Terminal Orientation in OFDM-based LiFi Systems
Ardimas Andi Purwita, Mohammad Dehghani Soltani, Majid Safari, Harald Haas
aa r X i v : . [ ee ss . SP ] A ug Terminal Orientation in OFDM-based LiFiSystems
Ardimas Andi Purwita,
Student Member, IEEE,
Mohammad Dehghani Soltani,
Student Member, IEEE,
Majid Safari,
Member, IEEE, and Harald Haas,
Fellow, IEEE
Abstract
Light-fidelity (LiFi) is a wireless communication technology that employs both infrared and visiblelight spectra to support multiuser access and user mobility. Considering the small wavelength of light,the optical channel is a ff ected by the random orientation of a user equipment (UE). In this paper, arandom process model for changes in the UE orientation is proposed based on data measurements. Weshow that the coherence time of the random orientation is in the order of hundreds of milliseconds.Therefore, an indoor optical wireless channel can be treated as a slowly-varying channel as its delayspread is typically in the order of nanoseconds. A study of the orientation model on the performanceof direct-current-biased orthogonal frequency-division multiplexing (DC-OFDM) is also presented. Theperformance analysis of the DC-OFDM system incorporates the e ff ect of di ff use link due to reflectionand blockage by the user. The results show that the di ff use link and the blockage have significant e ff ects,especially if the UE is located relatively far away from an access point (AP). It is shown that the e ff ectis notable if the horizontal distance between the UE and the AP is greater than . m in a typical × . × m indoor room. Index Terms
LiFi, measurement, random orientation, random process model, OFDM.
I. I ntroduction
The authors are with School of Engineering, Institute for Digital Communications, LiFi R&D Centre, The University ofEdinburgh, Edinburgh EH9 3JL, U.K. (e-mail: { a.purwita, m.dehghani, majid.safari, h.haas } @ed.ac.uk). L ight-fidelity (LiFi) has recently attracted significant research interest as the scarcity inthe radio frequency (RF) spectrum becomes a major concern, see [1] and [2]. Based onpredictions of mobile data tra ffi c, the number of cell sites and achievable spectral e ffi ciency, theentire RF spectrum in the US will be fully utilized in around the year 2035 [3]; hence, the use ofoptical wireless communications is of great interest. The benefit of LiFi over other optical wire-less communication systems, such as visible light communication (VLC), is that LiFi supportsmulti-user connections and bi-directionality. In other words, LiFi provides similar functionalityas the other Institute of Electrical and Electronics Engineers (IEEE) 802.11 technologies, e.g.,handover and multiple access. Therefore, a working group for LiFi in IEEE 802.11 already exists[4] as well as a task group for LiFi in IEEE 802.15 [5].In an indoor room, the quality of the optical channel highly depends on the geometry pa-rameters of a user equipment (UE), an access point (AP) and the dimensions of the room [6].Therefore, a significant change in the parameters due to the mobility of the users greatly a ff ectsthe channel. The main focus of this paper is the random orientation of the UE. Meanwhile, themajority of studies on LiFi or VLC only consider the case where the UE faces upward, see [2]or [7] and references therein. The facing-upward assumption is practically supported by LiFiuniversal serial bus (USB) dongles used by a laptop or a tablet computer. LiFi USB dongles havebeen commercialized, and this use case is already deployed. The next natural step for LiFi isfor it to be integrated into mobile devices, such as smartphones and indeed tablets or laptops. Inpractice, the orientation of the mobile devices is random in nature. Therefore, it is of importanceto study the characteristics of the random orientation.Over the past few years, only a few papers have been published which have considered therandom orientation of the mobile terminal, see [8]–[17]. The authors in [8], [11] and [12] focus onthe bit error ratio (BER) performances of an on-o ff keying (OOK) system with a random receiverorientation. Handover probability in a LiFi network with randomly-oriented UEs is studied in[9] and [16]. The studies of the VLC channel capacity and the e ff ect of random orientation tonon-orthogonal multiple access (NOMA) are presented in [10] and [13], respectively. All theauthors assume that the random orientation follows a certain probability density function (PDF)without any support from data measurements. In our initial work [14], [18], the PDF of therandom orientation based on a series of experiments is presented. A generalized random waypoint model is also proposed in [18] considering the e ff ect of orientation using an autoregressive(AR) model. Another experiment result is reported in [19]; however, the authors only focus on the rate of change of orientation. In this paper, a more comprehensive analysis of the experimentalresults first reported in [14] is provided.The proposed PDFs in [14] and [18] model the random orientation as a random variable bydirectly counting the frequency of data, which are assumed to be uncorrelated. In other words,temporal characteristics of the random orientation, e.g., the autocorrelation function (ACF), arenot described. Moreover, the noise from the measurement device is ignored. In this paper, therandom orientation is characterized based on a random process (RP) model. The main challengeis that the time sampling of data measurements is not evenly-spaced. Therefore, the ACF cannotbe directly estimated from the sample data, and the conventional Fourier analysis cannot beused since the sinusoids are no longer orthogonal. Therefore, the least-squares spectral analysis(LSSA) [20]–[24] is used to estimate the spectral characteristics of the data measurements. Inaddition, a Wiener filter is used to filter the noise in the data measurement [25], and the CLEAN algorithm is applied to eliminate the partial-aliasing in the power spectrum, see [23] and [26].Based on our proposed RP model, it is shown that the channel is highly-correlated withinthe order of hundreds of milliseconds. The RP model is suitable for the type of studies whichconsider the movement of the users inside a room, such as the studies of handover probabilityin a LiFi network [9] and [16]. In addition, the RP model can be used in mobility models suchas the orientation-based random waypoint model proposed in [18]. In this paper, the randomorientation model is applied to an orthogonal frequency-division multiplexing (OFDM)-basedLiFi system [2]. The main advantage of OFDM over other typical modulation systems, such asOOK, is that it can mitigate the inter-symbol interference (ISI) which is caused by multipathpropagation of the indoor optical channel, see [6] and [27].As a use case, this paper focuses on the comparison of the analysis of the LiFi system withand without the di ff use link considering the random orientation model. The reason for this isthat most studies in LiFi or VLC, see [8]–[14] and [16], neglect the di ff use link, and onlythe line-of-sight (LOS) channel is considered due to the fact that the received signal poweris dominated by the power from the LOS link. It will be shown later that this is not alwaysthe case, and it will significantly a ff ect the performance of our LiFi system in some scenarios.This result is consistent with other results in [6], [27] and [28] which consider the di ff use link.However, these studies only focus on the OOK modulation scheme. In this paper, the e ff ect of To the best of authors’ knowledge, it is not an abbreviation and first introduced as CLEAN algorithm. (a) (b)Fig. 1. (a) System model and (b) block diagram of a DC-OFDM-based system. the di ff use link in the OFDM-based LiFi system is investigated. We will also consider a humanbody as both blocking and reflector objects since the random orientation is modeled based ondata measurements that were collected while the participants were using the UEs.In Section II, our system model is presented. Our experimental setups and results are discussedin Section III and IV, respectively. The use cases of the random orientation model to the OFDM-based LiFi system are presented in Section V and VI. In Section V, the performances of theLiFi system with fixed locations of the UEs and the users are studied. The results in Section Vare then generalized to the case where the locations and the orientations of the UEs are randomin Section VI. Section VII concludes our work.II. S ystem M odel An indoor room with several optical APs, known as the optical attocell [2], and a mobileuser using his LiFi-enabled device, referred to as a UE, is assumed as depicted in Fig. 1(a).Throughout this paper, the AP acts as a transmitter (Tx), and the UE acts as a receiver (Rx). AUE is assumed to have a photodiode (PD) on the front screen and held in a comfortable manner,which will be discussed in the next section. A direct-current-biased OFDM (DC-OFDM) basedsystem is used in this paper; the block diagram of the system is shown in Fig. 1(b). In thissection, we first explain our OFDM transmission system and then the channel model.
