  We study constructive interference based block-level precoding (CI-BLP) in
the downlink of multi-user multiple-input single-output (MU-MISO) systems.
Specifically, our aim is to extend the analysis on CI-BLP to the case where the
considered number of symbol slots is smaller than that of the users. To this
end, we mathematically prove the feasibility of using the pseudo-inverse to
obtain the optimal CI-BLP precoding matrix in a closed form. Similar to the
case when the number of users is small, we show that a quadratic programming
(QP) optimization on simplex can be constructed. We also design a
low-complexity algorithm based on the alternating direction method of
multipliers (ADMM) framework, which can efficiently solve large-scale QP
problems. We further analyze the convergence and complexity of the proposed
algorithm. Numerical results validate our analysis and the optimality of the
proposed algorithm, and further show that the proposed algorithm offers a
flexible performance-complexity tradeoff by limiting the maximum number of
iterations, which motivates the use of CI-BLP in practical wireless systems.
