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

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

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?