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

A coplanar waveguide (CPW)-fed third iteration inner tapered tree-shaped ultra-wideband (UWB) fractal antenna for polarization diversity applications is presented. The antenna comprises of two orthogonal fractal antenna structures to achieve polarization diversity performance across the frequency spectrum of 4.7 – 19.4 GHz. An isolation of more than 15 dB is accomplished. The designed antenna has a nearly omnidirectional radiation pattern with an average gain of 2.45 dB, very low values of envelope correlation coefficient and capacity loss, nearly constant diversity gain (DG) and mean effective gain (MEG) values. The time domain analysis results illustrated the low dispersion in the radiated pulse. The designed antenna has advantages of wider bandwidth and miniaturized dimensions along with good diversity performance. These advantages make the designed antenna a promising candidate for future wireless communication systems having multipath fading as a major concern.


Introduction
In 2002, FCC allocated the unlicensed frequency spectrum from 3.1 to 10.6 GHz for ultra-wideband (UWB) technology [1]. After this allocation, ultra-wideband has received attention from wireless communication experts owing to its advantageous features like wider bandwidth, low cost, low susceptibility to multipath fading, reduced probability of detection and intercept and potentially high data rates. In a highly dense and dynamic environment, the UWB systems suffer from multipath fading due to reflection and diffraction. This multipath fading results into the degradation of signal-to-noise ratio (SNR) and channel capacity.
An effective method to resolve these multipath fading issues is the incorporation of antenna diversity techniques in wireless communication systems. Several types of diversity, such as space/spatial, pattern and polarization diversity, have been already proposed and implemented to receive multiple signals [2][3][4].
In a diversity scheme, the power or signal-to-noise ratio of the received signal is optimized by the selection or combining of output signals in several ways like selection combining, equal gain combining or maximal ratio combining. The detailed description of diversity combining techniques is available in [5,6].
For good diversity performance, the received signals should have very low correlation between them [7]. An increase in correlation reduces the combining efficiency. In a spatial diversity scheme, a large separation (compared to wavelength) between the antennas is used to achieve decoupling between signals. This large space requirement limits the use of this diversity method. To overcome this drawback, other techniques such as pattern or polarization diversity [8,9] are investigated. These alternate techniques involve the use of two or more antenna elements with different radiation patterns [10]. An UWB system with polarization diversity technique has potential applications in advanced instruments used for microwave imaging, radar and high-speed data transfer. Some UWB polarization diversity antennas are already reported in the literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. However, the application of those available structures is limited due to their large dimensions, multilayer structure, complex feedline, complex geometries, etc.
Among the various bandwidth enhancement techniques, the use of fractal geometries is proven to be a good method. Fractal antenna structures have a compact size and wideband performance due to properties of self-similarity, space filling and effective energy coupling properties [29].
In this chapter, a compact CPW-fed UWB fractal antenna with polarization diversity performance is presented. The bandwidth of the antenna structure [29] is enhanced by loading the coplanar ground planes with a quarter wavelength long rectangular notches. Two identical copies of this antenna structure are arranged orthogonally to achieve good interport isolation and orthogonal polarization diversity performance without affecting the UWB performance. In the following sections, antenna design description is followed by discussion of frequency domain analysis results, time domain analysis results and diversity performance parameter calculation. Finally, it is concluded with major findings of this chapter.

Antenna design
The geometry of the antenna structure is demonstrated in Figure 1, and its optimized dimensions are listed in Table 1. It is etched on a 1.6 mm thick FR-4 epoxy substrate having a relative permittivity of 4.4 and loss tangent of 0.02. All the dimensions are optimized by using finite element method (FEM)-based Ansoft's high-frequency structure simulator (HFSS) [30]. During simulation, the radiating patch and ground planes are assumed to be perfect electrical conductors. The antenna structure is designed in two steps.
The fourth iterative fractal geometry of radiator is derived from a rectangular monopole by loading it with a pair of triangular notches on its edges. The flow chart of designing the intermediate design steps is presented in Figure 2. The intermediate design steps for radiator geometry are shown in Figure 3. The iteration structure dimensions are governed by Eq. (1):   where: n = iteration number = 2 or 3. R 1 = dimension of the first iteration, i.e. L 1 , W 1 and W m1 . R n = dimension of the nth iteration. r = iterative ratio = 0.4. In the first step, the dimensions of radiating patch are unaltered. The bandwidth of inner tapered tree-shaped fractal antenna is enhanced by loading the ground plane with quarter wavelength rectangular notches to excite an additional resonance at 18.6 GHz. The dimensions of notch are governed by Eq. (2): L r = electrical length of slot for resonance. f r = resonance frequency = 18.6 GHz.
In the second step, two identical structures designed in the first step are placed orthogonal to each other. The air gap between the two structures and their locations are optimized. All the frequency domain results are calculated by using HFSS. The time domain results and diversity performance parameters are analysed by using CST MWS [31].

