I.Introduction The use of the radio spectrum is regulated by governmental rules. Almost allparts of the radio spectrum are licensed today. The FCC published a thesis in [1] where the spectrum use in the United States is presented in the aim of betterspectrum utilization.On the other hand, studies have shownthat major licensed bands are largely underutilized. This hasinitiated the idea of cognitive radio (CR), where secondaryusers are allowed to utilize the licensed bands without causing armful interference to the licensed or primary users [2].The CR technology has the potential to significantly increasethe efficiency of the spectrum utilization while maintaining the QoS requirement of the primary users. Multi-Input Multi-Output (MIMO) is the most widelyused technology in current and future wireless communicationsystems. Since OFDM can naturally provide flexibility to fill inspectrum holes over a wide bandwidth, it has been considered as one of the best candidates for the physical layer of CR systems [3], [4].The channel state information (CSI) is crucial for CR systems [5].In practice, the CSI can be estimated by using pilot tones. The selection of pilot tones will significantly affect the channel estimation performance. For conventional OFDM systems where all subcarriers can be used for transmission, the issue of pilot design has been well studied [6]. However, these methods are not effective for OFDM-based CR systems, since the subcarriers used by the primary users cannot be employed by the secondary users. Hence the available subcarriers for the secondary users may be non-contiguous which brings new challenges to pilot design.The simplest pilot design for OFDM-based CR system is to predesign pilot tones for the conventional OFDM system and then deactivates those tones already used by the primaryusers according to the result of spectrum sensing. At the receiver, the remaining activated pilot tones are used forchannel estimation. Directly implementing channel estimationbased on such pilot pattern leads to poor performance [7].To obtains satisfactory channel estimation performance, a shift pilot scheme is proposed in [7]. After predesigning pilot tonesand deactivating some of them according to the spectrumsensing result, this scheme selects some activated data subcarriersas the new pilot tones. Specifically, when a pilot toneis deactivated, its nearest activated data subcarrier is then usedas the new pilot tone. The similar idea can be also found in [8], [9]. Although such a scheme outperforms the aforementioned done, it cannot provide satisfactory performance in all cases.This is mainly because the positions of pilot tones are notoptimized.In this thesis, we propose a new practical pilot design method for MIMO-based CR systems. Unlike the above twoschemes, the proposed one does not predesign the pilot tones.The pilot design is performed after spectrum sensing (i.e.,after the set of activated subcarriers is obtained). To obtaina low-complexity method, we first formulate the pilot designin terms of a new optimiza...