Most existing transceivers are Fourier-centric where complex sinusoids play a central role in the internals of the core building blocks. From the channel perspective, complex sinusoids constitute the fundamental effects in the wireless baseband equivalent channel model; exemplified by the time-invariant and time-varying transfer functions in static and time-varying channel conditions respectively. In addition, complex sinusoids are used as signaling waveforms for data transmission through the channel. The dominant mode of transmission in modern communications is in the form of finite time duration blocks having approximately finite bandwidth. As a result, the time-frequency space becomes projected to a time-frequency subspace having essentially limited support where complex sinusoids suffer from leakage effects due to the finite time extent of a block. In addition, Kronecker delta signals (duals of complex sinusoids) suffer from the same vulnerability due to the finite extent bandwidth. Gabor signaling bases using non-rectangular pulse shapes can attain good confinement in the time-frequency space, however, at the expense of completeness which reduces the utilization efficiency of the time-frequency signaling resources. Over a signaling block period, a doubly dispersive (DD) channel is projected onto an essentially limited time-frequency subspace. In this subspace, the Discrete Prolate Spheroidal (DPS) basis matched to the channel parameters is known to be optimally compact in representing the channel using a basis expansion decomposition. Unlike the Discrete Fourier Transform (DFT) basis which lacks compactness due to the leakage effect. Leakage in the expansion coefficients of a particular channel using the DFT basis has a direct correspondence with the Inter-Symbol Interference (ISI) between the DFT signaling components when transmitted through the same channel. For the DPS basis, however, the correspondence is not as obvious. Nevertheless, DPS when used for signaling results in ISI compactness in the form of an exponential decay of distant ISI components. The efficacy of DPS signaling in DD channels in addition to its efficiency in modeling DD channels motivates the investigation of a new transceiver baseband architecture where DFT is supplanted by DPS. / Ph. D. / Radio communication technology is undeniably a vital organ in modern societies, witnessed by its compelling socio-economic impact. Social media terms such as Facebook and Twitter, etc., have spurred a trans-geographical neologism in the vernacular of nations across the globe. This is all thanks to the seamless ubiquity afforded by untethered wireless communication technology. High data rate wireless communication for nomadic modes of operation, movement across locations with intermittent dwelling, has been an uncontested success. However, the quality of communications while on the move at ambitiously high speeds, up to 500Km/h, is a completely different state of affairs. Orthogonal Frequency Division Multiplexing (OFDM) is the working horse technology driving all modern communication systems including Bluetooth, WiFi, 4G Long Term Evolution (LTE), High Definition TV broadcast (HDTV) and more. As the adage goes “no one size fits all”, OFDM so far has been the size that fits nomadic and relatively slow mobility modes of operation which correspond to the majority of behavior patterns of communicating entities. However, scenarios that rely on high mobility modes are gradually moving out of the fringes and into the center scene, examples being Wide-band Vehicle-to-Vehicle (V2V) and Vehicle-to-Anything (V2X) communication. Because of OFDM’s inadequacy in such high mobility conditions, both academic and industrial bodies have embarked on their research efforts to investigate signaling schemes resilient to hostile channel effects that arise in high mobility conditions. The thesis of this work is that Discrete Prolate Spheroidal (DPS) Sequences is the most suitable candidate from the list of competitors, DPS being our discovery, that has been presented by the v research community so far. We provide both theoretical arguments to demonstrate the essential merits of DPS as well as case-specific simulations to demonstrate its efficacy.