detection of signals in noise
Download
Skip this Video
Download Presentation
Detection of signals in Noise

Loading in 2 Seconds...

play fullscreen
1 / 11

Detection of signals in Noise - PowerPoint PPT Presentation


  • 101 Views
  • Uploaded on

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:.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

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


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
detection of signals in noise

Detection of signals in Noise

指導老師:黃文傑

姓名:吳政修

outline
outline
  • Review Bayes’ formula
  • Decision rules
  • Maximum a posteriori probability (MAP)
  • ML detection in AWGN channel
review bayes formula
Review Bayes’ formula
  • Conditional probability:
  • Total probability:
  • Bayes’ formula:
slide4
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.
decision rules
Decision rules
  • The optimum detector chooses to minimize

or equivalently, to maximize

  • The corresponding probability of being correct is
maximum a posteriori probability map
Maximum a posteriori probability (MAP)
  • 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
MAP detection rule
  • 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
In an AWGN channel
  • 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
Optimum receiver
  • For a correlator receiver, we consider that

1.equally likely source symbols

2.AWGN channel

Received signal

Performed by a correlator receiver

slide10
procedure
  • Set if for all
ad