This research focuses on channel modeling and uplink detector design for the emerging multiple-input multiple-output (MIMO) paradigm deployed with an extremely large aperture array (ELAA). ELAA-MIMO represents a key technology for next-generation mobile networks, offering the potential to enhance spectral efficiency by more than an order of magnitude compared to current massive-MIMO systems. However, the significantly large array dimensions render the wireless channel spatially non-stationary, creating challenges for efficient ELAA-MIMO channel modeling and uplink detector design. More specifically, these MIMO detectors can be categorized into those that achieve linear optimality (i.e., linear minimum mean square (LMMSE) performance) and those that approach global optimality (i.e., maximum likelihood detection (MLD) performance). This thesis delves into uplink communication in ELAA-MIMO systems, focusing on the following three fundamental research problems:

1) How to develop an efficient channel model that accurately represents all the key ELAA-MIMO spatial non-stationarities?

2) How to design a low-complexity detector that can achieve LMMSE performance?

3) How to design a low-complexity detector that can approach MLD performance?

In response to these problems, three significant contributions are made in this thesis. First, a novel fading channel model is proposed for ELAA-MIMO, incorporating three key factors contributing to channel spatial non-stationarities: link-wise path loss, shadowing effects, and inconsistent line-of-sight (LoS)/non-LoS states. This model generates simulated channel data that aligns closely with published measurements from practical ELAA channels. Second, a method called user-wise singular value decomposition (UW-SVD) is proposed to speed up the convergence of current algorithms to LMMSE performance. Simulation results demonstrate that UW-SVD can accelerate existing linearly iterative algorithms by more than tenfold. Finally, projected-Jacobi (p-Jacobi) method is proposed to approach MLD performance even in semi-symmetric MIMO channels. With a strategically designed initialization vector, p-Jacobi quickly converges to MLD-optimality within a few iterations. Moreover, computer simulations show that p-Jacobi is robust to the spatial non-stationarities in ELAA channels. All these contributions advance the practical realization of ELAA-MIMO systems, potentially revolutionizing future wireless communication networks.