  Numerous linear and non-linear data-detection and precoding algorithms for
wideband massive multi-user (MU) multiple-input multiple-output (MIMO) wireless
systems that rely on orthogonal frequency-division multiplexing (OFDM) or
single-carrier frequency-division multiple access (SC-FDMA) require the
computation of the Gram matrix for each active subcarrier. Computing the Gram
matrix for each active subcarrier, however, results in excessively high
computational complexity. In this paper, we propose novel, approximate
algorithms that significantly reduce the complexity of Gram-matrix computation
by simultaneously exploiting correlation across subcarriers and channel
hardening. We show analytically that a small fraction of Gram-matrix
computations in combination with approximate interpolation schemes are
sufficient to achieve near-optimal error-rate performance at low computational
complexity in massive MU-MIMO systems. We also demonstrate that the proposed
methods exhibit improved robustness against channel-estimation errors compared
to exact Gram-matrix interpolation algorithms that typically require high
computational complexity.
