Decentralizing the optimal multi-cell beamforming via large system analysis

Abstract

A multi-cell minimum power beamforming problem is considered. It is known that the inter-cell interference (ICI) terms couple the base stations (BS) and inter-cell coordination is required for global optimal solution. The cooperation can be realized by exchange of instantaneous channel state information (CSI) or terms related to the ICI values via a backhaul link. However, the limited backhaul capacity and delay constraints put a limit on achievable performance when the number of antennas and users grow large or when dealing with a fast fading scenario. In this work, we demonstrate that the ICI terms coupling the coordinating BSs can be approximated using the random matrix theory (RMT) tools when the problem dimensions grow large, and that the approximated ICI values depend only on channels statistics, i.e., spatial load and user specific path loss values. This leads to a significant reduction in the information exchange rate among BSs. Furthermore, processing is simplified because with a fixed approximated ICI values the beamforming vectors can be obtained locally at each BS. The proposed solution guarantees the feasibility of the target signal-to-interference-plus-noise ratios (SINR) without any major loss of performance as compared to the optimal centralized design.

Decentralizing Multicell Beamforming via Deterministic Equivalents

“…which along with (28) l)). On the other hand, we notice thatm b M ,M (−(1 + l)) at l = 0 is equal tom b M ,M in (24)…”

“…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.…”

Large System Analysis of Base Station Cooperation for Power Minimization

“…A known problem with the asymptotic analysis is that the target rates are not guaranteed to be achieved when N is finite and relatively small (e.g., [14]). This is because the approximation errors translate into fluctuations of the resulting SINR values.…”

“…Applying the matrix inversion lemma first [26] and then using (14) we have that the numerator in the right-hand-side of the above equation takes the form:…”