I. Previously on IET

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