  In this paper we address the problem of finding the sensing capacity of
sensor networks for a class of linear observation models and a fixed SNR
regime. Sensing capacity is defined as the maximum number of signal dimensions
reliably identified per sensor observation. In this context sparsity of the
phenomena is a key feature that determines sensing capacity. Precluding the SNR
of the environment the effect of sparsity on the number of measurements
required for accurate reconstruction of a sparse phenomena has been widely
dealt with under compressed sensing. Nevertheless the development there was
motivated from an algorithmic perspective. In this paper our aim is to derive
these bounds in an information theoretic set-up and thus provide algorithm
independent conditions for reliable reconstruction of sparse signals. In this
direction we first generalize the Fano's inequality and provide lower bounds to
the probability of error in reconstruction subject to an arbitrary distortion
criteria. Using these lower bounds to the probability of error, we derive upper
bounds to sensing capacity and show that for fixed SNR regime sensing capacity
goes down to zero as sparsity goes down to zero. This means that
disproportionately more sensors are required to monitor very sparse events. Our
next main contribution is that we show the effect of sensing diversity on
sensing capacity, an effect that has not been considered before. Sensing
diversity is related to the effective \emph{coverage} of a sensor with respect
to the field. In this direction we show the following results (a) Sensing
capacity goes down as sensing diversity per sensor goes down; (b) Random
sampling (coverage) of the field by sensors is better than contiguous location
sampling (coverage).
