  A new approach to distributed cooperative beamforming in relay networks with
frequency selective fading is proposed. It is assumed that all the relay nodes
are equipped with finite impulse response (FIR) filters and use a
filter-and-forward (FF) strategy to compensate for the transmitter-to-relay and
relay-to-destination channels.
  Three relevant half-duplex distributed beamforming problems are considered.
The first problem amounts to minimizing the total relay transmitted power
subject to the destination quality-of-service (QoS) constraint. In the second
and third problems, the destination QoS is maximized subject to the total and
individual relay transmitted power constraints, respectively. For the first and
second problems, closed-form solutions are obtained, whereas the third problem
is solved using convex optimization. The latter convex optimization technique
can be also directly extended to the case when the individual and total power
constraints should be jointly taken into account. Simulation results
demonstrate that in the frequency selective fading case, the proposed FF
approach provides substantial performance improvements as compared to the
commonly used amplify-and-forward (AF) relay beamforming strategy.
