Communications over the Best Singular Mode of a Reciprocal MIMO Channel

We consider two nodes equipped with multiple antennas that intend to communicate i.e. both of which transmit and receive data. We model the responses of the communication channels between these nodes as linear and reciprocal (time invariant or with very slow time variations). In practice, we exploit the closed loop conversation between these nodes and present an efficient algorithm allowing to adaptively identify the Best Singular Mode (BSM) of the channel. We consider two scenarios. In the first scenario, the initial communication link is established over the BSM assuming that the exchanged data is partially known at both nodes. This scenario is suitable for channel training. In the second scenario, the BSM is adaptively updated while the real unknown data is exchanged between the nodes i.e. no capacity is wasted for channel identification. The proposed adaptive algorithm is robust to noise as the involved step-size allows a trade-off to reduce the impact of the additive noise at the expense of some estimation delay. Our computer simulations show that the proposed algorithm works efficiently in both modes of operations (training mode and simultaneous training/data transmission mode) for both static and slow fading MIMO channels and for both white and colored noises.