There is an increasing need for a cognitive radio (CR) that is capable of observing its environment and modifying its transmission characteristics to transmit on unused frequency bands in ways that cause no harmful interference to the primary users (PU). In this paper, we assume that the PU transmits using a conventional OFDM system. We present a non-contiguous OFDM (NC-OFDM) and a multi-block OFDM system as two possible modulation schemes for the SU. We formulate the theoretical expressions of the frequency spectrum for these two CR OFDM systems as a systematic way to study the side-lobe interference caused by the PU to the SU, and vice versa. Lastly, we discuss their implementation, complexity issues, and their BER performance.
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