  We study in this paper a two-hop relaying network consisting of one source,
one destination, and three amplify-and-forward (AF) relays operating in a
half-duplex mode. In order to compensate for the inherent loss of capacity
pre-log factor 1/2 in a half-duplex mode, we consider alternate transmission
protocol among three relays where two relays and the other relay alternately
forward messages from source to destination. We consider a multiple-antenna
environment where all nodes have $M$ antennas. Aligning the inter-relay
interference due to the alternate transmission is utilized to make additional
degrees of freedom (DOFs) and recover the pre-log factor loss. It is shown that
the proposed relaying scheme can achieve $\frac{3M}{4}$ DOFs compared with the
$\frac{M}{2}$ DOFs of conventional AF relaying. In addition, suboptimal linear
filter designs for a source and three relays are proposed to maximize the
system achievable sum-rate for different fading scenarios when the destination
utilizes a linear minimum mean-square error filter for decoding. We verify from
our selected numerical results that the proposed filter designs give
significant improvement over a naive filter or conventional relaying schemes.
