An SNR balancing approach to two-way relaying

Abstract

We consider a relay network which consists of two transceivers and r relay nodes. Assuming that the transceivers and the relays are all equipped with single antennas, we devise a two-way amplify-andphase-adjust relaying scheme. In this scheme, each relay multiplies its received signal by a complex weight and transmits the so-obtained signal thereby participating in a distributed beamforming process. We deploy an SNR balancing technique where the smallest of the two transceiver SNRs is maximized while the total transmit power is kept below a certain power budget. We show that this problem has a unique solution which can be obtained through an iterative procedure with a linear computational complexity per iteration. We also prove that for any channel realization, this approach leads to a power allocation scheme where half of the maximum power budget is allocated to the two transceivers and the remaining half will be shared among all the relay nodes. We further devise a distributed implementation of our proposed scheme which requires a minimal cooperation among the two transceivers and the relays. In fact, we show that our technique can be implemented such that the bandwidth required to obtain the beamforming weights in a distributed manner remains constant as the size of the network grows.

A semi-closed form solution to the SNR balancing problem of two-way relay network beamforming

“…As the optimal beamforming vector is unique(i.e., w(p o As a simple suboptimal solution, one can choose p o 1 =P /4. In[1], the authors have shown thatp o 1 + p o 2 =P /2, we obtain that p o 2 = p o 1 =P /4.Although this solution is suboptimal, if different diagonal entries of D1 and D2 are drawn from the same pdf, the choice of p o 1 = p o 2 =P /4 can be close to the optimal solution thus alleviating the need for solving (20). We will evaluate the performance of both (optimal and suboptimal) solutions via numerical examples.…”

“…It is shown in [1] that the maximum is achieved when SNR1 = SNR2 holds true, and hence, the optimization problem (6) is equivalent to…”

“…, nr. It has been shown in [1] that the phase of wi has to match to the phase of the ith entry of h which is equal to the aggregated phase of the channel coefficients from the ith relay to the two transceivers. That is θi = φi = ∠fi1 + ∠fi2 where φi denotes the phase of the ith entry of h and ∠z represents the phase of the complex number z. Consequently, the amplitude of different entries of w can be obtained by solving the following optimization problem:…”

“…In light of Lemma 1, a steepest descent algorithm has been proposed in [1] to obtain the global solution to (11). We denote this solution as αo.…”

“…In [11], the problem of network beamforming design has been studied for a twoway wireless relay network. The networks considered in [11] consists of two transceivers and multiple relay nodes (see also [1,12]). Two different approaches are used in [11] to develop two network beamformers.…”