  As communication systems advance towards the future 6G era, the incorporation
of large-scale antenna arrays in base stations (BSs) presents challenges such
as increased hardware costs and energy consumption. To address these issues,
the use of one-bit analog-to-digital converters (ADCs)/digital-to-analog
converters (DACs) has gained significant attentions. This paper focuses on
one-bit multiple-input multiple-output (MIMO) detection in an uplink multiuser
transmission scenario where the BS employs one-bit ADCs. One-bit quantization
retains only the sign information and loses the amplitude information, which
poses a unique challenge in the corresponding detection problem. The
maximum-likelihood (ML) formulation of one-bit MIMO detection has a challenging
likelihood function that hinders the application of many high-performance
detectors developed for classic MIMO detection (under high-resolution ADCs).
While many approximate methods for the ML detection problem have been studied,
it lacks an efficient global algorithm. This paper fills this gap by proposing
an efficient branch-and-bound algorithm, which is guaranteed to find the global
solution of the one-bit ML MIMO detection problem. Additionally, a new
amplitude retrieval (AR) detection approach is developed, incorporating
explicit amplitude variables into the problem formulation. The AR approach
yields simpler objective functions that enable the development of efficient
algorithms offering both global and approximate solutions. The paper also
contributes to the computational complexity analysis of both ML and AR
detection problems. Extensive simulations are conducted to demonstrate the
effectiveness and efficiency of the proposed formulations and algorithms.
