Correlation properties of large scale fading based on indoor measurements

Correlation properties of large scale fading based on indoor measurements Niklas Jaldén, Per Zetterberg, Björn Ottersten Signal Processing, Wireless@KTH, S3 Royal institute of Technology 44 Stockholm Email: niklas.jalden@ee.kth.se Aihua Hong, Reiner Thomä Institute for Information Technology Technische Universität Ilmenau PSF 565, D-98684 Ilmenau, Germany Email: aihua.hong@tu-ilmenau.de Abstract Statistical channel models are attractive for their simplicity but sometimes lack in precision. In order to improve modelling accuracy, statistical model parameters, which are dependent on the environment, are extended to include spatial and temporal correlation. In outdoor scenarios these parameters are assumed constant over large areas of several wavelengths hence the name large scale parameters. This paper studies the large scale fading (LSF) and the applicability of bringing this previously used outdoor variable to the indoor case. The impacts of the model of the LSF on the outdoor system-performance have been studied and several relevant models have been proposed for outdoor cases. We present the intra-site autocorrelation as well as the inter-site cross correlation of the LSF for an indoor channel. The results are based on two separate measurement campaigns conducted at KTH, Stockholm and TUI, Ilmenau, using a single mobile station (MS) and multiple base stations (BSs) to investigate such models. We observe that the areas under which the LSF could be assumed constant are, in indoor scenarios, so small that it can be assumed independent from one local area to another. Furthermore, we find results that point towards the existence of inter-site correlation in some specific scenarios. I. INTRODUCTION As the demand for higher capacity in wireless communication increases the cell sizes decreases. It is getting more common to use pico-cells to supply connection on a single floor in a building and a previous study [] pointed toward the gain that could be achieved by using multiple base stations on a single floor. There are several different methods to model the wireless channels. Statistical models are computationally efficient compared to ray-tracing for example, but might lack in precision. One way to improve this is to use parameters describing the channel which are then extended to include some spatial and temporal correlation. In outdoor scenarios the parameters are assumed constant over large areas and are therefore termed Large Scale (LS) parameters. The name large scale parameters was probably coined within the European WINNER project for a collection of parameters such as shadow fading, angle spread, delay spread and so on. Using this way of modelling it is of key interest to derive information on the spatial variability of the LS parameters, i.e. auto correlation, from measured data to get reliable models that reflect the true propagation environment. Furthermore it could be as important to evaluate the correlation of these parameters for one area but between different channels, as in the case of one mobile station (MS) and multiple base stations (BSs), i.e. inter-site cross correlation. The impacts of the model of the large scale fading on the outdoor system-performance have been studied in [2], [3], other relevant models have been investigated and reported in [4], [5], [6], [7], [8], [9], []. Current existing channel models treat the different channels from one MS to several BSs as independent, with the exception of the WINNER I, and the SCM model which is the ground for WINNER I, which has a fixed of []. It is not clear where this value comes from, hence even the new WINNER model assumes zero correlation. There are several papers describing the use of large scale parameters for outdoor scenarios,for example [4], but to the authors knowledge there are few, if any, that evaluates if this way of outdoor channel modelling can be applied to indoor scenarios as well. In this paper we discuss the use of the large scale fading parameter for indoor channel modelling and study its correlation properties on the same link and in links between one MS and several BSs. This paper is structured as follows: In Section II we give a short description of the measurement campaigns, followed by the introduction to the large scale fading and its extraction procedures in Section III. Section IV gives the results, and finally we give some conclusions in V. II. MEASUREMENT CAMPAIGNS In this section the two channel measurement equipments and measured scenarios are briefly described. A. KTH measurements The KTH measurement equipment is custom made, narrow band CW with a center frequency of 8MHz. It is equivalent to the equipment described in []. The simplicity of the equipment enables change in the setup for specialization of the measurements. For these measurements one 4-element uniform linear array (ULA) was used on the receiver (Rx) MS side, and two 2-element BSs were used as transmitters (Tx). The BSs were placed in different locations on the same floor to investigate correlations in the LS parameters of the different channels with respect to BS position. The transmission and reception was simultaneous on all channels, thus resulting in

