# Towards a Performance Boundary in Calibrating Indoor Ray Tracing Models

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## Abstract

This paper investigates the performance boundaries of a calibrated deterministic indoor channel model. From a propagation modeling point of view, this process allows to assess the weakness of ray tracing and sets the boundary conditions for a such modeling method. The principle of the deterministic model calibration used in this work focuses upon the estimation of optimal material parameters by means of a few pilot measurements and a simulated annealing method. This technique improves the accuracy of the prediction model for all measurement positions including those not considered by the calibration. The performance of the calibrated ray tracing model and the sensitivity of the calibration to the number of pilot measurements have been investigated. For this investigation, a measurement campaign has been conducted within an indoor office building at 2.45 GHz with 100 MHz bandwidth. Furthermore, the model performance has been compared to empirical indoor models.

### Keywords

Path Loss Measurement Campaign Directional Antenna Channel Impulse Response Power Delay Profile## 1. Objective and Introduction

The blind prediction, based on a priori approximate knowledge of material parameters, often shows an obvious mismatch with the measurements. Even if predicted path loss values are accurate enough like, for example, in [1], time dispersion parameters could show a significant mismatch. Ray tracing-based conventional deterministic modeling methods use geometrically accurate data and rely on tabulated values for the electrical parameters of the building materials. For instance, the authors in [2] made direct measurements of the building materials. However, the material parameters remain approximate and impossible to define accurately for each building, especially when the building materials are a heterogeneous mixture of unknown components, for which no electromagnetic measurement values are available. Therefore, a calibration of these material parameters, reducing the mismatch between the model and the measurements, is required. The issue of deterministic modeling calibration has been addressed in very few works. In [3], only the dielectric constant of each wall have been tuned separately and the gradient method is used to estimate the solution. However, using the gradient method in conjunction with this tuning provides generally a local minimum and does not necessarily provide the optimal solution.

As the relation between power taps and material parameters is a nonlinear combinatorial relationship, the simulated annealing approach used in this paper provides the general optimal solution by simultaneously changing the dielectric constant and loss tangent of all material parameters with a changing step at each range of iterations. The method proposed converges to a global solution and avoids to be dropped into a local minimum as the gradient method does. The performance and robustness of this calibration procedure is analyzed in this paper by means of an indoor measurement campaign within an office building.

This paper is organized as follows. Section 2 presents the ray tracing model. Section 3 investigates the calibration process and the calibration algorithm. Subsequently, the conducted measurement campaigns and the calibration results for an indoor office environment are highlighted in Section 4. Finally, Section 5 addresses the sensitivity of the calibration to the measurements and assesses the boundary of the modeling methods.

## 2. The Wideband Semideterministic Prediction Model

The prediction model has been presented earlier by the authors in [4, 5, 6]. It has been derived by means of two core components; a geometric engine and an electromagnetic engine. While the geometric engine derives the propagation paths based on the accurate information of the 3D building database, the electromagnetic engine computes the propagation mechanisms and integrates the antenna radiation patterns.

The model requires an accurate 3D indoor database with detailed information describing the scattering objects (walls, doors, and windows), their thickness and their dielectric properties. The required building parameters introduced in the database are the relative dielectric constant Open image in new window and the loss tangent Open image in new window . According to their electromagnetic material properties, the structures of the building are classified into *N* different classes with common dielectric material parameters.

Besides free-space propagation, the propagation tool computes the Fresnel equations, considering multiple reflections and transmission through walls. Depending on whether the antennas is horizontally or vertically polarized, the system considers the corresponding reflection/transmission coefficients and also the angle of departure (AoD) and angle of arrival (AoA) corresponding to each path. Interactions up to the Open image in new window order reflection have been considered. Many simulations have confirmed that this order provides a compromise between the accuracy of channel parameter (path loss and delay dispersion) and the reasonable computation time, which is also in accordance with [7]. The tool supports as much transmissions as the wave encounters in its propagation path. It accounts for the single diffraction using the uniform theory of diffraction (UTD) [8].

whereby Open image in new window is the number of MPCs clustered together to form the Open image in new window tap.

