Propagation model

To know the quality of the channel between transmitter and receiver, we need to know how the signals behave when they travel from the transmitter to the receiver: the channel response. As mentioned in Chapter 2, the channel re- sponse generally consists of three components: path loss, slow fading and fast fading. For the fast fading component we need channel traces for a number of TTI and for a certain number of transmit- and receive antennas. The fast fading component of the MIMO channel between a transmitter and receiver is represented by a matrix H that defines for n receive- and m transmit anten- nas all possible channel responses between the transmit and receive antennas denoted by hi,j at time t [42]. Equation 5.2 shows such a channel matrix for

2 receive- and 4 transmit antennas, conforming to our model parameters. Fig- ure 5.4 shows a graphical representation of the paths between the transmit- and receive antennas, as specified by our model parameters.

H(t) = h1,1(t) h1,2(t) h1,4(t) h1,4(t) h2,1(t) h2,2(t) h2,3(t) h2,4(t) (5.1) The channel response matrices can be generated by the use of standard- ized models such as SCM, SCME or WINNER (I and II) [42, 43, 37, 44]. The main difference between the three models is that both WINNER models and the SCME model support larger bandwidth and both WINNER models are appli- cable for more scenarios. All models can theoretically be applied to our system- level simulations because they all provide random delay and angle spreads for

5.4. PHYSICAL LAYER ABSTRACTION 39

Figure 5.4: Paths between BS and UE antennas in a system with four transmit antennas and two receive antennas

different users [37], making the choice of the models largely dependent on the availability of the knowledge how to generate the channel traces.

The channel matrix is generally determined by path loss, shadowing and multipath fading. The path loss component is calculated by the use of a path loss model, such as Okumura-Hata, COST-231 or WINNER II [37, 44, 45]. The path loss models are sets of algorithms, mathematical expressions and diagrams representing the radio characteristics of a certain environment. These models are either empirical or deterministic and are targeted to a certain environment like urban or rural. Empirical models are based on real-life measurements, taking the environmental influences implicitly into account. The correctness of an empirical model depends on the quality of the measurements and the applicability of the original measurement environment. Most empirical models provide different parameters for usage in different environments e.g. WINNER II provides parameters for rural-, urban- and suburban environments, among others. Deterministic models, however, are based on the physical properties of signal propagation in different environments and can as such be applied to different environments without affecting accuracy. The downside is that the algorithms are computationally complex and are thus most used in small scale simulations or for indoor propagation simulation [46]. Shadowing is applied separately, and is often modelled using a log-normal distribution. The WINNER II includes different formulas for shadowing in various environments. Multipath fading is applied next, and is included in the SCM, SCME and WINNER models. Spectrum-wise there are many bands that can be chosen to deploy LTE in. In Japan, 800 MHz, 1500 MHz and 1700 MHz bands are in planned or deployed phase; the United States and Canada mainly use 700 MHz and 2100 MHz while in Europe the deployed and planned networks are mainly situated at 800 MHz and 2600 MHz. Furthermore, the idea of reusing the spectrum originally assigned to GSM are also frequently raised. As we aim to simulate a European urban environment, we choose to simulate the 2600 MHz frequency. This frequency is more applicable in an urban environment than for instance 800 MHz since in urban areas operators prefer to use the higher capacity of 2600 MHz over the larger coverage of 800 MHz as there is larger population density than in rural areas.

40 CHAPTER 5. MODELLING

The choice of a propagation environment and frequency band limits the choice of path loss models. The Okumura-Hata and COST-231 path loss models are not applicable in this scenario because their frequency range is limited to respectively 50 MHz - 1500 MHz and 1500 MHz - 2000 MHz [47, 48, 49]. For the 2600 MHz band, the Stanford University Interim (2500 MHz - 2700 MHz) model or the WINNER II (2000 MHz - 6000 MHz) path loss model is applicable [44]. Both are applicable to urban terrain, but as the WINNER II is more advanced and Fraunhofer-Gesellschaft (FhG) is willing to calculate the channel matrices for this model, we use this model in our simulations. These channel matrices are generated for the parameters of our system model, and this full set of channel matrices will be referred to as channel traces, as they describe the channel for our users in the modelled time.

As calculation of the channel traces is computationally complex and resource intensive, we cannot model too many TTIs. The length of the channel trace has to be chosen carefully as it has to be long enough to be able to see effects of slow- and fast fading, yet it must not be too long as the data size increases linearly with the number of TTIs. Furthermore, this would lead to delay in the data delivery, surely delaying this study. Therefore, we set the number of TTIs included in the channel trace to 1000. This is enough to see effects from slow- and fast fading. As the a replication of the simulation typically takes more than one second, we can repeatedly loop over the channel traces from front to back and back again to simulate longer timespans.