  In this paper, we propose a new type of array antenna, termed the Random
Frequency Diverse Array (RFDA), for an uncoupled indication of target direction
and range with low system complexity. In RFDA, each array element has a narrow
bandwidth and a randomly assigned carrier frequency. The beampattern of the
array is shown to be stochastic but thumbtack-like, and its stochastic
characteristics, such as the mean, variance, and asymptotic distribution are
derived analytically. Based on these two features, we propose two kinds of
algorithms for signal processing. One is matched filtering, due to the
beampattern's good characteristics. The other is compressive sensing, because
the new approach can be regarded as a sparse and random sampling of target
information in the spatial-frequency domain. Fundamental limits, such as the
Cram\'er-Rao bound and the observing matrix's mutual coherence, are provided as
performance guarantees of the new array structure. The features and
performances of RFDA are verified with numerical results.