A. Transmission System
In the Tx, N inverse discrete Fourier transform IDFT operations are performed to obtaindiscrete time and parallel OFDM symbols, which are expressed by: x p [ k ] = N − X n = X n e j π nk / N , k = , , . . . , N − , where X n is the symbol that is transmitted at the n th subcarrier [29]. The symbol X n is chosenfrom an M n -ary quadrature amplitude modulation (QAM) constellation with the average power E h | X n | i = P n . Moreover, X n should follow the Hermitian symmetry, i.e., X n = X ∗ N − n . In thispaper, the constellation size and the power per symbol at each subcarrier are fixed, i.e., M n = M and P n = N , is large, it is widely known that x p [ k ] follows a Gaussiandistribution with zero mean and variance, σ = (cid:16) N − (cid:17) [29]. Furthermore, for a given bit rate R b , the OFDM symbol rate is R s = R b / log M . After adding the cyclic prefix (CP), the OFDMsampling rate is: f s = r os R s N + N cp N , (1)where N cp is the length of CP, and r os is the oversampling ratio, i.e., r os = N / N u , where N u isthe number of subcarriers that are used. Zero padding in the frequency domain is applied forthe unused subcarriers. The bandwidth of the OFDM symbol is defined as f s / (2 r os ).Let’s now define x [ k ] as a discrete time OFDM signal after parallel-to-serial conversion andadding the CP. The signal x [ k ] needs to be clipped because (i) to meet the dynamic range ofthe digital-to-analog converter (DAC) and the analog-to-digital converter (ADC), (ii) to meet thenon-negative constraint of the intensity modulation (IM) and (iii) to avoid the nonlinearities ofthe LED. Let x c [ k ] be a discrete time clipped signal of x [ k ] at levels − r σ and r σ , where r and r denote the clipping ratios. It is assumed that a predistortion is employed such the P-I curve of the LED in the non-clipped region is linear [30]. Using the Gaussian approximation,i.e., x [ k ] follows the Gaussian distribution, the Bussgang’s Theorem can be applied; therefore, x c [ k ] can be written as x c [ k ] = K x [ k ] + d [ k ], where d [ k ] is a random process that is uncorrelatedwith x [ k ], and K is defined as K = − ( Q ( r ) + Q ( r )), where Q ( · ) is the tail distribution function Recall that the DC subcarrier is used for the DC bias. The factor 2 is due to the Hermitian symmetry. of a normal distribution [29]. In other words, K shows the attenuation level due to the clippingprocess.The zero-order hold is used to model the DAC. Let H DAC ( f ) be a frequency response of it withthe cuto ff frequency is equal to the bandwidth of the OFDM symbols. Note that the low-passfrequency in the zero-order hold is modeled by a fifth order Bessel filter [29]. A DC bias isperformed after the DAC to meet the non-negative constraint and defined as 2 r P N − n = | H DAC ( f n ) | ,where f n denotes the frequency of the n th subcarrier. The frequency response of the LED isdenoted by H LED ( f ) and modeled as a low pass filter using a first order Butterworth filter withcuto ff frequency f c LED . The output signal of the LED, which is in the optical domain, is transmittedover a channel with a channel impulse response (CIR) h ( t ) whose frequency response is H CIR ( f ).In the receiver, the frequency responses of the PD and the transimpedance amplifier (TIA)are represented by the frequency response of an antialiasing filter in the ADC, H ADC ( f ), as itis typically narrower than the others. Note that the PD has a responsitivy denoted by R whosephysical unit is Ampere per Watt (A / W). As in the DAC, the cuto ff frequency of ADC is chosento be equal to the bandwidth of the OFDM symbols. We mainly vary the cuto ff frequency ofthe LED, f c LED , as it is typically the main limiting factor in the front-ends of an optical wirelesscommunication system [7]. In this paper, only the thermal noise is considered, and its single-sided power spectral density (PSD) is denoted by N . A single tap equalizer is used to estimatethe transmitted symbols.In general, the BER at the n th subcarrier, P b n , can be approximated as follows [29]: P b n ≈ M − √ M ! Q r γ n M − , (2)where γ n is the electrical signal-to-noise ratio (SNR) at the n th subcarrier, which can be expressedas follows: γ n = K R | H DAC ( f n ) H LED ( f n ) H CIR ( f n ) H ADC ( f n ) | f s N | H ADC | / (2 N ) . (3)The average BER for all OFDM symbols is denoted by P b which is simply the average of P b n over all subcarriers. B. Channel Impulse Response, h ( t )The multipath propagation in an indoor optical wireless channel is described by the CIR h ( t )and its frequency response H CIR ( f ). A widely used method to calculate the CIR is proposed by Kahn and Barry in [27]. This method is significantly improved by Schulze in [31] by takinginto account all reflections. This method is used in this paper since our interest is not to observehow adding an increased number of high order reflections a ff ects the LiFi analyses, but insteadto observe how neglecting the reflections a ff ect the analyses.In this paper, an empty o ffi ce room with dimensions length ( L ) × width ( W ) × height ( H ) m is assumed. A human body will be modeled as a rectangular prism, which is similar to [32], i.e.,the iterative version of Kahn and Barry’s method. Considering an object as a rectangular prismusing Schulze’s method is straightforward, and it will be discussed later. A similar approach ispresented in [33], but the authors also model other common body parts. From our observations,adding such details is less significant to our analyses than focusing on the reflectivities of thosebody parts. In addition, di ff ractions on the edge of a human body are ignored in this paper sincethe wavelengths of the infrared and visible light spectrum are relatively short compared to thedimension of the edge of a human body. Blockages due to other people are not considered inthis paper.The CIR h ( t ) can be decomposed into the LOS and the di ff use links [31]. That is, it can bewritten as: h ( t ) = h Rx,Tx ( t ) + h di ff ( t ) F ⇐⇒ F − H CIR ( f ) = H Rx,Tx ( f ) + H di ff ( f ) , (4)where F denotes the Fourrier transform. Let’s define an attenuation factor between the Rx andthe Tx as follows: G Rx,Tx = m + π cos m (cid:0) φ Rx,Tx (cid:1) A Rx cos (cid:0) ψ Rx,Tx (cid:1) d v Rx,Tx (FoV) , (5)where m is the Lambertian index, A Rx denotes the receiver area and ψ Rx,Tx is the incident angleor angle of arrival between the normal vector n u and the position of the Rx. Note that theorientations of an LED in the Tx and a PD in the RX are shown by the unit normal vector n u and n a , respectively. The radiant angle or angle of departure between the normal vector n a andthe position of the Tx is denoted by φ Rx,Tx . The distance between the Tx and Rx is denoted by d Rx,Tx . The term v Rx,Tx has a binary value that denotes a visibility factor of the link between anRx and a Tx, i.e., v Rx,Tx is one if 0 ≤ φ Rx,Tx ≤ π/ v Rx,Tx (FoV) is one if 0 ≤ ψ Rx,Tx ≤ FoV.
