Duality and Optimization for Generalized Multi-Hop MIMO Amplify-and-Forward Relay Networks With Linear Constraints

We consider a generalized multi-hop MIMO amplify-and-forward (AF) relay network with multiple sources/destinations and arbitrarily number of relays. We establish two dualities and the corresponding dual transformations between such a network and its dual, respectively, under single-network linear co...

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Vydané v:	IEEE transactions on signal processing Ročník 61; číslo 9; s. 2356 - 2365
Hlavní autori:	An Liu, Lau, V. K. N., Youjian Liu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.05.2013 Institute of Electrical and Electronics Engineers
Predmet:	Algorithm design and analysis Amplify and forward Applied sciences Covariance matrix Detection, estimation, filtering, equalization, prediction duality Exact sciences and technology Information, signal and communications theory MIMO MIMO precoder optimization multi-hop MIMO networks Network topology Optimization relay Relays Signal and communications theory Signal, noise Spread spectrum communication Telecommunications and information theory MIMO system Non convex programming Relay Relay network Amplify and forward Coding circuit Transmission protocol multi-hop MIMO networks Dual transformation duality Optimization Multihop network Covariance Signal processing MIMO precoder optimization Routing protocols Fast algorithm
ISSN:	1053-587X, 1941-0476
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Abstract	We consider a generalized multi-hop MIMO amplify-and-forward (AF) relay network with multiple sources/destinations and arbitrarily number of relays. We establish two dualities and the corresponding dual transformations between such a network and its dual, respectively, under single-network linear constraint and per-hop linear constraint. A unified optimization framework is proposed to find a stationary point for an important class of nonconvex optimization problems of AF relay networks based on a local Lagrange dual method, where the primal algorithm only finds a stationary point for the inner loop problem of maximizing the Lagrangian w.r.t. the primal variables. The input covariance matrices are shown to satisfy a polite water-filling structure at a stationary point of the inner loop problem. The duality and polite water-filling are exploited to design fast primal algorithms. Compared with the existing algorithms, the proposed optimization framework with duality-based primal algorithms can be used to solve more general problems with lower computation cost.
AbstractList	We consider a generalized multi-hop MIMO amplify-and-forward (AF) relay network with multiple sources/destinations and arbitrarily number of relays. We establish two dualities and the corresponding dual transformations between such a network and its dual, respectively, under single-network linear constraint and per-hop linear constraint. A unified optimization framework is proposed to find a stationary point for an important class of nonconvex optimization problems of AF relay networks based on a local Lagrange dual method, where the primal algorithm only finds a stationary point for the inner loop problem of maximizing the Lagrangian w.r.t. the primal variables. The input covariance matrices are shown to satisfy a polite water-filling structure at a stationary point of the inner loop problem. The duality and polite water-filling are exploited to design fast primal algorithms. Compared with the existing algorithms, the proposed optimization framework with duality-based primal algorithms can be used to solve more general problems with lower computation cost.
Author	Lau, V. K. N. Youjian Liu An Liu
Author_xml	– sequence: 1 surname: An Liu fullname: An Liu email: eewendaol@ust.hk organization: Dept. of Electr. & Comput. Eng., Hong Kong Univ. of Sci. & Technol., Hong Kong, China – sequence: 2 givenname: V. K. N. surname: Lau fullname: Lau, V. K. N. email: eeknlau@ece.ust.hk organization: Dept. of Electr. & Comput. Eng., Hong Kong Univ. of Sci. & Technol., Hong Kong, China – sequence: 3 surname: Youjian Liu fullname: Youjian Liu email: eugeneliu@ieee.org organization: Dept. of Electr., Comput., & Energy Eng., Univ. of Colorado at Boulder, Boulder, CO, USA
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Keywords	MIMO system Non convex programming Relay Relay network Amplify and forward Coding circuit Transmission protocol multi-hop MIMO networks Dual transformation duality Optimization Multihop network Covariance Signal processing MIMO precoder optimization Routing protocols Fast algorithm
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SubjectTerms	Algorithm design and analysis Amplify and forward Applied sciences Covariance matrix Detection, estimation, filtering, equalization, prediction duality Exact sciences and technology Information, signal and communications theory MIMO MIMO precoder optimization multi-hop MIMO networks Network topology Optimization relay Relays Signal and communications theory Signal, noise Spread spectrum communication Telecommunications and information theory
Title	Duality and Optimization for Generalized Multi-Hop MIMO Amplify-and-Forward Relay Networks With Linear Constraints
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