Monotonic Optimization Framework for Coordinated Beamforming in Multicell Networks

Utschick, Wolfgang; Brehmer, Johannes

doi:10.1109/tsp.2011.2182343

Cited by 71 publications

(81 citation statements)

References 27 publications

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“…Furthermore, if the optimal solution g * to the original problem satisfies g * ≥ s, then the perturbation will not impact the solution accuracy. The reason for the perturbation is to prevent numerical convergence issues, for example, when searching for solutions close to an axis [275,276]. We have the following result.…”

Section: Polyblock Outer Approximation (Pa) Algorithmmentioning

confidence: 89%

“…17 This line-search approach was suggested in [218,274,275] and utilized for multi-cell resource allocation with single-antenna interference channels in [206], coordinated MISO beamforming in [153,276], and general multi-cell MISO systems in [26]. Other types of curves r(τ ) can also be used to capture certain properties of f (·) -one should always try to utilize any structure that exists in the problem.…”

Section: Lower and Upper Bounds In A Boxmentioning

confidence: 99%

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Optimal Resource Allocation in Coordinated Multi-Cell Systems

Björnson

2013

FNT in Communications and Information Theory

302

317

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The use of multiple antennas at base stations is a key component in the design of cellular communication systems that can meet high-capacity demands in the downlink. Under ideal conditions, the gain of employing multiple antennas is well-recognized: the data throughput increases linearly with the number of transmit antennas if the spatial dimension is utilized to serve many users in parallel. The practical performance of multi-cell systems is, however, limited by a variety of nonidealities, such as insufficient channel knowledge, high computational complexity, heterogeneous user conditions, limited backhaul capacity, transceiver impairments, and the constrained level of coordination between base stations. This tutorial presents a general framework for modeling different multi-cell scenarios, including clustered joint transmission, coordinated beamforming, interference channels, cognitive radio, and spectrum sharing between operators. The framework enables joint analysis and insights that are both scenario independent and dependent.The performance of multi-cell systems depends on the resource allocation; that is, how the time, power, frequency, and spatial resources are divided among users. A comprehensive characterization of resource allocation problem categories is provided, along with the signal processing algorithms that solve them. The inherent difficulties are revealed: (a) the overwhelming spatial degrees-of-freedom created by the multitude of transmit antennas; and (b) the fundamental tradeoff between maximizing aggregate system throughput and maintaining user fairness. The tutorial provides a pragmatic foundation for resource allocation where the system utility metric can be selected to achieve practical feasibility. The structure of optimal resource allocation is also derived, in terms of beamforming parameterizations and optimal operating points.This tutorial provides a solid ground and understanding for optimization of practical multi-cell systems, including the impact of the nonidealities mentioned above. The Matlab code is available online for some of the examples and algorithms in this tutorial. IntroductionThis section describes a general framework for modeling different types of multi-cell systems and measuring their performance -both in terms of system utility and individual user performance. The framework is based on the concept of dynamic cooperation clusters, which enables unified analysis of everything from interference channels and cognitive radio to cellular networks with global joint transmission. The concept of resource allocation is defined as allocating transmit power among users and spatial directions, while satisfying a set of power constraints that have physical, regulatory, and economic implications. A major complication in resource allocation is the inter-user interference that arises and limits the performance when multiple users are served in parallel. Resource allocation is particularly complex when multiple antennas are employed at each base station. However, the throu...

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Section: Polyblock Outer Approximation (Pa) Algorithmmentioning

confidence: 89%

Section: Lower and Upper Bounds In A Boxmentioning

confidence: 99%

Optimal Resource Allocation in Coordinated Multi-Cell Systems

Björnson

2013

FNT in Communications and Information Theory

302

317

View full text Add to dashboard Cite

show abstract

“…There are many variations on the PA algorithm that might improve the convergence speed: (a) An improved vertex update rule is suggested in [275, Proposition 4.2] to remove more in each iteration; (b) the line-search accuracy δ can be a function of the number of iterations and the vertex g (n) [118,276]; (c) the original problem can be perturbed in an adaptive manner to further avoid shallow cuts and jamming [39,275]; (d) scheduling can be included in the algorithm [39,276]; and (e) the algorithm can be restarted from the current best solution if the number of vertices grows too large [274].…”

Section: Remark 212 (Variations)mentioning

confidence: 99%

“…Output: Final interval [f min , f max ] on optimal value; Output: Feasible point g * ε = g feasible with f min = f (g * ε ); coordinated beamforming in [153,276]. The convergence of the PA algorithm to the global optimum is established by the following theorem.…”

mentioning

confidence: 99%

“…For any given accuracy ε > 0, the PA algorithm finds an interval [f min , f max ] for the optimal value of (2.1) that satisfies Proof. The original proof in [274] assumed ideal line-search δ = 0, but can be relaxed using the guidelines in [276]. Suppose for the purpose of contradiction that the algorithm requires infinitely many iterations, then it generates at least one infinite sequence of vertices…”

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confidence: 99%

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