Prediction, Estimation and Detection Problems with Quantization Considerations: Applications to Financial Markets and Wireless Communication
Problems involving prediction, estimation and detection of signals are three broad categories of problems occurring in statistical signal processing. In this work, we address these problems in specific contexts where quantization of observations plays an important role. Firstly we consider mid-price prediction in present day financial markets called limit order book markets. We propose several nonparametric predictors of the sign of mid-price movements in such markets. These sign predictors are based on different features constructed from the order book data observed contemporaneously and in the recent past. Using historical market data, we evaluate our predictors through an order execution task. We construct order execution strategies that incorporate these predictors and show that the predictors can be used to obtain statistically and economically significant improvements in execution costs. Secondly, we consider wireless spectrum sharing techniques that have become very important due to the increasing demand for spectrum. Hence there is growing interest in using real-time auctions for economically incentivizing users to share their excess spectrum. However, prior literature has not considered critical constraints such as bid price quantization, communication overheads and error prone bid revelation that would pose serious problems in implementing secondary spectrum auctions. We propose auction schemes where a central clearing authority auctions spectrum to bidders, while explicitly accounting for these communication constraints. We consider several scenarios where the clearing authority's objective is to award spectrum to bidders who value spectrum the most. We prove that this objective is asymptotically attained by our scheme when bidders are non-strategic with constant bids. We propose separate schemes to make strategic users reveal their private values truthfully, auction multiple sub-channels among strategic users, and track slowly time-varying bid prices.Thirdly, spectrum shortage has also increased the necessity to use high frequency millimeter wave (mmWave) bands for 5G communication systems. Analog to digital converters (ADCs) contribute significantly to the implementation cost and power consumption of such receivers. The use of large antenna arrays in mmWave communications causes these costs to rise even further. These costs can be reduced if low precision quantizers are used in ADCs. As part of this work, we propose a novel receiver design using low precision quantizers drawing ideas from the parallel ADC design literature. Utilizing structural similarities between multi-antenna receivers and parallel ADCs, we show that the signal-to-noise ratio and achievable rate respectively scale linearly and logarithmically with the number of antennas. We also extend the idea where multiple streams can be transmitted simultaneously. All our designs depend only on symbol rate sampling, which eliminates costly oversampling of high bandwidth signals.
Love, Purdue University.
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