The LOS link, H Rx,Tx ( f ), can be expressed by [31]: H Rx,Tx ( f ) = G Rx,Tx exp (cid:0) − j π f d Rx,Tx / c (cid:1) , (6)where c is the speed of light. The di ff use component can be calculated by partitioning eachsurface into discrete smaller elements, i.e., p = , , . . . , P , and treating them as another radiatoror receiver. These discrete elements include the partition of the surfaces of the blocking objectsas they are modeled by rectangular prisms. This is the reason why the calculation of h ( t ) whena human body is modeled by a rectangular prism is straightforward. The smaller elements actas a radiator with the Lambertian index m =
1. The gain of the reflected light has an additionalattenuation factor, which is called the reflectivity, ρ .The frequency response of the di ff use component can be calculated as follows [31]: H di ff ( f ) = r T ( f ) G ρ (cid:16) I − G ( f ) G ρ (cid:17) − t ( f ) . (7)The vector r T ( f ) = (cid:0) H RX,1 ( f ) H RX,2 ( f ) · · · H RX, P ( f ) (cid:1) is called the receiver transfer vector. Thetransmitter transfer vector is denoted by t ( f ) = (cid:0) H ( f ) H ( f ) · · · H P ,TX ( f ) (cid:1) T . The roomintrinsic frequency response for each small element is described by a P × P matrix G ( f ) whoseits i th row and j th column represent the LOS frequency response between the i th and the j th elements. The matrix G ρ denotes the reflectivity matrix where G ρ = diag ( ρ , ρ , . . . , ρ P ).III. E xperiment A. Assumptions
The unit normal vector of the transceiver is denoted by the vector n u , and spherical coordinatesare used to describe its orientation. A polar angle is denoted by θ , and an azimuth angle is denotedby ω , see the inset in Fig. 1(a). It is clear that from (4-7), as the normal vector n u changes,so does the CIR. Therefore, it is important to have the random orientation model to study theCIR’s behavior. In this section, our experimental results on the random orientation of a UE arediscussed.From our experimental data, it is observed that the noisy measurement of θ , which is denotedby m θ ( t ), fluctuates around its mean as depicted in Fig. 2. Note that discussions about ourexperimental setups are given in the next section. In this paper, the random orientation is modeledas the change of orientation that is caused by user behavior such as hand movements and otheractivities, such as typing or scrolling. Therefore, we can write it as: m θ ( t ) = µ θ + θ ( t ) + n θ ( t ) , (8) (a) (b)Fig. 2. Samples of noisy measurement: (a) m θ ( t ) and m ω | ˜ ω ( t ) for the sitting activity and (b) m θ ( t ) and m ω | ˜ ω ( t ) for the walkingactivity. where µ θ denotes the mean of m θ ( t ), the subscript ‘0’ refers to the corresponding RP whosemean is zero and n θ ( t ) denotes the noise of the measurement. Furthermore, we assume that both θ ( t ) and n θ ( t ) are wide-sense stationary (WSS) and independent to each other. While the WSSRP asserts the mean to be constant, it will be shown later that our proposed model gives areasonable match with the experimental data in terms of the ACF and the power spectrum.For ω , it needs a di ff erent assumption as it highly depends on the directions of the users. Thatis, for a di ff erent sample, ω might no longer fluctuate around 40 ◦ as in Fig. 2(b), and it couldfluctuate around − ◦ if the participant faced the other way. This does not happen in the θ caseas all measurement data θ generally fluctuate around µ θ . For the azimuth angle ω , conditionedon the direction of the UE, ˜ ω , we use following noisy measurement model: m ω | ˜ ω ( t ) = ˜ ω + ω ( t ) + n ω ( t ) , (9)where ˜ ω is the angle direction of the UE and will be modeled as a RV following the uniformdistribution over the interval ( − π, π ] as shown in [18] and [34]. Therefore, the subscript on ˜ ω denotes that m ω | ˜ ω ( t ) is valid for a given value of ˜ ω . The physical meaning of ˜ ω is the directionof a UE, which will later be used to define the direction of a user who holds it. The descriptionsof ω ( t ) and n ω ( t ) are the same as in (8). B. Experimental Setup
The same experimental setup has been presented in [14] and [18]. It will be provided here forthe convenience of the reader. We asked 40 participants from the Alexander Graham Building, University of Edinburgh to conduct a series of experiments. Nine of them were left-handed,and none su ff ered from a severe hand tremor. After being briefed on the procedure and thepurpose of the experiments, they were asked to browse the Internet and watch videos as theystreamed for a minute. Both activities are chosen to emulate the typical data that is obtainedduring activities requiring Internet services. To support our WSS assumption, the time limit wasset to be one minute since the participants might get tired and change the means drastically ifthe experiment was longer. To be able to conduct the series of the experiments while measuringthe data, the Physics Toolbox Sensor Suite application is used [35]. The application is installedon two di ff erent Samsung Galaxy S5 smartphones.The participants were also asked to sit, which is referred to as the sitting activity , and walk,which is referred to as the walking activity , during the experiments. The walking activity wasconducted in a straight corridor with dimensions 40 m ×
15 m. There was a total of 222measurements that were collected, which comprise 148 data measurements for the sitting activityand 74 data measurements for the walking activity.IV. E xperimental R esults and A nalysis The Physics Toolbox Sensor Suite application captures real values of rotations of a UE interms of pitch, roll and yaw rotations. These values are then transformed into the sphericalcoordinates [9]. It is important to note here that time sampling of the application is not evenlyspaced and random in each data measurement. The time sampling duration can range from 1 msto 0 .
65 s. In fact, the most frequent time sampling durations from all data measurements are, inthe order, 1 ms, 18 ms and 64 ms, for a minute experiment, each data measurement has around2 ,
000 to 3 ,
000 samples. Instead of the conventional Fourier analysis, the LSSA that is basedon the Lomb-Scargle method is used in this paper [21].It should be noted here that several preprocessing steps are performed as the analysis is verysensitive to the time sampling. First, it is observed that some time samplings are not unique.That is, from the measurement data, there are some time samplings that are the same, and theygive slightly di ff erent values. In this case, one sampling time is randomly chosen among them.Second, we noticed that a few participants already got tired keeping their arms up. Hence, wedid not process the measurement data for that case since we are interested in the scenario wherethe mean of a measurement data is relatively constant (or we are interested in the slight hand movement about the mean). None of these steps are performed in [14], [18] or [34] as the authorsonly focus on occurrence of the orientation sampling.Fig. 2 shows some samples of data measurements that were collected. Notice that the samplesfluctuate around their means. The mean µ θ , is calculated as follows: µ θ = N N X i = ˆ µ ( i ) θ , (10)where ˆ µ ( i ) θ is the estimated mean of the i th data measurement. By taking average of all datameasurements, we obtain µ θ = . ◦ for the sitting activity and µ θ = . ◦ for the walkingactivity. These results show that when the participants sit, they tilt the phone to the back morethan they would when they walk. The reason for this is because most of the participants puttheir elbows on a desk while using their phones. For the rest of paper, a comfortable manner isdefined as the position where the user holds the UE with θ in the vicinity of µ θ .Unlike µ θ in (8), if the user holds the UE in a normal position as depicted in Fig. 1(a), then˜ ω in (9) depends on which direction the user sits or walks. As also shown in [18] and alsothrough an uncontrolled measurement in [34], the PDF of the unconditional azimuth angle ω is dominated by the random direction of the UE (i.e., ˜ ω ) and it can be modelled as uniformlydistributed in ( − π, π ]. Therefore, the measurement average for azimuth angle does not providea physical intuition. A. Noise Measurements
The characteristics of the data measurements with no activity are first observed; in otherwords, the noise of the application is measured. In particular, the spectrum and the behavior ofthe noise will be investigated. For the random sampling, it is suggested by [21], [23] and [24]that we need to be concerned about the spectrum of the random sampling. Let w ( t ) be a windowfunction of the random sampling as expressed by: w ( t ) = , t = t k , t , t k . (11)where { t k } N − k = is the random sampling. It is important because there might be pseudo-aliasing orpartial-aliasing of signals (see Figs. 13 and 14 in [24] for clear examples). For these purposes,we collected 15 data measurements containing noise samples with di ff erent time intervals fromthe same smartphones used in the experiments. (a) (b)(c) (d)(e)Fig. 3. Results of measurements with no activity: (a) samples of θ ( t ), (b) PSD of θ ( t ) in dB-degree / rad / sample, (c) samplesof ω ( t ), (b) PSD of ω ( t ) in dB-degree / rad / sample and (e) PS of w ( t ). The red curves in (b) and (d) are the average of manygenerated white noises with the same variances as the respected figures to show the consistency of the model. Some samples of the results from noise measurements are shown in Fig. 3. Note that the othersamples also show similar results as in Fig. 3 except Fig. 3(e) as the sampling times are random;thus, the spectrum of the window is also random. The power spectrum (PS) of w ( t ) is calculatedby the LSSA. Our equivalent definitions of the PS and the PSD in uniform time sampling areprovided in the Appendix.By comparing Figs. 3(a) and (c), notice that the fluctuations of ω ( t ) are stronger. This fact issupported by their PSDs shown in Figs. 3(b) and (d), respectively; the PSDs resemble those ofwhite noises, and their variances are − .
71 dB-degree and 0 .
