CSI definition.pdf

Chapter 2 Understanding of Channel State Information Abstract Channel State Information (CSI) is one of the major types of data used in wireless sensing, thanks to its fine subcarrier-level granularity and easy access with commodity Wi-Fi devices. While it is feasible to simply process CSI as numer...

Chapter 2 Understanding of Channel State Information Abstract Channel State Information (CSI) is one of the major types of data used in wireless sensing, thanks to its fine subcarrier-level granularity and easy access with commodity Wi-Fi devices. While it is feasible to simply process CSI as numeric data, understanding the underlying model can guide the development of more effective wireless sensing algorithms. In this chapter, we aim to introduce CSI and its main components, including various signal features and error terms. Devices supporting the CSI collection are listed at the end of this chapter. 2.1 Definition of CSI In a general indoor environment, a signal sent by the transmitter arrives at the receiver via multiple paths. Along each path, the signal experiences a certain delay, attenuation, and phase shift. The received signal is the superimposition of multiple alias versions of the transmitted signal. Therefore, the complex baseband signal voltage measured at the receiver at a specific time is : N  V = ||Vi ||e−j θi , (2.1) i=1 where Vi and θi are the amplitude and phase of the ith multipath component (note that the modulation scheme of the signal is implicitly considered), and N is the total number of components. RSSI is then simply the received power in decibels (dB): RSSI = 10 log2 (||V ||2 ). (2.2) As the superimposition of multipath components, RSSI not only varies rapidly with propagation distance changing at the order of the signal wavelength but also fluctuates over time even for a static link. A slight change in certain multipath com- ponents may result in significant constructive or destructive multipath components, leading to considerable fluctuations in RSSI as a consequence. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 11 Z. Yang et al., Smart Wireless Sensing, https://doi.org/10.1007/978-981-16-5658-3_2 12 2 Understanding of Channel State Information The essential drawback of RSSI is the failure of reflecting the multipath effect. To fully characterize individual paths, the wireless channel is modeled as a temporal linear filter, known as Channel Impulse Response (CIR). Under the time-invariant assumption, CIR h(τ ) is represented as: N  h(τ ) = ai e−j θi δ(τ − τi ), (2.3) i=1 where ai , θi , and τi are the amplitude, phase, and time delay of the ith path, respectively. N is the total number of multipath and δ(τ ) is the Dirac delta function. Each impulse represents a delayed multipath component, multiplied by the corresponding amplitude and phase. In the frequency domain, the multipath effect also causes frequency-selective fading, which is characterized by Channel Frequency Response (CFR). CFR is essentially the Fourier transform of CIR. It consists of both amplitude response and phase response. Figure 2.1 shows a multipath scenario, the transmitted signal, the received signal, and the illustrative channel responses. Both CIR and CFR depict the small-scale multipath effect and are used for fine-grained channel measurement. Note that the CIR and CFR are concerning complex amplitudes, while another pair of parameters in terms of the signal power is Power Delay Profile (PDP) and Power Spectrum Density (PSD). CIR and CFR are measured by decoupling the transmitted signal from the received signal. Specifically, in the time domain, the received signal r(t) is the temporal convolution of transmitted signal s(t) and channel impulse response h(t): r(t) = s(t) ⊗ h(t). (2.4) In the respective frequency domain, the received signal spectrum R(f ) is the multiplication of the transmitted signal spectrum S(f ) and the channel frequency response H (f ): R(f ) = S(f ) × H (f ). (2.5) As demonstrated in Equations 2.4 and 2.5, CIR can be derived with the deconvolution of received and transmitted signals, while CFR is the ratio of the received and the transmitted spectrums. Since the calculation of convolution is nontrivial, the CIR is usually derived from the CFR using the inverse Fourier transform. In the case of a flat transmission power spectrum, CIR is approximated by : 1 −1 ∗ h(t) = F S (f )R(f ), (2.6) Ps  2.1 