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# Detection of signals in Noise - PowerPoint PPT Presentation

Detection of signals in Noise. 指導老師 : 黃文傑 姓名 : 吳政修. outline. Review Bayes’ formula Decision rules Maximum a posteriori probability (MAP) ML detection in AWGN channel. Review Bayes’ formula. Conditional probability: Total probability: Bayes’ formula:.

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## PowerPoint Slideshow about ' Detection of signals in Noise' - anais

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### Detection of signals in Noise

• Review Bayes’ formula

• Decision rules

• Maximum a posteriori probability (MAP)

• ML detection in AWGN channel

• Conditional probability:

• Total probability:

• Bayes’ formula:

Decision rules observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• The optimum detector chooses to minimize

or equivalently, to maximize

• The corresponding probability of being correct is

Maximum a posteriori probability (MAP) observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• The probability of the decision be correct, given that observing vector x, is

• The probability of error is as follows

• Thus the optimum decision observes the particular received vector X=x and the output chooses to maximize the .

MAP detection rule observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• MAP

if for all

Thus if all transmitted symbols occur equally likely, i.e.

Then the decision is equivalent to the maximum likelihood decision rule.

if for all

In an AWGN channel observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• In an AWGN channel

• AWGN ML detection

if for all

The decision is to choose a message point closest to the received signal point, which is intuitively.

Optimum receiver observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• For a correlator receiver, we consider that

1.equally likely source symbols

2.AWGN channel