A mobile communication system employs binary phase shift keying with rectangular
pulses

to transmit information at a rate of one bit per seconds over a channel with (time-invariant) baseband-equivalent impulse response

Furthermore, the channel adds white Gaussian noise of spectral height . The receiver is designed under the assumption that and hence is simply a filter matched to the transmitted pulses . In summary, the communication system can be described by the following block diagram.

The objective of this problem is to determine the parameters of the equivalent tapped delay-line model between the input sequence and the output sequence . A generic block diagram for a tapped delay-line model is given below.

- Compute the convolution of the pulse shaping filter with the channel impulse response .
- How many memory elements are there in the tapped delay-line?
- What are values for the coefficients in the tapped delay-line model?
- Find the distribution (type, mean, variance, etc.) of the additive noise samples in the tapped delay line model.

2003-12-08