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dB in Software Creation Code 3 of 9 in Software dB




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2 dB generate, create bar code 39 none with software projects Microsoft Office Excel Website (2.45). Performance in lo g-normal shadowing is typically parameterized by the log mean dB , which is refered to as the average dB path loss and is in units of dB. With a change of variables we see that the distribution of the dB value of is Gaussian with mean dB and standard deviation dB : p( dB ) = ( dB dB )2 1 exp . 2 2 dB 2 dB (2.

46). The log-normal di ANSI/AIM Code 39 for None stribution is de ned by two parameters: dB and dB . Since = Pt /Pr is always greater than one, dB is always greater than or equal to zero. Note that the log-normal distribution (2.

43) takes values for 0 . Thus, for < 1, Pr > Pt , which is physically impossible. However, this probability will be very small when dB is large and positive.

Thus, the log-normal model captures the underlying physical model most accurately when dB >> 0. If the mean and standard deviation for the shadowing model are based on empirical measurements then the question arises as to whether they should be obtained by taking averages of the linear or dB values of the empirical measurements. Speci cally, given empirical (linear) path loss measurements {p i }N , should the mean path loss i=1 1 1 be determined as = N N pi or as dB = N N 10 log10 pi .

A similar question arises for computing the i=1 i=1 empirical variance. In practice it is more common to determine mean path loss and variance based on averaging the dB values of the empirical measurements for several reasons. First, as we will see below, the mathematical justi cation for the log-normal model is based on dB measurements.

In addition, the literature shows that obtaining empirical averages based on dB path loss measurements leads to a smaller estimation error [64]. Finally, as we saw in Section 2.5.

4, power falloff with distance models are often obtained by a piece-wise linear approximation to empirical measurements of dB power versus the log of distance [1]. 43. Most empirical st udies for outdoor channels support a standard deviation dB ranging from four to thirteen dB [2, 17, 35, 58, 6]. The mean power dB depends on the path loss and building properties in the area under consideration. The mean power dB varies with distance due to path loss and the fact that average attenuation from objects increases with distance due to the potential for a larger number of attenuating objects.

The Gaussian model for the distribution of the mean received signal in dB can be justi ed by the following attenuation model when shadowing is dominated by the attenuation from blocking objects. The attenuation of a signal as it travels through an object of depth d is approximately equal to s(d) = e d , (2.47).

where is an att bar code 39 for None enuation constant that depends on the object s materials and dielectric properties. If we assume that is approximately equal for all blocking objects, and that the ith blocking object has a random depth d i , then the attenuation of a signal as it propagates through this region is s(dt ) = e . = e dt ,. (2.48). where dt = i di i s the sum of the random object depths through which the signal travels. If there are many objects between the transmitter and receiver, then by the Cental Limit Theorem we can approximate d t by a Gaussian random variable. Thus, log s(dt ) = dt will have a Gaussian distribution with mean and standard deviation .

The value of will depend on the environment. Example 2.4: In Example 2.

3 we found that the exponent for the simpli ed path loss model that best ts the measurements in Table 2.3 was = 3.71.

Assuming the simpli ed path loss model with this exponent and the same K = 31.54 2 dB, nd dB , the variance of log-normal shadowing about the mean path loss based on these empirical measurements. Solution The sample variance relative to the simpli ed path loss model with = 3.

71 is.
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