two 2x4 channel matrices for each MS position. The environment can be characterized as modern multi-floor single-office building, with a concrete and brick outer shell. The floors and roofs are made of reinforced concrete and the inner walls of wood and plaster. The layout is two main corridors with several rooms on the sides. Fig. shows the floor plan of the KTH measurements as well as the routes covered by the moving MS. Three differen BS setups were considered for these measurements. These are: setup where both BSs are located at point A with.3m spacing, setup 2 where BS: is located at A and BS:2 at position B and finally setup 3 where BS: is located at A and BS:2 at position C. The long corridors are close to 5m and the short ones, perpendicular to the long, are 6m. The measured routes in Fig. were measured twice for each BS setup -3, one in each moving direction for the MS. This means that the corridors were measured 6 times in total. This results in three different classification types of the scenarios. The line of sight (LOS) classification is used when there is a visible path between MS and BS. Non line of sight (NLOS) is when there is no visible path between the BS and the MS due to obstruction by walls and floors etc, and finally the semi line of sight (SemiLOS) is when the LOS path is obstructed by measurement equipment and personnel. This means that this classification is used in the same corridor as the LOS case, but when the MS is moving away from the BS, hence the measurement equipment blocks the visible path from BS to MS. Fig.. B. TUI measurements KTH measurement scenario The second measurement campaign has been performed in a foyer room at TUI in the summer of 24 using a RUSK channel sounder [2]. The investigated room is a large open area with the dimension of 5m x 3m x 8m. The foyer walls are constructed with a mixture of concrete, steel, and glass. These measurements were done in uplink using one MS with 6-element uniform circular array (UCA), and one BS with an 8-element ULA. A center frequency of 5.2GHz and a bandwidth of 2MHz was utilized. The Tx array was mounted on top of a trolley at the height of.3m, while the Rx was located on a tripod 3m above ground. In order to get meaningful statistical results, a large set of measurement data has been collected by locating the BS at different positions. The exact BS positions are shown in the Fig. 2 by the points labelled with numbers from to. The pointing direction, of the antenna broadside, is indicated by the arrows next to the numbered locations. For each BS position, the measurement was performed by driving the trolley along the same route. The dashed line in Fig. 2 is the trolley s movement trajectory. The label S indicates the start point of measurement route, and F the final point. The whole route is about 92m long. These measurements were unfortunately not simultaneous from MS to multiple BS channels. For most of the measurement positions, the MS was in LOS to all BSs. Fig. 2. TUI measurement scenario III. PARAMETER DEFINITION AND EXTRACTION PROCEDURES At the beginning of this section a short description to the large scale fading which is studied in this paper is given. For further explanations we refer to [3]. After this, the methods used to extract the large scale fading from the measurement data are described. A. definition of Large scale fading In a majority of the channel models, the propagation loss is defined as the product of three factors, namely the path loss (P L ), large scale fading (LSF ) and small scale fading (SSF ) as in [4]. Small scale fading is rapid fluctuations in the received power due to multipath propagation, and changes in a distance of λ/2, while path loss f(d) is the loss in power due to the propagation distance d between transmitter and receiver. Large scale fading describes variation in the local mean during a relative long observation. Knowing this the fraction of the received power to the transmitted can be formulated as: ( ) Pr P L [db] = log P t = LSF + SSF + log f(d), () In outdoor channel models the most common way of modelling the path loss f(d) is as linearly decreasing with log distance, while in indoor there seems to be no commonly accepted model. Some papers use the same model as in the outdoor case, for example in [5], while some assume the power to be decreasing linearly with linear distance as in [6]. In this paper we do not choose a model for f(d), but estimates it by calculating the local mean over a large area, as in [7], see Section III-B.. According to Eqn., the two values which should be removed from the measured received power to estimate the LSF component are SSF and path loss.

