基本情况：李同学，复旦大学，电子工程本科，GPA 3.69，TOEFL 105，GRE 328 

录取学校：Purdue University, West Lafayette Ph.D. in Electrical and Computer Engineering 

My keen interest and strength in Electrical Engineering are tempered through leading team to participate in scientific research innovation contest and performing researches under the supervision of faculty. It is also through such kind of practices that my determination to pursue a doctoral degree in Electrical Engineering is strengthened. I expect to equip myself with the leading-edge knowledge and research methods pertinent to communications and networking, particularly, in optimization. 

In recent years, 5G innovation has compelled the attention of researchers and engineers from all over the world. The blueprint of 5G combines massive MIMO with Heterogeneous Networks (HetNets), which relies on ultra-dense and irregular operator- deployment of Base Stations (BSs) together. However, such combination leads to certain problems. For instance, with the growing number of BSs, the electricity bill has become a major part of the operational expenditure of cellular networks. Meanwhile, on one hand, massive MIMO can significantly improve the spatial degree of freedom and thus bring higher throughput; on the other hand, the super-fast data rate leaves the network controller a huge challenge: how to make the network stable with limited loss inperformance? 

From my current knowledge, the soaring electricity bill could be solved through the using of smart grid. While, with only limited (or none) knowledge of the distribution of the harvested energy in the network planning of smart grid, a stochastic optimization problem could be formulated. And to solve this problem, an online Stochastic Gradient Decent (SGD) solver or the Lyapunov method could be employed. The Lyapunov method minimizes the drift plus penalty and can guarantee the strong stability of the queues with only a bounded loss of performance. Considering the virtue queues of Lyapunov method and the subgradient of SGD are mutual connected, one of my future goal is to identify these connections. 

At graduate school, I will put effort into the research on Convex Optimization, Stochastic Optimization, in addition accompanied by Machine Learning and Online Convex Optimization. I have ever performed mixed integer programming in the joint base station activation project, and have a grasp of Convex Optimization and Stochastic Optimization. Through graduate work, I also want to take into a deeper dive into related fields, and position myself for cutting-edge researches in network planning and design, for example, massive MIMO, integration of renewable energy/smart power grids and wireless communication, beamforming, power allocation, design of sensor network, and so forth. 

Based on the above factors, I have decided to apply to the Ph.D. in Electrical and Computer Engineering program in your ECE department. The researches in the field of Communications, Networking, Signal & Image Processing in your department can satisfy my interests and fulfill my study plan. Particularly, after carefully reading your faculty’s websites, I am interested in Professor Borja Peleato-Inarrea’s research in convex optimization, as well as Professor Saul B. Gelfand and Stanley Chan’s research in optimization. I am looking forward to getting more exposure to their research and performing doctoral study under their guidance. 

My undergraduate experience has well prepared me for further studies in the aforementioned areas. To be specific, the bachelor’s curriculum has familiarized me with the concepts and methods in linear algebra, signal and system, digital signal processing, probability, principles of communication and signal detection. Furthermore, a thorough understanding of theorem proving processes and derivations of conclusions strengthened my knowledge. Making mention of programming, I have a good command of MATLAB and C++ skills, and I am proficient in applying them to deal with real problems. Besides, my mastery of hardware description languages and assembly language can add to my qualifications to fulfill your program. 

With an inner drive, I conducted researches in the areas I am passionate about. In my junior year, I worked alongside a faculty advisor and a graduate student in a project centered on joint base station activation and downlink beamforming in HetNets. At the beginning, we developed a mixed integer programming, and reformulated the problem to a semidefinite programming (SDP) at a later point. However, the simulation results got from both attempts were not satisfactory. To make improvements, we employed Gibbs sampling, yet the results were still not as ideal as supposed. Through a further analysis, I found that the reason led to such results was that we had oversimplified this problem, for which we could not make the best of spatial degrees of freedom. 

I also had research experience concerning uplink power allocation. To get a thorough understanding of certain system and identify the underlying factors that influence the performance of uplink cellar system, I conducted a simulation using MATLAB, assuming the number of antennas is extremely large at BS and only one antenna at each user equipment. The total power is limited in one cellar and equal power allocation among users. Based on the results achieved, Inoticed that with MMSE receiver, if the channel is estimated perfectly, the inter-cell inferences do not have too much impact on system performance. However, when there exists pilot contamination with MMSE channel estimation, a gap between single cell and multicells cellar systems would emerge. Thus, I demonstrated the demand of the uplink power allocation and pilot design in multicell- multiuser massive MIMO systems. 

To earn a Ph.D. degree from Purdue University will be a big challenge for me. But, on the strength of my strong passion for and academic background in performing research, I have faith in myself that I will thrive as a researcher who can lead innovations in communications and networking, and through my experience of Purdue.