3.2 Time domain

During time domain analysis, two identical antenna structures are arranged in two major configurations, i.e. face to face and side by side as shown in Figure 10. In each of these configurations, one port is excited, whereas the other port is terminated with a matched load. The antenna structure is excited with a Gaussian pulse having a centre frequency of 13 GHz and bandwidth of 1–25 GHz. The normalized amplitudes of the transmitted and received signals are presented in Figure 11. From these normalized amplitudes, the correlation between the two signals, i.e. system fidelity factor, is calculated by using Eq. (3). The calculated values of system fidelity factor for four cases are listed in Table 5. The values listed in Table 5 indicate that the signal is slightly distorted in side-by-side configuration in comparison to faceto-face configuration for both cases.

Inner Tapered Tree-Shaped Ultra-Wideband Fractal Antenna with Polarization Diversity DOI: http://dx.doi.org/10.5772/intechopen.86071

$$F = \max\left[\frac{\int\_{-\infty}^{\infty} s\_t(t)s\_r(t+\tau)d\tau}{\int\_{-\infty}^{\infty} |s\_t(t)|^2 dt \int\_{-\infty}^{\infty} |s\_r(t)|^2 dt}\right] \tag{3}$$

where st(t) and sr(t) are the transmitted and received pulses and τ is the group delay. The variations of group delay with respect to frequency for all four cases are illustrated in Figure 12. It is observed that the group delay has its variations less than 1 ns over the entire band of operation.

#### 3.3 Diversity performance

To analyse the diversity performance of the designed antenna, various parameters like envelope correlation coefficient, diversity gain (DG) and mean effective gain (MEG) are to be calculated from s-parameters or farfield patterns. The envelope correlation coefficient (ECC) signifies the correlation between the radiation patterns of two antenna elements. For the designed antenna structure, ECC (ρe) is

Figure 7. Radiation patterns of the two antenna elements in XY, YZ and ZX planes.

3.2 Time domain

Table 4.

48

Table 3.

Bandwidth of two ports.

UWB Technology - Circuits and Systems

to-face configuration for both cases.

Comparison of designed antenna with other UWB diversity antenna.

During time domain analysis, two identical antenna structures are arranged in two major configurations, i.e. face to face and side by side as shown in Figure 10. In each of these configurations, one port is excited, whereas the other port is terminated with a matched load. The antenna structure is excited with a Gaussian pulse having a centre frequency of 13 GHz and bandwidth of 1–25 GHz. The normalized amplitudes of the transmitted and received signals are presented in Figure 11. From these normalized amplitudes, the correlation between the two signals, i.e. system fidelity factor, is calculated by using Eq. (3). The calculated values of system fidelity factor for four cases are listed in Table 5. The values listed in Table 5 indicate that the signal is slightly distorted in side-by-side configuration in comparison to face-

Figure 8. Peak realized gain versus frequency characteristics.

Figure 9. Radiation and total efficiencies of the two antenna elements.

#### Figure 10.

Time domain analysis configurations of the diversity antenna. (a) Face to face (b) Side by side.

calculated by using Eq. (4) [32]. The calculated values of ECC are plotted in Figure 13.

$$\rho\_{\mathbf{e}} = \frac{\left| \mathbf{S}\_{\mathbf{1}\mathbf{1}}^{\*} \mathbf{S}\_{\mathbf{1}\mathbf{2}} + \mathbf{S}\_{\mathbf{2}\mathbf{1}}^{\*} \mathbf{S}\_{\mathbf{2}\mathbf{2}} \right|^{2}}{\left( \mathbf{1} - \left( \left| \mathbf{S}\_{\mathbf{1}\mathbf{1}} \right|^{2} + \left| \mathbf{S}\_{\mathbf{2}\mathbf{1}} \right|^{2} \right) \right) \left( \mathbf{1} - \left( \left| \mathbf{S}\_{\mathbf{2}\mathbf{2}} \right|^{2} + \left| \mathbf{S}\_{\mathbf{1}\mathbf{2}} \right|^{2} \right) \right)} \tag{4}$$

From Figure 13, it is observed that the ECC values are less than 0.005 in the entire band of operation. These low values of ECC (<0.5) signify that the designed antenna is a good candidate for the UWB applications with polarization diversity [16].

System fidelity factor for four configurations of the designed antenna.

