Precoding and Reception for ULA-Based Wide-Aperture MIMO

An approach is presented to compute the capacity-achieving precoder and receiver for wide-aperture MIMO with uniform linear arrays in
${\mathcal {O}}(N^{2}_{\textsf {min}})$
operations as opposed to the
${\mathcal {O}}(N^{2}_{\textsf {min}} {N_{\textsf {max}}})$
required by the singular-value decomposition of the channel matrix;
${N_{\textsf {min}}}$
and
${N_{\textsf {max}}}$
are the smallest and largest of the numbers of transmit and receive antennas. This hefty reduction in complexity comes at no cost in performance provided a parabolic wavefront model applies over the arrays, which is the case if the array apertures are not overly large relative to the range. Then, as the number of antennas grows larger, the proposed approach evolves into DFT-based precoders and receivers that are even more easily computable.