  We investigate the effects of finite sky coverage on the spectral resolution
$\Delta\ell$ in the estimation of the CMBR angular power spectrum $C^{\ell}$. A
method is developed for obtaining quasi-independent estimates of the power
spectrum, and the cosmic/sample variance of these estimates is calculated. The
effect of instrumental noise is also considered for prototype interferometer
and single-dish experiments. By proposing a statistic for the detection of
secondary (Doppler) peaks in the CMBR power spectrum, we then compute the
significance level at which such peaks may be detected for a large range of
model CMBR experiments. In particular, we investigate experimental design
features required to distinguish between competing cosmological theories, such
as cosmic strings and inflation, by establishing whether or not secondary peaks
are present in the CMBR power spectrum.
