  Channel Estimation is an essential component in applications such as radar
and data communication. In multi path time varying environments, it is
necessary to estimate time-shifts, scale-shifts (the wideband equivalent of
Doppler-shifts), and the gains/phases of each of the multiple paths. With
recent advances in sparse estimation (or "compressive sensing"), new estimation
techniques have emerged which yield more accurate estimates of these channel
parameters than traditional strategies. These estimation strategies, however,
restrict potential estimates of time-shifts and scale-shifts to a finite set of
values separated by a choice of grid spacing. A small grid spacing increases
the number of potential estimates, thus lowering the quantization error, but
also increases complexity and estimation time. Conversely, a large grid spacing
lowers the number of potential estimates, thus lowering the complexity and
estimation time, but increases the quantization error. In this thesis, we
derive an expression which relates the choice of grid spacing to the
mean-squared quantization error. Furthermore, we consider the case when
scale-shifts are approximated by Doppler-shifts, and derive a similar
expression relating the choice of the grid spacing and the quantization error.
Using insights gained from these expressions, we further explore the effects of
the choice and grid spacing, and examine when a wideband model can be well
approximated by a narrowband model.
