**7. Real world antennas**

The real world antennas which match the elevation characteristics over frequency of the optimized synthesized antennas can be found in [1]. Two dual orthogonal polarized antennas are used along with a 180◦ hybrid coupler to form the two subchannels. The comparison of the radiation pattern over frequency of the synthesized antennas and the real world antennas is shown in Fig. 7 .

**Figure 6.** Capacity analysis for the aperture size 5×5×5 cm3. (Image taken from [29])

10 Will-be-set-by-IN-TECH

**Figure 5.** Resulting synthesized antenna radiation pattern for a transmit-receive pair (horizontal polarization) for subchannel 1 (S1), with line-of-sight propagation, and subchannel 2 (S2), with propagation paths reflected from the ceiling and floor, for the aperture size 5×5×5 cm3 with 5×5×<sup>5</sup>

Three averaging strategies were used, namely averaging over frequency, over location, and of transmitter and receiver radiation patterns. The first averages all radiation patterns obtained at frequency points between 3.1 to 10.6 GHz to obtain a pattern which is valid for the UWB. The second averages the radiation pattern obtained from random points around the scenario so that the resulting radiation pattern is valid for use in the whole scenario. The third averaging is done if the resulting transmitter and receiver radiation patterns look qualitatively

The capacity for the averaged synthesized patterns according to the number of sampling antennas across the ECC (Electronic Communications Committee) standard's UWB band was analyzed using (26). The term *pi* is taken from the power spectral density levels of the ECC UWB spectral mask, *λ<sup>i</sup>* is the Eigenvalue of the subchannel from the matrix **S** and

noise = *kTB*, where *k* is the Boltzmann constant, *T* = 297 K and *B* = 100 MHz. Fig. 6 shows the capacity of the synthesized radiation pattern using 2×2×2 till 5×5×5 sampling antenna elements within the defined 5×5×5 cm3 physical space. It can be seen that the higher the number of sampling antennas, the more the capacity increases, agreeing with the theory in [18]. Noting that the rise in the capacity is decreasing with the higher element configuration used, we conclude that the 5×5×5 configuration is nearing the capacity saturation limit.

The real world antennas which match the elevation characteristics over frequency of the optimized synthesized antennas can be found in [1]. Two dual orthogonal polarized antennas are used along with a 180◦ hybrid coupler to form the two subchannels. The comparison of the radiation pattern over frequency of the synthesized antennas and the real world antennas

the array according to the Cartesian coordinate system.

elements, (left) side view and (right) bottom view. (Image taken from [29])

similar, so that both can use the same antennas.

*E*single is the electric field of the sampling antenna used (a dipole in this case), *N*ant is the total number of transmitter or receiver antennas (since they both use the same sampling antenna configuration), *β* is the wave number, *d* is the distance from the origin of the sampling antenna to a far-field observation point, *ai*∠*ζ<sup>i</sup>* is the weighting from the **U** and **V** beamforming matrices, *di* − *d* = Δ*ϕ* in (27) and Δ*xi*, Δ*yi*, Δ*zi* are the position of the individual elements in

where

*Averaging strategy*

**6.1. Capacity analysis**

**7. Real world antennas**

is shown in Fig. 7 .

*σ*2

(b) Real world antennas (left) subchannel 1 (right) subchannel 2

**Figure 7.** Synthesized antennas vs. real world antennas: radiation pattern (elevation) over frequency
