# Downlink Power Optimization for Heterogeneous Networks with Time Reversal-based Transmission under Backhaul Limitation

## TL;DR

This paper proposes a novel downlink power minimization scheme for heterogeneous networks using time reversal beamforming at femtocells and zero-forcing at macrocells, addressing backhaul limitations and channel estimation errors.

## Contribution

It introduces a combined beamforming approach with closed-form solutions and robust optimization for imperfect channels in HetNets.

## Key findings

- Time reversal outperforms zero-forcing in beamforming efficiency.
- The proposed power minimization scheme effectively reduces power consumption.
- Robust optimization accounts for channel estimation errors, enhancing reliability.

## Abstract

In this paper, we investigate an application of two different beamforming techniques and propose a novel downlink power minimization scheme for a two-tier heterogeneous network (HetNet) model. In this context, we employ time reversal (TR) technique to a femtocell base station (FBS) whereas we assume that a macrocell base station (MBS) uses a zero-forcing-based algorithm and the communication channels are subject to frequency selective fading. Additionally, HetNet's backhaul connection is unable to support a sufficient throughput for signaling information exchange between two tiers. Given the considered HetNet model, a downlink power minimization scheme is proposed, and closed-form expressions concerning the optimal solution are provided, taking this constraint into account. Furthermore, considering imperfect channel estimation at TR-employed femtocell, a worst-case robust power minimization problem is formulated. By devising TR worst-case analysis, this robust problem is transformed into an equivalent formulation that is tractable to solve. The results presented in our paper show that the TR technique outperforms the zero-forcing one in the perspective of beamforming methods for femtocell working environments. Finally, we validate the proposed power loading strategy for both cases of perfect and imperfect channel estimations.