<p>High PAPR is one of the major challenges in using OFDM for communication, resulting in using inefficient linear amplifiers at the transmitter, or distortion if nonlinear amplifiers are used. Means of reducing PAPR in OFDM waveforms have been extensively researched, but those methods still have some need to avoid distortion. Using a pair of complementary sequences, an OFDM signal can be created that is constant in envelope, reducing the PAPR to unity and allowing the use of nonlinear amplifiers. Sequence pairs restricted to a particular alphabet are information-inefficient so instead a means of encoding onto a pair of complementary sequences is developed such that the length of the sequence increases linearly with the number of information symbols. The structure of this constant-modulus OFDM signal can also be used at the receiver to deal with channel fading and improve performance in noise. All of these concepts are extended to two-dimensional complementary sequence pairs for use in MIMO or broadcast applications using a uniform linear array while maintaining constant modulus on all antennas. This extension also includes exploration of additional structure imposed by the method of construction in multiple dimensions.</p>

In this thesis study, joint frequency offset and channel estimation methods for single-input single-output (SISO) systems are examined. The performance of maximum likelihood estimate of the parameters are studied for different training sequences. Conventionally training sequences are designed solely for the channel estimation purpose. We present a numerical comparison of different training sequences for the joint estimation problem. The performance comparisons are made in terms of mean square estimation error (MSE) versus SNR and MSE versus the total training energy metrics. A novel estimation scheme using complementary sequences have been proposed and compared with existing schemes. The proposed scheme presents a lower estimation error than the others in almost all numerical simulations. The thesis also includes an extension for the joint channel-frequency offset estimation problem to the multi-input multi-output systems and a brief discussion for multiple frequency offset case is also given.