Wimax standards and Security The Wimax

FIGURE 5.2
Actual RSSI measured at customer locations versus predicted RSSI from the planning model.

100 m 1 km 10 km

40
1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0

50

RSSI (dBm)
60

70

80
PR = 27.36 log (d/1km) 70.9

Average RSSI Linear fit
90

100
log (d/1km)

FIGURE 5.3
Received power level signal strength indicator (in dBm) as a function of distance (on a logarithmic scale).

100 m 1 km 10 km

160

Empirical path loss
Free-space path loss
Erceg B predicted path loss Linear (empirical path loss)

150

140

130
PL = 27.24 log (d/1km) + 127.2

Path loss (dB)
120

110

100

90

80
1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0
log (d /1km)


FIGURE 5.4
Empirical path loss as a function of distance (on a logarithmic scale) and comparison to prediction models.

station power, cable loss, antenna pattern, and even (to a small extent) on the deviation from boresight of the sector’s antenna.^∗ Path loss estimates are represented in Figure 5.4.

Approximation of path loss to a one-slope model leads to the following equation:
PL(dB) = 127.2 + 27.24 × log(d/d₀) (5.6)

=
with d₀ 1 km. The trial environment is compared to typical cellular models as discussed below.

• 
  
  =
  
  =
  Path loss exponent is approximately n 2.7. The Walfish–Ikegami model for line-of-sight in urban corridors predicts n 2.6. Other reports have shown similar results for 3.5 GHz: Ref. 25 reports val- ues of n between 2.13 and 2.7 for rural and suburban environments, Ref. 27 reports n = 3.2. However, many other models predict higher
  

^∗ Deviation from boresight may be easily estimated for fixed access where customer locations were previously geocoded. From geocoded data, a bearing with respect to the serving base combined with the known orientation of the sectors antennas yield an angle off boresight for every customer. A specific attenuation number can then be included for a better path loss estimate. In most designs, sectors will overlap around the 3 dB beam width, and omitting this term would not result in more than 3 dB error in the path loss estimate. Nevertheless, the calculations involved are easy enough to improve the path loss estimate.

exponents for n, between 3.5 and 4.5 (see path loss exponents in Table 5.1).

• 
  Otherwise, approximations are fairly good with Erceg-B and C models. Erceg-B is the best fit and is represented in Figure 5.4.
  

The most popular method to compute slope estimate is a least squares error estimate. In that method, a set of error terms {e_i} is defined between each data point and a linear estimate. Minimizing the sum of these errors yields the slope and intercept, which intuitively gives a good approxima- tion of the data set. That method also benefits from the following important properties [37]:

1. 
   Least squares estimated slope and intercept are unbiased estimators.
   
2. 
   Standard deviations of the slope and intercept depend only on the known data points and the standard deviation of the error set {e_i}.
   
3. 
   Estimated slope and intercept are linear combinations of the errors {e_i}.
   

From the last point, if we assume that the errors are independent normal random variables (as in a log-normal shadowing situation), the estimated slope and intercept are also normally distributed. If we assume more generally that the data points are independent, the central limit theorem implies that for large data sets, the estimated slope and intercept tend to be normally distributed.

For the last assumption to be true, very low correlation of the wireless channel must exist between data points. This is the case when data points are measured at fixed locations tens or hundreds of meters apart—in which case measurements show very low correlations between the respective fading channels. Similarly, this is the case even in a mobile cellular environment, from one cell to another.
The important conclusion is that path loss exponent is approximated by a normal (or Gaussian) random variable.
We also verify a few more key findings as in Ref. 13, for a 3.5 GHz fixed link:

1. 
   
   = ×
   Free-space approximation (PL₀ 20 log(4πd₀/λ)) works well within 100 m.
   
2. 
   Path loss exponent depends strongly on height of transmitter (mobile height being more or less constant throughout).
   
3. 
   Variations around median path loss are Gaussian within a cell (log- normal shadowing) with standard deviation σ ≈ 11.7 dB.
   
4. 
   Unfortunately, our limited number of cells do not allow us to quan- tify the nature of the variations of σ over the population of macro cells.
   

8
6

Throughput (Mbps)
4
2
0
0.50 1.50 2.50 3.50
Distance (km)