B. Extraction procedure of large scale fading from measurement data Below we describe the procedure for extracting the LSF from the measurement data. The methods differ slightly between the two campaigns due to the fact that one is narrow-band measurements while the other is wide-band. ) Extraction procedures KTH: First, the small scale fading is averaged out by filtering the data over all 4 receiver antennas, both transmitting antennas, and a spatial window of m. This is similar to the distance of λ proposed as a good window size in [6] to average out small scale fading without distorting the large scale fade patterns. Second, the path loss is estimated and removed on a point by point basis. An individual mean for each point is estimated by taking the mean received power from all points within a radius of 4m from the given location. This corresponds to a window of 5λ. Since the moving speed of the MS is close to constant this gives that the same number of samples is used to estimate each local mean. 2) Extraction procedures TUI [9]: First, the small scale fading is removed by in each snapshot summing the power of all frequency bins and then averaging over all multiple input multiple output (MIMO) sub-channels. The blue points in Fig. 3 depict the results after summing and averaging. These values reveal that the SSF is completely removed. Second, the path loss component is estimated in similar manner as in the KTH analysis. A long averaging window of 5 snapshots, which is close to 8m in distance, or 4λ in wave length, [9]. This area is of the same size in meters as that used in the KTH analysis. After this filtering, the path loss component has been acquired (seen as the red line in Fig. 3). Finally, the LSF component is obtained by subtracting the path loss component from the short term filtered data (see the black points in Fig. 3). propagation loss [db] variation [db] 65 7 75 8 85 5 5 PL+LSF PL 2 3 4 5 6 snapshot number 2 3 4 5 6 snapshot number Fig. 3. Estimation of the large scale fading component from measurement data, one example measurement place/type LOS SemiLOS NLOS KTH 2.3.8 2.8 TUI 2. - - TABLE I STANDARD DEVIATION OF LARGE SCALE FADING IV. EXPERIMENTAL RESULTS A. Statistical distributions of LSF The large scale fading in db can, as generally found in literature, be modelled by a zero-mean normal distribution, and this proved to give a good fit for these measurements as well. In Table. I the standard deviations of the LSFs are shown for the two measurement campaigns and environments. If we look at the KTH measurements we see that the LOS scenario has higher variations than the SemiLOS. One possible explanation for this is that the larger dynamic changes in received power in LOS are due to loosing or gaining strong multipaths while passing by for example doorways or large metallic white-boards. The SemiLOS on the other hand had a constant blocking of the visible LOS path by personnel and measurement equipment, hence the dynamic changes in the received power were smaller. The largest variations in the large scale fading was found in the NLOS case where the blocking of the signal changed drastically during a measurement run. These variations in received signal power are heavily dependent on location of the MS relative to the corridor walls. The TUI measurements were made in a big open area and the mobile was further away from the nearby walls than in the KTH measurements. Furthermore, since the MS is in LOS to all BSs most of the time the variations on all paths are similar, and the standard deviation is a bit smaller than the KTH LOS. B. Spatial autocorrelation properties of LSF The autocorrelation of the large scale fading was analyzed for different channel conditions. The curve in Fig. 4, which shows the estimated autocorrelation for the TUI measurements, could be well modelled using an exponential decay as reported earlier [4], [6], [7], [8], [9], []. Similar results are obtained when looking at the KTH measurements, and the decorrelation distances for both campaigns are shown in Table. II. The decorrelation distance in this paper is defined as the distance to which the correlation coefficient has dropped to e, a commonly used value in the literature. correlation coefficient Fig. 4. large scale fading autocorrelation 2 3 4 5 distance [m] BS BS 2 BS 3 BS 4 BS 5 BS 6 BS 7 BS 8 BS 9 BS BS Autocorrelation properties of large scale fading

Scenario LOS SemiLOS NLOS KTH 2.2 2.7.7 TUI.3-.8 - - TABLE II DECORRELATION DISTANCES IN METERS FOR THE DIFFERENT MEASUREMENT CAMPAIGNS AND SCENARIOS It is observed that the decorrelation distance is in the order of -2 meters which means that the large scale fading changes almost completely between every other local area (remember that in the KTH campaign the small scale fading is averaged out over a distance close to m). Furthermore we note that the decorrelation distance is largest in the SemiLOS scenario from KTH which goes well in hand with that fact that these measurements had the smallest large scale fading variations. With this in mind the large scale fading can be seen as independent over distance travelled by the MS. To further show the importance of the MS location within the hallway the power on the same measurement route is plotted against the distance in Fig. 5. These three measurements were made on separate days, with the BS in the exact same position (the BS placed at A, see Fig., and the MS moving towards the BS, route 4, hence LOS scenario). The amount of movent by people in building was not controlled but was fairly constant on all days, so the only likable explanation is the MS position relative to the wall within the corridor. 