Numerical optimization has played a central role in addressing key signal processing (SP) problems. Highly effective methods have been developed for a large variety of SP applications such as communications, radar, filter design, and speech and image analytics, just to name a few. However, optimization algorithms often entail considerable complexity, which creates a serious gap between theoretical design/analysis and real-time processing. In this paper, we aim at providing a new learning-based perspective to address this challenging issue. The key idea is to treat the input and output of an SP algorithm as an unknown nonlinear mapping and use a deep neural network (DNN) to approximate it. If the nonlinear mapping can be learned accurately by a DNN of moderate size, then SP tasks can be performed effectively-since passing the input through a DNN only requires a small number of simple operations. In our paper, we first identify a class of optimization algorithms that can be accurately approximated by a fully connected DNN. Second, to demonstrate the effectiveness of the proposed approach, we apply it to approximate a popular interference management algorithm, namely, the WMMSE algorithm. Extensive experiments using both synthetically generated wireless channel data and real DSL channel data have been conducted. It is shown that, in practice, only a small network is sufficient to obtain high approximation accuracy, and DNNs can achieve orders of magnitude speedup in computational time compared to the state-of-the-art interference management algorithm.
Bibliographical noteFunding Information:
Manuscript received December 3, 2017; revised April 19, 2018 and July 19, 2018; accepted July 26, 2018. Date of publication August 23, 2018; date of current version September 14, 2018. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Chandra Ramab-hadra Murthy. The work of H. Sun, X. Chen, and M. Hong was supported in part by the National Science Foundation under Grants CMMI-1727757 and CCF-1526078, and in part by the Air Force Office of Scientific Research under Grant 15RT0767. The work of N. D. Sidiropoulos was supported by the National Science Foundation under Grant CIF-1525194. The work of Q. Shi was supported in part by NSFC under Grants 61671411, U1709219 and 61374020, in part by the Fundamental Research Funds for the Central Universities, and in part by Zhejiang Provincial NSF of China under Grant LR15F010002. This paper was presented in part at the 18th IEEE International Workshop on Signal Processing Advances in Wireless Communications, Sapporo, Japan, July 2017 . (Haoran Sun and Xiangyi Chen contributed equally to this work.) (Corresponding author: Mingyi Hong.) H. Sun, X. Chen, and M. Hong are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,firstname.lastname@example.org; email@example.com; firstname.lastname@example.org).
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- Optimization algorithms approximation
- WMMSE algorithm
- deep neural networks
- interference management