Definition of CSI Fig. 2.1 Multipath propagations, received signals, and channel responses. ACM Computing Surveys, Vol. 46, ©2013 ACM, Inc. https://doi.org/10.1145/ 2543581.2543592 13 14 2 Understanding of Channel State Information where F−1 denotes the inverse Fourier transform. R(f ) is the Fourier transform of the received signal r(t), i.e., the frequency spectrum. S ∗ (f ) is the complex conju- gate of the Fourier transform of the transmitted signal s(t). And Ps approximates the transmitted signal power, which, under the flat transmission assumption, is nearly a constant within the frequency band of interest. Precisely measuring and modeling the wireless channel often need dedicated infrastructures such as Vector Network Analyzer (VNA) or Software Defined Radio (SDR) [2, 3, 6]. Moreover, although the derivation of CIR and CFR is independent of the modulation scheme of the transmitted signal, it is still more convenient to implement the process on commercial devices with specific modulation schemes. For instance, if OFDM is adopted, such as in IEEE 802.11a/g/n, the receivers are then readily capable of calculating CIR and CFR, since the amplitudes and phases on each subcarrier provide a sampled version of the signal spectrum, while Fourier transform is implemented in OFDM receivers. Recent advances in the wireless community have taken this one step further. Using off-the-shelf Wi-Fi NICs, the sampled version of CFR within the Wi-Fi bandwidth is available to upper layers, which is known as Channel State Information (CSI). Each sample of CSI depicts the amplitude and phase of a subcarrier:  H (fk ) H (fk ) = ||H (fk )||e , (2.7) where H (fk ) is the CSI sample at the subcarrier with the central frequency fk , and  H (fk ) denotes its phase. Hence a group of CSI samples H (fk ), (k = 1, · · · , K), represent K sampled CFRs at the granularity of subcarrier level. 2.2 Noise in CSI In practice, CSI measured by wireless devices consists of not only the theoretical value in Equation 2.7, but also various random phase errors. These phase errors are mainly due to the asynchronization of the local oscillators of the transmitter and the receiver. In general, the measured CSI phase of the subcarrier fk can be represented as:  Ĥ (fk ) =  H (fk ) + 2πfk (δ1 + δ2 ) + β + θ, (2.8) where  H (fk ) is the theoretical phase as in Equation 2.7, δ1 and δ2 are the packet boundary detector (PBD) phase error and sampling frequency offset (SFO), β is the carrier frequency offset (CFO), and θ is the constant unknown initial phase introduced by the antenna RF chain. The sources of these phase offsets are briefly discussed. Packet boundary detection (PBD) error. A Wi-Fi receiver detects the boundary of a packet by correlating ideal training symbols with the received signal. Peaks 2.3 Signal Features in CSI 15 will appear when the training symbols in the packet are processed and the packet boundary is thus determined. However, due to interference and noise, the detected boundary may not coincide with the real boundary. The time shift between two boundaries introduces a random phase error 2πfk δ1 to the CSI. Sampling frequency offset (SFO). The sampling frequency offset between the transmitter and the receiver scales the received signal in both the time and frequency domains. As a result, a random phase error approximately proportional to the subcarrier frequency is introduced, i.e., 2πfk δ2. Carrier frequency offset (CFO). The carrier frequency offset between the transmit- ter and the receiver introduces a phase offset when the receiver downconverts the received signal to the baseband frequency. Since the CFO is orders of magnitude smaller than the absolute carrier frequency, the phase error is approximately constant across subcarriers and termed as β. Unknown initial phase. Different antennas and the corresponding RF chains intro- duce different unknown initial phase theta to the CSI, due to various imple- mentation factors such as unequal lengths of transmission lines and PLL locking mechanism. The initial phase is unknown but constant each time the device starts up and only needs one-time calibration. The phase errors discussed above severely distort the CSI measurements and jeopardize the signal processing procedure. Besides the phase noise, CSI is also distorted by random amplitude noise called power control uncertainty, which is induced by the imperfection of the Automatic Gain Controller (AGC) that compensates the transmitted power level. All these phase errors need to be filtered out to achieve robust and reliable wireless sensing. 