1 Reference Signaling Conventional Channel Estimation In - - PDF document

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Physical Layer Security Overview

Yao Zheng

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

4 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

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transmitter receiver eavesdropper

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Reference Signaling

• In wireless communications, we use reference signals to help

estimate channel information

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transmitter receiver

Downlink reference signaling Amp. Amp. reference signal channel estimate channel

Conventional Channel Estimation

• Uplink and downlink channel estimation

8 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

Channel Estimation for Secrecy

• Q: Is uplink reference signaling enough?

9 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

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 11

Random Property

• We often model the as random variables
• For example, let be a Bernoulli random variable

12 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 13 noise + =

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

15 Capacity The whole transmission will be ruined

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

16 1940s Hamming Codes 1990s Turbo Codes 50 years

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.,

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…

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

19 … … … … … … transmitter receiver … codeword

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”

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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.,

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transmitter receiver eavesdropper

Interpretation of Secrecy Capacity

• Information theoretic points of view

26 This portion is used to

• verwhelm the eavesdropper

This remaining portion is the secrecy capacity

receiver eavesdropper

Interpretation of Secrecy Capacity

• Modulation points of view

– Suppose that the eavesdropper has a worse resolution on the transmitted symbol

27 Transmitter’s 16QAM constellation transmitted symbol Receiver Eavesdropper

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

28 00 00 00 00

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

30 transmitter receiver uplink reference signals Channel 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

32 transmitter receiver eavesdropper

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

33 transmit stop

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

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.5 1 1.5 2 2.5 g Rs (bits) No CSIRE No CSIRE lowerbound CRSNR CSIRE CRSNR CSIRE lowerbound FCSI with optimal alloc. FCSI with onoff alloc.

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2 4 6 8 10 12 14 16 18 20 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 P (dB) Rs (bits) No CSIRE No CSIRE lowerbound Practical CSIRE Practical CSIRE lowerbound FCSI 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

40 transmitter receiver eavesdropper …

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

0.5 1 1.5 2 2.5 3 3.5 4 1 2 3 4 5 6 g Rs (bits) No CSIRE Practical CSIRE Full CSI with onoff alloc.

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• vs. P with Optimal and

2 4 6 8 10 12 14 16 18 20 1 2 3 4 5 6 7 8 9 P (dB) Rs (bits) No CSIRE Practical CSIRE Full CSI with onoff alloc.

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Backup Slides

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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
• f the CSIT affect the achievable rate a lot?

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