Decorrelation distance characterization of long term fading of CW MIMO channels in urban multicell environment

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1 Decorrelation distance characterization of long term fading of CW MIMO channels in urban multicell environment Alayon Glazunov, Andres; Wang, Ying; Zetterberg, Per Published in: 8th International Conference on Alied Electromagnetics and Communications, 2. ICECom 2. DOI:.9/ICECOM Link to ublication Citation for ublished version (APA): Alayon Glazunov, A., Wang, Y., & Zetterberg, P. (2). Decorrelation distance characterization of long term fading of CW MIMO channels in urban multicell environment. In 8th International Conference on Alied Electromagnetics and Communications, 2. ICECom 2. (. -4). IEEE--Institute of Electrical and Electronics Engineers Inc.. DOI:.9/ICECOM General rights Coyright and moral rights for the ublications made acceible in the ublic ortal are retained by the authors and/or other coyright owners and it is a condition of acceing ublications that users recognise and abide by the legal requirements aociated with these rights. Users may download and rint one coy of any ublication from the ublic ortal for the urose of rivate study or research. You may not further distribute the material or use it for any rofit-making activity or commercial gain You may freely distribute the URL identifying the ublication in the ublic ortal Take down olicy If you believe that this document breaches coyright lease contact us roviding details, and we will remove acce to the work immediately and investigate your claim. L UNDUNI VERS I TY PO Box7 22L und

2 Decorrelation Distance Characterization of Long Term Fading of CW MIMO Channels in Urban Multicell Environment Andres Alayon Glazunov, Ying Wang Mobile Networks R&D TeliaSonera Sweden AB 2386 Farsta Per Zetterberg Signal Proceing, S3 Royal Institute of Technology 44 Stockholm Abstract- An analysis of long-term fading roerties of 4 4 CW MIMO channels is resented in this aer. The main focus has been on the long-term variability of MIMO channels in urban cellular environments, with emhasis on the decorrelation distance over mid range distances along the mobile trajectory for different base station antenna heights. A model that characterizes the decorrelation distance at different robability levels of distribution of the decorrelation distance is roosed. The model redicts that at some robability level all measured decorrelation distances will be within ½ and 2, where is the decorrelation distance at the e - level of the autocorrelation function. INTRODUCTION Knowledge of the behavior of the radio channel is of vital imortance to roer wirele communication system design. Multile Inut Multile Outut (MIMO) techniques use multile elements antenna (MEA) at both link ends. These new degrees of freedom anticiate otential increase of both caacity and link reliability In this aer we focus on the autocorrelation of the lognormally distributed long term fading, which is also known as shadowing. Shadowing has a direct imact on traditional cellular system lanning, since it variability ut constraints on as well cell coverage through coverage robability and signal quality (signal to noise ratio, SNR) variability as hand-off and scheduling algorithms, among many other asects. Our analysis is based on a measurement camaign resented in []. Here we roose a model that further extends the widely acceted exonential decaying correlation model in [2], to handle the fact that the autocorrelation is also a stochastic function itself. The main idea here is to study the decorrelation of the lognormal fading over a range corresonding to the faster comonent of the bi-exonential model [3]. 2 MIMO MEASUREMENT CAMPAIGN This MIMO measurement camaign uses the Wirele Develoment Laboratory (WIDELAB) test bed develoed by the signal-roceing grou at the Royal Institute of Technology (KTH), Sweden. A detailed descrition of the hardware equiment can be found in [4].The measurement camaign was conducted in the city center of Stockholm, Sweden. The oerating frequency was MHz in the ulink band in an urban area. The mobile station and the base stations were equied with the antenna arrays. Three receiver (BS) arrays are used, with one at Kårhuset and two at Vanadis. The schematic scenario of the three-sector structure is drawn in Fig., []. Vanadis Karhuset MS moving direction TX3 TX4 MS TX2 TX Figure The ma of the outdoor driving measurement. The two red dots denote the locations of the BS sites Kårhuset and Vanadis. The blue trajectory is the MS driving route during the measurement. The ointing directions of four TX antennas on the MS are also illustrated. The ointing directions of the three receiver arrays are labeled with three letters, with A for the one at Kårhuset, and B, C for the two at Vanadis. A oints ~ 2 counter-clock-wise off the direction of Vanadis. B and C oint 6 clock-wise and counterclock-wise off the direction of Kårhuset, resectively. The BS array A is about to 3 meters above roofto, and the BS arrays B and C are about meters above roofto, by this means two different BS antenna heights are emulated. During the outdoor driving measurement, the mobile terminal was mounted on to

