Outline • Research Problem Statement Physical Layer Security Overview • Introduction to Achievable Rate and Capacity • Physical Layer (PHY) Security Yao Zheng • Some Research Results • Conclusions and Future work 2 Wireless Environment • Open-access medium Ally Enemy Research Problem Statement Signaler 3 4 Wiretap Channel Modeling Channel State Information • The received signals are modeled as • In convention, the channel state information (CSI) are assumed to be known to all the nodes where are channel coefficients and are Gaussian noises transmitter receiver eavesdropper transmitter receiver • However, letting the eavesdropper know the CSI can be problematic by increasing her ability in eavesdropping eavesdropper 18 6 1
Reference Signaling Conventional Channel Estimation • In wireless communications, we use reference signals to help • Uplink and downlink channel estimation estimate channel information Channel state information Channel state information uplink reference signals at the transmitter (CSIT) at the receiver (CSIR) Downlink reference signaling transmitter receiver downlink reference signals transmitter receiver Amp. Amp. channel estimate reference signal Not realistic channel Channel state information at the eavesdropper (CSIE) 7 8 eavesdropper Channel Estimation for Secrecy • Q: Is uplink reference signaling enough? Introduction to Achievable Rate and Channel state information Channel state information Capacity uplink reference signals at the transmitter (CSIT) at the receiver (CSIR) downlink reference signals transmitter receiver Not realistic Channel state information at the eavesdropper (CSIE) 9 10 eavesdropper Random Property Rate without Noises and Channel Uncertainty • Let’s take a look at the point-to-point channel • We often model the as random variables • For example, let be a Bernoulli random variable channel Degenerate case Randomized case receiver transmitter • If there are no channel uncertainty and noise, e.g., , we can Message: 01011100101… deliver infinite information through the channel in a unit time, i.e., Message: 111111111… 10110011001… … infinitely long message 11 12 2
Channel Uncertainty and Noises Overcome the Noise • Assume a Gaussian channel, i.e., where • However, channel uncertainty and noises make it impossible to deliver messages at a infinite rate • To overcome the noise, we can quantize the transmitted symbol channel noise + = receiver transmitter • That is , where is the channel coefficient and is the additive noise • Since the transmit power, i.e., , is limited, the number of quantization levels is limited => rate is limited • Reference signaling can help eliminate the channel uncertainty 13 14 Rate and Capacity Channel Coding • With the noise, we know that the transmission rate cannot be infinite • Channel coding is essential for achieving the capacity • Q: How large can the rate be? Or is there a capacity (maximum • Channel coding: Ways to quantize and randomize the transmitted achievable rate)? symbol to tolerate noises and convey as much information as possible The whole transmission • The notion of capacity will be ruined Capacity • The channel coding design is generally not easy 50 years 1940s Hamming Codes 1990s Turbo Codes 15 16 Random Coding Some Assumptions • Random coding: randomly generate the quantization according to a • We want to transmit at a rate of , i.e., each symbol represents specific distribution bits • In the theoretical development, random coding saves the struggle of • As the signals are sent through time, let where designing a channel coding scheme is the time index … • Random coding is generally not good in the practical use … t + + + + = bits • Therefore, we convey a message from a set, e.g., 17 18 3
Codebook Generation Achievable Rate • In random coding, we need to randomly generate a codebook • 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 codeword … • For example, with the CSI known to both the transmitter and the receiver transmitter receiver, it turns out that the capacity of the channel … … … … … subject to the power constraint , is given by … • For each message candidate, there is a randomly generated codeword associated with it 19 20 Converse • Capacity proofs usually consist of two parts – Achievability Physical Layer (PHY) Security – 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 21 22 Physical Layer Security Gaussian Wiretap Channel • Scenario: The transmitter wants to send secret messages to the • The received signals are modeled as receiver without being wiretapped by the eavesdropper subject to the power constraint where are the channel coefficients and transmitter receiver eavesdropper • In 1975, Wyner showed that channel coding is possible to protect the secret messages without using any cryptography methods transmitter receiver • The corresponding maximum rate of the secret message is referred to as the “secrecy capacity” eavesdropper 23 18 4
Secrecy Capacity Interpretation of Secrecy Capacity • Suppose that the CSI are known to all the terminals. The • Information theoretic points of view secrecy capacity turns out to be This remaining portion is the secrecy capacity where This portion is used to overwhelm the eavesdropper transmitter receiver receiver eavesdropper eavesdropper • To have a positive secrecy capacity, the receiver should experience a better channel than the eavesdropper, i.e., 25 26 Interpretation of Secrecy Capacity Random Modulation • Modulation points of view • Use 4PSK to transmit the secret message while randomly choosing the quadrants to confuse the eavesdropper – Suppose that the eavesdropper has a worse resolution on the transmitted symbol • For example, to transmit the 00 symbol, we have four candidates to Transmitter’s 16QAM constellation select transmitted symbol 00 00 Receiver Eavesdropper 00 00 • 2-bit degrees of freedom are used to confuse the eavesdropper 27 28 Realistic Channel Assumption Secrecy with CSIT Only • An essential assumption for achieving the secrecy capacity is for the transmitter to know the CSI from the eavesdropper Channel state information Channel state information uplink reference signals at the transmitter (CSIT) at the receiver (CSIR) • However, as a malicious node, the eavesdropper will not feed its channel information back • What we are interested in is “Secrecy with CSIT only” transmitter receiver Channel state information at the eavesdropper (CSIE) 29 30 eavesdropper 5
SISO Wiretap Channel Model • The received signals are modeled as Some Research Results where , , and transmitter receiver eavesdropper 31 32 Case 1: Reversed Training without CSIRE Resulting Channel and Achievable Rate • Suppose that the transmitter knows but doesn’t know • The resulting received signals at the receiver and eavesdropper are • We take the strategy of channel inversion with a channel quality threshold for transmission, i.e., where • We want to find an achievable secrecy rate for this scheme as • and are first revealed to the receiver and eavesdropper where the mutual information is obtained by numerical integration transmit stop 33 34 Achievable Secrecy Rate Case 2: Reversed Training with Practical CSIRE • Here, we assume that the receiver and eavesdropper know their • It turns out that the achievable secrecy rate is given by respective received SNR, i.e., and where • So the transmitter only has to null the phase to the receiver. The and resulting channel is given by where is a uniform phase random variable 35 36 6
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