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ece4305_L10

ece4305_L10 - Quantitative Performance Analysis ECE4305...

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Quantitative Performance Analysis ECE4305: Software-Defined Radio Systems and Analysis Professor Alexander M. Wyglinski Department of Electrical and Computer Engineering Worcester Polytechnic Institute Lecture 10 Professor Alexander M. Wyglinski ECE4305: Software-Defined Radio Systems and Analysis

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Quantitative Performance Analysis Probability of Bit Error Signal Space Concepts Mathematical Framework I Suppose that a signal s i ( t ), i = 1 , 2, was transmitted across an AWGN channel with noise signal n ( t ) I A receiver intercepts r ( t ) and needs to determine whether s 1 ( t ) or s 2 ( t ) was sent I This situation can be evaluated using Hypothesis Theory : H 1 : r ( t ) = s 1 ( t ) + n ( t ) , 0 t T H 0 : r ( t ) = s 2 ( t ) + n ( t ) , 0 t T where H 0 and H 1 are “Hypothesis 0” and “Hypothesis 1” Professor Alexander M. Wyglinski ECE4305: Software-Defined Radio Systems and Analysis
Quantitative Performance Analysis Probability of Bit Error Signal Space Concepts Decision Rule I Suppose that s 1 ( t ) was transmitted I In general, we can determine the level of correlation between two signals x ( t ) and y ( t ) over the time interval 0 t T using the expression: T Z 0 x ( t ) y ( t ) dt I Consequently, our decision rule on whether s 1 ( t ) or s 2 ( t ) was transmitted given that we observe r ( t ) is defined as: T Z 0 r ( t ) s 1 ( t ) dt T Z 0 r ( t ) s 2 ( t ) dt (1) where we assume that s 1 ( t ) was transmitted I The received signal r ( t ) is more correlated to s 1 ( t ) than s 2 ( t ) Professor Alexander M. Wyglinski ECE4305: Software-Defined Radio Systems and Analysis

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ece4305_L10 - Quantitative Performance Analysis ECE4305...

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