enhancing secrecy with channel knowledge
DESCRIPTION
Enhancing Secrecy With Channel Knowledge. Presenter: Pang-Chang Lan Advisor: C.-C. (Jay) Kuo May 2, 2014. Outline. Research Problem Statement Introduction to Achievable Rate and Capacity Physical Layer (PHY) Security Some Research Results Conclusions and Future work. - PowerPoint PPT PresentationTRANSCRIPT
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Enhancing Secrecy With Channel Knowledge
Presenter: Pang-Chang LanAdvisor: C.-C. (Jay) Kuo
May 2, 2014
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Outline• Research Problem Statement
• Introduction to Achievable Rate and Capacity
• Physical Layer (PHY) Security
• Some Research Results
• Conclusions and Future work
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RESEARCH PROBLEM STATEMENT
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Wireless Environment• Open-access medium
Ally Enemy
Signaler
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Wiretap Channel Modeling• The received signals are modeled as
where are channel coefficients and are Gaussian noises
transmitter receiver
eavesdropper
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Channel State Information• In convention, the channel state information (CSI) are assumed
to be known to all the nodes
• However, letting the eavesdropper know the CSI can be problematic by increasing her ability in eavesdropping
transmitter receiver
eavesdropper
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Reference Signaling• In wireless communications, we use reference signals to help
estimate channel information
transmitter receiverDownlink reference signaling
Amp. Amp.reference signal
channel estimate
channel
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Conventional Channel Estimation• Uplink and downlink channel estimation
transmitter receiver
uplink reference signals
downlink reference signals
Channel state information at the transmitter (CSIT)
Channel state information at the receiver (CSIR)
eavesdropper
Channel state information at the eavesdropper (CSIE)
Not realistic
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Channel Estimation for Secrecy• Q: Is uplink reference signaling enough?
transmitter receiver
uplink reference signals
downlink reference signals
Channel state information at the transmitter (CSIT)
Channel state information at the receiver (CSIR)
eavesdropper
Channel state information at the eavesdropper (CSIE)
Not realistic
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INTRODUCTION TO ACHIEVABLE RATE AND CAPACITY
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Rate without Noises and Channel Uncertainty
• Let’s take a look at the point-to-point channel
• If there are no channel uncertainty and noise, e.g., , we can deliver infinite information through the channel in a unit time, i.e.,
transmitter receiver
channel
infinitely long message
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Random Property• We often model the as random variables
• For example, let be a Bernoulli random variable
Degenerate case Randomized case
Message: 111111111… Message: 01011100101… 10110011001……
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Channel Uncertainty and Noises• However, channel uncertainty and noises make it impossible to
deliver messages at a infinite rate
• That is , where is the channel coefficient and is the additive noise
• Reference signaling can help eliminate the channel uncertainty
transmitter receiver
channel noise
+ =
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Overcome the Noise• Assume a Gaussian channel, i.e., where
• To overcome the noise, we can quantize the transmitted symbol
• Since the transmit power, i.e., , is limited, the number of quantization levels is limited => rate is limited
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Rate and Capacity• With the noise, we know that the transmission rate cannot be infinite
• Q: How large can the rate be? Or is there a capacity (maximum achievable rate)?
• The notion of capacity
Capacity
The whole transmission will be ruined
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Channel Coding• Channel coding is essential for achieving the capacity
• Channel coding: Ways to quantize and randomize the transmitted symbol to tolerate noises and convey as much information as possible
• The channel coding design is generally not easy
1940s Hamming Codes 1990s Turbo Codes
50 years
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Random Coding• Random coding: randomly generate the quantization according to a
specific distribution
• In the theoretical development, random coding saves the struggle of designing a channel coding scheme
• Random coding is generally not good in the practical use
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Some Assumptions• We want to transmit at a rate of , i.e., each symbol represents
bits
• As the signals are sent through time, let where is the time index
• Therefore, we convey a message from a set, e.g.,
…t
+ + + +… = bits
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Codebook Generation• In random coding, we need to randomly generate a codebook
• For each message candidate, there is a randomly generated codeword associated with it
… … ……
…
…
transmitter receiver
…
codeword
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Achievable Rate• A rate is said to be achievable if there exists a channel coding
scheme (including random coding) such that the message error probability, i.e., , is zero as
• For example, with the CSI known to both the transmitter and the receiver, it turns out that the capacity of the channel
subject to the power constraint , is given by
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Converse• Capacity proofs usually consist of two parts
– Achievability
– Converse
• The converse part helps you identify that a certain achievable rate is in fact the maximum rate (capacity), i.e., any rate above it is not achievable
• Usually, the converse part of the proof is difficult and may not be always obtained
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PHYSICAL LAYER (PHY) SECURITY
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Physical Layer Security• Scenario: The transmitter wants to send secret messages to the
receiver without being wiretapped by the eavesdropper
• In 1975, Wyner showed that channel coding is possible to protect the secret messages without using any cryptography methods
• The corresponding maximum rate of the secret message is referred to as the “secrecy capacity”
transmitter receiver
eavesdropper
