  In this work, a new transmission scheme, signal space cognitive cooperation,
is introduced by applying the idea of signal space diversity in an underlay
spectrum sharing decode-and-forward multi-relay cooperative network. In the
proposed structure, the secondary source signal is rotated by a certain angle
and then the source and the secondary best relay transmit the in-phase and the
quadrature components of the rotated signal. As a consequence, two source
signals, rather than one, are transmitted in two-time slots which improves data
rates considerably, compared to the conventional cognitive cooperative schemes.
In this work, proactive relaying mode is used in which the best relay is
selected based on the max-min selection criterion before executing the
transmission. Considering both statistical and the instantaneous channel state
information of the feedback channel between the primary receiver and the
secondary network, two power allocation methods are adopted at the source. For
both methods, closed-form expressions of error probability are derived.
Moreover, asymptotic analysis is performed and diversity gain is obtained to
provide further insights about the system performance. Finally, analytical
expressions are verified by Monte-Carlo simulations.
