**2.1. Specific parameters for UWB antennas**

In UWB systems, the previous fundamental and classical parameters must be considered in designing antennas but there are more challenges to monitor them and some additional parameters.

**Bandwidth** - First of all, what distinguishes a UWB antenna from other antennas is its ultra wide frequency bandwidth. According to the FCC's definition, a suitable UWB antenna should be able to yield an absolute bandwidth of not less than 500 MHz or a fractional bandwidth of at least 0.2. Moreover, UWB antenna must be operable and must have stable impedance matching over the entire 3.1-10.6 GHz frequency range in the case of I-UWB following the FCC defined spectral mask. Sometimes, it is also demanded (e.g., in Europe) that the UWB antennas should provide the band-rejected characteristic to coexist with other narrowband devices and services occupying the same operational band [11].

**Radiation Pattern** - Directional or omni-directional radiation properties are needed depending on the practical application. Omni-directional patterns are normally desirable in mobile and hand-held systems. For radar systems and other directional systems where high gain is desired, directional radiation characteristics are preferred. High radiation efficiency is usually required for antennas but it is imperative and essential for an ultra wideband antenna because the transmit power spectral density is excessively low. Therefore, any excessive losses incurred by the antenna could potentially compromise the functionality of the system.

**Size and Cost** - A suitable antenna needs to be small and of light weight enough to be compatible to the application. As we are projecting UWB for the applications that include

especially mobile and portable devices, therefore it is highly desirable that the antenna should feature low profile and compatibility for integration with printed circuit board (PCB).

Multiple-Input Multiple-Output Antennas for Ultra Wideband Communications 213

In summary for the applications of portable devices, general specifications required to

Gain Smooth in the band of interest Phase Linear ; nearly constant group delay

Physical profile Small, compact, planar

Like the case of UWB, there are also some additional parameters other than the fundamental

**Mutual Coupling and Isolation** - In MIMO applications, the signals transmitted by multiple antenna elements are generally supposed to be independent or uncorrelated. But in reality, the current induced on one antenna produces a voltage at the terminals of nearby elements, termed as mutual coupling [13]. It means there is always mutual coupling present between nearby antenna elements. However, for MIMO applications, the mutual coupling should be minimized to as low value as possible. In a contradictory way, it should be noted that it is also studied that mutual coupling can help to reduce the correlation between the different channel coefficients in nearby placed antenna elements scenario, thus escalating the capacity [14]. This is an important issue for the antenna community. In a general way the coupling

The port-to-port isolation is defined as the transmission of power between two of the input ports of the multiport antenna under test. It is characterized by |���| parameter. It must be

��������� � ��������|���|

In MIMO systems, to maximize the energy radiated by an antenna, it should be ensured that negligible amount of transmitted energy is lost into the ports of other antennas terminated by the matched impedances. In other words, MIMO systems require the |���| to be minimized to as low value as possible as isolation is directly related to the antenna efficiency. A lot of research has been done on the reduction of mutual coupling and the enhancement of the isolation. It is worth mentioning that the mutual coupling is characterized most of the times by the isolation in the literature. However, in [16], it is stated that isolation is not the exact representation of mutual coupling, as it is possible that there is very good isolation but it is not necessary for mutual coupling to be low in this case. Hence, to evaluate the mutual coupling, it is better to observe the surface current distributions on the non-excited radiating element, when nearby radiating element, is excited. Although the

� (2)

**Table 1.** Characteristics of UWB antenna for portable devices.

parameters to be taken into account while designing MIMO antennas.

has an adverse effect and mutual coupling has to minimize [15].

noted that isolation is a positive quantity and is given as

**2.2. Specific parameters for MIMO antennas** 

design UWB antennas under the FCC regulations can be summarized in Table 1.

Parameter Value VSWR bandwidth 3.1-10.6 GHz Radiation pattern Omnidirectional Radiation efficiency High (> 70%)

Specific parameters to be required to characterize UWB antennas are now described.

