  A major challenge in sparsity pattern estimation is that small modes are
difficult to detect in the presence of noise. This problem is alleviated if one
can observe samples from multiple realizations of the nonzero values for the
same sparsity pattern. We will refer to this as "diversity". Diversity comes at
a price, however, since each new realization adds new unknown nonzero values,
thus increasing uncertainty. In this paper, upper and lower bounds on joint
sparsity pattern estimation are derived. These bounds, which improve upon
existing results even in the absence of diversity, illustrate key tradeoffs
between the number of measurements, the accuracy of estimation, and the
diversity. It is shown, for instance, that diversity introduces a tradeoff
between the uncertainty in the noise and the uncertainty in the nonzero values.
Moreover, it is shown that the optimal amount of diversity significantly
improves the behavior of the estimation problem for both optimal and
computationally efficient estimators.