11 dB-degree, respectively. Notethat these values are determined from their linear scales instead of decibel scales to get a moreaccurate result. These variances will be used as parameters in our filter for estimating a desiredsignal from a noisy measurement. Note that the narrow red curves in Figs. 3(b) and (d) arethe average of the PSDs of many generated white noise with corresponding variances. Theseempirical observations are done to show their resemblances to white noise.To gain insight into the window function w ( t ), recall that for an evenly sampled case, we haveDirac combs as the window functions both in the time and frequency domains. Sampling in the time domain is equivalent to taking a convolution of the signal of interest in the frequencydomain with a Dirac comb; therefore, the aliasing after the Nyquist frequency can be seen. Fora random sampling, the window function will also be random, and the definition of the Nyquistfrequency might not exist depending on the characteristics of the random sampling [24]. Basedon [36], the Nyquist frequency for random sampling is κ , where κ is the largest factor such thateach spacing of the time sampling is an integer multiple of κ . In our case, κ exists, and κ = . partial-aliasing in [24], and thewindow function from our data measurements falls into the periodic nonuniform sampling class.This class of window function commonly occurs in the instrumentations as the trigger signalperiodically changes (see [37] and [23]), and this phenomenon is relevant in our case.Up to this point, it can be concluded that the noise in our measurement resembles white noisewhose variances are − .
71 dB-degree for θ ( t ) and 0 .
11 dB-degree for ω ( t ), respectively. Wecan also expect that there will be partial-aliasing in the frequency domain and an aliasing after500 Hz in the PSD of our data measurement. B. Data Measurements
Moving forward from the discussion of noise measurements, we are now ready to discuss ourdata measurements. The fluctuations in Fig. 2 is also shown in many tremor-related publications,such as [38] or [39]. Note that the fluctuation not only occurs for subjects who su ff er fromsevere tremors or Parkinson’s disease, but the same thing also occurs for healthy subjects witha relatively smaller amplitude as the tremor is defined as rapid involuntary oscillations of partsof the human body [39]. One of the frequently used models to describe such a phenomenonis the harmonic RP, i.e., sinusoids in white noise and with random phases [38]. Therefore, ourwork will be based on the harmonic RP. An additional advantage is that it is relatively easy toanalyze in terms of peak detection, see the appendix for a more detailed explanation.Fig. 4 shows the power spectra that are estimated by LSSA and the interpolation methods.The dashed line in Fig. 4 shows a false alarm probability of 0 .
1% denoting that the peaks thatare above the line have 0 .
1% probability of an error being mistaken as the real peak. Both PSs (a) (b)Fig. 4. Power spectrums of the noisy measurements m θ ( t ) from one of the participants, where: (a) the LSSA is applied, and (b)the interpolation is applied. are calculated with the same Nyquist frequency, i.e., 500 Hz. Since the results for the ω , i.e., m ω | ˜ ω ( t ), show the same characteristics, the results are not presented here.As previously mentioned, both aliasing and partial-aliasing can be seen in Fig. 4(a). Thelower inset Fig. 4(a) shows the PS of the window function. Notice that the frequency gaps ofthe reliable peaks, i.e., the peaks that are located above the false alarm probability line, have thesame frequency gaps as those of the PS of the window function. Therefore, a cleaning algorithmmust be performed to detect the real peaks.Our empirical observation on the PSDs shows that the noise floor is also increasing. Therefore,we assume that there are two white noise sources, i.e., one of them comes from the noise ofthe measurement, and the other one is inherent from the participant’s unsteady hand. The noisefloor is also detected in [39], and it also agrees with the model in [38]. In this paper, we willonly filter the measurement noise that is explained in the previous subsection.The e ff ect of the linear interpolation can be seen in Fig. 4(b), which is a typical smooth-ing e ff ect. Interpolating unevenly sampled data is equivalent to filtering out a high frequencycomponent. Recall that the cuto ff frequency of the linear interpolation is inversely proportionalto the number of upsampling ratios. Since our random sampling can range from an order ofmilliseconds to hundreds of milliseconds, the upsampling ratio is very high; thus, the cuto ff frequency of the linear interpolation is quite low. Therefore, quantities, such as ACF, that arederived from the filtered data will be significantly a ff ected. For more detailed expositions of whythe interpolation method is unfavorable than the LSSA, the readers could consult to [20], [21], [23], [24] or [37].Before discussing our model, an independency test between m θ ( t ) and m ω | ˜ ω ( t ) in our measure-ment data needs to be carried out. Note that the random sampling is not an issue here becausethe test is performed for both m θ ( t ) and m ω | ˜ ω ( t ) which have the same sampling time. A testgiven by [40] is applied. The output of the test is the p-value with the null hypothesis whethertwo tested RPs are independent. By calculating the p-value for each measurement, we have aminimum p-value of 0 .
13 for the sitting activity and 0 .
19 for the walking activity. Recall thatthe smaller the p-value, the stronger the evidence that the null hypothesis should be rejected. Inaddition, a p-value equal to 0 .
05 is used as a rule-of-thumb; hence, p-value larger than 0 .
13 isdeemed significant. In other words, both m θ ( t ) and m ω | ˜ ω ( t ) can be treated as independent RPs.Based on [38], θ ( t ) is modeled as a harmonic RP in white noise, that is: θ ( t ) = A θ sin (2 π f θ t + φ ) + v θ ( t ) , (12)where A θ is the amplitude, f θ is the fundamental frequency of θ ( t ), φ is a RV that is uniformlydistributed from − π to π and v θ ( t ) is a white noise with the variance σ v θ . We will focus on θ ( t ),but keep in mind that the same model can also be applied for ω ( t ), and we provide the finalresult for ω ( t ) together with that for θ ( t ).Recall that the unnormalized ACF of (12) is: R θ ( τ ) = E (cid:2) θ ( t ) θ ∗ ( t + τ ) (cid:3) = A θ π f θ τ ) + σ v θ δ ( τ ) , (13)where δ ( · ) is an impulse function. The normalization is taken such that the ACF at τ = R θ ( τ ) / R θ (0). This model agrees with our observation and will be shown later. Our empiricalobservation for all of our data measurements shows that one sinusoid is su ffi cient.It is clear that to estimate θ ( t ), the noise, n θ ( t ), and the partial aliasing due to the randomsampling need to be filtered. For the former case, we use a Wiener filter [25], and for the lattercase, we use the CLEAN algorithm, see [26] and [23]. The CLEAN algorithm is an iterativemethod that uses the knowledge of a window function to perform deconvolution in the frequencydomain. The output of the algorithm is the spectrum as if it were taken from evenly sampleddata.In this paper, a first-order Wiener filter is applied, which is denoted as a finite impulse response(FIR) F ( z ) = f + f z − . A more complicated filter is also possible, but we want to show that even (a) (b)Fig. 5. (a) A power spectrum of ˆ θ ( t ) from Fig. 4 after being filtered and (b) an ACF of ˆ θ ( t ) from Fig. 4. with a simple optimal filter our model can closely match the experimental data. The polynomialof the filter F ( z ) can be easily calculated by solving following the Wiener-Hopf equation [25]: A θ + σ v θ + σ n θ A θ cos (2 π f θ τ ) A θ cos (2 π f θ τ ) A θ + σ v θ + σ n θ f f = A θ + σ v θ A θ cos (2 π f θ τ ) . (14)All parameters in (14) can be obtained by calculating both the PSD and PS of the zero-meannoisy measurement. The values of the parameters will be explained in the next paragraph.Fig. 5(a) shows the PS of the estimated θ ( t ), ˆ θ ( t ), after being filtered by both the FIR filterand the CLEAN algorithm. It is clear that the partial aliasing no longer exists. From Fig. 5(a),the peak can be detected at f θ = .
32 Hz, and the amplitude is A θ = . ◦ .Based on (13), σ v θ can be estimated as: σ v θ ≈ R θ (0) A θ (1 − R θ ( ǫ ) / R θ (0))2 R θ ( ǫ ) , (15)for a small ǫ . Fig. 5(b) shows the normalized ACF that is calculated by taking the inverse Fouriertransform of the PSD of ˆ θ ( t ). For Fig. 5(b), R θ ( ǫ ) / R θ (0) is 0 . σ v θ isapproximately 9 . ◦ ( σ v θ = .
