What Path Loss Models Have to Do with Financial Models?
September 15, 2011
I was recently asked by a business associate how to estimate the capital costs of an LTE network. Inevitably our discussion led to estimating the number of sites required to cover a market. Designing to meet coverage requirements along with its complement, capacity requirements, form the basis for estimating the size, and consequently cost, of the radio access network. This is something that differentiates the financial modeling service provided by Telesystem Innovations. So I like to expand in this post on a few general principles related to path loss models which play a critical part is determining cell size.
Path loss models can be classified in one of three categories:
- Empirical models: models based on field measurement data collected in different environments (urban, rural, etc.) and at different frequencies from which curve fitted equations are derived. These models are simple to use and include a few parameters such as transmitter and receiver height, carrier frequency and correction factors for different types of terrain. Because these models are statistical they have variable accuracy.
- Physical models (deterministic): site-specific models which require enormous number of geometry information about the site. They are computationally intensive but provide good accuracy.
- Hybrid models (semi-deterministic): these models combine empirical and deterministic aspects so while they require lower computational complexity than deterministic models, they also provide higher accuracy than purely empirical models.
|Empirical Models||Okumura-Hata (150 – 1500 MHz)
Cost 231 Hata (1500 – 2000 MHz)
Modified Cost 231 Hata (2000 – 3500 MHz)
Erceg/SUI (broadband wireless)
Dual Slope (micro-cell model)
|Physical Models||Ray tracing: ray imaging & ray launching
Two ray model (micro-cell)
|Hybrid Models||COST 231-Walfisch-Ikegami|
Empirical models are most typically used in the wireless industry, so I like to expand further on this category. When deciding on which model to use, it’s critical to pay attention to a few parameters:
- Range: some models were developed for macrocells and they start from about 1000 m from the transmitter (base station). Other models are targeted at microcells and start at lower initial breakpoint.
- Frequency range: models are typically validated for a certain frequency range. For example, the Okumura-Hata model which is one of the most popular models caps out at 1500 MHz. To use this model at higher frequencies, one needs to consider the Cost 231 Hata model which is valid between 1.5 GHz and 2 GHz.
- Transmitter and receiver heights: typically macro-cells are placed high above ground (e.g. 30-90 meters), while micro-cell are placed low above ground (e.g. 10-20 meters). Mobile systems are characterized by handhelds at low height above ground (e.g. 1.6 m) while in fixed wireless access systems outdoor CPEs are placed at higher elevation above ground (e.g. 5 m). The model needs to have been validated over the height range in which the transmitter and receiver will be located.
Having said this, what sort of error do we get with empirical models? The answer is that it depends on the model and morphology. For example, the Hata model provides the best precision for 900 MHz in urban environment. Tests done in Lithuania at 160, 450, 900 and 1800 MHz show that the standard deviation of error is 5-7 dB in urban and suburban areas and 15 dB in rural areas. Tests in Brazil show an average error of 4.4 dB with a standard deviation of 2.6 dB. To further illustrate, 4.4 dB error results in around 25% error in cell radius leading to 44% error in cell size! (Imagine the cost impact of such an error on the financial model.)
Similarly, the Erceg model (some refer to it by the SUI – Stanford University Interim – models) which is based on measurements done at 1900 MHz in suburban areas in the United States has been shown to over-predict the loss at 3.5 GHz in all environments (of course, frequency correction factor has been included). I cite this example, because the Erceg model is used extensively in predicting the cell size for WiMAX and other fixed wireless access networks.
In summary, a good knowledge of propagation models is very important to provide a good approximation of the coverage area of a cell, and consequently number of sites and cost of the radio access network. The financial models developed by TSI incorporate such subtleties which differentiate them from other canned tools.
And this is what path loss models have to do with financial models.