is equivalent to that for a four-phase PSK signal.

(1)

$2(1)

1-1-10

1.10

$₁,(1)

$2(1)

S4(1)

0

Q2. Consider the two 8-point QAM signal constellation shown below. The minimum distance between

adjacent symbol is 2 in both constellations.

(-2,2)

(2,2)

Constellation A

$3(1)

(2,-2)

(-2./3) (013) (2,3)

(0,√3)

(-1,0) (1.0)

(2.-√3)

Constellation B

i Determine the average transmitted energy per symbol for each constellation, assuming that all

the signal points in each constellation are equally likely.

ii Which of the above two constellations would you prefer to use on an AWGN channel and why?