ORCID

https://orcid.org/0000-0001-6904-996X

Date of Award

Summer 2025

Language

English

Embargo Period

7-2-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Electrical and Computer Engineering

Program

Electrical and Computer Engineering

First Advisor

Aveek Dutta

Committee Members

Aveek Dutta, Dota Saha, Daphney Stavroula Zois, Marc Sanchez Net

Keywords

Wireless Communications, Modulation, Precoding, Non-stationary Channels, OFDM, MIMO

Subject Categories

Signal Processing | Systems and Communications

Abstract

Waveform design aims to achieve orthogonality among data signals/symbols across all available Degrees of Freedom (DoF) to avoid interference while transmitted over the channel. Precoding involves the decomposition of the channel matrix into orthogonal components for the purpose of constructing a precoding matrix that is then combined with the data signal to achieve orthogonality in the spatial dimension. On the other hand, modulation uses orthogonal carriers in a certain signal space to carry data symbols with minimal interference from other symbols. However, it is widely evident that next Generation (xG) wireless systems will experience very high mobility, density and time-varying multi-path propagation that will result in a highly non-stationarity of the channel states. Conventional precoding methods using SVD or QR decomposition, are unable to capture these joint spatio-temporal variations as those techniques treat the space-time-varying channel as separate independent spatial channel matrices and hence fail to achieve joint spatio-temporal orthogonality. Meanwhile, the carriers in Orthogonal Frequency Division Multiplexing (OFDM) and Orthogonal Time Frequency Space (OTFS) modulations are unable to maintain the orthogonality in the frequency and delay-Doppler domain respectively, due to the higher order physical variation like velocity (Doppler effect) or acceleration (time-varying Doppler effect). In this thesis, we derived a High Order Generalized Mercer's Theorem (HOGMT) for the orthogonal decomposition of multi-dimensional non-stationary channels, where the decomposed eigenfunctions are able to completely characterize the stochastic behavior of the channel. Based on this novel decomposition method, we proposed a joint spatio-temporal precoding, HOGMT-Precoding, which achieves interference-free communication with Channel State Information known at the Transmitter (CSIT). Further, the precoded signal is able to directly reconstruct the data signal at the receiver without complementary steps such as post-coding, so as to reduce the computational complexity at the receiver. We show that the proposed precoding is still optimal when the channel degrades to stationary cases. Through the theoretical analysis of the evolution of modulation techniques, we proposed a generic modulation method that investigates orthogonal subcarriers in eigenspace using HOGMT, referred to as Multidimensional Eigenwave Multiplexing (MEM) modulation. The modulated symbols orthogonal in the eigenspace are able to maintain their orthogonality across all the DoF when transmitting through the channel, thereby mitigating interference in channels under the multi-dimensional variation. The implementation of HOGMT using linear algebra entails high computational complexity. To address this, we proposed an explainable Neural Network (NN) to implement HOGMT, significantly reducing the complexity of MEM. Furthermore, we introduced an adaptive NN architecture by integrating the Augmented Lagrange Method (ALM). The proposed decomposition, characterization, precoding, modulation, and NN methods collectively enable a practical, reliable, and robust communication system for xG non-stationary channels.

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This work is licensed under the University at Albany Standard Author Agreement.

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