3 4 5 LOS Day LOS Day 2 LOS Day 3 The LOS locations for BS:2 are in area, the blue area, as shown in Fig. 6. The overall inter-site cross correlation for this Fig. 6. Correlation areas, KTH scenario area is close to zero which can seem evident since BS:2 is in LOS while BS: is not. However, if we only look at the small subset of area labelled area 2, the green area in Fig. 6, which is the last part of this corridor, the signals to the two BSs have some propagation path in common. In this area we find indeed a correlation of the large scale fading of. Similarly if we look at area 3 for measurement setup 3 the inter-site cross correlation is -5. This is not so surprising if we study the floor plan in Fig. 6. When the MS is in the middle of area 3, the paths to BS position A and C are identical. Moving towards A the path to C changes exactly in the same way as the path to A would if the MS was moving towards C. To show the dependence of the position of the MS on the correlation, we study the inter-site cross correlation of the large scale fading as a function of distance for area of measurement setup 3. The correlation is calculated once every m using all large scale fading values within the distance of 2m from the MS, hence there is some overlap between the windows. This distance is larger than that over which small scale fading was averaged but smaller than the area used to calculate the path loss. In Fig. power (db) 6 Correlation vs distance 7.8 8.6 9 5 5 2 25 3 35 4 45 5 distance from BS (m) Fig. 5. Received power in LOS scenario C. inter-site cross correlation properties of LSF Even though the large scale fading is almost independent from one local area to another there might exist inter-site cross correlation in the different links from the same MS to two different BSs. This correlation is of interest while evaluating for example coverage, co-channel interference, and handover algorithms etc. Below, the results from the two different measurement campaigns are described. ) KTH s case: Taking the overall correlation for the different antenna positions we find the LSF between the two BSs to be uncorrelated for setup scenarios 2 and 3, see Fig. and close to full correlation for scenario. The full correlation for scenario is not surprising since the BSs are closely located and see practically the same channel, while the channels for the other scenarios are more different. Segmenting the data in smaller parts however we see some correlation even for wide BS separation. To show this consider setup 3 as explained earlier in Section II-A, where BS: is at A and BS:2 is at C..4.2.2.4 2 3 4 5 Distance from BS2 Fig. 7. Correlation as a function of distance 7 we see the correlation of the large scale fading component between the two BSs as a function of distance to BS:2. The correlation seems to increase with distance, but there are clear dips in the correlation at around 5 and 35 meters which are when the MS passes by the perpendicular hallways connecting the corridor that the MS is in with the upper corridor, which is the LOS corridor for BS:. It is reasonable to assume that the MS at this point receives another strong multipath component from BS:, and this has also been verified by investigating scatter-plots. 2) TUI s case: based on the TUI measurement data, the inter-site cross correlation behaviors have been analyzed. Three factors have been investigated to figure out their effects on the correlation coefficient: the distance between two BSs

d BS, the angle seen from the MS to two BSs θ, and the distance difference between MS-BSa MS-BSb links d diff. the experiential results are shown in Figs. 8, 9 and. The results indicate that the LSFs from two different sites are correlated when the two BSs are near to each other or they are in the same direction from the MS. Almost no dependence on the inter-site correlation from the distance difference between two links has been observed in Fig.. In the TUI measurement scenario, the dimension of the considered environment is limited. Therefore, no large distance difference could be provided, and no obvious dependence could be obtained. However, in outdoor case, especially in macro-cell case, this effect should be much greater. Fig. 8. Fig. 9. BSs cross correlation 5 5 2 25 3 distance between two BSs Cross correlation as a function of the distance between BSs Correlation coefficient 5 5 2 angle seen from MS to two BSs [deg.] Cross correlation as a function of the angle seen from BS to two Correlation coefficient 5 5 2 25 3 distance difference between two links: MS-BSa and MS-BSb Fig.. Cross correlation as a function of the distance difference between MS-BSa and MS-BSb One issue that could have an impact on the correlation calculations for the TUI analysis is that the measurements are not simultaneous on the separate BSs. Since the decorrelation distance is on the order of m, accurate positioning is of key essence. V. CONCLUSION This paper has studied the correlation properties of the large scale fading in indoor scenarios. 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