Distributed energy spectral efficiency optimization for partial/full interference alignment in multi-user multi-relay multi-cell MIMO systems

Abstract

The energy spectral efficiency maximization (ESEM) problem of a multi-user, multi-relay, multi-cell system is considered, where all the network nodes are equipped with multiple antenna aided transceivers. In order to deal with the potentially excessive interference originating from a plethora of geographically distributed transmission sources, a pair of transmission protocols based on interference alignment (IA) are conceived, which may be distributively implemented in the network. The first, termed the full-IA protocol, avoids all intra-cell interference (ICI) and other-cell interference (OCI) by finding the perfect interferencenulling receive beamforming matrices (RxBFMs). The second protocol, termed as partial-IA, only attempts to null the ICI. Employing the RxBFMs computed by either of these protocols mathematically decomposes the channel into a multiplicity of non-interfering multiple-input–single-output (MISO) channels, which we term as spatial multiplexing components (SMCs). The problem of finding the optimal SMCs as well as their power control variables for the ESEM problem considered is formally defined and converted into a convex optimization form with the aid of carefully selected variable relaxations and transformations. Thus, the optimal SMCs and power control variables can be distributively computed using both the classic dual decomposition and subgradient methods. The performance of both protocols is characterized, and the ESEM algorithm conceived is compared to a baseline equal power allocation (EPA) algorithm. The results indicate that indeed, the ESEM algorithm performs better than the EPA algorithm in most cases. Furthermore, surprisingly the partial-IA protocol outperforms the full-IA protocol in all cases considered, which may be explained by the fact that the partial-IA protocol is less restrictive in terms of the number of available transmit dimensions at the transmitters. Given the typical cell sizes considered in this paper, the path-loss sufficiently attenuates the majority of the interference, and thus the full-IA protocol over-compensates, when trying to avoid all possible sources of interference. We have observed that, given a sufficiently high maximum power, the partial-IA protocol achieves an energy spectral efficiency (ESE) that is 2.42 times higher than that attained by the full-IA protocol.

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ORCID for Lajos Hanzo: orcid.org/0000-0002-2636-5214

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