3 of a car at about.8 m above ground. The environment can be characterized as the heavily built u area with a uniform density of buildings, ranging from 4-6 floors. The driving seed varied aroximately from m/s to 2 m/s. The measurement was erformed in the forenoon when the traffic was heavy. Fig. also shows the mobile driving route during the measurement, together with the ointing directions of four TX antennas on the mobile. TX4 and TX2 oint forward and backward to the mobile moving direction, resectively, while TX and TX3 oint erendicular to the moving direction. 3 CHANNEL MODEL Ignoring the noise term, the relationshi between the received signals, y (t) and transmitted signals, s (t) is modeled as, y ( t) H( t) s( t) () where the narrowband MIMO channel matrix is N t denoted as r N H C. We model the channel having N r antennas at the base station (receiver) array and N t antennas at the mobile station (transmitter) array. The overall channel variability between the n-th transmitter and m-th receiver antenna is further modeled according to the claical three-stage model ) the deterministic art of the local area mean, which stands for the distance ath lo law, PL, 2) the stochastic art of the local area mean, which is the shadow fading, S and suerimosed fast fading characterized by the normalized (instantaneous ower normalized to the unit) comlex channel imulse resonse H. Thus, the overall channel variability may be studied by reresenting the channel transfer function as follows, 2 S H H (2) PL Our further focus will be on shadow fading, S exreed in db. 4 SHADOW FADING AUTOCORRELATION The long-term fading is caused by obstacles in the roagation ath between the mobile and the base station like buildings, mountains, other objects and humans. The long-term fading is also called slow fading or shadow fading. Shadow fading effect causes random variations in the local average received ower We denote the enveloe in db of the shadow fading comonent by S db, which has been found to follow a Gauian distribution. S db is often considered a zeromean Gauian random variable with standard deviation σ s (also in db), which has also been aumed in the resent aer. To measure how fast the shadow fading comonent varies as the mobile moves along a certain route, we calculate the satial autocorrelation as S ( x), S ( x + ) (3) db db where x is the satial searation along the mobile route, and S db (x) is the samled shadow fading enveloe (S ) in db, with S db ( x). A widely acceted model for the autocorrelation function is the exonential model, [2], e (4) where the decorrelation distance defined as the smallest distance traveled by the mobile such that the autocorrelation falls to e -, ( ) e.3679 () A short decorrelation distance indicates that the shadow comonent varies quickly as the mobile moves, while a longer decorrelation distance corresonds to a more slowly shadowing. Further, since the channel reveals a stochastic behavior we have a number of realizations of the autocorrelation (x) for each, then we can obtain (x) defined as the autocorrelation at a certain df level, { Pr( ( < ) } ) (6) Based on the above we roose the autocorrelation model defined at the df level to have the general form,. e + sign(.) e (7). + sign(.) e where sign(.) is the signum function,, / is the decorrelation distance at. ( ) e and C. is a constant in but is an even function of.. Hence, for., (7) agrees with model (4) ) (. e (8) with /,, that is at the % df level of the distribution. The decorrelation distance of our model and model in [2] agree. If, then. e ± e ( ) (9). ± e It is easy to see that equation (9) above works for almost all values of, excet in the limit case when tends to infinity. In that case C. must also tend to infinity in order to give a satisfactory result. Namely,

4 that for zero decorrelation distance any consecutives values will remain uncorrelated. Now, let aume that C.. Thus equation (9) becomes e ± () e ± Hence, the decorrelation distances, + (>) and (<) defined at e, > < () Clearly, for such as C the decorrelation. distance will be within the interval [½, 2 ] at the e - level of the autocorrelation function, where is the decorrelation distance for. at the same level. MEASUREMENT RESULTS The shadow fading roerties of all 6 channels in the 4 4 MIMO channel matrix are analyzed. The distance traveled by the MS during a measurement round varies from 8 m to 2 m. Furthermore, we resamle the extracted shadow fading comonents at a satial distance of (about.8m) to get equally saced data along the mobile route. The fast fading was filtered using a window of 6 m in average. Within each one-minute measurement run, the satial autocorrelation sequence () is calculated using equation (3), and the corresonding decorrelation distance is estimated according to equation (). Combining results from all measurement rounds, we select the autocorrelation curves at three df levels, % (), % () and 99% (), as defined by equation (6). We also estimate the decorrelation distance from the % () curve, which we will refer to as the median decorrelation distance x. It is worthwhile to notice that the usual aroach is to extract data over larger distances along the mobile trajectory and the normalization is done relative the overall ath lo trend. Obviously, in that case no variability of the decorrelation distance would be observed. Fig. 2 and Fig. 3 show the emirical % (), % (), and 99% () of 6 channels, for base station A and B resectively. For comarison, we also lot () according to equation (4). The estimated x (in meters) of 6 channels for base station A are listed in Table I and base station B in Table II. Several observations may be done from the resented lots. As can be seen from Fig. 2 and Fig. 3 the model fits the measured data very well for.. However, due to lack of data we do not validate the resented model for. and.99. However, there is a trend that shows that this model could rovide good agreement with observed data. Further, we see that in average (median) the decorrelation distance does not deend that strongly on the BS antenna height as shown in Table and 2. On the other hand, the variance is larger for the BS with higher height. This may be exlained by the fact that at lower BS antenna height the roagation environments is more homogeneous, basically, the Non Line Of Sight (NLOS) scenario revails between the MS and the BS, hence the lower variance. For the same reason at higher BS antennas the sight conditions between the MS and BS is more heterogeneous since the LOS robability is higher in this case. Table Median of shadow decorrelation distance in meters (estimated from the % () curve), and standard deviation in meters, of 6 channels for base station A. A Tx µ σ µ σ µ σ µ σ Rx 8., Rx2 7.6, Rx Rx Table 2 Ibid. Table, Base station B. B Tx µ σ µ σ µ σ µ σ Rx Rx Rx Rx Tx. Rx Rx Rx Rx Base Station A, () vs. (meters) Figure 2 Shadow fading satial autocorrelations of 6 channels. The lower and the uer dashed lines are % () and 99% (), resectively. The solid and the dotted lines are % () and (), resectively. Base station A. From Table and 2 it follows that, the antenna air ointing arallel to the MS ath direction (TX2 and TX4) exerience a faster-varying shadow fading, while the antenna air ointing erendicular to the MS movement direction (TX and TX3) exerience a more stable shadowing environment. A lausible exlanation could be found in the orientation of the MS relative the BS. Since, the BS antenna has a relatively

