Decentralized multi-cell beamforming with QoS guarantees via large system analysis

Abstract

This work focuses on the power minimization prob- lem while ensuring target rates in the downlink of a multi-cell multi-user MIMO system wherein L base stations (BSs) of N antennas serve in total K single-antenna user equipments. We assume that the transmit antennas at each BS are correlated and propose a decentralized solution to compute an approximation of the optimal beamforming vectors. The analysis is conducted in the asymptotic regime in which N and K grow large with a given ratio K/N. In particular, the proposed solution relies on the exchange of intercell interference terms whose large system approximations are computed at each BS using knowledge of local transmit correlation matrices and non-local pathlosses. Numerical results are used to evaluate the performance loss of the proposed solution compared to the optimal one and to investigate its accuracy in systems of finite size

Deterministic equivalent for max-min SINR over random user locations

“…− −−− → 0 via a contradiction argument as in [25], [33] where a sketch of the proof is presented in Appendix A.…”

“…where as in the corollary. We still need one more step to show the derivedλ k with independence assumption is a deterministic equivalent for λ k which can be proved via a contradiction argument as in [25], [33] APPENDIX B PROOF OF COROLLARY 1 First we evaluate the error due to plugging 1 1+τj instead of and ς j η bj /η b . Now, writing each term inside the summation of (9) as 1 1+τj + ι j , the error terms {ι j } are averaged out by the summation, and hence, converge to E{ι} due to strong law of large number (SLLN).…”

Decentralizing Multicell Beamforming via Deterministic Equivalents

“…Parts of this paper have been published in the conference publications [28]- [30]. The decentralized solution relying on deterministic ICI values is investigated in an i.i.d Rayleigh fading model in [28] and in the correlated scenario in [29], [30].…”

“…Parts of this paper have been published in the conference publications [28]- [30]. The decentralized solution relying on deterministic ICI values is investigated in an i.i.d Rayleigh fading model in [28] and in the correlated scenario in [29], [30]. Specifically, the large system analysis is sketched in [29], [30] while the precise proofs along with derivation details are presented in the current work.…”

“…The decentralized solution relying on deterministic ICI values is investigated in an i.i.d Rayleigh fading model in [28] and in the correlated scenario in [29], [30]. Specifically, the large system analysis is sketched in [29], [30] while the precise proofs along with derivation details are presented in the current work. In addition, the analysis is extended to the case where UEs are grouped on the basis of their statistical properties.…”