Results and discussion
The intermediate antenna design steps are compared in terms of their S 11 curves in Figure 4. It is observed that the bandwidth is increasing with an increase in iteration. For further increase in iteration, no significant improvement is observed. The reflection coefficient curves for the initial antenna structure with and without ground notches are illustrated in Figure 5. Its quantitative analysis is listed in Table 2. It is observed that the lower band edge frequency is negligibly changed, whereas the higher band edge frequency is shifted from 16.4 GHz to 19.4 GHz in the case of notch-loaded ground plane. The initial resonances are slightly shifted to higher frequency with an additional resonance.

Frequency domain
The designed diversity antenna structure is simulated by using HFSS and CST MWS simulators. The variations of simulated scattering parameters with frequency are demonstrated in Figure 6. The quantitative analyses of bandwidth for two antenna elements used in designed antenna structure are presented in Table 3. From Figure 6 and Table 3, it is observed that there are some discrepancies among the two simulation results. These discrepancies can be attributed to the different mesh size suitable for numerical techniques on which the simulators are designed. In addition to mesh size, it is also important to mention that in CST MWS the structure can be solved in single pass instead of solution for different frequency spectrum, i.e. 1-2, 2-4, 4-8, 8-16 and 16-32 GHz in HFSS. The differences between the S 11 and S 22 characteristics are due to asymmetrical structure with respect to substrate. A good isolation of more than 15 dB is achieved. The designed antenna has resonances at the frequencies of 6, 8, 10.8, 15.8 and 18.8 GHz.
The comparison among the designed antenna and previously reported polarization/pattern diversity antenna structures is listed in Table 4. It is observed that the designed antenna has wider bandwidth, good isolation and miniaturized dimensions than other structures.
The simulated radiation patterns of two antenna elements at the resonance frequencies of 6, 8, 10.8, 15.8 and 18.8 GHz in all three planes are illustrated in Figure 7. From Figure 7, it is observed that the antenna structures have bidirectional and omnidirectional patterns at lower frequencies. At higher frequencies, the patterns are distorted omnidirectional in nature due to the excitation of higher-order modes at those frequencies. It is also clearly observable that the patterns of both antenna structures have a phase difference of 90°in each plane as desirable.    The variations of radiation and total efficiencies with frequency for both antenna elements are shown in Figure 9. The radiation efficiencies of both antenna elements are more than 0.7 with an average of more than 0.86. Similarly, the total efficiencies have an average of 0.83. The efficiencies are decreasing with an increase in frequency due to the use of lossy FR-4 substrate.

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. Table 3. Bandwidth of two ports.
where s t (t) and s r (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.

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 (ρ e ) is calculated by using Eq. (4) [32]. The calculated values of ECC are plotted in Figure 13. 1 À S 11 j j 2 þ S 21 j j 2 1 À S 22 j j 2 þ S 12 j j 2 (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].  Table 5. System fidelity factor for four configurations of the designed antenna.
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.
where XPR represents the cross-polarization ratio, G θ and G φ are the θand φcomponents of the antenna power gain patterns and P θ and P φ are the θand 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.  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.
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].  where ψ R is the correlation matrix of the receiving antenna and is expressed mathematically as 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.

Conclusion
A compact third iteration fractal antenna with notch-loaded ground plane for UWB applications is investigated and analysed. By using orthogonal arrangement of two antenna elements, polarization diversity performance is achieved. The designed antenna has an impedance bandwidth of 4.7-19.4 GHz, isolation of more than 15 dB, a size miniaturization up to 92% over previously reported structures and good diversity performance parameters values like ECC < 0.005, almost constant DG = 10 and channel capacity loss of less than 0.3 b/s/Hz which makes it suitable for UWB polarization applications in future wireless communication systems to mitigate the multipath fading.