1. I. Previously on IET

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

3. 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

4. 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

5. 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

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

7. Union Bound for BER Performance

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

9. 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

10. Exact vs Union Bound BER Performance10