We consider two transceivers equipped with multiple antennas that intend to communicate i.e. both of which transmit and receive data in a TDD fashion. Assuming that the responses of the physical communication channels between these two nodes are linear and reciprocal (time invariant or with very slow time variations), and by exploiting the closed loop conversation between these nodes, we have proposed efficient algorithms allowing to adaptively identify the Best Singular Mode (BSM) of the channel (those algorithms are for training, blind, and semi-blind channel identification). Unlike other proposed algorithms, our proposed adaptive algorithms are 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. In practice, however, the reciprocity of the equivalent channels is lost because of the mismatch between the transmit and the receive filters of the communicating nodes. This mismatch causes significant degradation in the performance of the BSM estimation. Therefore, we have also proposed adaptive self-calibrating algorithms (which do not require any additional RF circuitry) that account for such a mismatch. In addition, we have conducted a convergence analysis of the BSM algorithm and extended it to estimate multiple modes simultaneously. Finally, we have also proposed an adaptive, iterative algorithm that is capable of allocating power in such a way that maximizes the capacity of a SISO OFDM communication system. / Thesis (Ph.D, Electrical & Computer Engineering) -- Queen's University, 2010-07-21 16:53:33.077