**3.2. Derivation of the model parameters**

For the derivation of the model parameters, a series of measurements with synthetic arrays at both transmitter (Tx) and receiver (Rx) have been conducted in three different office and lab scenarios in the IHE building of the Karlsruhe Institute of Technology. Two are office scenarios (scenario B and D), where the number of details in both rooms is small. The third scenario (scenario C) is a cluttered lab scenario [25]. Here, a large number of small details such as cables, tools, books etc. is distributed over the tables and shelves. These small objects were neglected in the scenario model. The transmitter is placed within a 0.12 m long linear positioner, and the receiver is moved on a 1.2 m by 0.6 m rectangle. Thus, a linear and a rectangular virtual array are obtained. The spacing between two consecutive antenna positions in both Tx and Rx arrays is 3 cm. With the exception of the antennas, the measurement setup used is identical with the setup described before. The simulation settings are also the same.

For the derivation of the model parameters, the behavior of the channel characteristics (path loss *L* and delay spread *σ*D) in the measurements and the simulations are analyzed and compared [25]. To find adequate model parameters, simulations with different parameter sets are conducted and compared with the measurements. As the test of all possible parameter combinations would be computationally prohibitive, an initial parameter set has been chosen based on previous work findings in [23] and the parameters have been varied one by one.

The scatterer generation is done only once in each realization for Tx position in the middle of the Tx array and for Rx position in the middle of the Rx arrays. For each other Tx/Rx configuration the same scatterers are used.

Due to the statistical nature of the model, some variation of the simulated channel parameters for consecutive simulations with the same model parameter set is to be expected. Hence, for each parameter set 5 realizations are then simulated and the channel parameters derived from them are averaged. This number is small enough to be simulated quickly, and large enough to give approximate mean values for a given parameter set.

To derive the model parameters, their influence on the chosen channel characteristics is analyzed. It can be observed that:


Considering this observation, first *p* is set to 0.03 because it has the strongest influence on the error. Thus, values of *a* = 0.2 and *N* = 16 are chosen which give a good tradeoff between path loss and delay spread errors. Finally, the scattering radius is set to *r* = 1 m.

Another indirect model parameter is the order of reflection which is considered in the scatterer placement. The influence of the considered reflection order on the delay spread is shown for a single position in the middle of the Rx and Tx array of an office scenario. The measured delay spread for this point is 3.8 ns.

**Figure 12.** Influence of the considered reflection order on the delay spread in scenario 2.

The curves show that depending on the chosen model parameter (*a* and *p* have the strongest influence here) the inclusion of reflections of up to 3rd order influences the delay spread. The same has been observed in other scenarios and for the path loss. Thus, in the following the scatterers will be placed around the reflection points of up to the 3rd order.
