1. Wireless Communication
Lecture 4
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2. Channel Capacity
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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
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4. AWGN Channel Capacity
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5. Power and Bandwidth Limited Regimes
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6. Band limited regime SNR>>1
N0=1 assumed
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7. Power limited regime SNR<<1
N0=1 assumed
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8. Capacity Curve
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9. Shannon Limit in AWGN channel
What is the minimum SNR per bit (Eb/N0) for reliable communications?
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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
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11. Capacity of Fading Channels
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12. Capacity of fading channel
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13. Fading channel, only Rx knows CSI
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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:
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15. Optimal Adaptive Scheme
Power Adaptation
Capacity
Waterfilling 1 g g0
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16. An equivalent approach: power allocation over time
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17. Optimal Solution The water-filling solution is given by
To define the water level, solve:
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18. Asymptotic results
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19. Performance Comparison
At high SNR, water-filling does not provide any gain.
Transmitter knowledge allows rate adaptation and simplifies coding.
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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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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
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