无线通信中的最优资源分配―复杂性分析与算法设计

Optimal resource allocation for wireless communications:Complexity analysis and algorithm design

最优资源分配问题是无线通信系统设计中的基本问题之一.最优地分配功率、传输波形和频谱等资源能够极大地提高整个通信系统的传输性能.目前,相对于通信技术在现实生活中的蓬勃发展,通信系统优化的数学理论和方法显得相对滞后,在某些方面已经成为影响其发展和应用的关键因素.无线通信中的最优资源分配问题常常可建模为带有特殊结构的非凸非线性约束优化问题.一方面,这些优化问题常常具有高度的非线性性,一般情况下难于求解;另一方面,它们又有自身的特殊结构,如隐含的凸性和可分结构等.本文着重考虑多用户干扰信道中物理层资源最优分配问题的复杂性刻画,以及如何利用问题的特殊结构设计有效且满足分布式应用等实际要求的计算方法.

Resource allocation is a fundamental problem in the design of wireless communication systems. The mutual interference among users, which is a major factor of limiting the performance of communication systems, can be efficiently mitigated by carefully allocating wireless resources such as transmission power, transmission waveforms, and frequency bands. Current mathematical theories and methods for the design of communication systems lag behind the rapid development of communication technologies, and sometimes influence their devel- opments and applications. Most of the resource allocation problems arising from wireless communications boil down to non-convex nonlinear constrained optimization problems with special structures. On one hand, these op- timization problems are often non-convex and highly nonlinear, and thus are difficult to solve; on the other hand, these problems have their own special structures such as （hidden） convexity and separability. This paper focuses on the optimal physical layer resource allocation problems for the multi-user interference channel, especially on characterizing the computational complexity of these problems, and designing efficient algorithms （satisfying some practical requirements like distributed implementation） for these problems by the use of their special structures.