2.3 Signal Features in CSI 2.3.1 Time of Flight ToF is the time duration where the signal propagates from the transmitter to the receiver along a certain path. Given the frequency f , the phase shift introduced by the ToF τ is:  ToF = −2πf τ. (2.9) As the superimposition of multipath signals, CSI is modeled as: K  H (f ) = αk e−j 2πf τk , (2.10) k=1 16 2 Understanding of Channel State Information Path 1 Rx Channel Impulse Response LOS Path 2 Time Tx Fig. 2.2 The relationship between ToF and CIR of signal features where K is the total number of multipath, and αk and τk are the complex attenuation factor and time of flight (ToF) for the k-th path, respectively. Theoretically, the ToF of all paths can be identified in CIR, which can be calculated by applying the inverse Fourier transform to CSI samples of all subcarriers. However, since the transmitter and the receiver lack synchronization, non-zero temporal shifts exist in CIR and the absolute ToF is not available. The relationship between signal propagation path, ToF, and CIR is showed in Fig. 2.2. 2.3.2 Angle of Arrival and Angle of Departure When a device has multiple antennas, a local coordinate at the device can be created. As shown in Fig. 2.3, for a transmitter, the angle of departure (AoD) ϕ represents the direction in the local coordinate along which the transmitted signal is received by the receiver. For a receiver, the angle of arrival (AoA) φ represents the direction in the local coordinate along which the received signal is transmitted by the transmitter. Since the antennas are spatially separated, non-zero phase shifts between antennas Rx antennas Tx antennas Fig. 2.3 Angle of Arrival and Angle of Departure 2.3 Signal Features in CSI 17 are introduced. The phase shifts depend on the AoA/AoD. Specifically, suppose the relative location between two antennas is Δl = [Δx , Δy ] and the unit direction vector of AoA is e = [cos φ, sin φ], the phase shift between the two antennas is: 2π  AoA = Δl · e. (2.11) λ Then CSI can be modeled as: K  2π H (i) = αk e−j λ Δl(i)·e , (2.12) k=1 where i represents the i-th antenna at the receiver. The same model applies to the AoD at the transmitter side and the 3D space with azimuth and elevation angles. In practice, algorithms such as Capon and MUSIC can be used to estimate the AoA/AoD of multiple paths from the CSI of the antenna array. MUSIC analyzes the incident signals on multiple antennas to find out the AoA of each signal. Specifically, suppose D signals F1 , · · · , FD arrive from directions θ1 , · · · , θD at M > D antennas. The received signal at the ith antenna element, denoted as Xi , is a linear combination of the D incident wavefronts and noise Wi : ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ X1 F1 W1 ⎢ X2 ⎥ ⎢ F2 ⎥ ⎢ W2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢.. ⎥ = a(θ1) a(θ2 )... a(θD ) ⎢. ⎥+⎢.. ⎥ ⎣. ⎦ ⎣.. ⎦ ⎣. ⎦ XM FD WM or X = AF + W, (2.13) where a(θi ) is the array steering vector that characterizes added phase (relative to the first antenna) of each receiving component at the ith antenna. A is the matrix of steer vectors. As shown in Fig. 2.3, for a linear antenna array with elements well synchronized, ⎡ ⎤ 1 ⎢ e−j Δl(1)·e ⎥ 2π ⎢ λ ⎥ ⎢ −j Δl(2)·e ⎥ 2π a(θ ) = ⎢ ⎢ e λ ⎥. ⎥ (2.14) ⎢.. ⎥ ⎣. ⎦ −j λ Δl(M−1)·e 2π e 18 2 Understanding of Channel State Information Suppose Wi ∼ N(0, σ 2 ), and Fi is a wide-sense stationary process with zero mean value, the M × M covariance matrix of the received signal vector X is: S = XX∗ = AFF∗ A∗ + WW∗ (2.15) = APA∗ + σ 2 I, where P is the covariance matrix of transmission vector F. The notation (·)∗ represents conjugate transpose and (·) represents expectation. The covariance matrix S has M eigenvalues λ1 , · · · , λM associated with M eigenvectors e1 , e1 , · · · , eM. Sorted in a non-descending order, the smallest M − D eigenvalues correspond to the noise while the rest D correspond to the D incident signals. In other words, the M-dimension space can be divided into two orthogonal subspace, the noise subspace EN expanded by eigenvectors e1 , · · · , eM−D , and the signal subspace ES expanded by eigenvectors eM−D+1 , · · · , eM (or equivalently D array steering vector a(θ1), · · · , a(θD )). To solve for the array steering vectors (thus AoA), MUSIC plots the reciprocal of squared distance Q(θ ) for points along the θ continuum to the noise subspace as a function of θ : 1 Q(θ ) =. (2.16) a∗ (θ )EN EN ∗ a(θ ) This yields peaks in Q(θ ) at the bearing of incident signals. It is similar to applying MUSIC algorithm for AoD spectrum estimation. 