I Previously on IET Phase Shift Keying PSK

Phase Shift Keying (PSK) Modulation Base band Signal X(t) 1 0 1 Band Pass

PSK Demodulation X(t)[2 cos 2(2πfct)] X(t)cos(2πfct) x Low Pass Filter X(t) 2 cos(2πfct) X(t)[2

Orthogonality of sin and cos Functions X(t)cos(2πfct) X(t)[2 sin(2πfct)cos(2πfct)] x Low Pass Filter 0

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

QPSK Demodulation x Y(t) Low Pass Filter Parallel-to. Serial 2 cos(2πfct) x XI (t)

Modulation in Time-Limited Communications Binary Encoder Cosine Modulation Transmitting Filter Binary Symbols In Phase

Modeling of In phase Modulation Binary Encoder Cosine Modulation Transmitting Filter ES=A 2 -A

Modulation in Band-Limited Communications Binary Encoder Cosine Modulation Transmitting Filter Binary Symbols In Phase

Modulation in Time-Limited Communications Binary Encoder Binary Symbols Transmitting Filter Sine Modulation Rectangular Filter

Modeling of In phase Modulation Binary Encoder Sine Modulation Transmitting Filter ES=A 2 j.

Modulation in Band-Limited Communications Binary Encoder Binary Symbols Transmitting Filter Sine Modulation Raised Cosine

Modulation Constellations BPSK QPSK 1 b/s/Hz 8 -QPSK 16 QAM 3 b/s/Hz © Tallal

Basic Communication Model in AWGN N TX S + R Channel Model R=S+N Detection

BPSK Modulation over AWGN Channels ES Energy per Symbol © Tallal Elshabrawy

BPSK Modulation over AWGN Channels Gaussian Noise 0 © Tallal Elshabrawy

BPSK Modulation over AWGN Channels Received signal distribution given 0 © Tallal Elshabrawy transmitted

BPSK Modulation over AWGN Channels Error Calculation given Symmetry of Gaussian Distribution Let 0

BPSK Modulation over AWGN Channels Error Calculation given Let 0 © Tallal Elshabrawy transmitted

BPSK Modulation over AWGN Channels Signal Power & Symbol Error Performance 0 © Tallal

BER of PSK over AWGN Channels Notes: l Define N 0 Total Noise Power

QPSK Modulation over AWGN Channels ES Energy per Symbol Error given Noise on Cosine

BER of QPSK over AWGN Channels Notes: l Define N 0 Total Noise Power

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I. Previously on IET

Phase Shift Keying (PSK) Modulation Base band Signal X(t) 1 0 1 Band Pass Signal Y(t) © Tallal Elshabrawy 2

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

Orthogonality of sin and cos Functions X(t)cos(2πfct) X(t)[2 sin(2πfct)cos(2πfct)] x Low Pass Filter 0 2 sin(2πfct) X(t)[2 sin(2πfct)cos(2πfct)]=X(t) sin(4πfct)] High frequency content © Tallal Elshabrawy 4

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

QPSK Demodulation x Y(t) Low Pass Filter Parallel-to. Serial 2 cos(2πfct) x XI (t) Low Pass Filter X(t) XQ (t) 2 sin(2πfct) © Tallal Elshabrawy 6

Modulation in Time-Limited Communications Binary Encoder Cosine Modulation Transmitting Filter Binary Symbols In Phase Modulation Rectangular Filter ES=(1)2× 1=1 Time Representation 1 1 TS Frequency Representation TS 0 f -fc 0 Time Representation fc f ES=(-1)2× 1 TS -1 -fc 0 Frequency Representation f 0 0 fc f -TS © Tallal Elshabrawy 7

Modeling of In phase Modulation Binary Encoder Cosine Modulation Transmitting Filter ES=A 2 -A © Tallal Elshabrawy A

Modulation in Band-Limited Communications Binary Encoder Cosine Modulation Transmitting Filter Binary Symbols In Phase Modulation Raised Cosine Filter Time Representation ES=(1)2× 1=1 1 t Frequency Representation 1/RS -RS/2 0 RS/2 Time Representation f -fc- RS/2 -fc+ RS/2 0 fc- RS/2 -1 Frequency -RS/2 Representation 0 RS/2 f ES=(-1)2× 1 t t 0 fc fc+ RS/2 -fc- RS/2 -fc+ RS/2 0 Bit Rate = RS Bandwidth = RS 1 b/s/Hz fc- RS/2 fc fc+ RS/2 f -1/RS © Tallal Elshabrawy 9

Modeling of In phase Modulation Binary Encoder Cosine Modulation Transmitting Filter ES=A 2 -A © Tallal Elshabrawy A

Modulation in Time-Limited Communications Binary Encoder Binary Symbols Transmitting Filter Sine Modulation Rectangular Filter In Quadrature Modulation ES=(1)2× 1=1 Time Representation 1 1 TS Frequency Representation TS fc f -fc 0 Time Representation 0 f ES=(-1)2× 1 TS -1 Frequency Representation 0 0 -fc f -TS © Tallal Elshabrawy 0 fc f 11

Modeling of In phase Modulation Binary Encoder Sine Modulation Transmitting Filter ES=A 2 j. A -j. A © Tallal Elshabrawy

Modulation in Band-Limited Communications Binary Encoder Binary Symbols Transmitting Filter Sine Modulation Raised Cosine Filter In Quadrature Modulation Time Representation ES=(1)2× 1=1 1 t Frequency Representation fc 1/RS fc- RS/2 -RS/2 0 RS/2 Time Representation f -fc- RS/2 -fc+ RS/2 ES=(-1)2× 1 t -1 Frequency -RS/2 Representation 0 RS/2 f 0 t 0 fc+ RS/2 -fc- RS/2 -fc+ RS/2 Bit Rate = RS Bandwidth = RS 1 b/s/Hz 0 fc- RS/2 fc f fc+ RS/2 -1/RS © Tallal Elshabrawy 13

Modeling of In phase Modulation Binary Encoder Sine Modulation Transmitting Filter ES=A 2 j. A -j. A © Tallal Elshabrawy

Basic Communication Model in AWGN N TX S + R Channel Model R=S+N Detection Performance: l Correct Detection l S = S* l Erroneous Detection l S ≠ S* © Tallal Elshabrawy RX Detection S*

BPSK Modulation over AWGN Channels Error Calculation given Symmetry of Gaussian Distribution Let 0 © Tallal Elshabrawy transmitted

BER of PSK over AWGN Channels Notes: l Define N 0 Total Noise Power l N 0/2 Noise Power over Cosine axis, i. e. , σ2=N 0/2 l Each symbol corresponds to a single bit l Eb = E S l Pb = P e © Tallal Elshabrawy

QPSK Modulation over AWGN Channels ES Energy per Symbol Error given Noise on Cosine axis < or Noise on Sine axis < © Tallal Elshabrawy transmitted :

BER of QPSK over AWGN Channels Notes: l Define N 0 Total Noise Power l N 0/2 Noise Power over Cosine axis, i. e. , σ2=N 0/2 l N 0/2 Noise Power over Sine axis, i. e. , σ2=N 0/2 l Each symbol MOST LIKELY corresponds to a single bit (Gray Coding) l Eb = ES/2 l Pb ≈ Pe/2 © Tallal Elshabrawy 01 11 00 10 Gray Coding: Neighbor constellations points vary in only one bit