**Compliance with Spectral Masks** - A good design of UWB antenna should be optimal for the performance of overall system. To avoid the possible inband/outband interference between the UWB systems and existing electronic systems, the antenna should be designed such that the overall device (antenna and RF front end) complies with the mandatory power emission mask given by the FCC or other regulatory bodies. The emission limits will be determined by both the selection of source pulse and design of antennas in UWB systems.

**Impulse Response** - As the origin of UWB technology stems from time-domain electromagnetics, therefore UWB antenna is required to achieve good time domain characteristics (i.e., good impulse response). The idea is simply to characterize the LTI (Linear Time Invariant) system by its response to an impulsive excitation instead of amplitude and phase and measurements versus frequency (i.e., swept frequency response). For the narrowband case, it is approximated that an antenna has same performance over the entire bandwidth and the basic parameters, such as gain and return loss, have little variation across the operational band. In contrast, I-UWB systems often employ extremely short pulses for data transmission. In other words, enormous bandwidth has been occupied, thus the antenna can't be treated as a "spot filter" any more but a "band-pass filter". In this case, the antenna imposes more significant impacts on the input signal. As a result, a good time domain performance (i.e., minimum pulse distortion in the received waveform) is a primary concern of a suitable UWB antenna because the signal is the carrier of useful information [12]. Therefore, it is indispensable and important to study the antenna's characteristics in time domain.

**Group Delay** - It is an important parameter that represents the degree of distortion of UWB signal. Group delay is a measure of the slope of the transmission phase response. The linear portion of the phase response is converted to a constant value and deviation from linear phase are transformed into deviations from constant group delay. The variations in group delay cause signal distortion, just as deviations from linear phase cause distortion. It can be given as

$$group\ delay = -\frac{\Delta \phi}{\Delta \omega} \tag{1}$$

where ߮ is the total phase shift in radians, and ߱ is the angular frequency in radians per unit time, equal to ʹߨ݂, where ݂ is the frequency. The group delay variations induced by the radiation pattern of the antenna will affect the overall receiver system performance, since it can bring relatively large timing errors. An antenna gain versus frequency without nulls, means a linear phase response, hence a constant group delay.

In summary for the applications of portable devices, general specifications required to design UWB antennas under the FCC regulations can be summarized in Table 1.


**Table 1.** Characteristics of UWB antenna for portable devices.

## **2.2. Specific parameters for MIMO antennas**

212 Ultra Wideband – Current Status and Future Trends

(PCB).

systems.

time domain.

given as

especially mobile and portable devices, therefore it is highly desirable that the antenna should feature low profile and compatibility for integration with printed circuit board

**Compliance with Spectral Masks** - A good design of UWB antenna should be optimal for the performance of overall system. To avoid the possible inband/outband interference between the UWB systems and existing electronic systems, the antenna should be designed such that the overall device (antenna and RF front end) complies with the mandatory power emission mask given by the FCC or other regulatory bodies. The emission limits will be determined by both the selection of source pulse and design of antennas in UWB

**Impulse Response** - As the origin of UWB technology stems from time-domain electromagnetics, therefore UWB antenna is required to achieve good time domain characteristics (i.e., good impulse response). The idea is simply to characterize the LTI (Linear Time Invariant) system by its response to an impulsive excitation instead of amplitude and phase and measurements versus frequency (i.e., swept frequency response). For the narrowband case, it is approximated that an antenna has same performance over the entire bandwidth and the basic parameters, such as gain and return loss, have little variation across the operational band. In contrast, I-UWB systems often employ extremely short pulses for data transmission. In other words, enormous bandwidth has been occupied, thus the antenna can't be treated as a "spot filter" any more but a "band-pass filter". In this case, the antenna imposes more significant impacts on the input signal. As a result, a good time domain performance (i.e., minimum pulse distortion in the received waveform) is a primary concern of a suitable UWB antenna because the signal is the carrier of useful information [12]. Therefore, it is indispensable and important to study the antenna's characteristics in

