We consider the design of dynamic spectrum access (DSA) mechanism. Assuming heterogeneous primary channels with distinct availability statistics unknown to each secondary user (SU), we consider the auction-based approaches for spectrum access. We first apply a unit demand (UD) auction by exploring the instantaneous link condition of each SU for its throughput maximization. To address the disadvantages faced in the UD auction, we propose a learning-based unit demand (LBUD) auction. It incorporates a distributed learning of the primary channel availabilities into the auction mechanism to explore both primary channel availability statistics and instantaneous link gains of the SUs for their throughput maximization. The new mechanism not only substantially reduces communication overhead, but also improves the SUs' throughputs when the primary channels have dissimilar availability statistics. We show that the proposed LBUD auction for channel allocation among SUs preserves the strong property of the UD auction. We further propose an adaptive price increment algorithm to improve convergence speed of the iterative procedure used in the auction. Numerical results show the effectiveness of our proposed auction mechanism in terms of the throughput gain.