On the ergodic performance of a simple closed-loop spatial multiplexing architecture

We investigate a closed-loop spatial multiplexing architecture with linear array signal processing, which can be combined with off-the-shelf single-input single-output encoders/decoders. Rather than resorting to sophisticated interference cancellation schemes, excessive noise amplification due to ill-conditioned multiple-input multiple-output (MIMO) channels is evaded by retransmission of signal parts in critical subspaces, facilitated by a low-rate feedback channel. This lets the great capacities of MIMO channels be capitalized on with low system complexity, without requiring channel state information at the transmitter end. The closed-loop architecture involves a reverse propagation of the noise power, which we study using the theory of Markov chains. Conditions are defined under which stationarity is attained, considering both infinite and finite-rate feedback, and the constrained ergodic capacity of the system is expressed. It turns out that in the case of an (8 times 8) MIMO channel with uncorrelated Rayleigh fading, the constrained capacity comes as close as 4 dB to the unconstrained ergodic MIMO capacity.