78 dB-degree).By plugging in all these estimated parameters, the theoretical ACF can be calculated and it isshown in Fig. 5(b). Note that the estimated ACF is biased, and is calculated by taking the inverseFourier transform from the experimental data; it means that the ACF is decreasing over the timelag. Recall that in estimating the ACF, the biased estimation is preferable over the unbiasedone, as the unbiased one might have the normalized ACF value greater than one, which is not Table I. Average values of the estimated parameters.
Parameters Sitting Activity Walking Activity θ ( t ) ω ( t ) θ ( t ) ω ( t ) A ( ◦ ) 1 .
88 1 .
31 3 .
22 3 . f (Hz) 0 .
67 1 .
46 1 .
86 1 . σ v ( ◦ ) 5 .
91 3 .
22 7 .
59 9 . true (see [22] for an example). From Fig. 5(b), notice that the frequency f θ from one of themeasurement samples and our model shows a similarity, especially, in the low region of the timelag as it is the region of interest from the perspective of the wireless communication community.Such similarity is also seen for other measurement samples.To conclude, we first perform the CLEAN algorithm and the Wiener filter to estimate thevalues of A θ and f θ . By taking the inverse Fourier transform of the PSD that is the output ofthe CLEAN algorithm, we estimate the value of σ v θ . These procedures are performed for all ofour data measurements. By taking the average from all estimated values of the parameters, weobtain the values as shown in Table I.Based on the value of σ v from Table I, it is confirmed that the fluctuation of the experimentalresults for the walking activity is higher. The ACF will reach 0 for the first time at t = / (4 f ),and the lowest value is 0 .
13 s. Since the delay spread of the CIR h ( t ) is typically in the orderof nanoseconds [6]. Therefore, h ( t ) can still be considered slowly varying since the change oforientation is highly correlated in the timescale of nanoseconds.Let’s now define ω and θ as RVs whose realizations are chosen randomly and by takingevenly-spaced samples from their RP models without the measurement noise, i.e.: ω = ˜ ω + ω ( nT s ) ,θ = µ θ + θ ( nT s ) , where n ∈ N and T s is a sampling time. For ω , Table I and the results in [18] and [34] suggestthat ω can be accurately modeled as a uniformly distributed RV as ω has a relatively smallvariance compared to ˜ ω , which is uniformly distributed in ( − π, π ]. For modeling conditionalazimuth angle (i.e., ω | ˜ ω ), ω ( t ) can be generated based on the harmonic RP discussed aboveusing, for example, a Gaussian white noise.Regarding the RV θ , it is shown in [14] and [18] that the PDF of θ for the sitting activity iscloser to the Laplace distribution, and it is closer to the Gaussian distribution for the walking Fig. 6. Samples PDFs of θ with evenly spaced sampling and the fitted distributions. activity in terms of Kolmogorov-Smirnov distance (KSD). Recall that v θ ( t ) in (12) is kept generalin the sense that the white noise RP can be generated from any independent and identicallydistributed RV. We observe that to match it with the RV models in [14], [18], v θ ( t ) can bemodeled to be v θ ( t ) = X , where X is a zero-mean RV that follows either a Laplace distributionor a Gaussian distribution depending on the activity as shown in Fig. 6.The closed-form PDF of θ is hard to obtain since the derivation involves an integration of afunction that has non-elementary functions. That is, the PDF of θ is the convolution of a Laplaceor a Gaussian distribution and an arcsine distribution, which has the term ∝ / √ C − x , where C >
0. Therefore, the moments matching method is used, and the result is shown in Fig. 6. TheKSDs are used to measure the di ff erences between the evenly-spaced generated samples basedon our model and the fitting Gaussian or Laplace distributions. Based on the KSDs, we canobserve that generated samples of θ as a RV follow either a Laplace or a Gaussian distribution.It is straightforward to calculate the moments of the fitted distribution, e.g., the mean of theGaussian distribution is µ G = µ θ , and the variance is σ = σ v + A /
2. The same equation isalso applied for the Laplace distribution by replacing the subscript ‘G’ with ‘L’ to denote whichdistribution is being used. It is worth noting that this RP model can be used in conjunction withthe generalized random way point model proposed in [18] for modeling the mobility of the usersin LiFi networks. (a) (b)Fig. 7. (a) Description of the locations and the directions of users and UEs and (b) configurations of locations and directions ofthe users and the UEs. V. F ixed L ocation and O rientation In this paper, before discussing the general case where the locations and the directions ofthe users are random, several specific cases are discussed so that a deeper understanding bothin specific and general cases can be obtained in the end. Particularly, we will first discuss thebehavior of the CIR and its e ff ect on our OFDM system in terms of the BER and the receivedSNR to achieve a certain forward error correction (FEC) threshold. A. Channel Impulse Response
In this section, the CIR behavior for di ff erent configurations will be discussed. Fig. 7(a)shows the parameters to describe configurations of interest in this paper. The location of the APis denoted by ( x a , y a , z a ). Since a human body is modeled as a rectangular prism with dimensionsof L b × W b × H b , its location is represented by one of the locations of its vertices as denoted by( x u , y u ) without the z -axis coordinate. The location of a UE is relative to the location of the userwho holds it. In other words, we assume that the users hold the UEs in front of their chests.These are described in the insets of Fig. 7(a). The direction of the UE is denoted by ω , and thedirection of the user is assumed to be Ω = ω + π as depicted in Fig. 7(a).As in the experiments, two activities are considered, i.e., the sitting and the walking activities.Note that the term ‘walking activity’ is used throughout the rest of the paper so that it is consistentwith the term used in the experiments even though it is more intuitively correct to view it as acase where the user stands while holding the UE with a certain direction. We will use θ = . ◦ for the sitting activity, and θ = . ◦ for the walking activity, which are equal to the meansobtained in the experiments. For the walking activity scenario, we define L b = .
66 m, W b = .
2m and H b = .
75 m [41]. The UE is placed 0 .
35 m in front of the user’s chest, whose height iscalculated as 1 . ff erences are that H b = . . L = W = . H = ρ = .
3, the reflectivity of the ceiling is ρ = .
69 and thereflectivity of the floor is ρ = .
09 [27]. The reflectivities of the surfaces of a human body areassumed to be ρ = .
6, which is the reflectivity of a cotton fabric [42]. Note that a smallerrectangular prism can also be used to model the head of a human to distinguish it from the mainbody. However, this is not included in this paper. In addition, the reflectivity of human skin isalso around 0 . ρ = . m =
1, FoV = ◦ , A Rx = are used and the resolution of the partition is 10 to generate the CIR.For this specific case, 5 di ff erent configurations are chosen as denoted by C i for the i th configuration, see Fig. 7(b). These configurations are picked to describe several scenarios ofinterest which will be explained later. The location of the AP is (0 , , C , the user is located at ( − . , .
55) and his direction is
Ω = − ◦ , i.e., the direction ofthe UE is ω = ◦ .The configuration C represents the case where the LOS link still exists with ψ = . ◦ forthe walking activity and ψ = . ◦ for the sitting activity. The configuration C represents thecase where the LOS link is blocked by the user for the walking activity, but the LOS link existsfor the sitting activity with ψ = . ◦ . The configuration C represents the case where the UE islocated underneath the AP. The configuration C represents the case where the user is locatedat the corner of the room and the LOS link still exists for both activities with ψ = . ◦ forthe walking activity and ψ = . ◦ for the sitting activity. The configuration C represents thecase where the LOS link is blocked. However, unlike in C , there are two walls near the UE.Fig. 8 shows the magnitude response of the CIR with configurations described in Fig. 7(b).It is obvious that the configuration C gives a higher channel gain compared to the others dueto its shortest distance. Recall that the participants tend to tilt the UEs to the front during the (a) (b)Fig. 8. (a) Magnitude responses of H CIR with configurations depicted in Fig. 7(b) and (b) magnitude responses of H CIR for C and the sitting activity. The terms sitting and walking are used here to relate them with our previous discussions, while thephysical meanings of them are merely that the person holding the UE sits or stands and, the UE is oriented to the mean value. walking activity than that during the sitting activity. Therefore, the incident angle ψ is smaller;hence, the channel gain is higher for the walking activity. The results for C are comparablewith those for C . With full FoV, the channel gain for C is 10 dB lower than that for C . Itwill be shown later how this di ff erence a ff ects the performance of our OFDM system.The results for C show the case when the user is located near the wall. The channel gaindi ff erence between the results for the sitting activity (the LOS link exists) and the walkingactivity (the LOS link is blocked) varies between 20 to 30 dB. This result is consistent withthe result of the shadowing e ff ect in [6]. Fig. 8(b) shows the zoom-in figure of the result for C and the sitting activity. When LOS link exists, observe that the CIR fluctuates around theDC channel gain of its LOS link, especially, in a higher frequency region. It is also interestingto note that the channel gain for the sitting activity with C is slightly higher than that for thewalking activity with C . This is due to the incident angle ψ is much smaller; hence, the channelgain is higher as it is proportional to cos ( ψ ), see (5). The results for C have the worst channelgain of all. These channel gains will be used to determine the number of CP for our OFDMsystem.As in [7], we are also interested in the ratio between the power from the LOS link denotedby P LOS and the total power denoted by P tot . Table II shows the ratio in percentage. Note that to Table II. The contribution of the power from the LOS link in percentage. C , s C , w C , s C , s C , w C , s C , w P LOS P tot (%) 61.53 73.28 88.41 89.78 92.51 40.96 60.24 Table III. Values of parameters.