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Gaussian Wiretap Channel• The received signals are modeled as
subject to the power constraint where are the channel coefficients and
transmitter receiver
eavesdropper
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Secrecy Capacity• Suppose that the CSI are known to all the terminals. The
secrecy capacity turns out to be
where
• To have a positive secrecy capacity, the receiver should experience a better channel than the eavesdropper, i.e.,
transmitter receiver
eavesdropper
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Interpretation of Secrecy Capacity• Information theoretic points of view
This portion is used to overwhelm the eavesdropper
This remaining portion is the secrecy capacity
receiver eavesdropper
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Interpretation of Secrecy Capacity• Modulation points of view
– Suppose that the eavesdropper has a worse resolution on the transmitted symbol
Transmitter’s 16QAM constellation
transmitted symbol
Receiver Eavesdropper
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Random Modulation• Use 4PSK to transmit the secret message while randomly choosing
the quadrants to confuse the eavesdropper
• For example, to transmit the 00 symbol, we have four candidates to select
• 2-bit degrees of freedom are used to confuse the eavesdropper
0000
00
00
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Realistic Channel Assumption• An essential assumption for achieving the secrecy capacity is for the
transmitter to know the CSI from the eavesdropper
• However, as a malicious node, the eavesdropper will not feed its channel information back
• What we are interested in is “Secrecy with CSIT only”
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Secrecy with CSIT Only
transmitter receiver
uplink reference signalsChannel state information at the transmitter (CSIT)
Channel state information at the receiver (CSIR)
eavesdropper
Channel state information at the eavesdropper (CSIE)
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SOME RESEARCH RESULTS
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SISO Wiretap Channel Model• The received signals are modeled as
where , , and
transmitter receiver
eavesdropper
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Case 1: Reversed Training without CSIRE• Suppose that the transmitter knows but doesn’t know
• We take the strategy of channel inversion with a channel quality threshold for transmission, i.e.,
where
• and are first revealed to the receiver and eavesdropper
transmit
stop
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Resulting Channel and Achievable Rate
• The resulting received signals at the receiver and eavesdropper are
• We want to find an achievable secrecy rate for this scheme as
where the mutual information is obtained by numerical integration
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Case 2: Reversed Training with Practical CSIRE• Here, we assume that the receiver and eavesdropper know their
respective received SNR, i.e., and
• So the transmitter only has to null the phase to the receiver. The resulting channel is given by
where is a uniform phase random variable
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Achievable Secrecy Rate• It turns out that the achievable secrecy rate is given by
where
and
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Asymptotic Bounds on the Achievable Rates
• Since the achievable rates above rely on the numerical integration, explicit asymptotic bounds are also useful for performance evaluation.
• Based on the techniques in [1], we can derive the asymptotic lower bounds for the above achievable secrecy rates as
[1] A. Lapidoth, “On phase noise channels at high SNR,” in Proceedings of IEEE Information Theory Workshop 2002, Oct. 2002, pp. 1–4
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vs. with P = 10 dB and
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
Rs
(bits
)
No CSIRENo CSIRE lowerboundCRSNR CSIRECRSNR CSIRE lowerboundFCSI with optimal alloc.FCSI with onoff alloc.
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0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
P (dB)
Rs
(bits
)
No CSIRENo CSIRE lowerboundPractical CSIREPractical CSIRE lowerboundFCSI with onoff alloc.Full CSI with optimal alloc.
vs. P with Optimal and
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MISO Wiretap Channel Model• Suppose that the transmitter has antennas, and the legitimate
receiver and the eavesdropper have respectively one antenna
• The MISOSE wiretap channel is modeled by
where , , and
transmitter receiver
eavesdropper
…
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Case 1: Reversed Training without CSIR
• Suppose that the transmitter knows but doesn’t know
• The transmitter applies the channel inversion strategy with a channel quality threshold, i.e.,
where
• and are first revealed to the receiver and eavesdropper
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Resulting Channel and Achievable Rate
• The resulting received signals at the receiver and eavesdropper are
• The achievable secrecy rate for this scheme can still be found by
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Case 2: Reversed Training with Practical CSIR
• Here, we assume that the receiver and eavesdropper know their respective received SNR, i.e., and
• So the transmitter only has to null the phase to the receiver. The resulting channel is given by
• It turns out that the achievable secrecy rate is also given by
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vs. with P = 10 dB and
0 0.5 1 1.5 2 2.5 3 3.5 40
1
2
3
4
5
6
Rs
(bits
)
No CSIREPractical CSIREFull CSI with onoff alloc.
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vs. P with Optimal and
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
P (dB)
Rs
(bits
)
No CSIREPractical CSIREFull CSI with onoff alloc.
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CONCLUSIONS AND FUTURE WORK
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Conclusions• With CSIT only, we can achieve a higher secrecy rate than with full CSI
at all the nodes
• With multiple antennas at the transmitter, the gain on the achievable secrecy rate can be even increased
• By setting a channel gain threshold , i.e., transmit only when , the secrecy rate can be effectively improved
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Future Work• Design an efficient algorithm to find the optimal
• Find the achievable rate for the multi-antenna receiver and eavesdropper
• Work on the scenario with finite-precision CSIT. Will the imprecision of the CSIT affect the achievable rate a lot?