Capacity of flat-fading channels associated with a subspace-invariant detector

Space-time codes for multiple-input, multiple-output (MIMO) channels have received considerable attention due to the extraordinary spectral efficiencies offered by some space-time channels. In particular, the flat-fading channel, with identical, independently distributed gains between all transmitter and receiver pairs has been one of the space-time channels studied extensively. Most of these studies have focused on the capacity of the additive white Gaussian noise MIMO channel. When the noise-background has an unknown spatial covariance due, for example, interference, receivers that adapt to the noise background can be more robust. One way of achieving robustness involves building invariances into the receiver and channel coding. We consider receivers that are invariant both to the background covariance and to the MIMO channel transfer function. For the particular case of the flat-fading, additive white Gaussian noise channel, the MIMO capacity of the invariant receiver is calculated and compared with the capacity of the MIMO channel with an optimal receiver and known channel. The results indicate the cost of unsupervised (i.e., no training sequences) training for the combination of an unknown channel and unknown background.