Since typically only 2D radiation patterns (horizontal and vertical) are available, the developed model derives the 3D antenna radiation pattern through a bilinear interpolation knowing the measured 2D patterns in E- and H-planes [9]. Moreover, for a better accuracy, the system model integrates also 3D measured antenna patterns within an anechoic chamber.

## 3. Model Calibration

The calibration consists in extracting relevant multipath components (MPCs), for instance once reflected paths, simultaneously from the model and measurement. Afterwards, the simulated annealing is performed to optimize the material parameters.

### 3.1. Extraction of Parameters for Calibration

After identifying the direct path, according to the arrival time corresponding to the distance separating Tx and Rx, particular Open image in new window power taps (e.g., once reflected paths) with a power above the noise threshold have been extracted from the measurement and the model simultaneously. The noise threshold is computed from each measurement based on a dynamic noise clipping. Hence, two vectors of power taps have been formed which are Open image in new window and Open image in new window . The calibration uses the electromagnetic engine, the power tap matrices and the involved building structures to optimize the material parameters incorporated by the deterministic model.

### 3.2. Simulated Annealing Algorithm: Practical Implementation for Material Parameters Estimation

*N*classes) at a relatively high chosen temperature Open image in new window , a neighbor solution Open image in new window is afterwards generated as a next solution for which the evolution in cost, Open image in new window , is evaluated. If the cots decreases, the generated neighbor solution becomes the current one, otherwise the algorithm decides with a certain probability whether Open image in new window remains or Open image in new window becomes the current solution. The probability of accepting a transition, causing a decrease Open image in new window in the cost, is called the acceptance function and is set to Open image in new window . Open image in new window is the parameter that corresponds to temperature in the analogy with the physical annealing process. The algorithm runs Open image in new window steps with the same temperature. Afterwards, the changing step of the parameters is decreased geometrically with the factor Open image in new window towards zero. The process is stopped after ST steps if the objective function remains unchanged. The final solution is considered as the absolute optimum. The four configuration parameters ( Open image in new window , Open image in new window , Open image in new window , and Open image in new window ) considered by the algorithm are described in Table 1.

Simulated annealing algorithm parameters.

Notation | Meaning |
---|---|

A random solution as a set of material parameters | |

Objective function | |

Initial temperature of the stepped geometric decrease | |

Geometric decrease coefficient | |

Number of steps running with constant temperature | |

Maximum steps the algorithm runs without many changes |

where Open image in new window is the number of conducted measurements, Open image in new window is the number of paths within the measurement Open image in new window , and Open image in new window are the power taps from (1). The parameters Open image in new window and Open image in new window denote the predicted and measured powers of the MPCs, respectively.

## 4. Measurement Campaign and Calibration Results

### 4.1. Measurement Campaign

The offices where the measurements have been conducted are representative of the entire institute building and gather most of the building structures. Moreover, Open image in new window aligned measurements starting at Open image in new window m from the transmitter have been conducted on the floor (as depicted in Figure 2) due to its characteristics enabling LOS conditions and wave-guiding effects.

### 4.2. Calibration Performance

Summary of results for the three positions.

Position | Parameter | Measurement | Uncalibrated | Calibrated |
---|---|---|---|---|

Tx2-Rx1 | 10.3 | 2.8 | 8.1 | |

170 | 60 | 160 | ||

42.9 | 44.5 | 42.2 | ||

Tx1-Rx2 | 16 | 5.5 | 13.8 | |

170 | 70 | 120 | ||

41.2 | 43.8 | 40.4 | ||

Tx4-Rx1 | 11.8 | 1.3 | 7.9 | |

160 | 40 | 170 | ||

28.8 | 28.3 | 28.7 |

Though initially not included in the calibration, the measurements Tx1-Rx2 and Tx4-Rx1 show a good match with the calibrated model. As expected, the measurement Tx2-Rx1 shows a better match than the other measurements not included in the calibration. However, the advantage of the model resides in providing globally more accurate parameters at any location within the environment without need of huge measurement campaigns to cover the whole building. This is an advantage over the statistical modeling as presented, for example, in [6].

