On Parameter Estimation Employing Sinewave Fit andPhase Noise Compensation in OFDM Systems
Abstract: In today’s modern society, we are surrounded by a multitude of digital devices.The number of available digital devices is set to grow even more. As the trendcontinues, product life-cycle is a major issue in mass production of these devices.Testing and verification is responsible for a significant percentage of the productioncost of digital devices. Time efficient procedures for testing and characterization aretherefore sought for. Moreover, the need for flexible and low-cost solutions in thedesign architecture of radio frequency devices coupled with the demand for highdata rate has presented a challenge caused by interferences from the analog circuitparts. Study of digital signal processing based techniques which would alleviate theeffects of the analog impairments is therefore a pertinent subject.In the first part of this thesis, we address parameter estimation based on wave-form fitting. We look at the sinewave model for parameter estimation which iseventually used to characterize the performance of a device. The underlying goal isto formulate and analyze a set of new parameter estimators which provide a moreaccurate estimate than well known estimators. Specifically, we study the maximum-likelihood (ML) SNR estimator employing the three-parameter sine fit and derivealternative estimator based on its statistical distribution. We show that the meansquare error (MSE) of the alternative estimators is lower than the MSE of the MLestimator for a small sample size and a few of the new estimators are very close tothe Cramér-Rao lower bound (CRB). Simply put, the number of acquired measure-ment samples translate to measurement time, implying that the fewer the numberof samples required for a given accuracy, the faster the test would be. We alsostudy a sub-sampling approach for frequency estimation problem in a dual channelsinewave model with common frequency. Coprime subsampling technique is usedwhere the signals from both channels are uniformly subsampled with coprime pairof sparse samplers. Such subsampling technique is especially beneficial to lower thesampling frequency required in applications with high bandwidth requirement. TheCRB based on the co-prime subsampled data set is derived and numerical illus-trations are given showing the relation between the cost in performance based onthe mean squared error and the employed coprime factors for a given measurementtime.In the second part of the thesis, we deal with the problem of phase-noise (PHN).First, we look at a scheme in orthogonal frequency-division multiplexing (OFDM)system where pilot subcarriers are employed for joint PHN compensation, channelestimation and symbol detection. We investigate a method where the PHN statis-tics is approximated by a finite number of vectors and design a PHN codebook. Amethod of selecting the element in the codebook that is closest to the current PHNrealization with the corresponding channel estimate is discussed. We present simula-tion results showing improved performance compared to state-of-the art techniques.We also look at a sequential Monte-Carlo based method for combined channel im-pulse response and PHN tracking employing known OFDM symbols. Such techniqueallows time domain compensation of PHN such that simultaneous cancellation ofthe common phase error and reduction of the inter-carrier interference occurs.
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