INTRODUCTION
Over the past few years, the advancement in ultra-wideband (UWB) radio technology has played a significant role in the wireless telecommunication industry to fulfill the escalating needs of large bandwidth with high speed of data transfer at a low cost and low energy consumption [1]. In 2002, the Federal Communication Commission (FCC) has allocated the usage of unlicensed radio spectrum from 3.1-10.6 GHz (with a fractional bandwidth of 109.5% at 6.85 GHz center frequency) for commercial UWB applications [2]. Apart from the admirable properties of UWB technology, conventional UWB radio systems suffer from the problem of co-channel fading and interference due to multipath wave propagation from the transmitter to the receiver end. To curb the adverse effects of multipath fading, the UWB devices are designed with multiple-input multiple-output (MIMO) wireless technology which multiplies the capacity of radio channel using multiple antennas at transmitter and receiver. Equation (1) shows the linear relationship between the capacity and signal to noise ratio (SNR) of the MIMO antenna system.
\(C=B\left[\log_{2}\det\left(I_{\text{Nr}}+\frac{E_{t}}{\sigma_{n}^{2}+N_{t}}\right)\text{H.}H^{H}\right]\)(1)
where B, INr, Et, σn2, Nt, H and HH is the channel bandwidth, identity matrix, total input power, noise power, number of transmitter antennas, channel matrix and the hermitian transpose of the channel matrix respectively [3].
The integration of UWB-MIMO technologies has become an essential part of modern wireless systems to achieve a high data rate (about 1Gbps), superior radio link reliability, broad communication range and little interference in a rich multipath environment [4]. The physical size constraints of the portable and handheld gadgets pose a challenge to the antenna designers to develop small-sized and low-profile MIMO antennas. To meet these specifications, microstrip patch antenna (MPA) is a suitable choice due to its innate benefits of light-weight, simplicity, less cost, mechanically robust and planar/non-planar surface conformity [5]. For modeling compact user equipment, the inter-element spacing in the MIMO configuration is reduced which in turn degrades the array performance due to increased mutual coupling and alters the radiation pattern of actively radiating elements. Therefore, it is favored to incorporate fractal geometries in MPAs to achieve the desired compactness and multiband/wideband operation in a given restricted area due to its inherent self-similar, self-affine and space-filling characteristics [6]. Also, the combination of defected ground structure (DGS) approach with fractal MIMO antennas helps in achieving the desired size reduction, improved operational bandwidth and reduced mutual coupling between the actively radiating patches [7].
In past, researchers have reported many fractal geometries such as Sierpinski gasket [8], Pythagorean tree [9], Hilbert curve [10], Minkowski [11], etc. for designing MIMO antennas with the ultimate goal to achieve miniaturization and multiband/wideband frequency response. All the previously designed fractal MIMO antennas [8-11] had larger dimensions, less port-to-port isolation and were employed for multiband wireless systems. Based on the literature review, the primary objective of this article is to design, simulate and experimentally test a miniaturized fractal MPA array for high bandwidth and good diversity performance to support high data rate portable UWB systems. In this article, a Koch curve fractal (up to 2nd order of iteration) semi-circular antenna array with the DGS technique is proposed. The proposed fractal array is designed on a commercially available FR-4 substrate with relative permittivity (εr), loss tangent (tan δ) and height (ht) of 4.4, 0.024 and 1.57 mm respectively. The designing and simulation of the proposed fractal array is carried out in time domain solver of computer simulation tool microwave studio version 18 (CST MWS V’18) software with open boundary conditions. The proposed fractal MPA array covers the simulated frequency band from 4.395-10.184 GHz (79.4 % fractional bandwidth) with a peak return loss of -54.5 dB (at 9.4 GHz frequency) and isolation ≤ -16.8 dB. To justify the performance of the proposed fractal array for practical applications, it is fabricated (using photolithography process) and experimentally tested for S-parameters (S11, S22, S21, S12) using a vector network analyzer (VNA). The diversity performance parameters are computed using simulated and measured S-parameters which are found to lie within their acceptable limits.
ANTENNA GEOMETRY AND PARAMETRIC ANALYSIS
Figure 1 (a, b) shows the geometry of a dual-port semi-circular MPA array with Koch curve fractals and a minimized ground plane with DGS for MIMO implementation in UWB radio systems. The proposed fractal array is modeled on a low-cost FR-4 substrate (εr = 4.4, tan δ = 0.024 and ht = 1.57 mm) with the overall array dimensions of 30.5 × 47 mm2. As shown in Figure 1(a), the upper FR-4 substrate layer consists of two semi-circular radiating patches (copper), each joined with Koch curve fractal (up to 2nd order of iteration) on its upper edge. The separation distance between the fractal radiators is kept as λ/2 (21.2 mm). The optimized parametric values of the proposed fractal array are mentioned in Table 1. The semi-circular patches are designed for high resonating frequency where the radius of each semi-circle is calculated by Equation (2,3).
