5. Communication System Parameters [12 points]

Consider the following communication system with constellation with 16 points in 16 dimensions

as given in Question 1.5 (second set) of Chapter 1 of the textbook. The modulation is with the

orthonormal waveforms given by (t)= Po(t-nT), for n=1,2,3,..., 15, and po(t) is the

squarcroot raised cosine pulse with T = 0.0001 and a=0.5. Find the following parameters of

the system:

• Energy per bit Es

• Rate R

• Power P,

Bandwidth W.

The second set is attached below./nA second signal set with M = 16 signals in 16 dimensions that can transmit 4 bits of information has the following signals:

So = A(+1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1, +1)

$₁ = A(+1,-1, +1, −1, +1, −1, +1, −1, +1, −1, +1, −1, +1,-1, +1, -1)

$₂ = A(+1, +1,-1, −1, +1, +1, −1, −1, +1, +1, − 1, −1, +1, +1,-1,-1)

$3 = A(+1,-1,-1, +1, +1, −1, −1, +1, +1, −1, −1, +1, +1,-1,-1, +1)

$4 = A(+1, +1, +1, +1, −1, −1, −1, −1, +1, +1, +1, +1, −1, −1, −1, −1)

$5 = A(+1,-1, +1, −1, −1, +1, −1, +1, +1, −1, +1, −1, −1, +1, −1, +1)

S6 = A(+1, +1,-1, −1, −1, −1, +1, +1, +1, +1, −1, −1, −1, −1, +1, +1)

$7 = A(+1,-1,-1, +1, −1, +1, +1, −1, +1, −1, −1, +1, −1, +1, +1, −1)

$g = A(+1, +1, +1, +1, +1, +1, +1, +1, −1, −1, −1, -1,-1,-1,-1,-1)

$9 = A(+1,-1, +1, −1, +1, −1, +1, −1, −1, +1, −1, +1,-1, +1,-1, +1)

S10 = A(+1, +1,−1, −1, +1, +1, −1, −1, −1, −1, +1, +1, −1, −1, +1, +1)

S11 = A(+1,-1, −1, +1, +1, −1, −1, +1, −1, +1, +1, −1, −1, +1, +1, -1)

$12 = A(+1, +1, +1, +1, −1, −1, −1, −1, −1, −1, −1, −1, +1, +1, +1, +1)

S13 = A(+1,-1, +1, −1, −1, +1, −1, +1, −1, +1, −1, +1, +1, −1, +1, -1)

S14 = A(+1, +1,−1, −1, −1, −1, +1, +1, −1, −1, +1, +1, +1, +1, −1, −1)

S15 = A(+1,-1,-1, +1, −1, +1, +1, −1, −1, +1, +1, −1, +1, −1, −1, +1)