Virtual MIMO Beamforming and Device Pairing Enabled by Device-to-Device Communications for Multidevice Networks

Algorithm 2

Auction algorithm.

(1) Set for .

(2)   repeat

(3)   At device , calculate

,

,

,

     and update offer using with a certain positive constant and send it to device .

(4)     On receipt of at each device , calculate alternative rate gain using (26) and send it back to device .

(5)      .

(6)   until   All messages converge or max number of iterations are reached.

(7) At device , fix and for all to determine using (25), and find partner device such that .