Wimax standards and Security The Wimax

Link Budgets

Link budgets are essential for radio systems coverage and performance pre- dictions. Unfortunately, they depend largely on suppliers’ data and are often kept proprietary. Still, important common parameters valid for most fixed WiMAX systems are given in this section. Mobile WiMAX systems require a different link budget analysis and is not covered here.^∗
Radio parameter values are presented here for current fixed WiMAX sys- tems [1,2]. Some of these values, such as transmitted power and antenna gain, may change with local regulations; others, like received sensitivity, are com- monly discussed in the standard community and accepted as a minimum standard that suppliers must adhere to. Of course suppliers may improve upon such numbers.
A variety of diversity schemes may be employed in WiMAX systems; they have a significant impact on link budgets. Some early systems do not use any diversity; others use simple spatial or polarization diversity schemes; and some use advanced MIMO systems.

4. 
   Propagation Characteristics
   

Between transmitter and receiver, the wireless channel is modeled by several key parameters. These parameters vary significantly with the environment, rural versus urban, or flat versus mountainous. Different kinds of fading occur; they are often categorized into three types [15,16]:

Small-scale fading causes great variation within a half wavelength. It is caused by multipath and moving scatterers. Resulting fades are usually approximated by Rayleigh, Ricean, or similar fading statis- tics.^† Radio systems rely on diversity, equalizing, channel coding, and interleaving schemes to mitigate its impact.

Large-scale shadowing causes variations over larger areas because of terrain, building, and foliage obstructions; its impact on link budgets is detailed further in this section.

= ×
Distance dependence is approximated by PL 10n log(d), where n
is the path loss exponent that varies with terrain and environment.


^∗ Elements of mobile WiMAX are given, for instance, in Ref. 4, pp. 32–34.
^† Analyses in many published papers also show that Nakagami-m and Weibull distributions also lead to interesting results and convenient approximations.

We will see later in Section 5.3.4 that n itself typically follows a Gaussian distribution.

=
The large-scale fading due to various obstacles is commonly accepted to fol- low a log-normal distribution [18,20,21]. This means that its attenuation x measured in dB is normally distributed N(m, σ) with mean m x and stan- dard deviation σ. The probability density function of x is given by the usual Gaussian formula

p(x) = ¹ × exp ^{−(x − x)}2

(5.4)

σ^√2π
2σ²

With this Gaussian distribution model, the probability that the received power x at a distance d exceeds a threshold x₀ (the receiver threshold that provides an acceptable signal) is given by Ref. 22.



2

σ

2
P(x ≥ x₀) = ¹ erfc ^x0 √^{− x} (5.5)
where erfc is the complementary error function.^∗ Equation 5.5 is used to choose a fade margin, or excess margin, in a link budget to obtain a tar- get service reliability (percentage of acceptable signal at the edge of planned coverage). Without that excess margin, link budgets and propagation models only yield a median propagation loss, corresponding to 50% edge coverage reliability.^†

=

=
The mean of log-normal shadowing is usually incorporated in path loss model and its standard deviation σ is typically estimated by empirical mea- surements. Commonly accepted values for σ are between 6 and 12 dB. Measured values of σ seem to display Gaussian distribution as well and depend on: the radio frequency, the type of environment (rural, suburban, or urban), and base station and subscriber station height. Reports may be found in the literature [20–29] and are summarized in Table 5.1. The choice is somewhat arbitrary, but given the above experimental data we chose to follow an empirical value for suburban environment of σ 9.6 dB (e.g., for terrain category B in Ref. 13) and use that same estimate σ 9.6 dB for 3.5 GHz and 5.8 GHz. We then chose a fade margin or excess margin for a certain ser- vice reliability. For instance, service providers tend to impose a requirement of 90% edge coverage, which when following Jakes’ method [22] yields a fade margin of 12.3 dB.


^∗ The complementary error function is defined as erfc 1 erf, where erf is the error function erf(x) = ^{√2 ¸ x} e^−u2 du.

= −

π

0
^† Indeed, setting the excess margin to x₀ − m = 0 yields a coverage probability of P(x ≥ x) = 50%,
since erfc(0) = 1.