  In this work, the joint precoding across two distant transmitters (TXs),
sharing the knowledge of the data symbols to be transmitted, to two receivers
(RXs), each equipped with one antenna, is discussed. We consider a distributed
channel state information (CSI) configuration where each TX has its own local
estimate of the channel and no communication is possible between the TXs. Based
on the distributed CSI configuration, we introduce a concept of distributed
MIMO precoding. We focus on the high signal-to-noise ratio (SNR) regime such
that the two TXs aim at designing a precoding matrix to cancel the
interference. Building on the study of the multiple antenna broadcast channel,
we obtain the following key results: We derive the multiplexing gain (MG) as a
function of the scaling in the SNR of the number of bits quantizing at each TX
the channel to a given RX. Particularly, we show that the conventional Zero
Forcing precoder is not MG maximizing, and we provide a precoding scheme
optimal in terms of MG. Beyond the established MG optimality, simulations show
that the proposed precoding schemes achieve better performances at intermediate
SNR than known linear precoders.
