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notes12 - ECE 562 Fall 2010 Shannon’s Capacity Theorem...

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Unformatted text preview: ECE 562 Fall 2010 Shannon’s Capacity Theorem and Spectral Efficiency of Modulation Methods • Shannon’s Capacity Theorem. For the AWGN channel, the maximum rate at which reliable communication (P e → 0 for as block length goes to infinity) is possible for signal power P , noise power spectral density N , and bandwidth W Hz is given by C = W log 2 1 + P N W bits/s Note that P N W is the signal-to-noise ratio (SNR). Shannon’s result says that only information rates R < C bits/s can possibly result in reliable communication. Now, the result applies to coded systems, which we will study later, and for linear modulation schemes we need an outer code to drive the error probability to arbitrarily small values for at a given SNR. Interestingly, for orthogonal modulation, as we saw earlier we can drive the error probability to zero by letting M → ∞ . • Spectral Efficiency. The spectral efficiency of a signaling scheme over a communication channel is defined to the ratio of the information bit rate...
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notes12 - ECE 562 Fall 2010 Shannon’s Capacity Theorem...

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