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Auction based dynamic spectrum access is an efficient approach to solve the spectrum shortage problem. However, conventional spectrum auction algorithms mainly concentrated on maximizing the revenue, under which the dynamic spectrum access (DSA) users with poorer cognitive abilities are usually hard to win the auction for spectrum access. In this paper, we propose a novel waiting-time auction (WTA) algorithm to improve the winning probabilities for the DSA users with poorer cognitive abilities. Specifically, we formulate the spectrum allocation as an auction game. In the auction, all game users bid with waiting time to obtain the spectrum access opportunities, unlike the conventional approaches where users bid by using money. Correspondingly, users with poorer cognitive ability, usually having the lower time cost, can win the auction with higher probabilities through bidding longer waiting time. We prove that there exists a unique Nash equilibrium (NE) in the WTA based spectrum-allocation game and the NE is desirable for all game users. Both theoretical and simulation analyses show that our proposed WTA algorithm can effective improve the winning probabilities of users with lower cognitive abilities.