Monotonic and Sequential Fractional Programming for Performance - PowerPoint PPT Presentation

Monotonic and Sequential Fractional Programming for Performance Optimization in Interference Networks Eduard Jorswieck Communications Theory 16.05.2017

Joint work with • Alessio Zappone (University Cassino, Italy) • Emil Björnsson (Linköping University, Sweden) • Giacomo Bacci (Med. Broadband Infrastructure, Italy) • Luca Sanguinetti (Uni Pisa, Italy)

Resources in Wireless • Spectrum • Energy • Infrastructure • Data • Computational 
 Power • Channel Info… E. Jorswieck, L. Badia, T. Fahldieck, E. Karipidis and J. Luo, 
 "Spectrum sharing improves the network efficiency for cellular operators," 
 in IEEE Communications Magazine , vol. 52, no. 3, pp. 129-136, March 2014.

Heterogeneous Services • Conflicting performance metrics/requirements: ! • Data rate / throughput ! • Delay / latency ! • Energy efficiency ! • Security ! • Multi-Objective Programming (MOP) problem ! E. Björnson, E. Jorswieck, M. Debbah, B. Ottersten, "Multi-Objective Signal Processing Optimization: The Way to Balance Conflicting Metrics in 5G Systems", IEEE Signal Processing Magazine , vol. 31, no. 6, pp. 14-23, Nov. 2014.

http://www.nowpublishers.com/article/Details/CIT-088 A. Zappone and E. Jorswieck, " Energy Efficiency in Wireless Networks via Fractional Programming Theory ". Foundations and Trends in Communications and Information Theory, vol. 11, no. 3-4, June 2015, pp. 185-396. 5

Energy-Efficiency • The number of connected nodes will reach 50 billion by 2020 and that the energy demand will soon become unmanageable. • Bit-per-Joule energy efficiency , defined as the amount of bits which can be reliably transmitted per Joule of consumed energy. • Extensively studied for various systems without coupling. (1) G. Auer, V. Giannini, C. Desset, I. Godor, P. Skillermark, M. Olsson, M. Imran, D. Sabella, M. Gonzalez, O. Blume, and A. Fehske, “How much energy is needed to run a wireless network?” IEEE Wireless Communications , vol. 18, no. 5, pp. 40–49, Oct. 2011. (2) D. W. K. Ng, E. S. Lo, and R. Schober, “Energy-Efficient Resource Allocation for Secure OFDMA Systems,” IEEE Transactions on Vehicular Technology , vol. 61, no. 6, pp. 2572– 2585, July 2012. A. Zappone and E. Jorswieck, "Energy Efficiency in Wireless Networks via Fractional Programming Theory". Foundations and Trends in Communications and Information Theory , vol. 11, no. 3-4, June 2015, pp. 185-396.

Energy-Efficiency EE = f ( γ ( p )) α p + P c In line with the physical meaning of efficiency, the energy efficiency is defined as the system benefit-cost ratio in terms of amount of data reliably transmitted over the energy that is required to do so. A. Zappone and E. Jorswieck, "Energy Efficiency in Wireless Networks via Fractional Programming Theory". Foundations and Trends in Communications and Information Theory , vol. 11, no. 3-4, June 2015, pp. 185-396.

Energy-Efficiency of a Network • Global Energy-efficiency ! • Weighted arithmetic mean ! • Weighted geometric mean ! Observation: ! always ratios ! • Weighted minimum EE ! A. Zappone and E. Jorswieck, "Energy Efficiency in Wireless Networks via Fractional Programming Theory". Foundations and Trends in Communications and Information Theory , vol. 11, no. 3-4, June 2015, pp. 185-396.

Energy-Efficiency of a Network • Global Energy-efficiency ! • Weighted arithmetic mean ! • Weighted geometric mean ! Observation: ! always ratios ! • Weighted minimum EE ! Fractional Programming ! A. Zappone and E. Jorswieck, "Energy Efficiency in Wireless Networks via Fractional Programming Theory". Foundations and Trends in Communications and Information Theory , vol. 11, no. 3-4, June 2015, pp. 185-396.

Single Ratio: Concave Fractional Problem • The objective is pseudo-concave . • A local maximum is also a global maximum and KKT conditions are necessary and sufficient . C. Isheden, Z. Chong, E. Jorswieck, G. Fettweis, "Framework for Link-Level Energy Efficiency Optimization with Informed Transmitter", IEEE Trans. on Wireless Communications , vol. 11, no. 8, pp. 2946-2957, Aug. 2012.

Line between „easy“ and „difficult“ is not convex vs. non- convex A. Zappone and E. Jorswieck, "Energy Efficiency in Wireless Networks via Fractional Programming Theory". Foundations and Trends in Communications and Information Theory , vol. 11, no. 3-4, June 2015, pp. 185-396.

A. Zappone and E. Jorswieck, "Energy Efficiency in Wireless Networks via Fractional Programming Theory". Foundations and Trends in Communications and Information Theory , vol. 11, no. 3-4, June 2015, pp. 185-396.

