# MIT 6 661 - Types of Communication (23 pages)

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## Types of Communication

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- Pages:
- 23
- School:
- Massachusetts Institute of Technology
- Course:
- 6 661 - Receivers, Antennas, and Signals

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Types of Communication Analog continuous variables with noise P error 0 0 imperfect Digital decisions discrete choices quantized noise P error 0 usually perfect Message S1 S2 or SM Modulator v t channel adds noise and distortion M ary messages where M can be infinite Received message S1 S2 or SM Demodulator hypothesize H1 HN chooses one The channel can be radio optical acoustic a memory device recorder or other objects of interest as in radar sonar lidar or other scientific observations Lec14 10 1 2 6 01 A1 Optimum Demodulator for Binary Messages Hypothesis H1 Message S1 OK Probability H2 a priori ERROR P1 S2 ERROR vb va E G V1 P2 v Demodulator design 2 D case OK vb v measured t V2 va v V 1 H1 v V2 H2 Lec14 10 2 2 6 01 How to define V1 V2 vc A2 Optimum Demodulator for Binary Messages v vb E G V1 2 D case v measured va V2 vb t How to define V1 V2 va v V H 1 1 v V2 H2 vc Minimize Perror Pe P1 p v S1 dv P2 p v S2 dv V2 V1 replace with V 1 P1 P2p v S2 P1p v S1 dv V1 Note Lec14 10 3 2 6 01 V1 p v S1 dv V2 p v S1 dv 1 A3 Optimum Demodulator for Binary Messages Pe P1 P2p v S2 P1p v S1 dv V1 To minimize Perror choose V1 P1p v S1 P2p v S2 Very general solution i e choose maximum a posteriori P MAP estimate Lec14 10 4 2 6 01 A4 Example Binary Scalar Signal Case S1 A volts S2 O volts p v S1 p v S 2 2 2N 1 v A e 2 N p v S 2 If P1 P2 P2 bias choise toward H2 and a priori information noise 1 e v 2N 2 N p v S1 P1 0 Decision threshold if P1 P2 Lec14 10 5 2 6 01 2 n N Gaussian A 2 v A p v S P2 A 2 0 H2 P1 A Threshold if P1 P2 v A5 Rule For Defining V1 Binary Scalar Case Choose V1 P1p v S1 P2p v S2 1 v 2 2N p v S2 e 2 N binary case Likelihood ratio P A 2 V1 p v S2 P1 or equivalently An A An P2 P1 V1 p v S1 For additive Gaussian noise An A v A 2 2N v 2 2N 2vA A 2 2N An P2 P1 A 2 2NAn P2 P1 A N or v A n P2 P1 choose V1 if v 2A 2 A Lec14 10 6 2 6 01 bias A6 Binary Vector Signal Case For better performance use multiple independent samples v t S1 p v S1 P2 A p v S2 P1 t 0 1 2 m S 2 m Here

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