I need a help to review my statement of purpose. I major in ECE and I conducted research about communication system. Now, I move on Ph.D program in ECE specialized in financial engineering. Please give me a any type of feedback. Thank you so much in advance.
Looking back about 3 years ago, major investment firms and even insurance companies which had been proudly selling derivatives, had to file bankruptcies and finally caused economic crisis called 2nd great depression in history. Finally governments had to be involved to provide a bailout to the firms in such crisis but it was known that the quantitative analysts are the ones who to be blamed for causing that issue and eventually the ones who will have to recover the world economy. As a senior student majoring in engineering, I diagnosed the cause of this economic problem is that financial engineer ran economic models without fully investigating system input variances. In that statistical signal processing foresees system results with various signal inputs, it will be a key to designing more robust financial systems.
With this plan, I studied signal processing from which I had opportunities of creating various models, having to maximize performance and trying to find a better way to optimize channel performance of communication systems. I researched mainly for mathematical logic and analysis, a basic element of communication theory. However, I kept planning on my goal after the master's degree to study about application tools of engineering into real world economy and it became even more firm when I attended a seminar entitled "Introduction to Option Trading from a Control Perspective". Consequently, I learned that financial engineers use stochastic models to predict financial markets, as I also used a stochastic model to predict communication channel functioning. Indeed, both engineers develop algorithms to optimize performance. I soon found that an interdisciplinary approach is critical, as it creates creative, innovative, and synergetic results. Additionally, Dr. Derman encourages PhD students majoring in physics or engineering to study finance given that their research fits with the financial research in his book titled "Quant". This book gave me a more realistic goal and plan for my future in this field. Though I have researched communication theory for over three years and passed the PhD qualification exam, I am making this shift in research field given my clear passion and my strong interest in financial market movements.
To succeed on this trajectory, I plan to leverage my relevant background garnered from graduate-level courses, research, and computational skills. In particular, I enrolled and excelled in courses on modern probability theory, information theory, statistical signal processing, linear system, linear programming, applied linear algebra, and numerical linear algebra. Especially from the wireless communication course, I worked on a course assignment of comparison between OFDM-MIMO and CDMA-MIMO and had a strong motivation for studying more about developing statistical systems. By discussing my interesting research topics with Professor Akbar, I was able to start independent study under his guidance, from which I could develop phased MIMO radar with reconfigurable antennas. From this independent study, I found that the optimal antenna distance depends on scattering objects and I also designed a beam-pattern to minimize a false alarm rate as a result. Professor Akbar was satisfied with the results and recommended for me to join his research group as a research assistant and I then researched for continuous aperture phased-MIMO, an analog beam-forming communication system. In this research, I built a sparse multipath channel model, designed the pre-coder and filter to minimize interference and ultimately I was able to publish papers with this research findings, which were successfully decreasing complexity without any loss in performance from previously developed MIMO systems. For this project, I applied stochastic modeling with uniform distribution to spot positions of scattering objects, which will decide how the channel will work at each position. By examining the channel capacity and probability of an error, I finally designed pre-coder and filter increasing performance of the communication system. Indeed, during my research, I used statistical signal processing to determine the transmitted signal and find the position of the scattering objects, which is highly relevant to the Bayesian mechanism research of Professor Hartline. His research topic was based on maximizing surplus or benefit of winning a game or implementing an economic model. I envision that studying stock and foreign-exchange markets and auction biddings starts from building a stochastic model to mimic real economics. The first step will be establishing the performance measurement, which would be surplus, growth rate, or revenue of any financial objects. The next step would be developing algorithms to maximize system performance based on the stochastic economic model. Thus, mathematical analysis will have to be verified through computational simulation. Eventually after earning my doctorate, I plan to gain industry experience where I can apply such knowledge that I have gained from research.
At this point, I am ultimately finalizing a paper with the findings from the multipath channel model optimization research. Specifically, the ICASSP 2013 paper has been submitted and the IEEE transaction is in progress. Throughout the research process, I learned valuable techniques for conducting effective research and independent study. This entailed drafting a research plan at the first stage, presenting and writing research results, reviewing previous research and communicating with other team mates to decide a research direction. Also, I deepened and broadened my computer language skills such as Matlab, JAVA, C/C++ or Mathematica to the point of being proficient, because computational simulation is a main tool for experimentally implementing communication systems in our computational research group.
Given these goals, Northwestern University offers the ideal training, resources, and environment. It is the best place to study ECE with a finance specialization, and it is based in Chicago, one of the world's largest finance markets. Consequently, I can experience firsthand and up-to-date economic news and gain the insight needed to develop new applications for statistical signal processing. Further, Northwestern University has an economics group in ECE, which frequently interacts and communicates with the economic department, one of the best in the U.S. I therefore look forward to your program, as it offers an excellent education and research support that will allow me to become a professional independent researcher. Further, with more stability and family support from my family members living in Chicago, I am prepared for life in Chicago. In sum, it is with this background, mindset, and focus that I aim to prove an asset to Northwestern University and a promising contributor to this dynamic field.