I. Previously on IET

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

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

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

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)

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)

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

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

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

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

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

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

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

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

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

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

BPSK Modulation over AWGN Channels ES  Energy per Symbol

BPSK Modulation over AWGN Channels Gaussian Noise

BPSK Modulation over AWGN Channels Received signal distribution given transmitted

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

BPSK Modulation over AWGN Channels Received signal distribution given transmitted

BPSK Modulation over AWGN Channels Error Calculation given transmitted Let

BPSK Modulation over AWGN Channels Signal Power & Symbol Error Performance

BPSK Modulation over AWGN Channels Signal Power & Symbol Error Performance

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

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

BER of QPSK over AWGN Channels 01 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