Parameters Values UnitsBit rate ( R b ) 100 MbpsNumber of subcarriers ( N ) 128 -Number of used subcarriers ( N u ) 108 -Number of CPs (cid:16) N cp (cid:17) M ) 16 -Cuto ff frequency of the LED (cid:16) f c LED (cid:17)
20 or 40 MHzBER target (cid:16) P b,target (cid:17) . × − -Responsitivity of the PD ( R ) 0 . / W save the space, the subscripts ‘w’ and ‘s’ denote the results for the walking and sitting activities,respectively. Contrary to the results in [7] which considers only the case where the UE alwaysfaces upward, the power contribution of the LOS link is not always dominant which is shownby the results with the configuration C . The results of the power ratio will be generalized inthe next section for randomly-located users. B. OFDM Performance
In this paper, if the values of the parameters are not mentioned, the values are defined asshown in Table III. Given the values of OFDM parameters, the bandwidth of OFDM symbolsis around 28 MHz. These are chosen based on the value of f c LED that ranges between 20 to 40MHz, see [45], [46] and [7]. The number of CPs is chosen based on the worst channel in Fig. 8,which is C . The BER target is chosen such that it is lower than the FEC threshold, which isdefined as P b,target = . × − [47], and the responsitivity of the PD is R = . / W [48].Following [6] and [48], a received electrical SNR is defined as:SNR = R H (0) P N f s / , (16)where P t is the average optical transmitted power. The benefit of this definition is that theperformances of di ff erent modulation schemes can be fairly compared [48]. The SNR that isrequired to achieve P b = P b,target is denoted by SNR t . The BER comparisons for C is depictedin Fig. 9. The result follows our intuition that the multipath propagation makes the BER worse. Fig. 9. BER comparison for C where the subscript ‘s’ denotes sitting and ‘w’ denotes walking. The solid or dashed lines showthe theoretical results, and the markers show the simulation results.Table IV. Comparison of the received electrical SNR (in dB) at P b,target , which is denoted by SNR t , and the SNR penalty whenthe di ff use channel is neglected, which is denoted by SNR t,penalty . f c LED
40 MHz 20 MHz
C C , s C , w C , s C , w C , s C , w C , s C , w C , s C , w C , s C , w C , s C , w C , s C , w C , s C , w C , s C , w SNR t t,penalty In addition, as seen in Fig. 9, given the same rate and the same bandwidth of the OFDM symbols,decreasing the bandwidth of the LED such that it is less than bandwidth of the OFDM symbolswill also decrease the BER performance. Note that not all BER curves will be presented in thefigure since many configurations are investigated in this paper. Instead, only the SNR values at P b = P b,target are discussed in this paper, and they are given in Table IV.We are also interested in investigating the e ff ect of higher order reflections. In other words, thee ff ect of ignoring the di ff use link as in many published works, e.g., [10], [11], [14] or [12], willbe discussed. In terms of the BER target, we focus on the target SNR penalty, i.e., SNR t,penalty ,which is defined as the di ff erence between SNR t with both links and SNR t with the LOS linkonly. The values of SNR t,penalty can range from 0 .
58 to 10 . C , s has the biggest penalty, and thesmallest penalty is achieved for C , w . The flatness of the CIR is highly correlated to the powerratio as shown in Table II. We also observe that the power ratio of 75% is related to the SNRpenalty around 3 dB. For system designers who calculate a power budget of a LiFi system, thispenalty might significantly a ff ect the whole system cost. The e ff ect of the LED’s bandwidth can also be seen in the Table IV. For relatively flatchannels as in configurations C , decreasing the bandwidth increases the SNR penalty. On theother hand, decreasing the bandwidth reduces the SNR penalty for the other configurations. Thereason is that the level of fluctuation in the channel plays more significant role than the e ff ectof the subcarriers loss for the configurations other than C . More focused studies about theseobservations are subject of our future works. In the next section, we also discuss the consequenceof ignoring the di ff use link in terms of the outage probability, which is one of the main metricof the analyses in the network level or the cellular networks.VI. R andom L ocations and O rientations In this section, random locations and orientations of the UE are assumed. The benefit ofthis assumption is that the average performance can be obtained as the indoor optical wirelesschannel highly depends on the geometry of the UE and the AP, see Fig. 8 for an example. Toolsfrom the stochastic geometry are usually used to consider the case with randomly-located users.However, even with the LOS link, a closed form expression is hard to obtain and it typicallystill contains an integral expression, see [7] and [49]. In this section, a semi-analytic approachis used in the sense that the CIRs are generated by Monte Carlo simulations and the SNR targetis calculated analytically.We will assume that the locations of user and UE are uniformly distributed in an indoor roomwith the same dimensions used in the previous section. Since only a single channel is concerned,each realization has a user and a UE. This is further referred to as the binomial point process.As for the orientation, we assume that θ follows either a Laplace distribution or a Gaussiandistribution depending on the activity as depicted in Fig. 6, and the direction of the users, Ω ,follows a uniform distribution. We generated 1 ,
000 CIRs for each activity and observed that theprobability of the LOS link exists is 88 .
1% for the walking activity and 94 .
8% for the sittingactivity. In this section, the CIRs having the LOS links are used.First, we look at the cumulative distribution function (CDF) of SNR t,penalty for this ran-dom case. The result is depicted in Fig. 10(a). Since the results are quite similar, let’s focuson P h SNR t,penalty < i shown in the inset. P h SNR t,penalty < i for all configurations inFig. 10(a) are around 0 .
