ps2 - Problem Set #2 EECE-595, Section II Spring 2003,...

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Problem Set #2 EECE-595, Section II Spring 2003, Adaptive Filtering Date Assigned: 03/04/03 Date Due: 03/11/03 Background One of the important applications of adaptive filtering is in the area of channel equalization for the digital communications problem of channel multipath that arises when the delayed and attenuated copies of the transmit signal are also received. In this exercise we will study this application with respect to a BPSK- based communication system and a two-ray multipath channel of the form: h c ( t ) = δ ( t ) - αδ ( t - T b ) , | α | < 1 . The symbols that we desire to transmit are binary antipodal with equal prior probabilities, i.e., a [ k ] ∈ {- 1 , 1 } , p o = p 1 = 0 . 5 . A rectangular pulse shaping function of the form: p ( t ) = 1 t [0 ,T b ] 0 otherwise . is employed in the transmit process. The effective pulse amplitude modulated (PAM) signal is of the form: x pam ( t ) = X k = -∞ a [ k ] p ( t - kT b ) . The received signal after channel impairments is of the form:
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ps2 - Problem Set #2 EECE-595, Section II Spring 2003,...

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