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This paper provides an overview of the design of transmit and receive beam-formers and transmit power allocation for MIMO relays. Soft and hard methods for interference cancelation are presented, which play a critical role for all MIMO relays whether they are full-duplex or half-duplex, regenerative or non-regenerative, one-way relay or two-way relay. A perspective of MIMO relays in a network of many hops is illustrated. A distinction is made between feedback loop of energy and feedback loop of noise. Subspace computation and a Generalized Water-Filling (GWF) algorithm are shown as important building blocks for the design.
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