7. As previously discussed and shown in Table IV, using wider bandwidthresults in a better performance in terms of SNR t,penalty . Generally, considering that there is 0 . t,penalty can be greater than 3 dB, we believe that simply ignoring the di ff use (a) (b)Fig. 10. (a) CDFs of SNR t,penalty with randomly-located, randomly-oriented UEs and (b) CDFs of | H CIR (0) | with randomly-located, randomly-oriented UEs. link in BER analysis is too limiting. Alternatively, one can simply ignore the di ff use link incalculating the BER performance for a randomly-oriented UE for the case where the UE islocated near to the AP since the channel is relatively flat, see the results for C in Fig. 8.In a network-level analysis considering the interference and randomly-located UEs as in[7], [50] or [49], the received power is generally assumed to only come from the LOS link.Understanding the previous discussion, we get an insight that this is correct if the UE is locatednear the AP. Therefore, we are also interested in justifying the importance of the di ff use link inthe network-level analysis whose the main metric is the signal-to-interference-plus-noise ratio(SINR). Recall that the SINR is a function of the electrical received power which is proportionalto the DC channel gain, i.e., P r ∝ | H CIR (0) | , where P r is the average received optical power [6].The CDF of | H CIR (0) | is depicted in Fig. 10(b).Generally, the results for the walking activity are better than that of the sitting activity. Thereason is that the distance between the UE and the AP is shorter due to the vertical distancedi ff erence between both activities, i.e., the height is 1 . . | H CIR (0) | into two parts, i.e., thelow region where | H CIR (0) | < −
114 dB and the high region where −
114 dB ≤ | H CIR (0) | . Notethat −
114 dB is chosen such that the di ff erence of | H CIR (0) | with and without the di ff use linkis 3 dB. Notice that the gap is larger in the low region compared to that in the high region. InFig. 10(b), the maximum gap is around 25 dB in the low region. In the high region, the gap isnarrowing. This is expected since this region is typically obtained when the UE is located near the AP, and the power ratio is relatively high. For an example, see the CIR for C in Fig. 8(b).Based on these results, the studies of the interference power can be significantly improvedif the di ff use link is incorporated. This is true especially because the interfering transmittersare typically located far from the receiver. Being far from the receiver makes the fluctuationof H CIR ( f ) stronger, see H CIR ( f ) for C and C . Using only the LOS link in the studies of theinterference can be considered in a scenario where the UEs are located near the AP, for example,if the multiple access scheme used is NOMA as in [13] and [51]. The studies of the interferencein NOMA are typically focused on a single cell with multiple users, and the UEs are typicallylocated near an AP within a few meters away, see [51]. To relate it with our example, imaginewe draw a circle with the center being the AP, and the radius being around 1 . C to C are relatively flat, see Fig. 8.Another way to interpret results in Fig. 10(b) is by viewing it as the outage probability. Therelationship between | H CIR (0) | and the outage probability is obvious by looking at (16), i.e., thereceived electrical SNR is proportional to | H CIR (0) | . The outage event is typically defined as theevent when the received electrical SNR is less than a SNR target to achieve certain BER [8],[52]. Fig. 10(b) shows that a system with both links is significantly better than that with onlyLOS link, i.e., the outage events less frequently occur if the di ff use link is considered. In otherwords, reflected signal can help reducing the outage events up to 25 dB, especially, in the lowregion of the DC channel gain. VII. C onclusions This paper focused on modeling the random orientation and applying it in DC-OFDM-basedLiFi systems. A series of experiments were conducted with 40 participants, and 222 datameasurements were obtained while they browsed the Internet and watched streaming videos.The random orientation was modeled as user’s slight hand movement and other activities, suchas scrolling or typing. In addition, we observed that the sampling time of the sensors were notevenly-spaced. It was also shown that the ACF reached 0 for the first time when the time lagwas 0 .
13 s. Compared to the typical delay spread of the optical wireless channel which was inthe order of nanoseconds, the CIR could still be assumed to be slowly varying since the randomorientation was highly correlated in the order of nanoseconds.In this paper, we also applied the random orientation model to DC-OFDM-based LiFi systems.The RP model with a sinusoid in white noise was used to model the random orientation as an RV. The polar angle of the orientation of the UE was modeled as Laplace distribution for thesitting activity and a Gaussian distribution for the walking activity. In addition, the azimuthangle was modeled as a uniform distribution. Based on the RV model, the error performanceof the LiFi system was investigated. We showed that the probability of the SNR penalty whichwas larger than 3 dB was 30%. In terms of the DC channel gain, it was shown that the penaltycould range up to 25 dB in the low region of the DC channel gain which correlated to the casewhere the UE was located far from the AP. Therefore, a great care must be taken on when asimplification on reflection could be made.A ppendix : P ower S pectrum and P ower S pectral D ensity F or E venly -S paced S amples Throughout this paper, the spectral analysis is performed based on a LSSA that gives aperiodogram, which estimates either power spectral density (PSD) or power spectrum (PS). Forsimplicity, we can safely discuss and treat the PSD and the PS of the LSSA the same as theevenly-spaced counterpart, see [20], [21], [23], [24] or [37]. However, please bear in mind thatthe Lomb-Scargle method is used instead, not the conventional Fourier analysis.The PSD is mainly used to detect the noise level, and the PS is mainly used to detect thepower of a random signal at a certain frequency. Therefore for a discrete random process (RP) X [ n ] whose length is N , its two-sided PS with a rectangular window is expressed by: S X [ k ] = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N P j = X (cid:2) j (cid:3) e ( − π i )( j − k − / N (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N , k ∈ [0 , N − . Meanwhile, its PSD is expressed by: P X [ k ] = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N P j = X (cid:2) j (cid:3) e ( − π i )( j − k − / N (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N k ∈ [0 , N − . If X [ n ] is a sinusoid in a white noise with a random phase, i.e., X [ n ] = A sin (2 π f / F s n + φ ) + w [ n ],where f , F s is a frequency sampling, φ is a random variable (RV) which follows theuniform distribution from − π to π and w [ n ] is a zero-mean white noise whose variance is σ ,then the estimated power of X [ n ] at frequency f is 2 S X [ N f / F s ] = A . The white noise level is σ = U P j = L P X [ j ] / ( U − L + L , U ] is the interval outside the neighborhood of N f / F s . R eferences [1] Federal Communications Commission, Mobile Broadband: The Benefits of Additional Spectrum , Oct, 2010. [Online].Available: https: // apps.fcc.gov / edocs public / attachmatch / DOC-302324A1.pdf[2] H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?”
Journal of Lightwave Technology , vol. 34, no. 6, pp. 1533–1544,March 2016.[3] T. Cogalan and H. Haas, “Why would 5G need optical wireless communications?” in , Montreal, Canada, Oct 2017, pp. 1–6.[4] The Institute of Electrical and Electronics Engineers, Inc., “802.11bb - Standard for InformationTechnology–Telecommunications and Information Exchange Between Systems Local and Metropolitan AreaNetworks–Specific Requirements - Part 11: Wireless LAN Medium Access Control (MAC) and PhysicalLayer (PHY) Specifications Amendment: Light Communications,” accessed 2018-07-24. [Online]. Available:http: // / / pub / IEEE%20802 15%20WPAN%2015 7%20Revision1%20Task%20GroupOLD.htm[5] ——, “IEEE 802.15 WPANTM 15.7 Revision: Short-Range Optical Wireless Com-munications Task Group (TG 7r1),” accessed 2018-04-11. [Online]. Available:http: // / / pub / IEEE%20802 15%20WPAN%2015 7%20Revision1%20Task%20GroupOLD.htm[6] J. M. Kahn and J. R. Barry, “Wireless infrared communications,”