Normalized amplitudes of the transmitted and received pulses in all four configurations. (a) Face to face (b)

Inner Tapered Tree-Shaped Ultra-Wideband Fractal Antenna with Polarization Diversity

DOI: http://dx.doi.org/10.5772/intechopen.86071

Figure 11.

Side by side.

Table 5.

51

Inner Tapered Tree-Shaped Ultra-Wideband Fractal Antenna with Polarization Diversity DOI: http://dx.doi.org/10.5772/intechopen.86071

Figure 11. Normalized amplitudes of the transmitted and received pulses in all four configurations. (a) Face to face (b) Side by side.


#### Table 5.

calculated by using Eq. (4) [32]. The calculated values of ECC are plotted in

Time domain analysis configurations of the diversity antenna. (a) Face to face (b) Side by side.

<sup>2</sup> <sup>þ</sup> j j S21 <sup>2</sup>

11S12 <sup>þ</sup> <sup>S</sup><sup>∗</sup>

21S22

 2

<sup>2</sup> <sup>þ</sup> j j S12 <sup>2</sup> (4)

1 � j j S22

<sup>ρ</sup><sup>e</sup> <sup>¼</sup> <sup>S</sup><sup>∗</sup>

1 � j j S11

Figure 13.

50

Figure 10.

Figure 8.

Figure 9.

Peak realized gain versus frequency characteristics.

UWB Technology - Circuits and Systems

Radiation and total efficiencies of the two antenna elements.

System fidelity factor for four configurations of the designed antenna.

From Figure 13, it is observed that the ECC values are less than 0.005 in the entire band of operation. These low values of ECC (<0.5) signify that the designed antenna is a good candidate for the UWB applications with polarization diversity [16].

Another important parameter used to identify the suitability of an antenna for diversity applications is diversity gain. It is the difference between the selection combined cumulative distribution function (CDF) and one of the other CDFs at a certain CDF level. The commonly used CDF level is 1% [33]. The DG of the

Inner Tapered Tree-Shaped Ultra-Wideband Fractal Antenna with Polarization Diversity

DOI: http://dx.doi.org/10.5772/intechopen.86071

diversity antenna can be calculated approximately by Eq. (6) [34]. From Figure 15, it is observed that the diversity gain value is almost constant in the entire band of

DG <sup>¼</sup> <sup>10</sup> ffiffiffiffiffiffiffiffiffiffiffiffi

In the case of a rich multipath environment, the maximum rate of transmission for reliable transmission in a communication channel is estimated by calculating capacity loss (b/s/Hz). For a MIMO antenna, a channel capacity loss of less than 0.4 b/s/Hz is acceptable [35]. It is calculated by using the correlation matrix (7) [35].

1 � ρ<sup>e</sup>

p (6)

Closs ¼ � log <sup>2</sup> <sup>ψ</sup><sup>R</sup> � � (7)

operation.

Figure 14.

Figure 15.

53

Diversity gain versus frequency characteristic.

Mean effective gain versus frequency characteristics of the designed antenna.

Figure 12.

Group delay versus frequency characteristics of the diversity antenna for all four configurations.

Figure 13. Envelope correlation coefficient versus frequency characteristic.

The mean effective gain measures the antenna gain of each antenna element taking the radiation power pattern effects, the antenna total efficiency and the propagation effects into account. It is calculated by using Eq. (5) and is plotted for each antenna in Figure 14.

$$\text{LEG} = \int\_{0}^{2\pi} \left[ \frac{\text{XPR}}{\text{1} + \text{XPR}} \text{G}\_{\theta}(\theta, \varphi) P\_{\theta}(\theta, \varphi) + \frac{\text{XPR}}{\text{1} + \text{XPR}} \text{G}\_{\phi}(\theta, \varphi) P\_{\theta}(\theta, \varphi) \right] \sin\theta d\theta d\varphi \tag{5}$$

where XPR represents the cross-polarization ratio, Gθand Gφare the θ- and φcomponents of the antenna power gain patterns and P<sup>θ</sup> and P<sup>φ</sup> are the θ- and φcomponents of the angular density functions of the incident power, respectively. The MEG values for each antenna element in the case of isotropic radiation, i.e. XPR = 0 dB, are presented in Figure 14.