Parametric Approach: Dinkelbach Algorithm • This method allows to solve a CFP by converting it into a sequence of convex problems 
 • Solving a CFP is equivalent to • Superlinear convergence finding the zero of the 
 (Newton update) function . W. Dinkelbach, „On nonlinear fractional programming," Management Science , vol. 13, no. 7, pp. 492 - 498, March 1967

Energy Efficient Resource Allocation in 5G Wireless Networks A. Zappone, L. Sanguinetti, G. Bacci, E. Jorswieck and M. Debbah, "Energy- Efficient Power Control: A Look at 5G Wireless Technologies," in IEEE Transactions on Signal Processing , vol. 64, no. 7, pp. 1668-1683, April 1, 2016. A. Zappone, E. Björnson, L. Sanguinetti and E. Jorswieck, "Globally Optimal Energy-Efficient Power Control and Receiver Design in Wireless Networks," in IEEE Transactions on Signal Processing , vol. 65, no. 11, pp. 2844-2859, June1, 1 2017. 12

Energy Efficient Resource Allocation in 5G Wireless Networks A. Zappone, L. Sanguinetti, G. Bacci, E. Jorswieck and M. Debbah, "Energy- Efficient Power Control: A Look at 5G Wireless Technologies," in IEEE Transactions on Signal Processing , vol. 64, no. 7, pp. 1668-1683, April 1, 2016. A. Zappone, E. Björnson, L. Sanguinetti and E. Jorswieck, "Globally Optimal Energy-Efficient Power Control and Receiver Design in Wireless Networks," in IEEE Transactions on Signal Processing , vol. 65, no. 11, pp. 2844-2859, June1, 1 2017. 12

Contribution • A unified framework for EE optimization is developed for both centralized and decentralized networks with rate and power constraints which allows encompassing some of the emerging technologies for 5G and beyond . • The maximization of the GEE as well as of the minimum EE is considered in the network-centric case. • In the decentralized setting, the users in the network are modelled as rational, self-organizing agents that engage in a non-cooperative game wherein each one aims at maximizing its individual EE while targeting its own power and rate constraint. A. Zappone, L. Sanguinetti, G. Bacci, E. Jorswieck and M. Debbah, "Energy- Efficient Power Control: A Look at 5G Wireless Technologies," in IEEE Transactions on Signal Processing , vol. 64, no. 7, pp. 1668-1683, April 1, 2016.


 System Model (network view) • Individual EE of one user 
 • Constraints 
 • Global EE (GEE) 
 • Minimum weighted EE SINR expression 
 A. Zappone, L. Sanguinetti, G. Bacci, E. Jorswieck and M. Debbah, "Energy- Efficient Power Control: A Look at 5G Wireless Technologies," in IEEE Transactions on Signal Processing , vol. 64, no. 7, pp. 1668-1683, April 1, 2016.


 
 
 Application to 5G and Beyond • Massive MIMO • Relay-assisted CoMP Interference Network 
 J. Hoydis, S. ten Brink and M. Debbah, "Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?," in IEEE Journal on Selected Areas in Communications , vol. 31, no. 2, pp. 160-171, February 2013.

Centralized Optimization - Feasibility Lemma 1 : Let F be the following matrix with spectral radius . The solutions to global and minimum EE exist if and only if E. Seneta, Non-Negative Matrices and Markov Chains , 
 3rd ed. New York, NY, USA: Springer, 2006.

GEE Maximization First, for one block N=1: A. Zappone, L. Sanguinetti, G. Bacci, E. Jorswieck and M. Debbah, "Energy- Efficient Power Control: A Look at 5G Wireless Technologies," in IEEE Transactions on Signal Processing , vol. 64, no. 7, pp. 1668-1683, April 1, 2016.

GEE Maximization First, for one block N=1: SINR expression A. Zappone, L. Sanguinetti, G. Bacci, E. Jorswieck and M. Debbah, "Energy- Efficient Power Control: A Look at 5G Wireless Technologies," in IEEE Transactions on Signal Processing , vol. 64, no. 7, pp. 1668-1683, April 1, 2016.

GEE Maximization First, for one block N=1: SINR expression Does not result in concave denominator and not in concave fractional program A. Zappone, L. Sanguinetti, G. Bacci, E. Jorswieck and M. Debbah, "Energy- Efficient Power Control: A Look at 5G Wireless Technologies," in IEEE Transactions on Signal Processing , vol. 64, no. 7, pp. 1668-1683, April 1, 2016.

Sequential Programming • Instead of solving the difficult master problem, solve a sequence of easier problems . • Consider a problem P with objective f and a sequence of approximate problems P l with objectives f l such that the following properties hold • Then solving the sequence of problems, the value will converge and if the optimization variables converges, too, then to a point fulfilling the KKT conditions . B. R. Marks and G. P. Wright, “A general inner approximation algorithm for nonconvex mathematical programs,” Operations Research , vol. 26, no. 18 4, pp. 681–683, July–Aug. 1978.