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Fundamentals of wireless propagation channels
A radio communication system, as depicted in Fig. 2-1, aims to convey a message between two remote users through a propagation channel. At the transmitter side, the message is encoded into an electrical signal which is suited to ecient transmission and radiated into space by the antenna, in the form of an electromagnetic (EM) wave. On the other side, at the receiver, the original information is reproduced from the received EM waves, assuming it can be decoded without errors. The medium through which these signals propagate between the transmit and the receive antenna is called the wireless propagation channel. The wireless transmission channel is dened as the combination of the propagation channel and of the antennas. Fig. 2-2 depicts the dierence between the transmission and the propagation channels.
Channel reciprocity
The channel impulse response measured between two transceivers is the same re- gardless of the direction of transmission, since EM waves undergo the same physical interactions in both directions and there are usually no magnetic (non reciprocal) interactions. This is known by the channel \reciprocity » property, which holds in TDD systems where the same frequency band is used for both uplink and downlink [26, 27]. One benet of such a property in wireless communications is, e.g., intended to enhance transmission eciency such as throughput by providing channel state in- formation (CSI) at the transmitter side without additional feedback [28]. Recently, the reciprocity has been exploited in PhySec in such a manner that the shared CSI between two entities is exploited to protect exchanged data against an eavesdropper [22], in particular by extracting identical encryption keys. However, establishing radio reciprocity may be limited by some practical issues.
In fact, in TDD systems, the channel is required to remain invariable during the channel estimation phase in both directions. In other words, the channel should be estimated during the coherence time in order to reduce channel discrepancies.
Moreover, the asymmetric radio-frequency electronic hardware in the transmit and receive communication chains may break the reciprocity property [29, 30], owing to the unidirectional characteristics of certain components. This challenge is mostly addressed by performing calibration [31, 32, 33] and has been tested for SKG purposes in [34]. Nevertheless, although reciprocity is not valid in frequency-division duplex (FDD) systems, there have been attempts to mitigate its lack in such systems through alternative approaches, for example by using a frequency correction algorithm [35]. However, for instance, the reciprocity in FDD systems is not suciently resolved to sustain SKG algorithms. All over the thesis, we concentrate on a communication scheme appropriate for perfect reciprocity or nearly so, such as TDD. Then, any two entities (who may be legitimate terminals) may privately share common information extracted from the reciprocal channel, from which secure key bits may be established in order to encrypt data and thereby protect wireless communications. More clearly, because of the absence of an explicit feedback from receiver to transmitter, a third party (who may be a malicious attacker) has no access to the shared information considered as a source of secret keys, unless she exploits dierent methods, e.g. her own measurements.
Path loss, shadowing and small scale fading
Fig. 2-4 visually depicts the spatial variation of a propagation channel, which is often expressed in terms of three physically identied phenomena according to the spatial scale, i.e. the long distance path loss, the shadow fading and the small scale fading [36].
Path loss is explained by the average attenuation of the power of the EM wave with the transmitter-receiver separation distance d as the wave propagates through space. If we consider propagation between two isotropic antennas in free space, the signal experiences the following path loss (commonly known as the Friis transmission equation) in dB:
Channel degrees of freedom
In conventional communication system, the small scale fading is detrimental because the receiver is unable to correctly reproduce the original transmitted message when the channel is in a deep fade resulting from destructive multipath interference. In order to mitigate this eect, the transmitter sends several time the same message over the time-varying channel, until the fading turns toward constructive interference where the message is correctly received. This means that the message should be retransmitted after the channel coherence time, which is a statistical measure of the time duration over which the channel response is considered invariant. In other words, the coherence time is typically the time interval within which two channels measured over two dierent time instances are highly correlated. The coherence time is inversely proportional to the Doppler frequency, which is related to the rapidity of channel variations.
Table of contents :
1 Introduction
1.1 General motivations
1.2 Brief history of physical layer security
1.3 Thesis Context
1.4 Thesis objectives
1.5 New contributions
1.6 Organization of the dissertation
2 State of the art on secret key generation from random channels
2.1 Fundamentals of wireless propagation channels
2.1.1 Channel reciprocity
2.1.2 Path loss, shadowing and small scale fading
2.1.3 Channel degrees of freedom
2.1.4 Propagation channel models
2.2 Wireless channel-based secret key generation
2.2.1 SKG basics
2.2.2 Security versus an eavesdropper
2.2.3 Review of SKG
2.3 Conclusion
3 Secret key generation performance evaluation methods
3.1 Metrics for SKG assessment
3.1.1 Information theoretic bounds on key length
3.1.2 Channel correlations
3.1.3 Channel quantization performance
3.1.4 NIST tests
3.2 Channel quantization alternating (CQA) algorithm for SKG
3.2.1 State of the art
3.2.2 CQA description
3.3 Exploiting channel variability in SKG
3.3.1 Space variability
3.3.2 Frequency variability
3.3.3 Joint space-frequency variability
3.4 Conclusion
4 Performance of secret key generation in non-stationary channels
4.1 Shadowing
4.2 Disc of scatterers based channel model details
4.3 SKG performance evaluation
4.3.1 Channel correlations
4.3.2 Vulnerable key rate
4.3.3 CQA performance
4.4 Conclusion
5 Security behavior through ray tracing channel models
5.1 Environments and characteristics of the simulations
5.2 Propagation channel characteristics
5.2.1 Channel model
5.2.2 Small scale fading statistics
5.2.3 Delay and angular spreads
5.3 SKG from frequency variability
5.3.1 Available key bits
5.3.2 Evaluation of the degree of secrecy
5.4 SKG from space variability
5.4.1 Available key bits
5.5 Conclusion
6 Security performance in measured channels
6.1 Measuring systems and scenarios
6.2 Evaluation of errors between Alice, Bob and Eve keys
6.2.1 Dependence on the mapping
6.2.2 Alice-Bob disagreement vs. a simple channel model
6.2.3 Security performance with respect to Eve
6.3 Channel degrees of freedom for SKG
6.3.1 Space vs. time variability
6.3.2 Frequency variability
6.3.3 Joint space-frequency variability
6.3.4 Results
6.4 Information theoretic bounds on key length
6.4.1 SKG from frequency variability
6.4.2 SKG from space variability
6.4.3 Relative vulnerable key rate
6.5 Conclusion
7 Complete Secret Key Generation Scheme
7.1 Quantization
7.2 Information reconciliation
7.3 Privacy amplication
7.4 Results
7.4.1 Alice-Bob disagreement
7.4.2 Bob-Eve disagreement
7.4.3 Key randomness
7.5 Conclusion
8 Conclusion and perspectives
8.1 Conclusion
8.2 Perspectives
Resume en francais
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