Semi-deterministic Urban Canyon Models of Received Power for Microcells Jonathan S. Lu, Jeffrey N. Wu, Jian J. Zhu, Jerome A. Blaha Polaris Wireless Inc., Mountain View, U.S.A., [jlu, jwu, jzhu, jblaha]@polariswireless.com

Abstract— In this paper, line-of-sight (LOS) and non-line-ofsight (NLOS) models of the small-area average received power are presented for microcellular radio links. These computationally efficient models consider the propagation loss incurred by path loss and shadow fading through urban street canyons. The models are validated with microcellular measurements recorded at 850 and 1900 MHz in San Francisco. Comparisons are also performed with the Cost-231-WalfischIkegami model and show the importance of including urban canyon contributions in microcellular propagation prediction.

I.

II.

INTRODUCTION

In this work computationally efficient average power models for microcellular radio links are presented and compared with measurements and a standard microcellular model. The presented models can be used for tracking or optimizing cell coverage prediction in urban environments where previously proposed models are generally not suitable due to error or computation time constraints. To predict a 10 m resolution 2 km radius outdoor signal strength map for an urn microcellular cell site, the signal strength for roughly 125,000 locations must be predicted. For a city wide network deployment, depending on the city size, the number of prediction locations can potentially be in the tens of millions or more. For our application of tracking and/or optimizing network coverage in which frequency plans are frequently changed, and cell-site positions, pointing directions, etc. are changed on the order of weeks, computationally efficient models are needed. Empirical statistical models though computationally efficient, are prone to high error (e.g., standard deviation of error σ ~ 10 dB [1]) due to site-specific propagation effects. Deterministic models such as ray-tracing codes are more accurate (e.g., σ ~ 3 dB [2]), but are generally too computationally intensive or infeasible for large area predictions [3]. Semi-deterministic models such as the Cost-231-Walfisch-Ikegami model [4] are also computationally efficient, but typically only consider propagation over the rooftops. This can cause large errors when the dominant propagation paths travel through the street canyons rather than over the rooftops as discussed below. In this paper, we will (1) show the importance of accounting for propagation through the urban street canyons in microcellular propagation prediction, (2) present computationally efficient models which account for street canyon propagation and (3) present initial comparisons of

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these models with microcellular measurements and a standard microcellular propagation model. The presented semideterministic models are modified versions of previously proposed models for mobile-to-mobile radio links in urban environments [5]. These line-of-sight (LOS) and non-line-ofsight (NLOS) models selectively consider features in the environment, and account for road traffic and variable clutter near street intersections with heuristic parameters. URBAN CANYON RECEIVED POWER MODELS

In [5], the proposed LOS and NLOS path loss models are based on the two-ray model. For simplification in this paper, the free-space model is used to replace the two-ray model. Thus, the spatially-averaged power (i.e., inverse of path loss multiplied by transmitted power) for LOS radio links PLOS is given by the expression 2

⎛ λ ⎞ (1) PLOS = PTX GTX GRX ⎜ ⎟ , ⎝ 4π R ⎠ where λ is the wavelength and R is the radial distance from the transmit (TX) antenna to the receive (RX) antenna in meters. PTX is the transmitted power in dBm, and GTX and GRX are the TX and RX antenna gains in dBi, respectively. At 850 and 1900 MHz, λ is ≈ 0.35 and 0.16 m. For NLOS radio links where waves can propagate from the TX to the RX by just turning a corner at an intersection, the models assume that the vertical scatterers and diffraction edges are located at the center of the intersection. The contributions of these waves are expected to be dominant when the TX and RX are more than a street width away from the center of the intersection. The average power P1T from these contributions can then be written in the form 2

S ⎛ λ ⎞ , (2) P1T = PTX GTX GRX ⎜ ⎟ ⎝ 4π ⎠ R1 R2 ( R1 + R2 ) where the radial distance from the TX antenna to the diffraction point at the center of the intersection is R1 and the distance to the RX from the diffraction point is R2. A heuristic parameter S2 with units of m is used to account for the cumulative effect of the different scattering and diffraction coefficients. Note that this S2 parameter is taken as a constant which is equivalent to saying that waves propagate the same way at all intersections. In this work, a value of S2 = 0.36 m is used. This value is much lower than the values found in [5] and may be due to the absence of clutter at the height where the diffraction occurs.

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A similar expression to (2) can be used for radio links in which the propagating wave from the TX must turn two corners to reach the RX [5]. Cases in which the propagating wave must turn more corners are not considered because the over the rooftop contributions generally are more dominant in those scenarios. MEASUREMENT SETUP

IV.

