  This paper investigates adaptive signal shaping methods for millimeter wave
(mmWave) multiple-input multiple-output (MIMO) communications based on the
maximizing the minimum Euclidean distance (MMED) criterion. In this work, we
utilize the indices of analog precoders to carry information and optimize the
symbol vector sets used for each analog precoder activation state.
Specifically, we firstly propose a joint optimization based signal shaping
(JOSS) approach, in which the symbol vector sets used for all analog precoder
activation states are jointly optimized by solving a series of quadratically
constrained quadratic programming (QCQP) problems. JOSS exhibits good
performance, however, with a high computational complexity. To reduce the
computational complexity, we then propose a full precoding based signal shaping
(FPSS) method and a diagonal precoding based signal shaping (DPSS) method,
where the full or diagonal digital precoders for all analog precoder activation
states are optimized by solving two small-scale QCQP problems. Simulation
results show that the proposed signal shaping methods can provide considerable
performance gain in reliability in comparison with existing mmWave transmission
solutions.
