5. capacity of wireless channels
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1
5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
5. Capacity of Wireless Channels
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Information Theory• So far we have only looked at specific communication
schemes.• Information theory provides a fundamental limit to
(coded) performance.• It succinctly identifies the impact of channel resources on
performance as well as suggests new and cool ways to communicate over the wireless channel.
• It provides the basis for the modern development of wireless communication.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Historical Perspective
• Wireless communication has been around since 1900’s.
• Ingenious but somewhat adhoc design techniques
Claude ShannonGugliemo Marconi
•Information theory says every channel has a capacity.• Many recent advances based on understanding wireless channel capacity.
New points of views arise.
1901 1948
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Multipath Fading: A Modern View
Classical view: fading channels are unreliable
Modern view: multipath fading can be exploited to increase spectral efficiency.
16dB
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Capacity of AWGN Channel
Capacity of AWGN channel
If average transmit power constraint is watts and noise psd is watts/Hz,
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Power and Bandwidth Limited Regimes
Bandwidth limited regime capacity logarithmic in power, approximately linear in bandwidth.
Power limited regime capacity linear in power, insensitive to bandwidth.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Frequency-selective Channel
's are time-invariant.OFDM converts it into a parallel channel:
where is the waterfilling allocation:
with chosen to meet the power constraint.Can be achieved with separate coding for each sub-carrier.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Waterfilling in Frequency Domain
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Fading ChannelsDifferent notions of capacity, depending on scenarios:
• Slow fading channel: outage capacity
• Fast fading channel: “ergodic” capacity under infinitely deep time interleaving
• Capacity also depends on whether channel knowledge is known at the transmitter and/or receiver.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Slow Fading Channel
h random.
There is no definite capacity.
Outage probability:
outage capacity:
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Outage for Rayleigh Channel
Pdf of log(1+|h|2SNR) Outage cap. as fraction of AWGN cap.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Receive Diversity
Diversity plus power gain.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Time Diversity (I)
Coding done over L coherence blocks, each of many symbols.
This is a parallel channel. If transmitter knows the channel, can do waterfilling.
Can achieve:
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Time Diversity (II) Without channel knowledge,
Rate allocation cannot be done.
Coding across sub-channels becomes now necessary.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Fast Fading Channel Channel with L-fold time diversity:
As
Fast fading channel has a definite capacity:
Tolerable delay >> coherence time.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Capacity with Full CSI
Suppose now transmitter has full channel knowledge.
What is the capacity of the channel?
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Fading Channel with Full CSI This is a parallel channel, with a sub-channel for each
fading state.
is the waterfilling power allocation as a function of the fading state, and is chosen to satisfy the average power constraint.
where
Can be achieved with separate coding for each fading state.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Transmit More when Channel is Good
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Performance
At high SNR, waterfilling does not provide any gain. But transmitter knowledge allows rate adaptation and simplifies coding.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Performance: Low SNR
Waterfilling povides a significant power gain at low SNR.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Waterfilling vs Channel Inversion• Waterfilling and rate adaptation maximize long-term
throughput but incur significant delay.
• Channel inversion (“perfect” power control in CDMA jargon) is power-inefficient but maintains the same data rate at all channel states.
• Channel inversion achieves a delay-limited capacity.
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5: Capacity of Wireless Channels
Fundamentals of Wireless Communication, Tse&Viswanath
Summary• A slow fading channel is a source of unreliability: very
poor outage capacity. Diversity is needed.• A fast fading channel with only receiver CSI has a
capacity close to that of the AWGN channel. Delay is long compared to channel coherence time.
• A fast fading channel with full CSI can have a capacity greater than that of the AWGN channel: fading now provides more opportunities for performance boost.
• The idea of opportunistic communication is even more powerful in multiuser situations, as we will see.
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