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**Wireless Communication**

Lecture 4 Omar Abu-Ella

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Channel Capacity Omar 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 don’t know how to achieve) Depends on the channel characteristics We focus on AWGN channel with fading Omar Abu-Ella

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AWGN Channel Capacity Omar Abu-Ella

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**Power and Bandwidth Limited Regimes**

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**Band limited regime SNR>>1**

N0=1 assumed Omar Abu-Ella

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**Power limited regime SNR<<1**

N0=1 assumed Omar Abu-Ella

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Capacity Curve Omar Abu-Ella

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**Shannon Limit in AWGN channel**

What is the minimum SNR per bit (Eb/N0) for reliable communications? Omar 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 Omar Abu-Ella

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**Capacity of Fading Channels**

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**Capacity of fading channel**

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**Fading channel, only Rx knows CSI**

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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(g) can also be adapted Leads to optimization problem: Omar Abu-Ella

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**Optimal Adaptive Scheme**

Power Adaptation Capacity Waterfilling 1 g g0 Omar Abu-Ella

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**An equivalent approach: power allocation over time**

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**Optimal Solution The water-filling solution is given by**

To define the water level, solve: Omar Abu-Ella

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Asymptotic results Omar 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. Omar Abu-Ella

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**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 Omar Abu-Ella

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**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 Bc (like MCM). Independent fading in each subband Capacity is the sum of subband capacities 1/|H(f)|2 Bc P f Omar Abu-Ella

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