  We study the coexistence problem in a two-tier heterogeneous network (HetNet)
with cognitive small cells. In particular, we consider an underlay HetNet,
where the cognitive small base station (C-SBS) is allowed to use the frequency
bands of the macro cell with an access probability (AP) as long as the C-SBS
satisfies a preset interference probability (IP) constraint at macro users
(MUs). To enhance the AP (or transmission opportunity) of the C-SBS, we propose
a learning-based algorithm for the C-SBS and exploit the distance information
between the macro base station (MBS) and MUs. Generally, the signal from the
MBS to a specific MU contains the distance information between the MBS to the
MU. We enable the C-SBS to analyze the MBS signal on a target frequency band,
and learn the distance information between the MBS and the corresponding MU.
With the learnt distance information, we calculate the upper bound of the
probability that the C-SBS may interfere with the MU, and design an AP with a
closed-form expression under the IP constraint. Numerical results indicate that
the proposed algorithm outperforms the existing methods up to $60\%$ AP (or
transmission opportunity).
