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Wireless Communication

Wireless Communication. Lecture 4. Channel Capacity. 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

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Wireless Communication

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  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. 1 g g0 g Optimal Adaptive Scheme Waterfilling • Power Adaptation • Capacity 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. P Bc 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 f Omar Abu-Ella

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