Large-scale non-convex optimization in wireless communications
A central theme of wireless communication research is to allocate limited resources to achieve the best performance. Traditionally, these resources are time, bandwidth, power, spatial beam and code. In emerging and future applications, the resources may also include computing power, caching capability, edge resource, data offloading time, energy in robot, and machine learning accuracy. But no matter how the resource is defined, the resource allocation problems are usually formulated as constrained optimization problems.
Due to the appearance of data rate, SINR or energy efficiency, most wireless resource allocation problems are nonconvex constrained optimization problems. One prevalent way to handle nonconvex constrained optimization problems is to approximate them by convex counterparts (such as using successive convex approximation (SCA) or semidefinite relaxation (SDR)), and then apply off-the-shelf numerical solvers to solve the approximated convex problems. However, even we do not care about the performance loss due to approximations, most of the ready-to-use convex problem solvers are based on interior-point methods (IPMs), and their complexity orders are of O(S3.5), where S is the problem size. This makes them not suitable for large-scale problems.
On the other hand, it is possible to derive first-order methods (i.e., algorithms only involve gradient computation) for solving these problems. A celebrated example is the alternating direction method of multipliers (ADMM), but ADMM is only guaranteed to converge in convex problems. In order to take care of the nonconvex constraints in gradient-based methods, a variety of strategies such as variable splitting, converting constraints as penalty terms, iterative function linearization, projection, can be applied. Using these strategies judiciously, we have shown in various wireless systems that the computation time can be reduced by a factor of 100 while without sacrificing the system performance, compared to interior-point methods.
1. Zongze Li, Minghua Xia, Miaowen Wen, and Yik-Chung Wu, ``Massive Access in Secure NOMA under Imperfect CSI: Security Guaranteed Sum-rate Maximization with First-order Algorithm," to appear in IEEE Journal on Selected Areas in Communications (JSAC).
2. Fanqing Tan, Peiran Wu, Yik-Chung Wu, and Minghua Xia, ``Energy-efficient Non-orthogonal Multicast and Unicast Transmission of Cell-free Massive MIMO Systems with SWIPT," to appear in IEEE Journal on Selected Areas in Communications (JSAC).
3. Shuai Wang, Yik-Chung Wu, Minghua Xia, Rui Wang, and H. Vincent Poor, ``Machine Intelligence at the Edge with Learning Centric Power Allocation," IEEE Trans. on Wireless Communications. Vol. 19, no. 11, pp. 7293-7308, Nov. 2020. (the conference version of this paper received the best paper award in IEEE ICC 2020)
4. Shuai Wang, Miaowen Wen, Minghua Xia, Rui Wang, Qi Hao, and Yik-Chung Wu, ``Angle Aware User Cooperation for Secure Massive MIMO in Rician Fading Channel," in IEEE Journal on Selected Areas in Communications (JSAC), vol. 38, no. 9, pp.2182-2196, Sept. 2020, doi: 10.1109/JSAC.2020.3000837.
5. Yang Li, Minghua Xia, and Yik-Chung Wu, ``Caching at Base Stations with Multi-Cluster Multicast Wireless Backhaul via Accelerated First-Order Algorithm," IEEE Trans. on Wireless Communications, Vol. 19, no. 5, pp. 2920-2933, May 2020.
6. Yang Li, Minghua Xia, and Yik-Chung Wu, ``Energy-Efficient Precoding for Non-Orthogonal Multicast and Unicast Transmission via First-Order Algorithm," IEEE Trans. on Wireless Communications, Vol. 18, no. 9, pp. 4590-4604, Sep 2019.
7. Yang Li, Minghua Xia, and Yik-Chung Wu, ``Activity Detection for Massive Connectivity under Frequency Offsets via First-Order Algorithms," IEEE Trans. on Wireless Communications, Vol. 18, no. 3, pp. 1988-2002, Mar. 2019.
8. Yang Li, Minghua Xia, and Yik-Chung Wu, "First-Order Algorithm for Content-Centric Sparse Multicast Beamforming in Large-Scale C-RAN," IEEE Trans. on Wireless Communications, Vol. 17, no. 9, pp. 5959-5974, Sept. 2018.
9. Shuai Wang, Minghua Xia, and Yik-Chung Wu, "Multicast Wirelessly Powered Network with Large Number of Antennas via First-Order Method," IEEE Trans. on Wireless Communications, Vol. 17, no.6, pp. 3781-3793, June 2018.
10. Bin Luo, Lei Cheng, and Yik-Chung Wu, ``Fully-distributed Clock Synchronization in Wireless Sensor Networks Under Exponential Delays," Signal Processing, Vol. 125, pp. 261-273, Aug 2016.