# RP-HW3 - Kyung Hee University Department of Electronics and...

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1 Kyung Hee University Department of Electronics and Radio Engineering C1002900 Random Processing Homework 3: Sinusoid Estimation Spring 2010 Professor Hyundong Shin Issued: May 3, 2010 Due: May 17, 2010 (No acceptance of overdue submission) Reading: Course textbook Chapter 8 In this homework, we explore a basic problem involving sinusoid estimation. Specifically, given noisy observation of the form   cos , , , , nn YA n W n N  0 01 1 (3.1) we wish to estimate one or more of the nonrandom parameters A , 0 , or , where A 0 and   0 0 . In (3.1), we assume that the noises n W are i.i.d.   , 2 0 random variables. This model arises in a number of applications: analog communications, Doppler radar, noise cancel- lation, interference suppression, radio astronomy, and sonar direction-finding, for example. Analog Communication Amplitude Modulation (AM): In AM systems, the frequency 0 is known, but the am- plitude A varies with time and carries the information. In such systems, we can gener- ally approximate the amplitude as constant over the block of N samples, and consider the problem of recovering the amplitude for each block as an estimation problem. In such problems, the phase may be known, but more typically is an unknown parame- ter that, while not of interest, must be simultaneously estimated. Phase Modulation (PM): In PM systems, it is the phase that carries the information while the frequency 0 remains essentially fixed (and known). In such problems, the amplitude A is generally distorted by the channel and while similarly not of interest, must be jointly estimated as well. Frequency Modulation (FM): In FM systems, the frequency 0 carries the information and varies with time accordingly. In such systems, we then wish to estimate 0 , which is modeled as essentially constant over the block of length N . Typically, the communi- cation channel distorts both the amplitude A and phase , so these quantities must be simultaneously (i.e., jointly) estimated. Noise and Interference Cancellation A wide variety of noise and interference encountered in practice is inherently sinusoidal in nature. Examples include 60 Hz (line-frequency) interference in systems due to AC power

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2 supplies, noise from rotating machinery, propeller noise in aircraft or on ships, and nar- rowband jamming hostile or inadvertent in wireless communication systems. In such cases, the sinusoidal term in (3.1) may be the unwanted interference and n W may represent the (broadband) signal of interest. For these scenarios, an effective interference suppression strategy involves estimating the parameters of the sinusoidal interferer, then subtracting it out from the observations to recover the signal of interest.
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• Spring '10
• HyungdongShin
• Sinusoid Estimation, asymptotic ML estimation, asymptotic Cramér-Rao bounds, sinusoid estimation problem, ln fY y

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RP-HW3 - Kyung Hee University Department of Electronics and...

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