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Lecture 4 1Omar Abu-Ella

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Channel Capacity 2Omar Abu-Ella

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Shannon Capacity Defined as the maximum mutual information of channel Maximum error-free data rate a channel can support. Theoretical limit (usually dont know how to achieve) Depends on the channel characteristics We focus on AWGN channel with fading 3Omar Abu-Ella

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AWGN Channel Capacity 4Omar Abu-Ella

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Power and Bandwidth Limited Regimes 5Omar Abu-Ella

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Band limited regime SNR>>1 N 0 =1 assumed 6Omar Abu-Ella

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Power limited regime SNR<<1 N 0 =1 assumed 7Omar Abu-Ella

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Capacity Curve 8Omar Abu-Ella

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Shannon Limit in AWGN channel What is the minimum SNR per bit (Eb/N0) for reliable communications? 9Omar Abu-Ella

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Capacity of Flat-Fading Channels Capacity defines theoretical rate limit Maximum error free rate a channel can support Depends on what is known about channel CSI: channel state information CDI: channel distribution information Unknown fading: Worst-case channel capacity Fading Known at Receiver Only 10Omar Abu-Ella

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Capacity of Fading Channels 11Omar Abu-Ella

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Capacity of fading channel 12Omar Abu-Ella

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Fading channel, only Rx knows CSI 13Omar Abu-Ella

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Fading Known at both Transmitter and Receiver For fixed transmit power, same as only receiver knowledge of fading Transmit power P( ) can also be adapted Leads to optimization problem: 14Omar Abu-Ella

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15 Optimal Adaptive Scheme Power Adaptation Capacity 1 0 Waterfilling

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An equivalent approach: power allocation over time 16Omar Abu-Ella

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Optimal Solution The water-filling solution is given by To define the water level, solve: 17Omar Abu-Ella

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Asymptotic results 18Omar Abu-Ella

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Performance Comparison At high SNR, water-filling does not provide any gain. Transmitter knowledge allows rate adaptation and simplifies coding. 19Omar Abu-Ella

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20 Channel Inversion Fading inverted to maintain constant SNR Simplifies design (fixed rate) Greatly reduces capacity Capacity is zero in Rayleigh fading Truncated inversion Invert channel above cutoff fade depth Constant SNR (fixed rate) above cutoff Cutoff greatly increases capacity Close to optimal

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Omar Abu-Ella21 Frequency Selective Fading Channels For time-invariant channels, capacity achieved by water-filling in frequency Capacity of time-varying channel unknown Approximate by dividing into subbands Each subband has width B c (like MCM). Independent fading in each subband Capacity is the sum of subband capacities BcBc f P 1/|H(f)| 2

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