#### 4.2.1. Overall Analysis

Overall prediction error of the model before and after calibration.

Parameter | Statistics | Uncalibrated | Calibrated |
---|---|---|---|

8 | 4 | ||

5.1 | 4.7 | ||

1.5 | −5.6 | ||

22.8 | 18.1 | ||

46 | 11.9 | ||

48.1 | 30.1 | ||

−30 | |||

140 | 80 | ||

1.6 | 1.3 | ||

9.1 | 4 | ||

−23.5 | −10.5 | ||

21.1 | 7.3 |

#### 4.2.2. Performance over Cost 231 Models

Path loss prediction error statistics of COST 231 models and calibrated ray tracing.

Model | OSM | MWM | Ray tracing |
---|---|---|---|

−5.3 | −4.1 | 1.3 | |

10.5 | 9.2 | 4 | |

26.8 | 17.8 | 7.3 | |

−14.8 | −17.4 | −10.5 |

Originally, empirical models provide less accuracy compared to ray tracing models, as they only consider the direct path between the transmitter and the receiver. This is the main cause of their weakness especially within a rich multipath indoor environment.

## 5. Sensitivity of the Calibration to the Measurements

Analyzing the performance of the calibration reveals some investigations to be dealt with comprehensively. In this section, the degree of the model performance improvement added by the calibration is assessed as a function of the calibration set size. First, the effect of one measurement is investigated. Subsequently, the impact of increasing the calibration set size has been analyzed.

### 5.1. Single Measurement-Based Calibration

The uncalibrated plot (dashed line) is constant as it is the difference between the measurement and prediction for all the set of data before calibration. It is noticeable that the average error reaches an optimum of Open image in new window dB. However, at some other, less representative locations of the entire building, the calibration results are rather degraded.

### 5.2. Measurement Set Size Influence

Henceforth, the remarkable fact which flows from these results is that the error diminishes as the calibration set size increases. This error reaches a fluctuation status around the number of Open image in new window , where the modeling error starts to fluctuate around a constant value. This reveals effectively the performance boundary of this deterministic model. It is noteworthy that the prediction error of path loss and time dispersion parameters exhibits a general decay trend with increasing calibration set size. However, a judicious calibration requires a compromise between a best performance and a lower computation time and complexity.

## 6. Conclusions

This paper addresses the subject of a new deterministic model calibration technique based on simulated annealing, which improves the model performance by means of a few pilot measurements.

The basic facts that emerge from this paper are mainly the model performance improvement and the performance limit reached with more measurements. Indeed, the calibrated model outperforms the standard uncalibrated one with a mean error of Open image in new window dB and a standard deviation of Open image in new window dB. With an increasing size of the calibration set, the calibration reaches a steady state for a number of measurements of 10 and starts to deviate around a constant value which shows the performance limit of the ray tracing modeling method. The calibration positions should be chosen in a way to cover the different kinds of rooms in the building in order to enable the coverage of major structures within the environment.

Besides its advantage of compensating for the tedious task of manually tuning the building dielectric parameters plan, the calibration produces an optimized building plan that works for any conventional ray tracing model. It has been shown that, though the model accuracy improves with an increasing number of measurements used for the optimization, it is indeed bounded and tends to a steady state. The calibration modeling error starts to fluctuate around its extremum after a certain number of measurements, which obviously shows the limits of the deterministic modeling by means of ray tracing.

Directional antennas (as used in this paper) enhance the signal strength and the impinging waves from a certain direction. Omnidirectional antennas can also be used as in [6].

The more the structures a floor plan has the bigger the calibration set size should be in order to optimize all material parameters. Furthermore, the calibrating measurements should involve main propagation paths reflected on the structures to be calibrated.

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