Receptor ptimo

Receptor ptimoJulin Alemn

Others Assumptions

Others Assumptions

Geometrical Approach

Facilita Facilmente una visin

Representation of S1, S2

Procedure (4 steps)

Procedure (4 steps)

Procedure summary (4 steps)

Distance between the signals s2(t) and s1(t)

Generalized Procedure for M Orthonormal functions

Noise Representation 1

Noise Representation 2

Noise Representation 3

Noise Representation 4

Noise Representation 4

El conjunto de funciones base ortonormales que elegiriamos tendrn como primeras dos funciones las funciones fi usadas para representar las dos seales s1 y s2 exactamente.Optimun Receiver

Received signalAssumptions

Optimun Receiver

Criterion of the optimal receiver

Decision Regions

19Minimum Error Probability

For two mutually exclusive eventsBayes RulesProbability of received a zero give that a one is transmitted

20Likelihood Radio

if r are equal to R2 the error probability function is minimized, increasing the negative value in the integral, therefore:

21Probability with noise AWGN 1

22Probability with noise AWGN 2

Simplifying

23Probability with noise AWGN 3

Taking logarithm of both sides

24Probability with noise AWGN 3

25Receiver implementation

26Receiver implementationExpanding the terms of

Obtain:

27Receiver implementation

28Receiver implementation

29Receiver implementation

30Receiver implementation with correlator (a matched filter) Simplifier

31Receiver implementation with correlator (a matched filter) Simplifier

32Receiver implementation with correlator (a matched filter) Simplifier

33Receiver implementation with correlator (a matched filter) Simplifier

The threshold is:

34Receiver implementation with correlator (a matched filter) Simplifier35Receiver performancethe performance of the optimum receiver, which is measured in terms of its bit error probability.36