  In this paper we consider maximum-likelihood (ML) MIMO detection under
one-bit quantized observations and binary symbol constellations. This problem
is motivated by the recent interest in adopting coarse quantization in massive
MIMO systems--as an effective way to scale down the hardware complexity and
energy consumption. Classical MIMO detection techniques consider unquantized
observations, and many of them are not applicable to the one-bit MIMO case. We
develop a new non-convex optimization algorithm for the one-bit ML MIMO
detection problem, using a strategy called homotopy optimization. The idea is
to transform the ML problem into a sequence of approximate problems, from easy
(convex) to hard (close to ML), and with each problem being a gradual
modification of its previous. Then, our attempt is to iteratively trace the
solution path of these approximate problems. This homotopy algorithm is well
suited to the application of deep unfolding, a recently popular approach for
turning certain model-based algorithms into data-driven, and performance
enhanced, ones. While our initial focus is on one-bit MIMO detection, the
proposed technique also applies naturally to the classical unquantized MIMO
detection. We performed extensive simulations and show that the proposed
homotopy algorithms, both non-deep and deep, have satisfactory bit-error
probability performance compared to many state-of-the-art algorithms. Also, the
deep homotopy algorithm has attractively low computational complexity.
