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# DIGITAL COMMUNICATION EEL 6535

UF

GPA 3.75

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This 4 page Study Guide was uploaded by Brandon Douglas on Friday September 18, 2015. The Study Guide belongs to EEL 6535 at University of Florida taught by John Shea in Fall. Since its upload, it has received 19 views. For similar materials see /class/206811/eel-6535-university-of-florida in Electrical Engineering at University of Florida.

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Date Created: 09/18/15

EEL 6535 Study Guide for Exam I BINARY COMMUNICATION 0 Analysis of linear receiver Analyze performance determine distribution of decision statistic and use in error probability analysis for gtk arbitrary signals gtk arbitrary noise PSD gtk arbitrary lter shapes gtk be able to apply any techniques from EEL 5544 required to perform this analysis Design matched lter receiver Design correlator receiver based on matched lter Find decision regions and error probability performance for and know relationships among ML rule MAP Bayes rule gtllt gtllt gtk minimum probability of error rule gtk minimax rule Find a randomize minimax decision rule given the conditional density functions for the decision statistic given the transmitted signal Modify to create a non randomized minimax rule with the same performance 0 Calculate energies and correlation coef cient for signals Use to calculate error probs for matched lter ML detection 0 Calculate Euclidean distance between signals Use to calculate error probs for matched lter ML detection 0 Understand know how to construct and analyze common classes of binary modulation Antipodal Orthogonal on off Orthogonal equal energy SG 2 SIGNAL SPACE REPRESENTATIONS Determine the vector representation of a signal using a set of known basis waveforms Determine a minimal set of basis waveforms that can be used to represent a signal set Apply Gram Schmidt procedure to get basis waveforms and vector representation for a given signal set Determine the dimensionality of a signal set Understand relationship between norm and inner product of time domain signals and vector signal space representations Understand how antipodal and orthogonal signal sets appear in signal space representations Draw signal constellations APPLY SIGNAL SPACE REPRESENTATIONS TO COMMUNICATIONS Calculate error probabilities for binary signal sets with matched lterML detection Determine an optimal demodulator for an M aiy signal set Show that the noise at the output of different branches of the correlator demodulator is independent and identically distributed if it correlates with basis functions for the signal set Show that the noise that lies outside the signal space is independent of the signal and the signal space representation of the noise that lies in the signal space Use the signal constellation to determine the exact symbol or bit error probabilities Use the signal space constellation to determine union or nearest neighbors bounds on the error probabilities Express error probabilities in terms of the average symbol energy to noise density ratio E9 or the average bit energy to noise density ratio EbNO Apply Gray coding to a signal set to minimize the probabiltiy of symbol error Approximate the bit error probability for a Gray coded signal constellation LOW PASS EQUIVALENT SIGNALS Find the low pass equivalent signal for a bandpass signal Provide different interpretations of a LPE signal in terms of amplitude and phase real and imaginary parts etc SG 3 Find the bandpass signal from its LPE signal Provide interpretations of the bandpass signal based on the interpretations of the LPE signal mentioned above Convert between the energy of a signal and the energy of the LPE signal Find the low pass equivalent of a lter Convert between the autocorrelation function of a random process and the LPE random process SPECIFIC SIGNAL SETS Generate pulse position modulation signals and determine their performance Characterize the bandwidth ef ciency Generate equal energy M ary orthogonal amplitude modulation using Walsh Hadamard signals and determine the performance Characterize the bandwidth ef ciency Know the smallest EbNO for which error free communication is possible Provide a signal set that can achieve arbitrarily low error probability for EbNO above that limit Calculate the error probabilities and estimate the bandwidth ef ciency for BPSK Calculate the error probability under impairments such as imperfect carrier phase reference Calculate the symbol and bit error probabilities and estimate the bandwidth ef ciency for PAM Calculate performance for matched lterML detection or for other decision rules Apply Gray coding or natural coding to a signal set Calculate the exact bit error probabilities for a speci c bit coding Approximate the bit error probabilities for Gray coding Know relationships between bandwidth and energy ef ciency of BPSK and QPSK Calculate exact symbol and bit error probabilities for QPSK Calculate error probabilities and bandwidth ef ciency for M QAM Determine a 2 D Gray coding for M QAM BANDWIDTH EFFICIENCY Calculate bandwidth ef ciency using absolute bandwidth for Nyquist signaling or null to null bandwidth for square pulse shape Know Nyquist signaling rate for a given bandwidth and connection with Nyquist sampling rate SG 4 PRESENTATION OF DATA Convert from decibels to linear units and back Convert between ES and E5 Express performance differences between signal constellations or receiver structures in decibels Plot data with EbNO in decibel units on a linear X axis and the error probabilities on a logarithmic y axis

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