We investigate the problem of two-way network
beamforming and power allocation using the sum-rate maximization subject
to a total power budget in the network. We prove that solving this problem
is equivalent to solving the max-min fair problem (or the so-called max-min
fair design). Consequently the power allocation for
the sum-rate maximization leads to an SNR-balancing solution when applied to
the two-way relay network beamforming, as opposed to a water-filling type of
solution. To the best of our knowledge, such an equivalency between the
sum-rate maximization and max-min fair approaches has not been shown before for
any other communication scheme. In fact, the max-min fair approach is well
known to often result in a lower sum rate as compared to the maximum sum rate.
For the problem we consider in this paper, however, we have shown that these
two approached are equivalent.