In this paper, we consider a multi-pair two-way amplify-and-forward relaying system where multiple sources exchange information via a relay node equipped with largescale antenna arrays. Given that channel estimation is non-ideal, and that the relay employs either maximum-ratio combining/maximum-ratio transmission (MRC/MRT) or zeroforcing reception/zero-forcing transmission (ZFR/ZFT) beamforming, we derive two corresponding closed-form lower bound expressions for the ergodic achievable rate of each pair sources. The closed-form expressions enable us to design an optimal power allocation (OPA) scheme that maximizes the sum spectral efficiency under certain practical constraints. As the antenna array size tends to infinity and the signal-to-noise ratios become very large, asymptotically OPA schemes in simple closed-form are derived. The capacity lower bounds are verified to be accurate predictors of the system performance by simulations, and the proposed OPA outperforms equal power allocation (EPA). It is also found that in the asymptotic regime, when MRC/MRT is used at the relay and the link end-to-end large-scale fading factors among all pairs are equal, the optimal power allocated to a user is inverse to the large-scale fading factor of the channel from the user to the relay, while OPA approaches EPA when ZFR/ZFT is adopted. Index Terms-Massive MIMO, two-way relaying, amplifyand-forward, power allocation, linear processing, multi-pair communication.
Later, REF investigated the asymptotic SE with MR and ZF, and designed an optimal power allocation strategy to maximize the sum SE under certain practical constraints.
Power Allocation for Multi-Pair Massive MIMO Two-Way AF Relaying With Linear Processing
IEEE Transactions on Wireless Communications
IEEE Transactions on Wireless Communications
Mathematics Computer Science