1

Binary Signal Detection

In MATLAB we’ve worked some with AWGN noise and the concept of bit error probability. Let’s describe how this is measured.

2

Binary Signal Detection

3

Binary Signal Detection

)(tsi 1 logicfor Tt0 )(1 ts{ 0 logicfor T t0 )(2 ts

4

Binary Signal Detection

)(tsi 1 logicfor Tt0 )(1 ts{ 0 logicfor T t0 )(2 ts

Tt 0 2 1, i )()()( tntstr i

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Binary Signal Detection

)(tsi 1 logicfor Tt0 )(1 ts{ 0 logicfor T t0 )(2 ts

Tt 0 2 1, i )()()( tntstr i

2 ,1 )()()( 0 iTnTaTz i

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Binary Signal Detection

2 ,1 )()()( 0 iTnTaTz i

2 1, i 0 naz i

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Binary Signal Detection

2 ,1 )()()( 0 iTnTaTz i

2 1, i 0 naz i

z has two meanings (either a1 or a2), depending on whether s1(t) or s2(t) was sent.

z is sometimes called the test statistic.

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Binary Signal Detection

z has two meanings (either a1 or a2), depending on whether s1(t) or s2(t) was sent.

z is sometimes called the test statistic.

Compare z to λ ↓

λ is the threshold level of the threshold comparator

9

Binary Signal Detection

z has two meanings (either a1 or a2), depending on whether s1(t) or s2(t) was sent.

Compare z to λ ↓

λ is the threshold level of the threshold comparator

H1 z > λ H2 z < λ

10

Binary Signal Detection

z has two meanings (either a1 or a2), depending on whether s1(t) or s2(t) was sent.

λ is the threshold level of the threshold comparator

H1 z > λ H2 z < λ

11

Binary Signal Detection

z has two meanings (either a1 or a2), depending on whether s1(t) or s2(t) was sent.

λ is the threshold level of the threshold comparator

H1 z > λ H2 z < λ

z is here↑

Case 1

12

Binary Signal Detection

z has two meanings (either a1 or a2), depending on whether s1(t) or s2(t) was sent.

λ is the threshold level of the threshold comparator

H1 z > λ H2 z < λ

z is here↑

Case 2

13

Binary Signal Detection

z has two meanings (either a1 or a2), depending on whether s1(t) or s2(t) was sent.

λ is the threshold level of the threshold comparator

H1 z > λ H2 z < λ

z is here↑

Case 3