The radio spectrum is becoming increasingly congested everyday with emerging technologies and with the increasing number of wireless devices. Considering the limited bandwidth availability, accommodating the demand for higher capacity and data rates is a challenging task, requiring innovative technologies that can offer new ways of exploiting the available radio spectrum. Cognitive radio arises to be a tempting solution to the spectral crowding problem by introducing the notion of opportunistic spectrum usage. Because of its attractive features, orthogonal frequency division multiplexing (OFDM) has been successfully used in numerous wireless standards and technologies. We believe that OFDM will play an important role in realizing the cognitive radio concept as well by providing a proven, scalable, and adaptive technology for air interface. The goal of this dissertation is to identify and address some of the challenges that arise from the introduction of cognitive radio. Specifically, we propose methods for obtaining awareness about channel, spectrum, and waveform in OFDM-based cognitive radio systems in this dissertation. Parameter estimation for enabling adaptation, spectrum sensing, and OFDM system identification are the three main topics discussed. OFDM technique is investigated as a candidate for cognitive radio systems. Cognitive radio features and requirements are discussed in detail, and OFDM's ability to satisfy these requirements is explained. In addition, we identify the challenges that arise from employing OFDM technology in cognitive radio. Algorithms for estimating various channel related parameters are presented. These parameters are vital for enabling adaptive system design, which is a key requirement for cognitive radio. We develop methods for estimating root-mean-square (RMS) delay spread, Doppler spread, and noise variance. The spectrum opportunity and spectrum sensing concepts are re-evaluated by considering different dimensions of the spectrum which is known as multi-dimensional spectrum space. Spectrum sensing problem in a multi-dimensional space is addressed by developing a new sensing algorithm termed as partial match filtering (PMF). Cognitive radios are expected to recognize different wireless networks and have capability of communicating with them. Algorithms for identification of multi-carrier transmissions are developed. Within the same work, methods for blindly detecting transmission parameters of an OFDM based system are developed. Blind detection is also very helpful in reducing system signaling overhead in the case of adaptive transmission where transmission parameters are changed depending on the environmental characteristics or spectrum availability.