Orthogonal Frequency Division Multiplexing (OFDM) technique has gained increasing popularity in both wired and wireless communication systems, mainly due to its immunity to multipath fading, which allows for a significant increase in the transmission rate. By inserting a cyclic prefix (CP) before each transmitted block longer than the length of the channel, OFDM effectively transforms a frequency selective channel into a parallel of flat-fading channels. This greatly simplifies both channel estimation and data recovery at receiver. However, these advantages come at the cost of a loss of 10-25% spectral efficiency due to the insertion of CP, and an increased sensitivity to frequency offset and Doppler spread as well as transmission nonlinearity accentuated by non-constant modulus of OFDM signals. Additionally, due to the time-varying nature of wireless channels, training sequence needs to be transmitted periodically for the purpose of channel estimation. The overhead imposed by training sequence and CP can be up to 50 percent for fast fading channels, causing significant loss of spectral efficiency. In this proposal we aim to tackle these problems with the filter bank based multi-carrier system employing a special pulse shaping filter called IOTA (isotropic orthogonal transform algorithm) to yield good time and frequency localization properties so that inter-symbol interference (ISI) and inter-carrier interference (ICI) are avoided without the use of CP. We also investigate a linearly precoded IOTA system which facilitates blind channel estimation, resulting in a spectrally efficient multi-carrier system without the transmission of training sequence in addition to the elimination of CP. In order to effectively combat carrier frequency offset and high PAPR problems in the current orthogonal frequency division multiple access (OFDMA) and single carrier frequency division multiple access (SC-FDMA) based uplink communications, we propose a novel multiple access scheme which combines IOTA with low density signature (LDS) technique. The focus of our work will be on the study and utilization of some special properties of IOTA which have been overlooked by others. We aim to leverage these properties in the equalization, decoding and channel estimation design in order to achieve optimal performance and maximum capacity with affordable computational complexity. Our goal is to provide theoretical references and guidelines for successful implementation of IOTA systems for future wireless communications.