# An Alternating Optimization Algorithm for Energy Efficiency in Heterogeneous Networks

### Abstract

This paper studies the problems of precoding designs to achieve the energy efficiency (EE) in the uplink heterogeneous networks in which the multiple small cells are deployed in a macro-cell. We consider two design problems which maximize either the total system energy efficiency (SEE) or the minimum energy efficiency (MinEE) among users subject to the transmit power constraints at each user and interference constraints caused to the macro base station. Since the optimization problems are non-convex fractional programming in matrix variables, it cannot be straightforward to obtain the optimal solutions. To tackle with the non-convexity challenges of the design problems, we adopt the relationships between the minimum mean square error (MMSE) and achievable data rate to recast the EE problems into ones more amenable. Then, we employ the block coordinate ascent (BCA) and the Dinkelbach methods to develop efficient iterative algorithms in which the closed form solutions are obtained or the semi-definite programming (SDP) problems are solved at each iteration. Simulation results are provided to investigate the EE performance of the EE optimization as compared to those of the spectral efficiency (SE) optimization.

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### References

[2] W. C. Liao, M. Hong, Y. F. Liu, and Z. Q. Luo, “Base station activation and linear transceiver design for optimal resource management in heterogeneous networks,” IEEE Trans. Signal Process., vol. 62, pp. 3939–3952, Aug. 2014.

[3] B. Guler and A. Yener, “Uplink interference management for coexisting MIMO femtocell and macrocell networks: An interference alignment approach,” IEEE Trans. Wireless Commun., vol. 13, pp. 2246–2257, Apr. 2014.

[4] X. Kang, Y. C. Liang, and H. K. Garg, “Distributed power control for spectrum-sharing femtocell networks using stackelberg game,” in 2011 IEEE Int. Conf. Commun. (ICC), pp. 1–5, Jun. 2011.

[5] F. Pantisano, M. Bennis, W. Saad, M. Debbah, and M. Latvaaho, “Interference alignment for cooperative femtocell networks: A game-theoretic approach,” IEEE Trans. Mobile Computing, vol. 12, pp. 2233–2246, Nov. 2013.

[6] Y. Li, M. Sheng, C. Yang, and X.Wang, “Energy efficiency and spectral efficiency tradeoff in interference-limited wireless networks,” IEEE Commun. Letters, vol. 17, pp. 1924–1927, Oct. 2013.

[7] N. Zhao, F. R. Yu, and H. Sun, “Adaptive energy-efficient power allocation in green interference-alignment-based wireless networks,” IEEE Trans. Veh. Technol., vol. 64, pp. 4268– 4281, Sept. 2015.

[8] A. C. Cirik, S. Biswas, S. Vuppala, and T. Ratnarajah, “Energy efficient beamforming design for full-duplex MIMO interference channels,” in 2017 IEEE Int. Conf. Commun. (ICC), pp. 1–6, May 2017.

[9] S. He, Y. Huang, S. Jin, and L. Yang, “Coordinated beamforming for energy efficient transmission in multicell multiuser systems,” IEEE Trans. Commun., vol. 61, pp. 4961–4971, Dec. 2013.

[10] J. Xu and L. Qiu, “Energy efficiency optimization for MIMO broadcast channels,” IEEE Trans. Wireless Commun., vol. 12, pp. 690–701, Feb. 2013.

[11] Y. Li, P. Fan, and N. C. Beaulieu, “Cooperative downlink max-min energy-efficient precoding for multicell MIMO networks,”IEEE Trans. Veh. Technol., vol. 65, pp. 9425–9430, Nov.2016.

[12] Y. Li, Y. Tian, and C. Yang, “Energy-efficient coordinated beamforming under minimal data rate constraint of each user,” IEEE Trans. Veh. Technol., vol. 64, pp. 2387–2397, Jun. 2015.

[13] T. T. Vu, H. H. Kha, O. Muta, and M. Rihan, “Energy-efficient interference mitigation with hierarchical partial coordination for MIMO heterogeneous networks,” IEICE Trans. Commun., vol. E100.B, pp. 1023–1030, Jun. 2016.

[14] N. Zhao, F. R. Yu, and H. Sun, “Power allocation for interference alignment based cognitive radio networks,” in 2014 IEEE Conf. Computer Communications Workshops (INFOCOM WKSHPS), pp. 742–746, Apr. 2014.

[15] M. Cui, B. J. Hu, X. Li, H. Chen, S. Hu, and Y. Wang, “Energy-efficient power control algorithms in massive MIMO cognitive radio networks,” IEEE Access, vol. 5, pp. 1164–1177, Jan. 2017.

[16] Z. Xu, C. Yang, G. Y. Li, Y. Liu, and S. Xu, “Energy-efficient CoMP precoding in heterogeneous networks,” IEEE Trans. Signal Process., vol. 62, pp. 1005–1017, Feb. 2014.

[17] Q. Shi, M. Razaviyayn, Z. Q. Luo, and C. He, “An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,” in 2011 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), pp. 3060–3063, May 2011.

[18] D. P. Palomar, M. A. Lagunas, and J. M. Cioffi, “Optimum linear joint transmit-receive processing for MIMO channels with QoS constraints,” IEEE Trans. Signal Process., vol. 52, pp. 1179–1197, May 2004.

[19] J.-P. Crouzeix and J. A. Ferland, “Algorithms for generalized fractional programming,” Mathematical Programming, vol. 52, pp. 191–207, May 1991.

[20] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge university press, 2004.

[21] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.1.” http://cvxr.com/cvx, 2014.

[22] M. Razaviyayn, M. Hong, and Z. Q. Luo, “Linear transceiver design for a MIMO interfering broadcast channel achieving max-min fairness,” in 2011 Conf. Signals, Systems and Computers (ASILOMAR), pp. 1309–1313, Nov. 2011.

**Journal of Science and Technology: Issue on Information and Communications Technology**, [S.l.], v. 4, n. 1, p. 1-8, sep. 2018. ISSN 1859-1531. Available at: <http://ict.jst.udn.vn/index.php/jst/article/view/62>. Date accessed: 24 mar. 2023. doi: https://doi.org/10.31130/jst.2018.62.