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The growing demand on wireless communication systems to provide high data rates has brought with it the need for a flexible and efficient use of the spectrum resource, which is a scarce commodity. The regional spectrum allocation policy counteracts the free mobility of radio communication equipment. The vast majority of the available spectral resources have already been licensed, so it appears that there is little or no room to add any new services, unless some of the existing licenses are discontinued. Furthermore, recent studies and measurements have shown that vast portions of the licensed spectra are rarely used due to the inflexible spectrum regulations. The whole idea behind cognitive radio (CR) use is that it should prompt effective spectrum use, since intelligence and learning processes aid the radio system to access the spectrum effectively. The CR system has learning and understanding capabilities so that the stated goals may be achieved. In this article, we shall limit the scope of cognition to reduce mutual interference between CR-based rental (unlicensed) users (RUs) and licensed users (LUs) and in providing coexistence between them. It is expected that the rental users will be allowed to transmit and receive data over portions of spectra when primary (i.e., licensed) users are inactive. In this article, we will introduce the modulation strategies employed to realize a coexistence between the CR-based rental system and the licensed system. This is done in such a way that the RUs are invisible to the LUs. We consider the rental user accesses the unoccupied LU band in overlay fashion.