\(r=\ \frac{92\times 10^{9}}{f_{r}\sqrt{\varepsilon_{\text{eff}}}}\)(2)
\(\varepsilon_{\text{eff}}\approx\frac{\varepsilon_{r}+1}{2}\) (3)
where r, fr εr and εeffis the radius of the semi-circle, resonating frequency (GHz), the relative permittivity of the FR-4 substrate and effective dielectric constant of FR-4 substrate respectively [12].
The proposed MSA array is fed using two microstrip transmission lines with 50 Ω characteristic impedance (Zo). To realize the desirable matching performance between the radiating patch and microstrip line, the feedline width (b) is chosen according to the Equation (4,5) [5].
\(Z_{O}=\ \frac{120\pi}{\sqrt{\varepsilon_{\text{eff}}}\ \left[\frac{b}{h_{t}}+1.393+0.667ln\left(\frac{b}{h_{t}}+1.444\right)\right]}\), for \(\frac{b}{h_{t}}>1\) (4)\(\varepsilon_{\text{eff}}=\ \frac{\left(\varepsilon_{r}+1\right)}{2}+\ \frac{\left(\varepsilon_{r}-1\right)}{2}\left(1+\frac{12h_{t}}{b}\right)^{-1/2}\)(5)
A stub is added at the bottom of the feedline to achieve a wideband response with an improved impedance matching characteristic. The length of the stub is calculated using Equation 6 [4].
\(v=\frac{c}{2f_{r}\sqrt{\varepsilon_{\text{eff}}}}\) (6)
The recursive procedure followed to reach the 2ndorder of iteration of the Koch curve fractal is shown in Figure 1 (c). To construct the Koch curve fractal, initially, a straight line of length ‘l’ is considered (0th order of iteration). The length ‘l’ is further cut into three equal segments (each of length ‘l/3’) where the central segment is replaced by the two other segments of an equilateral triangle (each with length ‘l/3’) resulting in the 1st order of iteration. This process is iterated recursively to form the higher order of iterations. The self-similar repetitions of the proposed Koch curve fractal can be generated by iterated function system (IFS) approach, defined by generalized matrix Equation (7) using the set of affine linear transformations ‘W’.
\(W\par \begin{bmatrix}x\\ y\\ \end{bmatrix}=\par \begin{bmatrix}a&b\\ c&d\\ \end{bmatrix}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}+\par \begin{bmatrix}e\\ f\\ \end{bmatrix}\) (7)
where the variables ‘a’, ‘b’, ‘c’ and ‘d’ deals with rotation (θ) and scaling (s) operations and variables ‘e’ and ‘f’ deals with translations.
Using a=cos θ/s, b = -sin θ/s, c = sin θ/s and d = cos θ/s where s = 1/3 and θ = 60˚ for two segments of equilateral triangle (one in clockwise, other in anticlockwise direction), the required IFS transformation for Koch curve fractal is calculated by Equations (8-11) [13].
\(W_{1}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}=\par \begin{bmatrix}1/3&0\\ 0&1/3\\ \end{bmatrix}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}+\par \begin{bmatrix}0\\ 0\\ \end{bmatrix}\) for θ = 0˚ (8)
\(W_{2}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}=\par \begin{bmatrix}1/6&-\sqrt{3}/6\\ \sqrt{3}/6&1/6\\ \end{bmatrix}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}+\par \begin{bmatrix}1/3\\ 0\\ \end{bmatrix}\) for θ = 60˚ (9)
\(W_{3}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}=\par \begin{bmatrix}1/6&\sqrt{3}/6\\ -\sqrt{3}/6&1/6\\ \end{bmatrix}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}+\par \begin{bmatrix}1/2\\ \sqrt{3}/6\\ \end{bmatrix}\) for θ = -60˚ (10)
\(W_{4}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}=\par \begin{bmatrix}1/3&0\\ 0&1/3\\ \end{bmatrix}\par \begin{bmatrix}x\\ y\\ \end{bmatrix}+\par \begin{bmatrix}2/3\\ 0\\ \end{bmatrix}\) for θ = 0˚ (11)
The self-similarity dimension (D) of the proposed Koch curve fractal is calculated using Equation 12 [6]. In the proposed fractal configuration, four new non-overlapping copies (N) are generated with the scaling factor (s) of 1/3, resulting in a fractal dimension (D) of 1.262.
\(D=\frac{\log{(N)}}{\log{(1/s)}}\) (12)
As shown in Figure 1 (b), the lower FR-4 substrate layer consists of a reduced ground with DGS. A funnel-shaped decoupling structure extends vertically (at an angle 90˚) from the reduced ground plane. It obstructs the steady flow of current between the two radiating patches and hence minimizes the effect of cross-coupling. To further improve the isolation performance, two rectangular (each with dimensions 5 × 2.5) and L-shaped (11.6 × 0.5) slots, each with a length of λg/2 (where λg is the guided wavelength), is etched from the upper edge of the reduced ground. Figure 2 and Figure 4 show the geometrical variations in the patch and ground plane configuration of the proposed fractal array respectively for designing the final optimized geometry. The corresponding improvement in impedance bandwidth (S11/S22) and isolation (S21/S12) performance for variations in patch and ground plane geometries is depicted in Figure 3 and Figure 5 respectively.