# BU EECE 522 - Notes (17 pages)

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## Notes

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- Pages:
- 17
- School:
- Binghamton University
- Course:
- Eece 522 - Estimation Theory

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13 8 Signal Processing Examples Ex 13 3 Time Varying Channel Estimation Multi Path v t Tx y t Direct Path Rx Channel changes with time if Relative motion between Rx Tx Reflectors move change with time T y t ht v t d 0 T is the maximum delay Model using a time varying D T FIR system y n p hn k v n k k 0 Coefficients change at each n to model time varying channel 1 In communication systems multipath channels degrade performance Inter symbol interference ISI flat fading frequency selective fading etc Need To First estimate the channel coefficients Second Build an Inverse Filter or Equalizer 2 Broad Scenarios 1 Signal v t being sent is known Training Data 2 Signal v t being sent is not known Blind Channel Est One method for scenario 1 is to use a Kalman Filter State to be estimated is h n hn 0 hn p T Note h here is no longer used to notate the observation model here 2 Need State Equation Assume FIR tap coefficients change slowly h n Ah n 1 u n Assume FIR taps are uncorrelated with each other uncorrelated scattering A Q Ch are Diagonal Assumed Known That is a weakness cov h 1 M 1 1 cov u n 3 Need Observation Equation Have measurement model from convolution view x n p hn k v n k w n k 0 Known training signal zero mean WGN 2 x n v T h n w n Observation Matrix is made up of the samples of the known transmitted signal State Vector is the filter coefficients 4 Simple Specific Example p 2 1 Direct Path 1 Multipath h n Ah n 1 u n 0 99 A 0 0 0 0001 Q 0 0 999 Typical Realization of Channel Coefficients 0 0001 0 Q cov u n Note hn 0 decays faster and that the random perturbation is small Book doesn t state how the initial coefficients were chosen for this realization 5 Known Transmitted Signal Noise Free Received Signal It is a bit odd that the received signal is larger than the transmitted signal Noisy Received Signal The variance of the noise in the measurement model is 2 0 1 6 Estimation Results Using Standard Kalman Filter Initialization h 1 1 0 0 T M 1 1 100I Transient due to

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