  This paper considers the joint design of user power allocation and relay
beamforming in relaying communications, in which multiple pairs of
single-antenna users exchange information with each other via multiple-antenna
relays in two time slots. All users transmit their signals to the relays in the
first time slot while the relays broadcast the beamformed signals to all users
in the second time slot. The aim is to maximize the system's energy efficiency
(EE) subject to quality-of-service (QoS) constraints in terms of exchange
throughput requirements. The QoS constraints are nonconvex with many nonlinear
cross-terms, so finding a feasible point is already computationally
challenging. The sum throughput appears in the numerator while the total
consumption power appears in the denominator of the EE objective function. The
former is a nonconcave function and the latter is a nonconvex function, making
fractional programming useless for EE optimization. Nevertheless, efficient
iterations of low complexity to obtain its optimized solutions are developed.
The performances of the multiple-user and multiple-relay networks under various
scenarios are evaluated to show the merit of the paper development.
