Lecture 23

Assignment 4 (review) COMMUNICATION SYSTEMS

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Transmitter π (i − 1) ⎤ ⎡ , s i (t ) = cos ⎢ 2π f c t + 2 ⎥⎦ ⎣

Lecture # 23 2nd

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May 2007

i = 1, 2 ,3, 4 0 ≤ t ≤ Ts

The four symbols are s1,3 (t ) = ± cosωct , φ − shift o f 00 and 1800

Instructor

WASEEM KHAN

s2, 4 (t ) = ± sin ω c t , φ − shift o f 900 and 2700

Centre for Advanced Studies in Engineering

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Transmitter (another possible symbol set) π (i − 1) π ⎤ ⎡ + ⎥, s i (t ) = cos ⎢ω c t + 2 4⎦ ⎣

i = 1, 2 ,3, 4 0 ≤ t ≤ Ts

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This expression can be expanded as ⎡ π (i − 1) π ⎤ ⎡ π (i − 1) π ⎤ si (t ) = A cos ⎢ + ⎥ cos(ω c t ) − A sin ⎢ + ⎥ sin(ω c t ) 4⎦ 4⎦ ⎣ 2 ⎣ 2

In-phase part

i 1 2 3 4

⎡ π (i − 1) π ⎤ cos ⎢ + ⎥ 4⎦ ⎣ 2

0.707 -0.707 -0.707 0.707

Quadrature part ⎡ π (i − 1) π ⎤ sin ⎢ + ⎥ 4⎦ ⎣ 2

0.707 0.707 -0.707 -0.707

Quadrature Modulator

Example Run of QPSK Modulator I baseband 1 0.5 0

Baseband I and Q parts

Input bitstream

-0.5 -1

0

0.01

0.02

0.03

0.04 0.05 0.06 time(seconds) Q baseband

0.07

0.08

0.09

0.1

0

0.01

0.02

0.03

0.04 0.05 0.06 time(seconds)

0.07

0.08

0.09

0.1

1

1

0

1 0.5 0 -0.5 -1

bits =

I bandpass 1 0.5 0

Bandpass I and Q parts

-0.5 -1

0

0.01

0.02

0.03

0.04 0.05 0.06 time(seconds) Q bandpass

0.07

0.08

0.09

0.1

0

0.01

0.02

0.03

0.04 0.05 0.06 time(seconds)

0.07

0.08

0.09

0.1

1 0.5 0 -0.5 -1

1 0.5 0 -0.5 -1

0

0.05 time(seconds)

0.1

0

0

1

1

1

1

0