5 constant gain over the roagation area, the MS antenna attern orientation (directive antennas are used) may have a great imact not only on the fast fading but also on the long term fading. It is also well known that the main roagation mechanism in urban environments is diffraction over the roof tos. Now, for arallel orientation of antennas (TX2, TX4) in LOS conditions the decorrelation distance should be larger than in the NLOS case, since in LOS there are no larger shadowing objects in the roagation ath. But as we said, it is most robable that the signals reach the mobile over the roof to and therefore roagation ath will be shadowed by buildings besides the streets lowering the decorrelation distance. Similarly, for the orthogonally oriented antennas the main roagation mechanism is still the same and the received signal will variate the most at street croings or when turning around the corner. However, in this case the robability that the MS antennas are actually oriented towards the direction from which the main contribution to the received signal comes from is obviously higher. Hence, the received signals fade slower along the mobile ath comared to the case of arallel oriented antennas. Tx. Rx Rx Rx Rx Base Station B, () vs. (meters) Figure 3 Ibid. Fig. 2, Base station B. 6 DECORRELATION DISTANCE AND STANDARD DEVIATION The decorrelation distance describes how fast the shadow fading comonent varies, and the standard deviation σ s measures the severity of shadow fading. Here we look at the oible correlation between and σ s. Fig. 4 and Fig. lot (in meters) together with σ s (in db) observed at each TX, for base stations A and B, resectively. As is clear, σ s vary from db to 7 db and vary from 2 m to 28 m. In some measurement rounds, σ s and seem to have a ositive correlation, i.e., they increase and decrease at the same time. Namely, for values of σ s remarkably deviating from average the decorrelation distance also tends to increase but not vice versa. The value of o deends on local toology. Large σ s values usually occur when the mobile is turning around street corners, where the shadowing enveloe would most robably exerience some dee fades. Besides corner laces, large σ s may also occur as long as the shadowing environment has a shar change. A, (m) & σ s 2 Tx (m) 2 σ s Figure 4 x in meters (the blue curve) and σ in db s (the red curve), observed at TX, TX2, TX3, and TX4, resectively for Base station A. The x-axis labels the measurement round indices. Base Station A. B, (m) & σ s 2 Tx Figure Ibid. Fig. 4, Base station B. 7 DISCUSSION 2 (m) 2 σ s 2 2 A new model for the autocorrelation function of the long-term fading comonent has been rovided. The model describes the decorrelation distance as a stochastic variable for which a robability level of interest may be defined according to the modeling needs. For the % df level the model agrees with the exonentially shaed autocorrelation function. It is also shown that the base station antenna height has a larger imact on the variance of the decorrelation distance rather than on it average. Namely, the higher the BS the larger is the variance. Further, it was also observed that the orientation of the antenna lays a substantial role in the variability of the shadow fading. It is slower for antennas oriented erendicularly the MS ath. Finally, it was observed a weak correlation between the standard deviation of the shadow fading and the decorrelation distance, which was higher for the higher BS. 8 REFERENCES [] Y. Wang, Analysis of CW MIMO Channel Measurements in Urban Cellular Scenarios, MSc Thesis at TeliaSonera Sweden, Mobile Network R&D, and Deartment of S3, Royal Institute of Technology, Sweden, March 2 [2] M. Gudmundson, Correlation Model for Shadow Fading in Mobile Radio Systems, Elect. Lett. vol. 27, no. 23, Nov. 99, [3] A. Mawira, Models for the satial correlation functions of the log-normal comonent of the variability of VHF/UHF field strength in Urban environment, PIMRC 92, Boston, USA,. 3-7 [4] P. Zetterberg, Wirele Develoment Laboratory (WIDELAB) Equiment Base, Deartment of S3, Royal Institute of Technology, Stockholm, Sweden, 23