Opportunity detection at secondary transmitters (TXs) is a key technique enabling cognitive radio (CR) networks. Such detection however cannot guarantee reliable communication at secondary receivers (RXs), especially when their association distance is long. To cope with the issue, this paper proposes a novel MAC called sense-and-predict (SaP), where each secondary TX decides whether to access or not based on the prediction of the interference level at RX. Firstly, we provide the spatial interference correlation in a probabilistic form using stochastic geometry, and utilize it to maximize the area spectral efficiency (ASE) for secondary networks while guaranteeing the service quality of primary networks. Through simulations and testbed experiments using USRP, SaP is shown to always achieve ASE improvement compared with the conventional TX based sensing.