A WLAN design problem with known mobile device locations: a global optimization approach

Abstract

As wireless networks continue to see rapid growth, the next generation of networks needs to be designed to optimize fundamental capacity limits suggested by Shannon’s Information Theory. The use of simple coverage models and linear objective functions based on number of users will not provide optimal performance. This manuscript describes an optimization model and software tools that may be used to assist a network engineer in the design of a wireless local area network. The model uses Shannon’s channel capacity formula to calculate network capacity and is restricted to a single frequency with known locations for the mobile devices. Even under these assumptions, the model involves a complex nonlinear objective function with quadratic constraints. Multiple commercial software tools as well as a global optimizer developed by us are empirically evaluated on a set of test cases. One of the global solvers developed by LINDO Systems was found to work very well for all of the design cases tested.

Appendix: Derivation of attenuation formula

Several equations are required to determine the attenuation between a pair of locations. The path-loss is the signal attenuation given in dB, and is defined as the difference between the transmitted power at the source location and the received power at the destination location. Path-loss is given in Rappaport [13] on p. 108, by

$$ \mathit{PL}=10\log(P_t/P_r ) $$

(10)

where P _t is the transmitted power, and P _r is the received power.

This equation can be rewritten as

$$ P_r=P_t 10^{-\mathit{PL}/10} $$

(11)

Path loss can also be calculated directly between a pair of locations, given in Rappaport [13] on p. 161, by

$$ \mathit{PL}=\mathit{PL}_0+10n \log(d/d_0 )+X_\sigma $$

(12)

where PL ₀ is the known path-loss between locations at a distance of d ₀, d is the distance between the source and destination location, n is a constant determined by the medium of transfer, and X _σ is a random variable representing noise. For this analysis we use the expected value of X _σ , which is 0. The noise associated with MD m, N _m , used in this investigation is the root mean squared value of X _σ and is generally assumed to have a value of 10⁻¹⁰.

Rappaport [13] gives n as 3.27 on p. 165, and we will use that number. Rappaport also gives a value for PL ₀ for a d ₀ of 1 meter, which we will denote as PL _m . This value can be calculated from p. 166, giving a value for PL _m of 31.5 dB. As we are working in feet, we had to convert this value into the PL _f at 1 ft. As a meter is 3.28 feet:

$$ \mathit{PL}_f=\mathit{PL}_m+10\cdot3.27\log(1~\text{ft}/3.28~\text{ft}) = 14.6~\text{dB} $$

(13)

Therefore, the PL at d ft from the source is given by

$$ \mathit{PL}=\mathit{PL}_f+10\cdot3.27\log(d/1~\text{ft})=14.6+32.7 \log(d) $$

(14)

Combining (11) and (14) gives

$$ P_r=P_t 10^{-(14.6+32.7\log(d))/10}=P_t 10^{-1.46} d^{-3.27} $$

(15)