The Cost of Uncorrelation and Noncooperation in MIMO Channels

We investigate the capacity loss for using uncorrelated Gaussian input over a multiple-input multiple-output (MIMO) linear additive-noise channel. We upper-bound the capacity loss by a universal constant C* which is independent of the channel matrix and the noise distribution. For a single-user MIMO channel with n
_t
inputs and n
_r
outputs C* = min [ 1/2, n
_r
/n
_t
log
₂
(1+n
_t
/n
_r
) ] bit per input dimension (or 2C* bit per transmit antenna per second per hertz), under both total and per-input power constraints. If we restrict attention to (colored) Gaussian noise, then the capacity loss is upper-bounded by a smaller constant C
_G
= n
_r
/2n
_r
log
₂
(n
_t
/n
_r
) for n
_r
ges n
_t
/e, and C
_G
= 0.265 otherwise, and this bound is tight for certain cases of channel matrix and noise covariance. We also derive similar bounds for the sum-capacity loss in multiuser MIMO channels. This includes in particular uncorrelated Gaussian transmission in a MIMO multiple-access channel (MAC), and "flat" Gaussian dirty-paper coding (DPC) in a MIMO broadcast channel. In the context of wireless communication, our results imply that the benefit of beamforming and spatial water-filling over simple isotropic transmission is limited. Moreover, the excess capacity of a point-to-point MIMO channel over the same MIMO channel in a multiuser configuration is bounded by a universal constant.