  Multiple-user multiple-input multiple-output applications have recently
gained a lot of attention. Here, we show an efficient optimization formulation
for the design of all the temporal and spatial degrees of freedom of an
acoustic reconfigurable metasurface for the cocktail party problem. In the
frequency domain, the closed-form least square solution matches the optimal
time reversal solution for multiple emitter-receiver pairs, optimizing for each
frequency independently. This is more efficient than solving in the time domain
where the time convolution mixes all the degrees of freedom into a
resource-intensive optimization. We illustrate this methodology by optimizing
the frequency response of a design for two pairs of emitters-receivers using
the Green's functions of disordered media that are measured experimentally. We
report strong performance that will be put in perspective in future work, where
we will analyze the robustness of the design to noise in the data and design
the convolutional filters that match the optimal frequency response for
experiment validation of the design.