2.3.3 Doppler Frequency Shift Non-zero Doppler frequency shift fD is caused by the relative movement of the transmitter, receiver, or objects in the propagation path of the signal. It equals the changing rate of the path length of the signal, which is proportional to the changing rate of the phase shift: d DFS = fD. (2.17) dt When multiple packets are received in sequence, the CSI of the packet received at time t is: K  t H (t) = αk (t)e−j 2π 0 fDk (u)du , (2.18) k=1 2.4 CSI Data Collection 19 P1 P2 P2 P3 P3 LOS P1 Tx Rx Fig. 2.4 DFS for different moving status where fDk is the DFS of the kth path. Theoretically, DFS can be estimated by applying inverse Fourier transform to CSI samples from all packets. With packets collected during a longer period, the short-time Fourier transform (STFT) is often applied within sliding windows to generate the DFS spectrum. In practice, however, due to random phase shifts, it is impossible to directly obtain DFS from CSI samples of multiple packets. A compromise solution is to use the power of CSI H 2 (t), where the random phase shifts are removed. As a sacrifice, the positive and negative DFS spectrum are aliased. Figure 2.4 demonstrates the DFS spectrum for three different moving paths. 2.4 CSI Data Collection 2.4.1 Intel 5300 NIC CSI Tool This CSI Tool is built upon the Intel Wi-Fi Wireless Link 5300 802.11n MIMO radios, using a modified firmware and the open-source Linux wireless driver. It includes all the software and scripts required to collect, read, and parse CSI. The IWL5300 provides 802.11n CSI of 30 subcarrier groups. Each group contains 2 adjacent subcarriers given 20 MHz bandwidth or 4 given 40 MHz bandwidth. Each CSI sample is a complex number, with a signed 8-bit resolution for both real and imaginary parts. One CSI record is a A × 30 matrix, where M is the number of pairs of transmitting and receiving antennas. The homepage1 of this tool can be accessed for detailed information. 1 https://dhalperi.github.io/linux-80211n-csitool 20 2 Understanding of Channel State Information 2.4.2 Atheros-CSI-Tool Atheros-CSI-Tool is an open-source 802.11n measurement and experimentation tool. It enables the extraction of detailed PHY wireless communication information from the Atheros Wi-Fi NICs, including the Channel State Information (CSI), the received packet payload, and other information (the time stamp, the RSSI of each antenna, the data rate, etc.). Atheros-CSI-Tool is built on top of ath9k, which is an open-source Linux kernel driver supporting Atheros 802.11n PCI/PCI-E chips. Thus, this tool theoretically supports all types of Atheros 802.11n Wi-Fi chipsets. We have tested it on Atheros AR9580, AR9590, AR9344, and QCA9558. Atheros- CSI-Tool is open source and all functionalities are implemented in software without any modification to the firmware. Therefore, one is able to extend the functionalities of Atheros-CSI-Tool with his/her own codes under the GPL license. Atheros-CSI-Tool works on various Linux distribution, e.g., Ubuntu, OpenWRT, Linino, etc. Different Linux distribution works with different hardware. Ubuntu works for personal computers like laptops or desktops. OpenWRT works for embedded devices such as Wi-Fi routers. Linino works for IoT devices, such as Arduino YUN. The official website provides the source code for the Ubuntu version and OpenWRT version of the Atheros-CSI-tool. The homepage2 of this tool can be accessed for detailed information. 2.4.3 PicoScenes Platform PicoScenes is an advanced multi-purpose Wi-Fi sensing platform software. It supports the multi-NIC concurrent operation (including the packet injection, packet reception, and CSI measurement) of the Qualcomm Atheros AR9300 (QCA9300), Intel Wireless Link 5300 (IWL5300), and software-defined radio (SDR) devices. PicoScenes is architecturally versatile and flexible. It encapsulates all the low-level features into unified and hardware-independent APIs and exposes them to the upper- level plugin layer. Users can quickly prototype their own measurement plugins. 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