Inner Tapered Tree-Shaped Ultra-Wideband Fractal Antenna with Polarization Diversity DOI: http://dx.doi.org/10.5772/intechopen.86071

Another important parameter used to identify the suitability of an antenna for diversity applications is diversity gain. It is the difference between the selection combined cumulative distribution function (CDF) and one of the other CDFs at a certain CDF level. The commonly used CDF level is 1% [33]. The DG of the diversity antenna can be calculated approximately by Eq. (6) [34]. From Figure 15, it is observed that the diversity gain value is almost constant in the entire band of operation.

$$\mathbf{DG} = \mathbf{10}\sqrt{\mathbf{1} - \rho\_e} \tag{6}$$

In the case of a rich multipath environment, the maximum rate of transmission for reliable transmission in a communication channel is estimated by calculating capacity loss (b/s/Hz). For a MIMO antenna, a channel capacity loss of less than 0.4 b/s/Hz is acceptable [35]. It is calculated by using the correlation matrix (7) [35].

$$\mathbf{C}\_{loss} = -\log\_2\left(\boldsymbol{\psi}^R\right) \tag{7}$$

Figure 14. Mean effective gain versus frequency characteristics of the designed antenna.

Figure 15. Diversity gain versus frequency characteristic.

The mean effective gain measures the antenna gain of each antenna element taking the radiation power pattern effects, the antenna total efficiency and the propagation effects into account. It is calculated by using Eq. (5) and is plotted for

Group delay versus frequency characteristics of the diversity antenna for all four configurations.

� �

where XPR represents the cross-polarization ratio, Gθand Gφare the θ- and φcomponents of the antenna power gain patterns and P<sup>θ</sup> and P<sup>φ</sup> are the θ- and φcomponents of the angular density functions of the incident power, respectively. The MEG values for each antenna element in the case of isotropic radiation, i.e.

XPR

<sup>1</sup> <sup>þ</sup> XPR <sup>G</sup>φð Þ <sup>θ</sup>;<sup>φ</sup> <sup>P</sup>φð Þ <sup>θ</sup>;<sup>φ</sup>

sin θdθdφ

(5)

each antenna in Figure 14.

ð π

XPR

Envelope correlation coefficient versus frequency characteristic.

XPR = 0 dB, are presented in Figure 14.

<sup>1</sup> <sup>þ</sup> XPR <sup>G</sup>θð Þ <sup>θ</sup>;<sup>φ</sup> <sup>P</sup>θð Þþ <sup>θ</sup>;<sup>φ</sup>

0

2 ðπ

0

MEG ¼

52

Figure 13.

Figure 12.

UWB Technology - Circuits and Systems

Figure 16. Capacity loss versus frequency characteristic.

where ψ<sup>R</sup>is the correlation matrix of the receiving antenna and is expressed mathematically as

$$\boldsymbol{\Psi}^{\mathbb{R}} = \begin{bmatrix} \rho\_{11} & \rho\_{12} \\ \rho\_{21} & \rho\_{22} \end{bmatrix} \tag{8}$$

$$\rho\_{\acute{i}i} = \mathbf{1} - \left( |\mathbf{S}\_{\acute{i}i}|^2 + |\mathbf{S}\_{\acute{i}\bar{j}}|^2 \right) \tag{9}$$

$$\rho\_{\vec{i}\vec{j}} = -\left(\mathbf{S}\_{\vec{i}\vec{i}}^{\*}\mathbf{S}\_{\vec{i}\vec{j}} + \mathbf{S}\_{\vec{j}\vec{i}}^{\*}\mathbf{S}\_{\vec{i}\vec{j}}\right) \tag{10}$$

Author details

Sarthak Singhal<sup>1</sup>

55

Varanasi, Uttar Pradesh, India

provided the original work is properly cited.

\* and Amit Kumar Singh<sup>2</sup>

\*Address all correspondence to: sarthak.ece@mnit.ac.in

Institute of Technology, Jaipur, Rajasthan, India

1 Department of Electronics and Communication Engineering, Malaviya National

Inner Tapered Tree-Shaped Ultra-Wideband Fractal Antenna with Polarization Diversity

DOI: http://dx.doi.org/10.5772/intechopen.86071

2 Department of Electronics Engineering, Indian Institute of Technology (BHU),

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

i, j = 1 or 2.

Figure 16 shows that the channel capacity loss changes with the variation of frequencies. It can be seen that the capacity loss values are always less than 0.3 b/s/ Hz in the UWB operating range.
