# HW8 - ELEN 661 Modulation Theory Homework#8 Assignment Date Due Date 1 Sensitivity of PSK to Phase Errors(a Derive an expression for the

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ELEN 661 - Modulation Theory Homework #8 Assignment Date: 4/14/08 Due Date: 4/22/08 1. Sensitivity of PSK to Phase Errors. (a) Derive an expression for the probability of error of a coherent BPSK demodulator where the local oscillator used for demodulation is out of sync with respect to the carrier of the received sig- nal by a constant phase of . Suppose it is required to support a bit error rate of . How much phase error can be tolerated without causing more than 0.5dB loss in SNR? (b) Repeat part (a) for a QPSK system. 2. Analysis of Phase Estimation Errors. Suppose we are trying to estimate the phase of an unmodulated carrier in the presence of white Gaussian noise. That is, we are able to observe the low-pass equivalent signal , over some time interval , where is the usual white Gaussian noise with autocorrela- tion given by . As discussed in class, the ML estimate for the unknown carrier phase, , will form the complex statistic , and then estimate the phase according to . In this problem, we will attempt to work out the statistics of the error in this estimate.

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## This note was uploaded on 02/21/2012 for the course ECEN 611 taught by Professor Miller during the Spring '08 term at Texas A&M.

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HW8 - ELEN 661 Modulation Theory Homework#8 Assignment Date Due Date 1 Sensitivity of PSK to Phase Errors(a Derive an expression for the

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