**Group Delay** - It is an important parameter that represents the degree of distortion of UWB signal. Group delay is a measure of the slope of the transmission phase response. The linear portion of the phase response is converted to a constant value and deviation from linear phase are transformed into deviations from constant group delay. The variations in group delay cause signal distortion, just as deviations from linear phase cause distortion. It can be

݃ݑݎ݈݀݁ܽݕ ൌ െ οఝ

where ߮ is the total phase shift in radians, and ߱ is the angular frequency in radians per unit time, equal to ʹߨ݂, where ݂ is the frequency. The group delay variations induced by the radiation pattern of the antenna will affect the overall receiver system performance, since it can bring relatively large timing errors. An antenna gain versus frequency without nulls,

means a linear phase response, hence a constant group delay.

οఠ (1)

Specific parameters to be required to characterize UWB antennas are now described.

Like the case of UWB, there are also some additional parameters other than the fundamental parameters to be taken into account while designing MIMO antennas.

**Mutual Coupling and Isolation** - In MIMO applications, the signals transmitted by multiple antenna elements are generally supposed to be independent or uncorrelated. But in reality, the current induced on one antenna produces a voltage at the terminals of nearby elements, termed as mutual coupling [13]. It means there is always mutual coupling present between nearby antenna elements. However, for MIMO applications, the mutual coupling should be minimized to as low value as possible. In a contradictory way, it should be noted that it is also studied that mutual coupling can help to reduce the correlation between the different channel coefficients in nearby placed antenna elements scenario, thus escalating the capacity [14]. This is an important issue for the antenna community. In a general way the coupling has an adverse effect and mutual coupling has to minimize [15].

The port-to-port isolation is defined as the transmission of power between two of the input ports of the multiport antenna under test. It is characterized by |���| parameter. It must be noted that isolation is a positive quantity and is given as

$$Isolation = -10\log\_{10}|\mathbb{S}\_{21}|^2\tag{2}$$

In MIMO systems, to maximize the energy radiated by an antenna, it should be ensured that negligible amount of transmitted energy is lost into the ports of other antennas terminated by the matched impedances. In other words, MIMO systems require the |���| to be minimized to as low value as possible as isolation is directly related to the antenna efficiency. A lot of research has been done on the reduction of mutual coupling and the enhancement of the isolation. It is worth mentioning that the mutual coupling is characterized most of the times by the isolation in the literature. However, in [16], it is stated that isolation is not the exact representation of mutual coupling, as it is possible that there is very good isolation but it is not necessary for mutual coupling to be low in this case. Hence, to evaluate the mutual coupling, it is better to observe the surface current distributions on the non-excited radiating element, when nearby radiating element, is excited. Although the

$$MEG = \int\_0^{2\pi} \int\_0^{\pi} \left( \frac{XPR}{1 + XPR} G\_\theta(\theta, \varphi) P\_\theta(\theta, \varphi) + \frac{1}{1 + XPR} G\_\varphi(\theta, \varphi) P\_\varphi(\theta, \varphi) \right) \sin\theta d\theta d\varphi \tag{3}$$

$$XPR = \frac{\int\_0^{2\pi} \int\_0^{\pi} P\_\theta(\theta, \varphi) \sin \theta \, d\theta \, d\varphi}{\int\_0^{2\pi} \int\_0^{\pi} P\_\varphi(\theta, \varphi) \sin \theta \, d\theta \, d\varphi} \tag{4}$$

$$\int\_0^{2\pi} \int\_0^{\pi} P\_\theta(\theta, \varphi) \sin \theta d\theta d\varphi = 1\tag{5}$$

$$\int\_0^{2\pi} \int\_0^{\pi} \left( G\_{\theta}(\theta, \varphi) + G\_{\varphi}(\theta, \varphi) \right) \sin \theta \, d\theta \, d\varphi = 4\pi \tag{6}$$

