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Figure 21.5 The state diagram of the multipolling mechanism. (Reproduced by permission of IEEE [43].) (3) There is an equal probability BER for a bit error to occur due to the channel noise (interference, fading or multipath). Hence, ERRtype can be expressed as 1 (1 BER)ltype . (4) An STA becomes a nonbehaved one if the STA fails to receive the CTS frame from the PC. That is, = ERRCTS . If AvgD and AvgT denote the total number of bits in the data frames successfully sent from the polled STAs and the average complete time in time units for a poll, respectively, then the polling ef ciency is de ned as E = AvgD/AvgT. This represents the average uplink data rate during a poll. In the single poll, a polled STA contributes data frames if the STA successfully receives a CF-Poll frame and has pending data frames to be successfully transmitted. The polled STA may suffer frame error due to interference from external STAs. Therefore, AvgD = (1 ) frame num/2 ldata frame (1 ERRdata frame ) (1 ERRsingle

+ I(q)

(6.4.31)

The Green's function of the upper medium on the coarse grid is represented by Z;;{n. Then Eq. (6.4.23) for p = 1,2,3 becomes

(6.4.32)

1,2, ... ,Nsdg on the dense grid, while 'L.~~cl z;;;~ns)7~q) only has values of 1,2, ... ,Nscg on the coarse grid. Thus we first compute 'L.~~cl Z;;;~ns)

poll )

If we were to run this code, we would get something like the following:

q ).

Then we use linear interpolation of 'L.~~cl z~q~ns)7~q) on the coarse grid to find N sdg values on the dense grid. In Eq. (6.4.32), we use subscript intp to represent that interpolation. Thus the computational steps for matrix-vector multiplication are associated with the number of surface unknowns on the coarse grid. The algorithm is described pictorially in Fig. 6.4.2. The PBTG

I, Go CkoIrm - r;,1) I n ,

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Figure 6.4.2 Illustration of convolution of upper medium Green's function with surface fields on dense grid.

(21.5)

is also used in conjunction with the SMCG. The computational complexity of the combined algorithm of PBTG/SMCG is O(Nseg log(Nseg )). The numerical simulation results are presented in terms of the bistatic scattering coefficients normalized by the incident power. For an incident wave with a polarization (3, we have

(6.4.33)

pine = 21T" (3

(6 .. 34) 4

where k p = Jki + k~. The horizontal and vertical polarized scattered components of E; are, respectively, given by (6.3.46) and (6.3.47). The emissivity of the rough surface at incident angle (()i, cPi) is e(3 (()i , cPi) = 1 -

[:logging_service, :Logger, #<DRb::DRbObject:0x54204 @ref=206640, @uri="druby://192168112:55462">, "Primary Logger"] [:logging_service, :Logger, #<DRb::DRbObject:0x53c8c @ref=206640, @uri="druby://192168112:55462">, "Primary Logger"]

The polled STA will give a response to the PC after an SIFS period for a successful CF-Poll. If a polled STA does not respond to the PC after a PIFS period for a failed CF-Poll, the PC takes over the channel control and may send the next CF-Poll frame. In the HCF, the RTS/CTS frames should be exchanged before the data transmission to prevent the interference from other STAs. Since the HCF is being substituted for the PCF in the 802.11E, we consider the single poll of the HCF in our analysis. Therefore, AvgT = InitBT + (tsingle-poll + PIFS) ERRsingle-poll + [tsingle-poll + SIFS + tRTS + tCTS + 2SIFS + (1 ) frame num/2 (tdata + (tnull frame + SIFS)] (1 ERRsingle-poll )

[rh(3(()s, 1>s;

()i,

'Pi)

+ rV(3(()s, cPs;

()i,

+ SIFS) (21.6)

(6.4.35)

In this section, we illustrate the numerical simulation results of wave scattering from 2-D lossy dielectric rough surface. Simulations are based on Gaussian random rough surfaces with Gaussian correlation functions. All the cases are computed with the relative dielectric constants of 17 + i2 and 4.06 + iO.3, surface area of 8 free space wavelengths by 8 free space wavelengths, rms height from 0.05 to 0.3 wavelengths, and correlation length of 1.0 wavelength. The results of three methods will be shown: (i) single coarse grid of 8 points per free space wavelength with SMCG (SCG/SMCG), (ii) single dense gird of 16 points per free space wavelength with SMCG (SDG/SMCG), and (iii) PBTG/SMCG. Based on the experience of 1-D dielectric rough surfaces, the sampling density of 16 points per wavelength for the permittivity of 17 + i2.0 gives convergent results. Thus we regard (ii) as accurate results. We will show that (iii) is as accurate as (ii) and takes much less CPU time. First, we compare the bistatic scattering coefficients for one realization based on different methods. Next, the emissivities and CPU are compared. The results show that the dense grid is required for the case with large dielectric constant. Then the variation of brightness temperatures with observation angles is illustrated and compared with the second order small perturbation method. Finally, the brightness temperature as a function of rms height is shown for different observation angles. We use T = 300 K as the physical temperature. All the numerical results were computed on a DEC Alpha workstation.

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