SIMULATIONS AND ANALYSIS

REFERENCES [1] [2]

To predict the average power at the measurement locations, the building vector database shown in Fig. 1 was first rasterised. Next, each measurement point was classified on whether it had LOS with the TX antenna using a viewshed visibility algorithm [6]. Predictions for these points were computed using (1). For NLOS points, the centers of the intersections which were LOS with the TX were first found and then the visibility algorithm was applied from each LOS intersection to determine the 1-turn measurement points. A similar procedure was used to determine 2-Turn intersections and the visible points to each of them. Our implementation of the Cost-231-Walfisch-Ikegami (CWI) model, used b = 20 m, w = 20 m for San Francisco. LOS and NLOS classification was determined by the viewshed visibility algorithm mentioned in the previous paragraph. Antenna gains for NLOS locations were chosen using the location of the first significant shadowing building. All simulations were performed on a 64-bit PC computer with an Intel Xeon 3.6 GHz CPU and 16 GB of RAM. The 850 MHz predictions computation times for the urban canyon models presented in Section II and the CWI model are given in Table I. For a larger 450 thousand location simulation, the urban canyon model’s simulation time was ~24 minutes. Comparisons between the measurements to predictions using the urban canyon models had -1.5 dB mean error (predicted minus measured power in dBm) and 7.7 dB standard deviation of error. A grey scale map of absolute error is plotted in Fig. 1. Here locations with good prediction or locations where no measurements were collected have lighter colors, while locations with darker color denote locations with high prediction error. Comparisons between the CWI model and measurements had -20.7 dB mean error and 11.7 dB standard deviation of error.

[3] [4] [5]

[6]

C. Phillips, et. al, “Bounding the Error of Path Loss Models,” in Proc. IEEE Symp. New Frontiers in Dynamic Spect. Access Net., May 2011. G. E. Athanasiadou, et al., “A Microcellular Ray-Tracing Propagation Model and Evaluation of its Narrow-Band and Wide-Band Predictions,” IEEE Jnl. on Sel. Areas in Comm., Vol. 18, No. 3, pp. 322-335, 2000. E. M. Vitucci, et al., “The Truth about Ray Tracing: an unforgiving validation,” to be submitted to COST. E. Damosso, et. al. COST Action 231: Digital Mobile Radio Towards Future Generation Systems: Final Report. European Comm., 1999. J. S. Lu, et al., “Site-Specific Models of the Received Power for Radio Communication in Urban Street Canyons,” in IEEE Transactions on Antenna and Propagation, Vol. 62, No. 4, pp. 2192-2200, Apr. 2014. B. Kaucic and B. Zalik, “Comparison of viewshed algorithms on regular spaced points,” in Proc. of Conf. Computer Graphics, San Diego, CA, USA, pp. 177–183, 2003.

TABLE I. SUMMARY OF 850 MHZ SIMULATION RESULTS. Model

Mean Error [dB]

Standard Deviation of Error [dB]

Computation Time [s]

Urban Canyon

-1.5

7.7

339.0

CWI

-20.7

11.7

68.2

LOS Measurements NLOS Measurements Urban Canyon Model CWI Model

-20

-40 P ower [dBm ]

III.

An 850 MHz cell site and a 1900 MHz site were chosen for model validation. Base station characteristics were derived from surveying each of the target cell sites. Antenna heights were 9 and 20 m above ground level and effective isotropic radiated power (EIRP) were 40 and 20 dBm. At the RX side, a Rhode Schwarz scanner was placed inside a minivan while a PCTEL OP178H omni-directional antenna with 3 dBi gain was placed 1.8 m above the ground on top of the minivan. Using the scanner, the received signal strength indicator (RSSI) was recorded for the broadcast control channel (BCCH) of each site as the minivan drove in the vicinity. The measurements that were successfully decoded were then placed into approximately 2500 non-overlapping 10 m (i.e., 29λ) x 10 m bins and spatially averaged.

The cause of the error difference between the CWI and urban canyon models, can be attributed to the importance of propagation though the street canyons as seen in Figs. 1 and 2. In Fig. 2, the measurements near the LOS and the 1-Turn NLOS route depicted by the dashed line in Fig. 1 are plotted versus the distance R along the route. In this figure, it can be seen that the urban canyon model predictions are better able to track the distance dependence of the measured power in the NLOS region (R > 200 m). The CWI model on the other hand has a much stronger distance dependence which leads to larger errors farther from the intersection where the route changes from LOS to NLOS. Note that local variations in the urban canyon and CWI predictions are caused by LOS determination, antenna pattern sensitivity, and constructive interference from multiple 1-Turn or 2-Turn paths. In future works, a variable model for S will be investigated and a vertical plane model will be included to account for over-rooftop diffraction. In addition, the effect of out-of plane paths which vertically and horizontally diffract will be investigated.

-60

-80

-100

-120

Figure 1. Heat prediction error.

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200 400 600 800 Distance Along Route [m]

1000

Figure 2. Measured and predicted power for locations along the route shown in Fig. 1.