  Energy efficiency and its optimization constitute critical tasks in the
design of low-power wireless networks. The present work is devoted to the error
rate analysis and energy-efficiency optimization of regenerative cooperative
networks in the presence of multipath fading under spatial correlation. To this
end, exact and asymptotic analytic expressions are firstly derived for the
symbol-error-rate of $M{-}$ary quadrature amplitude and $M{-}$ary phase shift
keying modulations assuming a dual-hop decode-and-forward relay system,
spatially correlated Nakagami${-}m$ multipath fading and maximum ratio
combining. The derived expressions are subsequently employed in quantifying the
energy consumption of the considered system, incorporating both transmit energy
and the energy consumed by the transceiver circuits, as well as in deriving the
optimal power allocation formulation for minimizing energy consumption under
certain quality-of-service requirements. A relatively harsh path-loss model,
that also accounts for realistic device-to-device communications, is adopted in
numerical evaluations and various useful insights are provided for the design
of future low-energy wireless networks deployments. Indicatively, it is shown
that depending on the degree of spatial correlation, severity of fading,
transmission distance, relay location and power allocation strategy, target
performance can be achieved with large overall energy reduction compared to
direct transmission reference.
