Detecting Signals in Gaussian Noise

# Detecting Signals in Gaussian Noise - Detection and...

This preview shows pages 1–7. Sign up to view the full content.

Detection and Estimation (Spring , 2009) Detecting Signals in Gaussian Noise NCTU EE P.1 Detecting Signals in Gaussian Noise ~ Matched Filters Detecting a known deterministic signal in white Gaussian noise. s[n]: known w[n]: WGN with variance σ 2 We’ll decide H 1 if γ ’ is chosen to satisfy P

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Detection & Estimation (Spring, 2009) Detecting Signals in Gaussian Noise NCTU EE P.2 correlator (replica-correlator) Alternative Interpretation: matched filter For a linear, time-invariant filter, we have Let At n = N-1, Remark: For signals with unknown arrival times, we cannot use the matched filter in its present form.
Detection & Estimation (Spring, 2009) Detecting Signals in Gaussian Noise NCTU EE P.3 Example: In the frequency domain, Remarks: 9 The matched filter emphasizes the bands where there is more signal power. 9 When the noise is absent or X(f) = S(f), the matched filter output is just the signal energy.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Detection & Estimation (Spring, 2009) Detecting Signals in Gaussian Noise NCTU EE P.4 Maximum SNR Property Consider all possible FIR filter detectors. The output SNR is defined as s = [s[0] s[1] … s[N-1]] T h = [h[N-1] h[N-2] … h[0]] T w = [w[0] w[1] … w[N-1]] T By the Cauchy-Schwarz inequality, with equality if and only if h = c s . Hence, and the maximum output SNR is attained for Remarks: 9 For the detection problem of a known deterministic signal in WGN, the NP criterion and the maximum SNR criterion both lead to the matched filter detector. 9 For nonGaussian noise, the matched filter is not optimal in the NP sense but may still be said to maximize the SNR at the output of a linear FIR filter. (In the nonGaussian noise case, the NP detector is not linear!) 9 The matched filter maximizes the SNR at the output of any linear filter.
Detection & Estimation (Spring, 2009) Detecting Signals in Gaussian Noise NCTU EE P.5 Performance of Matched Filter Let

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Detection & Estimation (Spring, 2009) Detecting Signals in Gaussian Noise NCTU EE P.6 Remarks: 9 To improve the detection performance, we can always increase P
This is the end of the preview. Sign up to access the rest of the document.

### Page1 / 22

Detecting Signals in Gaussian Noise - Detection and...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online