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ece4305_L13

# ece4305_L13 - Correlator Receiver Structure ECE4305...

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Correlator Receiver Structure ECE4305: Software-Deﬁned Radio Systems and Analysis Professor Alexander M. Wyglinski Department of Electrical and Computer Engineering Worcester Polytechnic Institute Lecture 13 Professor Alexander M. Wyglinski ECE4305: Software-Deﬁned Radio Systems and Analysis

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Correlator Receiver Structure Optimal Decision in AWGN Channels Correlator Realization Receiver Structure AWGN Vector Channel I Refer to Lecture 11 regarding optimal detection I The optimal detector is equal to: max s i p ( ρ | s i ) P ( s i ) , for i = 1 , 2 ,..., M (1) I When P ( s i ) = 1 M for all i , we get: max s i p ( ρ | s i ) , for i = 1 , 2 M (2) I The received signal is equal to: r = s i + n (3) and if we isolate for n , we get: n = r - s i (4) Professor Alexander M. Wyglinski ECE4305: Software-Deﬁned Radio Systems and Analysis
Correlator Receiver Structure Optimal Decision in AWGN Channels Correlator Realization Receiver Structure Manipulating the Gaussian Noise PDF I Recall that the joint probability density function of the noise vector N is equal to: p ( n ) = p ( n 1 , n 2 ,..., n N ) = 1 (2 πσ 2 ) N / 2 e -|| n || 2 / 2 σ 2 (5) I We can easily show that the conditional probability density function of ρ given s i is equal to: p ( ρ | s i ) = p ( ρ - s i ) = p ( n ) = 1 (2 2 ) N / 2 e -|| ρ - s i || 2 / 2 σ 2 (6) I Vector s i is a ﬁxed quantity that is known I Vector ρ is simply the addition of s i with a Gaussian noise vector n Professor Alexander M. Wyglinski ECE4305: Software-Deﬁned Radio Systems and Analysis

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Correlator Receiver Structure Optimal Decision in AWGN Channels Correlator Realization Receiver Structure
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• Spring '10
• Wy
• probability density function, Professor Alexander M. Wyglinski, Professor Alexander M., Correlator Receiver Structure, Correlator Realization Receiver, Channels Correlator Realization

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ece4305_L13 - Correlator Receiver Structure ECE4305...

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