Examples with Matched Filters 2.10 2001/06/27 2005/09/20 10:50:56.733 GMT-5 Behnaam Aazhang aaz@ece.rice.edu Roy Ha rha@rice.edu Behnaam Aazhang aaz@ece.rice.edu Cauchy-Schwarz inequality correlator CSI linear matched filter signal-to-noise ratio SNR time-invariant Examples with the use of matched filters. The theory and rationale behind matched filter receivers can be found in Matched Filters.

s 1 t t for 0 t T s 2 t t for 0 t T h 1 t T t for 0 t T h 2 t T t for 0 t T

t 0 t 2 T s 1 ˜ t τ s 1 τ h 1 t τ s 1 ˜ t τ 0 t τ T t τ 0 t 1 2 T t τ 2 0 t 1 3 τ 3 t 2 2 T t 3 s 1 ˜ T T 3 3 Compared to the correlator-type demodulation ψ 1 t s 1 t E s s 11 τ 0 T s 1 τ ψ 1 τ τ 0 t s 1 τ ψ 1 τ 1 E s τ 0 t τ τ 1 E s 1 3 t 3

Assume binary data is transmitted at the rate of 1 T Hertz. 0 b 1 s 1 t s t for 0 t T 1 b -1 s 2 t s t   for   0 t T X t i P P b i s t i T