  This paper deals with the problem of jointly designing the source precoder,
the relaying matrices, and the destination equalizer in a multiple-relay
amplify-and-forward (AF) cooperative multiple-input multiple-output (MIMO)
wireless network, when partial channel-state information (CSI) is available.
Specifically, the considered approaches are based on the knowledge of
instantaneous CSI of the first-hop channel matrix, whereas only statistical CSI
of the second-hop channels is assumed. In such a scenario, with respect to the
case when instantaneous CSI of both the first- and second-hop MIMO channel
matrices is exploited, existing network designs exhibit a significant
performance degradation. Relying on a relaxed minimum-mean-square-error (MMSE)
criterion, we show that the design based on the potential activation of all
possible antennas for all available AF relays leads to a mathematically
intractable optimization problem. Therefore, we develop a joint
relay-and-antenna selection procedure that determines the best subset of the
available antennas possibly belonging to different relays. Monte Carlo
simulations show that, compared to designs based on the selection of the best
relay, the proposed strategy offers a significant performance gain, by also
outperforming other recently proposed relay/antenna selection schemes.
