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linkbud - 1 Link Budgets Intuitive Guide to Principles of...

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Link Budgets Copyright 1998 and 2002 Charan Langton www.complextoreal.com 1 Intuitive Guide to Principles of Communications www.complextoreal.com Link Budgets You are planning a vacation. You estimate that you will need $1000 dollars to pay for the hotels, restaurants, food etc.. You start your vacation and watch the money get spent at each stop. When you get home, you pat yourself on the back for a job well done because you still have $50 left in your wallet. We do something similar with communication links, called creating a link budget. The traveler is the signal and instead of dollars it starts out with °power±. It spends its power (or attenuates, in engineering terminology) as it travels, be it wired or wireless. Just as you can use a credit card along the way for extra money infusion, the signal can get extra power infusion along the way from intermediate amplifiers such as microwave repeaters for telephone links or from satellite transponders for satellite links. The designer hopes that the signal will complete its trip with just enough power to be decoded at the receiver with the desired signal quality. In our example, we started our trip with $1000 because we wanted a budget vacation. But what if our goal was a first-class vacation with stays at five-star hotels, best shows and travel by QE2? A $1000 budget would not be enough and possibly we will need instead $5000. The quality of the trip desired determines how much money we need to take along. With signals, the quality is measured by the Bit Error Rate (BER). If we want our signal to have a low BER, we would start it out with higher power and then make sure that along the way it has enough power available at every stop to maintain this BER. How we specify the quality of signal transmission The BER, as a measure of the signal quality, is the most important figure of merits in all link budgets. The BER is a function of a quantity called E b /N o , the bit energy per noise-density of the signal. For a QPSK signal in an additive white-gaussian-noise (AWGN) channel, the BER is given by ( ) BER erfc E N b = 1 2 0 /
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Link Budgets Copyright 1998 and 2002 Charan Langton www.complextoreal.com 2 This formula says that the BER of any signal is related to its E b /N o by the function, erfc . The function erfc, called the complimentary error function describes the cumulative probability curve of a gaussian distribution. It is found tabulated in most communications textbooks and is available as a built-in function in most math programs. The above equation when plotted has a classic waterfall shape when plotted on a log-log scale. The BER is inversely related to E b /N o . Higher E b /N o means better quality. Figure 1 - The Bit Error rate of a signal is a function of its E b /N o Although I started out talking about signal power as a measure of signal quality, you may have noticed that I have suddenly shifted to E b /N 0 . Instead of monitoring just the signal power as I said on the first page, we will actually monitor a ratio of the bit power to the noise power injected along the way.
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