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**Enhancing Secrecy With Channel Knowledge**

Presenter: Pang-Chang Lan Advisor: 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 Downlink reference signaling transmitter receiver Amp. Amp. channel estimate reference signal channel

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**Conventional Channel Estimation**

Uplink and downlink channel estimation Channel state information at the transmitter (CSIT) Channel state information at the receiver (CSIR) uplink reference signals downlink reference signals transmitter receiver Not realistic Channel state information at the eavesdropper (CSIE) eavesdropper

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**Channel Estimation for Secrecy**

Q: Is uplink reference signaling enough? Channel state information at the transmitter (CSIT) Channel state information at the receiver (CSIR) uplink reference signals downlink reference signals transmitter receiver Not realistic Channel state information at the eavesdropper (CSIE) eavesdropper

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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., channel transmitter receiver 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: … … Message: … …

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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 channel noise + = receiver transmitter

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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 The whole transmission will be ruined Capacity

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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 50 years 1940s Hamming Codes 1990s Turbo Codes

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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 codeword … receiver transmitter … … … … … …

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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 remaining portion is the secrecy capacity This portion is used to overwhelm the eavesdropper 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 00 00 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 Channel state information at the transmitter (CSIT) Channel state information at the receiver (CSIR) uplink reference signals transmitter receiver Channel state information at the eavesdropper (CSIE) eavesdropper

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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

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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

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vs. P with Optimal and

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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?

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