Proceedings of the IEEE , vol. 85, no. 2, pp. 265–298,Feb 1997.[7] C. Chen, D. A. Basnayaka, and H. Haas, “Downlink performance of optical attocell networks,”
Journal of LightwaveTechnology , vol. 34, no. 1, pp. 137–156, Jan 2016.[8] C. L. Bas, S. Sahuguede, A. Julien-Vergonjanne, A. Behlouli, P. Combeau, and L. Aveneau, “Impact of receiver orientationand position on visible light communication link performance,” in , Istanbul, Turkey, Sept 2015, pp. 1–5.[9] M. D. Soltani, X. Wu, M. Safari, and H. Haas, “Access point selection in Li-Fi cellular networks with arbitrary receiverorientation,” in , Valencia, Spain, Sept 2016, pp. 1–6.[10] J. Y. Wang, Q. L. Li, J. X. Zhu, and Y. Wang, “Impact of receiver’s tilted angle on channel capacity in VLCs,”
ElectronicsLetters , vol. 53, no. 6, pp. 421–423, 2017.[11] J. Y. Wang, J. B. Wang, B. Zhu, M. Lin, Y. Wu, Y. Wang, and M. Chen, “Improvement of BER performance by tiltingreceiver plane for indoor visible light communications with input-dependent noise,” in , Paris, France, May2017, pp. 1–6.[12] Y. S. Eroglu, Y. Yapici, and I. G¨uvenc¸, “Impact of random receiver orientation on visible light communications channel,”
CoRR , vol. abs / ArXiv e-prints , jan 2018.[14] A. A. Purwita, M. D. Soltani, M. Safari, and H. Haas, “Impact of terminal orientation on performance in LiFi systems,”in , Barcelona, Spain, April 2018, pp. 1–6.[15] M. D. Soltani, H. Kazemi, M. Safari, and H. Haas, “Handover modeling for indoor Li-Fi cellular networks: The e ff ectsof receiver mobility and rotation,” in , San Fransisco, USA, March 2017, pp. 1–6.[16] A. A. Purwita, M. D. Soltani, M. Safari, and H. Haas, “Handover probability of hybrid LiFi / RF-based networks withrandomly-oriented devices,” in , Porto, Portugal, June 2018, pp. 1–5.[17] M. D. Soltani, A. A. Purwita, I. Tavakkolnia, H. Haas, and M. Safari, “Impact of device orientation on error performanceof LiFi systems,”
IEEE Access (to be submitted) , 2018. [18] M. D. Soltani, A. A. Purwita, Z. Zeng, H. Haas, and M. Safari, “Modeling the random orientation ofmobile devices: Measurement, analysis and LiFi use case,” CoRR , vol. abs / // arxiv.org / abs / IEEE Transaction on Vehicular Technology , vol. 66, no. 5, pp. 3798–3811, May 2017.[20] P. Van´ıˇcek, “Approximate spectral analysis by least-squares fit,”
Astrophysics and Space Science , vol. 4, no. 4, pp. 387–391,Aug 1969.[21] J. D. Scargle, “Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaceddata,”
Astrophysical Journal , vol. 263, pp. 835–853, Dec. 1982.[22] M. R. Craymer, “The least-squares spectrum, its inverse transform and autocorrelation function: Theory and someapplications in geodesy,” Ph.D. dissertation, University of Toronto, Canada, 1998.[23] S. Baisch and G. H. Bokelmann, “Spectral analysis with incomplete time series: an example from seismology,”
Computers & Geosciences , vol. 25, no. 7, pp. 739 – 750, 1999.[24] J. T. VanderPlas, “Understanding the Lomb-Scargle Periodogram,”
ArXiv e-prints , Mar 2017.[25] M. H. Hayes,
Statistical Digital Signal Processing and Modeling , 1st ed. New York, NY, USA: John Wiley & Sons, Inc.,1996.[26] D. H. Roberts, J. Lehar, and J. W. Dreher, “Time Series Analysis with Clean - Part One - Derivation of a Spectrum,”
Astronomical Journal , vol. 93, p. 968, Apr 1987.[27] J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse responsefor indoor wireless optical channels,”
IEEE Journal on Selected Areas in Communications , vol. 11, no. 3, pp. 367–379,Apr 1993.[28] Z. Zhou, C. Chen, and M. Kavehrad, “Impact analyses of high-order light reflections on indoor optical wireless channelmodel and calibration,”
Journal of Lightwave Technology , vol. 32, no. 10, pp. 2003–2011, May 2014.[29] J. K. Perin, M. Sharif, and J. M. Kahn, “Modulation schemes for single-laser 100 Gb / s links: Multicarrier,” Journal ofLightwave Technology , vol. 33, no. 24, pp. 5122–5132, Dec 2015.[30] H. Elgala, R. Mesleh, and H. Haas, “Predistortion in optical wireless transmission using OFDM,” in , vol. 2, Shenyang, China, Aug 2009, pp. 184–189.[31] H. Schulze, “Frequency-domain simulation of the indoor wireless optical communication channel,”
IEEE Transaction onCommunications , vol. 64, no. 6, pp. 2551–2562, June 2016.[32] J. B. Carruthers and P. Kannan, “Iterative site-based modeling for wireless infrared channels,”
IEEE Transaction onAntennas and Propagation , vol. 50, no. 5, pp. 759–765, May 2002.[33] C. L. Bas, S. Sahuguede, A. Julien-Vergonjanne, A. Behlouli, P. Combeau, and L. Aveneau, “Human body impact onmobile visible light communication link,” in , Prague, Czech Republic,July 2016, pp. 1–6.[34] Z. Zeng, M. D. Soltani, H. Haas, and M. Safari, “Orientation model of mobile device for indoor VLC and millimetre wavesystems,” in , Chicago, USA, 2018.[35] V. Software, “Physics toolbox sensor suite,” accessed 2018-02-07. [Online]. Available:https: // play.google.com / store / apps / details?id = com.chrystianvieyra.physicstoolboxsuite[36] Eyer, L. and Bartholdi, P., “Variable stars: Which Nyquist frequency?” Astronomy and Astrophysics Supplement Series ,vol. 135, no. 1, pp. 1–3, 1999.[37] P. Babu and P. Stoica, “Spectral analysis of nonuniformly sampled data a review,”
Digital Signal Processing , vol. 20,no. 2, pp. 359 – 378, 2010. [38] M. Gresty and D. Buckwell, “Spectral analysis of tremor: understanding the results.” Journal of Neurology, Neurosurgery & Psychiatry , vol. 53, no. 11, pp. 976–981, 1990.[39] O. Dick, “From healthy to pathology through a fall in dynamical complexity of involuntary oscillations of the humanhand,”
Neurocomputing , vol. 243, pp. 142 – 154, 2017.[40] K. Chwialkowski and A. Gretton, “A kernel independence test for random processes,” in
Proceedings of the 31stInternational Conference on Machine Learning , vol. 32, no. 2. Bejing, China: PMLR, 22–24 Jun 2014, pp. 1422–1430.[41] J. Ilecko, “The simulation of human gait in Solid Works,” accessed 2018-02-07. [Online]. Available:http: // /
31 PRNT 2008 / Tecnic / et al. , “Cotton fabric GDS437 white descript,” accessed 2018-02-07. [Online]. Available:https: // crustal.usgs.gov / speclab / data / GIFplots / GIFplots splib07a / ChapterA ArtificialMaterials / splib07a Cotton Fabric GDS437 White ASDFRa AREF.gif[43] D. W. A. Catherine C. Cooksey, “Reflectance measurements of human skin from the ultraviolet to the shortwave infrared(250 nm to 2500 nm),” pp. 8734 – 8734 – 9, 2013.[44] T. van Kampen, “Optical properties of hair,” Master’s thesis, Technische Universiteit Eindhoven, Netherland, 1997.[45] J. Vucic, C. Kottke, S. Nerreter, K. D. Langer, and J. W. Walewski, “513 Mbit / s visible light communications link basedon DMT-modulation of a white LED,” Journal of Lightwave Technology , vol. 28, no. 24, pp. 3512–3518, Dec 2010.[46] H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb / s NRZ visible lightcommunications using a postequalized white LED,” IEEE Photonics Technology Letters , vol. 21, no. 15, pp. 1063–1065,Aug 2009.[47] M. S. Islim, R. X. Ferreira, X. He, E. Xie, S. Videv, S. Viola, S. Watson, N. Bamiedakis, R. V. Penty, I. H. White, A. E.Kelly, E. Gu, H. Haas, and M. D. Dawson, “Towards 10Gb / s orthogonal frequency division multiplexing-based visiblelight communication using a GaN violet micro-LED,” Photon. Res. , vol. 5, no. 2, pp. A35–A43, Apr 2017.[48] D. J. F. Barros, S. K. Wilson, and J. M. Kahn, “Comparison of orthogonal frequency-division multiplexing and pulse-amplitude modulation in indoor optical wireless links,”
IEEE Transaction on Communications , vol. 60, no. 1, pp. 153–163,January 2012.[49] L. Yin and H. Haas, “Coverage analysis of multiuser visible light communication networks,”
IEEE Transaction on WirelessCommunications , vol. PP, no. 99, pp. 1–1, 2017.[50] A. A. Purwita, C. Chen, D. A. Basnayaka, and H. Haas, “Aggregate signal interference of downlink LiFi networks,” in
GLOBECOM 2017 - 2017 IEEE Global Communications Conference , Singapore, Singapore, Dec 2017, pp. 1–6.[51] L. Yin, W. O. Popoola, X. Wu, and H. Haas, “Performance evaluation of non-orthogonal multiple access in visible lightcommunication,”
IEEE Transaction on Communications , vol. 64, no. 12, pp. 5162–5175, Dec 2016.[52] C. L. Bas, S. Sahuguede, A. Julien-Vergonjanne, A. Behlouli, P. Combeau, and L. Aveneau, “Human body impact onmobile visible light communication link,” in2016 10th International Symposium on CSNDSP