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Wireless Communication

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Presentation on theme: "Wireless Communication"— Presentation transcript:

1 Wireless Communication
Lecture 4 Omar Abu-Ella

2 Channel Capacity Omar Abu-Ella

3 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

4 AWGN Channel Capacity Omar Abu-Ella

5 Power and Bandwidth Limited Regimes
Omar Abu-Ella

6 Band limited regime SNR>>1
N0=1 assumed Omar Abu-Ella

7 Power limited regime SNR<<1
N0=1 assumed Omar Abu-Ella

8 Capacity Curve Omar Abu-Ella

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

10 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

11 Capacity of Fading Channels
Omar Abu-Ella

12 Capacity of fading channel
Omar Abu-Ella

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

14 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

15 Optimal Adaptive Scheme
Power Adaptation Capacity Waterfilling 1 g g0 Omar Abu-Ella

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

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

18 Asymptotic results Omar Abu-Ella

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

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 Omar Abu-Ella

21 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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