1. I. Previously on IET

2. Phase Shift Keying (PSK) Modulation1 1 1 1
Base band Signal
X(t)
Band Pass Signal
Y(t)

3. PSK Demodulation x X(t)[2cos2(2πfct)] =X(t)[1+cos(4πfct)]
Low Pass Filter x
X(t)
2cos(2πfct)
X(t)[2cos2(2πfct)] =X(t)[1+cos(4πfct)]
X(t)[2cos2(2πfct)]=X(t) +X(t)cos(4πfct)]
Base band Signal
(i.e., low frequency content)
High frequency content

4. Orthogonality of sin and cos Functions
X(t)[2sin(2πfct)cos(2πfct)]
X(t)cos(2πfct) x
Low Pass Filter
2sin(2πfct)
X(t)[2sin(2πfct)cos(2πfct)]=X(t) sin(4πfct)]
High frequency content

5. Quadrature- PSK Modulation (QPSK)
XI(t)cos(2πfct)
XI(t) x
Y(t)
cos(2πfct) +
X(t)
Serial-to-Parallel
XQ(t)
XQ(t)sin(2πfct) x
sin(2πfct)

6. QPSK Demodulation Parallel-to-Serial X (t ) x Low Pass Filter X(t) Y(t
2cos(2πfct) x
Low Pass Filter X (t ) Q
2sin(2πfct)

7. Modulation in Time-Limited Communications
Binary
Encoder
Transmitting
Filter
Cosine
Modulation
Binary
Symbols
Rectangular Filter
In Phase Modulation 
Time Representation
ES=(1)2×1=1 1 TS 1
Frequency Representation TS f f
-fc fc
Time Representation
ES=(-1)2×1 TS -1
Frequency Representation
-fc fc f f
-TS

8. Modeling of In phase Modulation
Binary
Encoder
Transmitting
Filter
Cosine
Modulation
ES=A2 -A A

9. Modulation in Band-Limited Communications
Binary
Encoder
Transmitting
Filter
Cosine
Modulation
Binary
Symbols
Raised Cosine Filter
In Phase Modulation 
Time Representation
ES=(1)2×1=1 1 t 1 t
Frequency Representation
1/RS f f
-RS/2
RS/2
-fc- RS/2
-fc+ RS/2
fc- RS/2
fc+ RS/2
-fc fc
Time Representation
ES=(-1)2×1 t t
Bit Rate = RS
Bandwidth = RS
1 b/s/Hz -1
Frequency Representation
-RS/2
RS/2
-fc- RS/2
-fc
-fc+ RS/2
fc- RS/2 fc
fc+ RS/2 f
-1/RS 9

10. Modeling of In phase Modulation
Binary
Encoder
Transmitting
Filter
Cosine
Modulation
ES=A2 -A A

11. Modulation in Time-Limited Communications
Binary
Encoder
Transmitting
Filter
Sine
Modulation
Binary
Symbols
Rectangular Filter
In Quadrature Modulation 
Time Representation
ES=(1)2×1=1 1 TS 1
Frequency Representation TS fc f
-fc f
Time Representation
ES=(-1)2×1 TS -1
Frequency Representation
-fc f f fc
-TS 11

12. Modeling of In phase Modulation
Binary
Encoder
Transmitting
Filter
Sine
Modulation
ES=A2 jA
-jA

13. Modulation in Band-Limited Communications
Binary
Encoder
Transmitting
Filter
Sine
Modulation
Binary
Symbols
Raised Cosine Filter
In Quadrature Modulation 
Time Representation
ES=(1)2×1=1 1 t 1 t
Frequency Representation
1/RS fc
fc- RS/2
fc+ RS/2 f f
-RS/2
RS/2
-fc- RS/2
-fc+ RS/2
-fc
Time Representation
ES=(-1)2×1 t t
Bit Rate = RS
Bandwidth = RS
1 b/s/Hz -1
Frequency Representation
-RS/2
RS/2
-fc- RS/2
-fc
-fc+ RS/2 f
fc- RS/2 fc
fc+ RS/2
-1/RS 13

14. Modeling of In phase Modulation
Binary
Encoder
Transmitting
Filter
Sine
Modulation
ES=A2 jA
-jA

15. Modulation Constellations
BPSK
QPSK
1 b/s/Hz
2 b/s/Hz
8-QPSK
16 QAM
3 b/s/Hz
4 b/s/Hz

16. Basic Communication Model in AWGNR S* TX RX
Detection +
Channel Model
R=S+N
Detection Performance:
Correct Detection
S = S*
Erroneous Detection
S ≠ S*

17. BPSK Modulation over AWGN Channels
ES  Energy per Symbol

18. BPSK Modulation over AWGN Channels
Gaussian Noise

19. BPSK Modulation over AWGN Channels
Received signal distribution given transmitted

20. BPSK Modulation over AWGN Channels
Error Calculation given transmitted
Symmetry of Gaussian Distribution
Let

21. BPSK Modulation over AWGN Channels
Received signal distribution given transmitted

22. BPSK Modulation over AWGN Channels
Error Calculation given transmitted
Let

23. BPSK Modulation over AWGN Channels
Signal Power & Symbol Error Performance

24. BPSK Modulation over AWGN Channels
Signal Power & Symbol Error Performance

25. BER of PSK over AWGN Channels
Notes:
Define N0 Total Noise Power
N0/2  Noise Power over Cosine axis, i.e., σ2=N0/2
Each symbol corresponds to a single bit
Eb = ES
Pb = Pe

26. QPSK Modulation over AWGN Channels
ES  Energy per Symbol
Symbol Error given transmitted :
Noise on Cosine axis <
or Noise on Sine axis <

27. BER of QPSK over AWGN Channels01 11
Notes:
Define N0 Total Noise Power
N0/2  Noise Power over Cosine axis, i.e., σ2=N0/2
N0/2  Noise Power over Sine axis, i.e., σ2=N0/2
Each symbol MOST LIKELY corresponds to a single bit (Gray Coding)
Eb = ES/2
Pb ≈ Pe/2 00 10
Gray Coding: Neighbor constellations points vary in only one bit