Optimal network beamforming for bi-directional relay networks

Havary-Nassab, Veria; Shahbazpanahi, Shahram; Grami, Ali

doi:10.1109/icassp.2009.4960074

Cited by 11 publications

(9 citation statements)

References 8 publications

(6 reference statements)

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“…In (35), α (k) and κ are the value of α at the kth iteration and the convergence-stability trade-off parameter, respectively. It follows from (20) and (34) that obtaining the matrix D(α) and the gradient vectorg(α) requires the calculation of four terms, namely α T D1α, α T D2α, α T α, and (8). It has been shown in [8] that as the SNR constraints in (36) are symmetric, the relay transmit power is half of the P min T =P at the optimum and the proof is complete.…”

Section: Lemma 1: the Optimization Problem (19) Does Not Have Any Locmentioning

confidence: 95%

“…It follows from (20) and (34) that obtaining the matrix D(α) and the gradient vectorg(α) requires the calculation of four terms, namely α T D1α, α T D2α, α T α, and (8). It has been shown in [8] that as the SNR constraints in (36) are symmetric, the relay transmit power is half of the P min T =P at the optimum and the proof is complete. Note that we assume that the two transceivers use the iterative algorithm in (35) to calculate the optimal value of α, say αo.…”

Section: Lemma 1: the Optimization Problem (19) Does Not Have Any Locmentioning

confidence: 95%

“…Also, distributed space-time coding scheme has been studied in the context of two-way relay networks in [7]. We have studied the problem of optimal two-way decentralized beamforming in [8]. The approach of [8] is based on the minimization of the total transmit power dissipated in the whole network while guaranteeing that the quality of service, measured by the signal-to-noise ratio (SNR), at the two ends of the link is above given thresholds.…”

Section: Introductionmentioning

confidence: 99%

“…We have studied the problem of optimal two-way decentralized beamforming in [8]. The approach of [8] is based on the minimization of the total transmit power dissipated in the whole network while guaranteeing that the quality of service, measured by the signal-to-noise ratio (SNR), at the two ends of the link is above given thresholds. In this paper, we use an SNR balancing approach to study the problem of optimal decentralized beamforming for two-way wireless relay networks.…”

Section: Introductionmentioning

confidence: 99%

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An SNR balancing approach to two-way relaying

Havary-Nassab

Shahbazpanahi

Grami

2009

2009 IEEE 10th Workshop on Signal Processing Advances in Wireless Communications

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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.

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Section: Lemma 1: the Optimization Problem (19) Does Not Have Any Locmentioning

confidence: 95%

Section: Lemma 1: the Optimization Problem (19) Does Not Have Any Locmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An SNR balancing approach to two-way relaying

Havary-Nassab

Shahbazpanahi

Grami

2009

2009 IEEE 10th Workshop on Signal Processing Advances in Wireless Communications

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“…We also assume that information symbols have unit power, i.e., Efjs 1 j 2 g = Efjs 2 j 2 g = 1. Total Transmit Power Minimization: We now summarize the total power minimization approach as studied in [1] and [13]. In this approach, the beamforming weights w and the transceivers' transmit powers p 1 and p 2 are obtained such that the total transmit power consumed in the whole network (denoted as P T ) is minimized while maintaining the received SNRs at both transceivers above certain levels 1 > 0 and 2 > 0, respectively.…”

Section: Preliminariesmentioning

confidence: 99%

A Semi-Closed-Form Solution to Optimal Distributed Beamforming for Two-Way Relay Networks

Shahbazpanahi

Dong

2012

IEEE Trans. Signal Process.

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In this correspondence, we present a computationally simple semi-closed-form solution to the problem of designing distributed beamformer for two-way (bi-directional) multi-relay networks. In such a network, the relay nodes use amplify-and-forward relaying protocol to help two transceivers exchange information in a bidirectional manner. We consider a total power minimization approach to optimally find the relay beamforming weights and the transceiver transmit powers. This approach is based on the minimization of the total transmit power, consumed in the whole network, subject to SNR constraints at the two transceivers. We show that as far as the relay beamforming weight vector is concerned, this minimization problem is equivalent to the minimization of the total transmit power for a one-way relay network where the target SNR of the receiving transceiver is equal to the sum of the target SNRs of the two transceivers in the original two-way relay network. Based on this observation, we show that the relay beamforming weight vector can be obtained in a closed from given that an intermediate parameter, namely the transmit power of the transmitter in the equivalent one-way relay network, is available. This intermediate parameter is shown to be the solution to a one-dimensional optimization problem, and thus, it can be obtained using a simple bisection method. Our semi-closed-form solution not only reveals the structure of the optimal beamforming weight vector, but also leads to a one-dimensional search regardless of the number of relays. This provides the computational advantage over the gradient based numerical method of Havary-Nassab et al., where the gradient dimension reflects the number of relays.Index Terms-bidirectional network beamforming, cooperative network, distributed beamforming, power control, relay selection, SNR balancing, two-way communications, two-way relaying.

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2010

Cooperative Communications

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Optimal network beamforming for bi-directional relay networks

Cited by 11 publications

References 8 publications

An SNR balancing approach to two-way relaying

An SNR balancing approach to two-way relaying

A Semi-Closed-Form Solution to Optimal Distributed Beamforming for Two-Way Relay Networks

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