Network beamforming based on second order statistics of the channel state information

Havary-Nassab, Veria; Shahbazpanahi, Shahram; Grami, Ali; Luo, Zhi-Quan

doi:10.1109/icassp.2008.4518182

Cited by 13 publications

(15 citation statements)

References 10 publications

(13 reference statements)

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“…Using (6), (7), and (8), the optimization problem (21) can be rewritten as subject to (22) To solve (22), let us write the weight vector as (23) where satisfies . The optimization problem (22) can be rewritten as subject to and (24) where the following definitions are used:…”

Section: A Total Power Constraintmentioning

confidence: 99%

Distributed Beamforming for Relay Networks Based on Second-Order Statistics of the Channel State Information

Havary-Nassab

Shahbazpanahi

Grami

et al. 2008

IEEE Trans. Signal Process.

395

288

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Abstract-In this paper, the problem of distributed beamforming is considered for a wireless network which consists of a transmitter, a receiver, and relay nodes. For such a network, assuming that the second-order statistics of the channel coefficients are available, we study two different beamforming design approaches. As the first approach, we design the beamformer through minimization of the total transmit power subject to the receiver quality of service constraint. We show that this approach yields a closed-form solution. In the second approach, the beamforming weights are obtained through maximizing the receiver signal-to-noise ratio (SNR) subject to two different types of power constraints, namely the total transmit power constraint and individual relay power constraints. We show that the total power constraint leads to a closed-form solution while the individual relay power constraints result in a quadratic programming optimization problem. The later optimization problem does not have a closed-form solution. However, it is shown that using semidefinite relaxation, this problem can be turned into a convex feasibility semidefinite programming (SDP), and therefore, can be efficiently solved using interior point methods. Furthermore, we develop a simplified, thus suboptimal, technique which is computationally more efficient than the SDP approach. In fact, the simplified algorithm provides the beamforming weight vector in a closed form. Our numerical examples show that as the uncertainty in the channel state information is increased, satisfying the quality of service constraint becomes harder, i.e., it takes more power to satisfy these constraints. Also our simulation results show that when compared to the SDP-based method, our simplified technique suffers a 2-dB loss in SNR for low to moderate values of transmit power.Index Terms-Convex feasibility problem, distributed beamforming, distributed signal processing, relay networks, semidefinite programming.

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Section: A Total Power Constraintmentioning

confidence: 99%

Distributed Beamforming for Relay Networks Based on Second-Order Statistics of the Channel State Information

Havary-Nassab

Shahbazpanahi

Grami

et al. 2008

IEEE Trans. Signal Process.

395

288

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“…Moreover, because the second and third lines of (30) are positive definite, a 2 > a 1 always holds and we can conclude directly that the first constraint of (32) is convex. By the fact that both the remaining constraints and the objective function are convex, we conclude that the problem (32) is convex and can be solved using the bi-section method [13,Sec. 3], [14].…”

Section: B Sub-optimal Joint Source and Relay Power Allocationmentioning

confidence: 98%

“…First, we derive a closed-form eigenvector solution to the relay transmit power allocation problem under a total relay transmit power constraint in Section IV-A. At the second step, we employ the bisection method [13], [14] to allocate the source transmit power and total relay transmit power with respect to a total transmit power and per-node transmit power constraints. The proposed power allocation algorithm is then stated as the process of solving the first and second steps iteratively until a stopping condition occurs, as described in Section IV-B.…”

Section: Proposed Power Allocation Schemementioning

confidence: 99%

Joint Power Allocation for Differentially Modulated Wireless Relay Networks

Pambudi

Lee

2012

IEEE Trans. Wireless Commun.

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This paper deals with the power allocation problem in a wireless relay network employing differential modulation technique and Alamouti distributed space-time code, where signals from both the direct and relay paths are taken into account in the detection process. We propose a sub-optimal power allocation scheme based on the maximization of an approximate receive covariance expression. The proposed scheme jointly allocates the transmit power of both the source and relay nodes under a total transmit power and per-node transmit power constraints. We can increase the effectiveness of the proposed power allocation algorithm by grouping the relays with respect to their individual covariances. Numerical experiments show that the proposed covariance maximization algorithm combined with the relay grouping algorithm offers a respectable BER performance improvement, compared to the conventional schemes. Finally, we demonstrate that the proposed scheme requires only a small number of iterations to achieve convergence, making it attractive to practical systems.

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“…Recently, decentralized beamforming techniques have been presented for relaying schemes where the relays re-transmit an amplitude-and phase-adjusted version of their received signals [3][4][5][6]. Also, the problem of joint uplink-downlink beamforming has been studied for a single-relay network where the relay is equipped with multiple antennas [7].…”

Section: Introductionmentioning

confidence: 99%

Optimal network beamforming for bi-directional relay networks

Havary-Nassab

Shahbazpanahi

Grami

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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We consider a relay network which consists of two transceivers and r relay nodes. We study a half-duplex two-way relaying scheme. First, the two transceivers transmit their information symbols simultaneously and the relays receive a noisy mixture of the two transceiver signals. Then each relay adjusts the phase and the amplitude of its received signal by multiplying it with a complex beamforming coefficient and transmits the so-obtained signal. Aiming at optimally calculating the beamforming weight vector as well as the transceiver transmit powers, we minimize the total transmit power subject to two constraints on the receive signal-to-noise ratios (SNRs) at the two transceivers. We show that the optimal weight vector can be obtained through a simple iterative algorithm which enjoys a linear computational complexity per iteration.Index Terms-Distributed beamforming, two-way relaying, distributed signal processing, bi-directional relaying, optimal power allocation, wireless relay networks.

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Network beamforming based on second order statistics of the channel state information

Cited by 13 publications

References 10 publications

Distributed Beamforming for Relay Networks Based on Second-Order Statistics of the Channel State Information

Distributed Beamforming for Relay Networks Based on Second-Order Statistics of the Channel State Information

Joint Power Allocation for Differentially Modulated Wireless Relay Networks

Optimal network beamforming for bi-directional relay networks

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