# Difference between revisions of "Channel Parameters"

Since channel measurement mechanisms are always virtually implemented in wireless commu- nication interfaces, PLS primitives are applicable and enable novel security approaches. For example, using channel profiles/parameter — measured by two bidirectionally communicating parties — is an attractive source of joint entropy. Channel profiles provide access to the random source originated by unpredictable character- istics of the channel. Therefore, they are the most essential part of CRKE. Next, we review CSI, RSSI, LQI , and others.

## Channel State Information (CSI)

Break-through techniques resort to finer-grained wireless channel measurement than RSSI. Using channel response, the PHY-layer is able to discriminate multipath characteristics, and thus holds the potential for better equalization of the receiver and transmitter filters. This more fine-grade channel parameter is called CSI. In IEEE 802.11 a/g/n it is defined as reflecting channel response. In a conceptual sense, Yang et al. said [The] channel response is to RSSI what a rainbow (color spectrum) is to a sunbeam, where components of different wavelengths are separated. [15]. CSI are mainly referred to CIR and Channel Transfer Function (CTF). Both have attracted many research efforts and some pioneer works have demonstrated a high performance increase for CRKE [16]. Furthermore, CSI-based key extraction has been exper- imentally proved to be immune to predictable channel attacks [17].

## Channel Impulse Response (CIR)

The wireless propagation channel modeled as a temporal linear filter is known as CIR. The CIR h(τ,t) is capable to fully characterize the individual paths (including the sum of all multipath components according to the tapped-delay-line model) and can be given as

$\displaystyle h(\tau,t) = \sum_{n=1}^{N(t)}\alpha_n(t)e^{-j\phi_n(t)}\delta(t- \tau_n(t))$

Calculation 2.11

and

$\displaystyle \phi_n(t) = 2\pi f_c\tau_n(t) - \delta D_n(t) - \delta_0$

Calculation 2.12

where $\displaystyle \alpha_n(t)$ is the amplitude attenuation, $\displaystyle \phi_n(t)$ the phase shift, and math>\tau_n(t)[/itex] the time delay of the n th tap. N(t) is the total path number $\displaystyle \delta(\cdot)$ the Diract function. CIR as a complex measure, are usually interpreted in its amplitude and phase information. Several schemes for key extraction were introduced using information of the phase shift $\displaystyle \phi_n(t)$ [18]. The proposed schemes differ in usage of wideband systems [19] and narrowband systems [20]. In narrow band systems, the phase is often decreased to a single-dimension parameter. Phase information is UWB settings have not been identified yet. The accumulation of more than one phase information collected in series leads to applications such as group and cooperative key extraction [21]. Except for the work of Mathur et al. [22] no practical system have been reported yet, especially not for wideband-based systems. The reason for this might be the high vulnerability of the phase to noise, carrier frequency offset, asynchronous clocks (or clock shift), an asynchronous clock drifts at the transmitter and receiver. The second approach for CIR-based key extraction is using the amplitude (of course a combination of both amplitude and phase is conceivable). Here the research focuses on UWB settings, where the amplitude can be estimated by sending a narrow approximation of a Dirac function) pulse signal [23]. Such systems are usually based on special hardware setups (far away from practical usage) using network analyzer, waveform generators and oscilloscopes. In narrow band systems, the amplitude of a CIR is often decreased to a single-dimension parameter, which represents the received power [24].

## Channel Transfer Function (CTF)

The CTF is the representation of the CIR in the frequency domain and can be given by its Fourier transform:

$\displaystyle H(f,t) = \int_0^{τ_{max}}h(τ,t)e^{−j2πfτ}\mathrm {dτ}$

Here $\displaystyle τ_max$ is the maximum channel delay. Measurements of the channel using Orthogonal Frequency-Division Multiplexing (OFDM) provide a noisy CTF Ĥ(f,t), which can be written as:

$\displaystyle \hat H(f,t) = H(f,t) + \hat n(f,t)$
Caluclation: (2.14)

where $\displaystyle \hat n(f,t)$ is the noise effect in the frequency domain. Most CTF-based key extraction systems have been implemented on top of IEEE 802.11 OFDM systems [25]. For practical implementations, it is recommended to use only the amplitude, due to the carrier frequency offset, asynchronous clocks (or clock shift), an asynchronous clock drifts at the transmitter and receiver. Unfortunately, the interfaces of most Wi-Fi chips do not provide (documented) CSI. A current exception is the Intel Wi-Fi Link 5300 [26]. Software-Defined Radio (SDR)s are also able to provide CSI, such as the Universal Software Radio Peripheral (USRP) [27] or Wireless open-Access Research Platform (WARP) [28].

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