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Detection of signals in NoisePowerPoint Presentation

Detection of signals in Noise

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Detection of signals in Noise

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Detection of signals in Noise

指導老師:黃文傑

姓名:吳政修

- Review Bayes’ formula
- Decision rules
- Maximum a posteriori probability (MAP)
- ML detection in AWGN channel

- Conditional probability:
- Total probability:
- Bayes’ formula:

- We apply the Bayes’ formula. First we assume that the 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

- 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
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
- AWGN ML detection
if for all

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

- For a correlator receiver, we consider that
1.equally likely source symbols

2.AWGN channel

Received signal

Performed by a correlator receiver

- procedure
- Set if for all