  In this paper, we propose a constructive interference (CI)-based block-level
precoding (CI-BLP) approach for the downlink of a multi-user multiple-input
single-output (MU-MISO) communication system. Contrary to existing CI precoding
approaches which have to be designed on a symbol-by-symbol level, here a
constant precoding matrix is applied to a block of symbol slots within a
channel coherence interval, thus significantly reducing the computational costs
over traditional CI-based symbol-level precoding (CI-SLP) as the CI-BLP
optimization problem only needs to be solved once per block. For both PSK and
QAM modulation, we formulate an optimization problem to maximize the minimum CI
effect over the block subject to a block- rather than symbol-level power
budget. We mathematically derive the optimal precoding matrix for CI-BLP as a
function of the Lagrange multipliers in closed form. By formulating the dual
problem, the original CI-BLP optimization problem is further shown to be
equivalent to a quadratic programming (QP) optimization. Numerical results
validate our derivations, and show that the proposed CI-BLP scheme achieves
improved performance over the traditional CI-SLP method, thanks to the relaxed
power constraint over the considered block of symbol slots.