$$MEG = \int\_0^{2\pi} \int\_0^{\pi} \left( \frac{1}{1+1} \frac{1}{4\pi} G\_\theta(\theta, \varphi) + \frac{1}{1+1} \frac{1}{4\pi} G\_\varphi(\theta, \varphi) \right) \sin\theta \,d\theta \,d\varphi = \frac{1}{2} \tag{7}$$

$$\rho\_c = \frac{\int\_0^{2\pi} \int\_0^{\pi} \left[ \chi \mathcal{P} \mathcal{R} E\_{\theta k}(\theta, \varphi) E\_{\theta l}^\*(\theta, \varphi) P\_\theta(\theta, \varphi) + E\_{\theta k}(\theta, \varphi) E\_{\varphi l}^\*(\theta, \varphi) P\_\varphi(\theta, \varphi) \right] \sin \theta d\theta d\varphi}{\sqrt{\sigma\_k^2 \sigma\_l^2}} \tag{8}$$

$$\rho\_c = \int\_0^{2\pi} \int\_0^{\pi} \left( XPRG\_{\theta k}(\theta, \varphi) P\_\theta(\theta, \varphi) + G\_{\varphi k}(\theta, \varphi) P\_\varphi(\theta, \varphi) \right) \tag{9}$$

$$G\_{\theta k}(\theta,\varphi) = E\_{\theta k}(\theta,\varphi)E\_{\theta l}^\*(\theta,\varphi) \tag{10}$$

$$G\_{\phi k}(\theta,\varphi) = E\_{\phi k}(\theta,\varphi)E\_{ol}^\*(\theta,\varphi) \tag{11}$$

$$
\rho\_{\mathbf{e}} = |\rho\_{\mathbf{c}}|^2 \tag{12}
$$

$$\rho\_e = \left| \frac{S\_{11}^\* S\_{12} + S\_{21}^\* S\_{22}}{\sqrt{1 - |S\_{11}|^2 - |S\_{21}|^2 \sqrt{1 - |S\_{22}|^2 - |S\_{12}|^2}}} \right|^2 \tag{13}$$


$$DG = \frac{(\text{SNR})\_c}{(\text{SNR})\_r} \tag{14}$$


$$DG = 10\sqrt{1 - |\rho|^2} \tag{15}$$

$$DG(dB) = 5.71 \exp\{-0.87\sqrt{\rho\_e} - 0.16\Delta\} \tag{16}$$

$$DG(dB) = -8.98 + 15.22 \exp\{-0.20 \sqrt{\rho\_e} - 0.04\Delta\} \tag{17}$$

$$DG(dB) = 7.14 \exp\{-0.59\sqrt{\rho\_e} - 0.11\Delta\} \tag{18}$$

$$
\Gamma\_a^t = \frac{available\ power - radiated\ power}{available\ power} \tag{19}
$$

$$
\Gamma\_a^t = \sqrt{\Sigma\_{l=1}^N |b\_l|^2} \Big/ \sqrt{\Sigma\_{l=1}^N |a\_l|^2} \tag{20}
$$

$$
\begin{pmatrix} b\_1 \\ b\_2 \end{pmatrix} = \begin{pmatrix} \mathbb{S}\_{11} & \mathbb{S}\_{12} \\ \mathbb{S}\_{21} & \mathbb{S}\_{22} \end{pmatrix} \begin{pmatrix} a\_1 \\ a\_2 \end{pmatrix} \tag{21}
$$

$$b\_1 = \mathbf{s}\_{11}a\_1 + \mathbf{s}\_{12}a\_2 = \mathbf{s}\_{11}a\_0e^{i\theta\_1} + \mathbf{s}\_{12}a\_0e^{i\theta\_2} = a\_1(\mathbf{s}\_{11} + \mathbf{s}\_{12}e^{i\theta})\tag{22}$$

