Network Performance

Network Performance - TELCOM 2120: Network Performance Fall...

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TELCOM 2120: Network Performance Fall 200 9 Homework 1 Solution Problem 1 (5 points) Consider a binary digital communication channel. To transmit a digital 0 the sender places a voltage of -1 volt on the channel for the symbol duration time. To transmit a digital 1 the sender places a voltage of +1 volt on the channel for the symbol duration time. The receiver detects the symbol on the communication channel as signal Y = v + N where v is 1 or -1 volt depending on the symbol transmitted and N is Gaussian white noise which is modeled as a Normally distributed random variable with mean 0 and variance 4. The receiver decides a 0 was sent if the voltage Y is negative and a 1 otherwise. (a) Find the probability of the receiver making an error if a digital 0 is sent. v is -1 when a digital 0 is transmitted. The receiver would make an error when Y > 0. That happens when N > 1. Since N is normally distributed with zero mean and variance 4, Pr[N > 1] = 1 - Pr[N ≤ 1] = 1 - Pr[Z ≤ (1 - μ ) / σ ] = 1 - Pr[Z ≤ (1 - 0) / 4] = 1 – (0.5+0.1915) = 0.3085 (b) What is the probability of making the correct decision if a digital 1 is transmitted? v is +1 when a digital 1 is transmitted. The receiver would make a correct decision when Y > 0. That happens when N > -1. Using the similar approach,
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Network Performance - TELCOM 2120: Network Performance Fall...

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