Post on 23-Sep-2015
description
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