Wimax standards and Security The Wimax

Propagation Environment

Propagation environments are certainly not specific to WiMAX, but WiMAX performance levels in different environments should be quantified. Propaga- tion characteristics depend on the bands of operations and are reviewed in this section.

1. 
   Propagation Modeling
   

Different spectrum bands have very different propagation characteristics and require different prediction models. Some propagation models are well-suited for computer simulation in the presence of detailed terrain and building data; others aim at providing simpler general path loss estimates [6].
A handful of empirical models were widely accepted for cellular communi- cations; their success being mostly due to their simplicity and their fairly good


^∗ Rules are similar to UNII-3, but with requirements around dynamic frequency selection (DFS) capability to protect Federal Government radar systems.

prediction for first-order modeling. The simplest approach is to estimate the power ratio between transmitter and receiver as a function of the separation distance d, that ratio is referred to as path loss. A physical argument like the Friis’ power transmission formula yields:

P_r
Pt =
^GtGrλ2 (5.1)
(4πd)²

= ×

=
where P_t and P_r are the transmitted and received power, G_t and G_r the trans- mitter and receiver gain, λ the wavelength of the signal, and d the separation distance. This equation shows a free-space dependence in 1/d². The exponent n 2 is referred to as the path loss exponent. If the path loss is measured in decibel (PL 10 log(P_t/P_r)), it varies logarithmically with the distance of separation. Simple models then consist of computing a path loss exponent n from some linear regression argument on a set of field data, and deriving a model like:


PL(dB) = PL₀ + 10n × log(d/d₀) (5.2)
where the intercept PL₀ is the path loss at an arbitrary reference distance d₀. Such models are referred to as empirical one-slope models and are countless in the literature. For instance, the above Friis equation leads to:

= =
PL(dB) = 32.44 + 20 × log( f /f₀) + 20 × log(d/d₀) (5.3) where f₀ 1 MHz and d₀ 1 km.
One such model by Okumura [7] was derived from extensive measure- ments in urban and suburban areas. It was later put into equations by Hata [8]. This Okumura–Hata model, valid for 150 MHz to 1.5 GHz, was later extended to PCS frequencies, 1.5–2 GHz, by the COST project [9,10] and is referred to as the COST 231-Hata model; it is still widely used by cellular operators. The model provides good path loss estimates for large urban cells (1–20 km) and a wide range of parameters like frequency, base station height (30–200 m), and environment (rural, suburban, or dense urban).
Another popular model is that of Walfish–Ikegami [11,12], which was also revised by the COST project [9,10] into a COST 231-Walfish–Ikegami model. It is based on considerations of reflection and scattering above and between buildings in urban environments. It considers both line-of-sight (LOS) and nonline-of-sight (NLOS) situations. It is designed for 800 MHz to 2 GHz, base station heights of 4–50 m, and cell sizes up to 5 km, and is especially convenient for predictions in urban corridors.
More recently, Erceg [13] proposed a model derived from a vast amount of data at 1.9 GHz, which makes it a preferred model for PCS and higher frequencies [14]. These models and their applications and domains of validity are well described and analyzed, for instance, in Refs. 15–18. They provide a first estimate used by service providers in wireless systems’ design phase.

Further refinements to these models in which multiple path loss exponents, n₁, n₂, ... , are used at different separation ranges provide some improve- ments, especially in heavy multipath indoor environments. It turns out, however, that variations from site to site are such that these multiple slope improvements are fairly small, and simple one-slope models are a good enough first approximation for outdoor propagation models. More detailed, site-specific models are required for better results, but require additional efforts and site-specific terrain or building data.

Two important points should be kept in mind about most propagation models though. The first is that large amounts of empirical data were collected at cellular and PCS frequencies (800 and 1900 MHz), and exten- sions to other frequencies may not have been well verified.^∗ The second is that these data points were collected while driving and may not accurately reflect fixed wireless links, which is discussed in more detail in the following section.

2.