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I. Previously on IET
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Phase Shift Keying (PSK) Modulation
1 1 1 1 Base band Signal X(t) Band Pass Signal Y(t)
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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
![PSK Demodulation x X(t)[2cos2(2πfct)] =X(t)[1+cos(4πfct)]](http://slideplayer.com/slide/13215890/79/images/3/PSK+Demodulation+x+X%28t%29%5B2cos2%282%CF%80fct%29%5D+%3DX%28t%29%5B1%2Bcos%284%CF%80fct%29%5D.jpg "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.")
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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
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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)
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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)
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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
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Modeling of In phase Modulation
Binary Encoder Transmitting Filter Cosine Modulation ES=A2 -A A
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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
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Modeling of In phase Modulation
Binary Encoder Transmitting Filter Cosine Modulation ES=A2 -A A
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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
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Modeling of In phase Modulation
Binary Encoder Transmitting Filter Sine Modulation ES=A2 jA -jA
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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
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Modeling of In phase Modulation
Binary Encoder Transmitting Filter Sine Modulation ES=A2 jA -jA
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Modulation Constellations
BPSK QPSK 1 b/s/Hz 2 b/s/Hz 8-QPSK 16 QAM 3 b/s/Hz 4 b/s/Hz
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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*
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BPSK Modulation over AWGN Channels
ES Energy per Symbol
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BPSK Modulation over AWGN Channels
Gaussian Noise
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BPSK Modulation over AWGN Channels
Received signal distribution given transmitted
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BPSK Modulation over AWGN Channels
Error Calculation given transmitted Symmetry of Gaussian Distribution Let
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BPSK Modulation over AWGN Channels
Received signal distribution given transmitted
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BPSK Modulation over AWGN Channels
Error Calculation given transmitted Let
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BPSK Modulation over AWGN Channels
Signal Power & Symbol Error Performance
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BPSK Modulation over AWGN Channels
Signal Power & Symbol Error Performance
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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
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QPSK Modulation over AWGN Channels
ES Energy per Symbol Symbol Error given transmitted : Noise on Cosine axis < or Noise on Sine axis <
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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
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