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I. Previously on IET

I. Previously on IET. QPSK Modulation over AWGN Channels. E S  Energy per Symbol. Symbol Error given transmitted : Noise on Cosine axis < or Noise on Sine axis <. BER of QPSK over AWGN Channels. Notes: Define N 0 Total Noise Power

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I. Previously on IET

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  1. I. Previously on IET

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

  3. BER of QPSK over AWGN Channels 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 01 11 10 00 Gray Coding: Neighbor constellations points vary in only one bit

  4. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 2 1 4 3

  5. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 2 1 d12 : Euclidian distance between constellation points 1 & 2 P12 : Probability received signal closer to constellation point 2 than constellation point 1 given constellation point 1 transmitted

  6. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 1 3 d13 : Euclidian distance between constellation points 1 & 3 P13 : Probability received signal closer to constellation point 3 than constellation point 1 given constellation point 1 transmitted

  7. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 1 4 d14 : Euclidian distance between constellation points 1 & 4 P14 : Probability received signal closer to constellation point 4 than constellation point 1 given constellation point 1 transmitted

  8. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 2 1 4 3

  9. Union Bound for BER Performance

  10. Union Bound for 8 PSK Modulation BER ES  Energy per Symbol M=8 001 011 000 dmin Θ 001 010 110 101 111

  11. Union Bound for 16 QAM Modulation BER ES  Energy per Symbol M=16 0010 0011 0001 0000 dmin 0110 0111 0101 0100 1110 1111 1101 1100 1010 1011 1001 1000

  12. Exact vs Union Bound BER Performance 12

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