$$b\_2 = \mathbf{s}\_{21}a\_1 + \mathbf{s}\_{22}a\_2 = \mathbf{s}\_{21}a\_0e^{l\theta\_1} + \mathbf{s}\_{22}a\_0e^{l\theta\_2} = a\_1\left(\mathbf{s}\_{21} + \mathbf{s}\_{22}e^{l\theta}\right) \tag{23}$$

$$\Gamma\_a^{\mathfrak{f}} = \sqrt{\frac{\left| \mathbf{S}\_{11} + \mathbf{S}\_{12}e^{\iota\theta} \right|^2 + \left| \mathbf{S}\_{21} + \mathbf{S}\_{22}e^{\iota\theta} \right|^2}{2}} \tag{24}$$

Multiple-Input Multiple-Output Antennas for Ultra Wideband Communications 219

(��|���|��|���|�)� (25)

� that takes into account

� − |���|

**3.1. Using Decoupling and Matching Networks (DMN)** 

for a reciprocal and symmetrical antenna system:

achieved by using a lossless decoupling network.

noticed.

of view, it is also important to consider the value of 1 − |���|

**Narrowband MIMO systems** - The achievement of low mutual coupling and good isolation using decoupling and matching networks is well explained by S. Dossche et al. in [28]. As earlier described in previous section, the envelope correlation can be calculated from the farfield radiation patterns as well as from the scattering parameters of the antenna system, assuming uniform propagation channel. The envelope correlation can be written as in (13)

�� <sup>=</sup> |�������

From above equation, it is clear that by changing the magnitude and phase of either ��� or ���, the correlation between the two antennas can be decreased. In practice, this can be achieved by using a matching network for connecting the antennas. From the system point

the effective radiated power by the antenna system, and it is maximized by minimizing |���| and |���|. Thus, two matching networks can be used at both sides to minimize ��� and ��� while a decoupling network can be used to make ��� in quadrature with ��� i.e., ��� is pure imaginary and thus the real part of mutual impedance ��� is equal to zero. This can be

Also, Weber et al. have used passive DMNs and studied them in detail [29]. In this context, the method for derivation of the admittance matrices of the DMN is explained. An important feature of this method is the formation of predefined orthogonal system port patterns. The admittance matrix can be converted to an actual circuit layout of the DMN in terms of capacitors and inductors. Recently, in [30], hybrid circuit is used as decorrelation circuit. This circuit provides a straightforward, frequency-independent, and feasible solution if the elements are symmetrically placed. This hybrid circuit introduces a 180° phase shift between the signals from the two antenna branches. A little variant of this technique can be observed in [31] where several parasitic elements have been employed between the radiating elements to reduce the isolation. The reduction is dependent on the length and number of the parasitic elements. At least 10 dB improvement, in isolation is

**UWB-MIMO Systems** - It can be noticed that lot of work has been presented to get better isolation using DMNs. However, this technique is not tractable for UWB-MIMO systems. The matching networks to design and to realize for multiband, wideband and ultra wideband MIMO systems are enough difficult. Thus, this technique is not employed yet for

As noted by Sievenpiper [32], an electromagnetic band gap (EBG) structure behaves as a high impedance surface. This structure consists of an array of metal protrusions on a flat metal sheet. They can be visualized as mushrooms or thumbtacks protruding from the

UWB-MIMO systems in the literature to the best of our knowledge.

**3.2. Using Electromagnetic Band Gap (EBG) structures** 

<sup>∗</sup> ����| �

The TARC of MIMO antenna is calculated by applying different combinations of excitation signals to each port. There is no need to define the TARC as a complex number since the phase reference plane does not have any physical meaning for a multiport antenna. The TARC is a real number between zero and one. When the value of the TARC is equal to zero, all the delivered power is radiated and when it is equal to one, all the power is either reflected back or goes to the other ports.

## **2.3. Summary on UWB MIMO antenna characteristics**

In context of UWB where the whole band approved by FCC is required to be covered in one shot, the design of antenna becomes challenging enough. The characteristics of the antennas are required to be stable for the wide frequency band. Moreover, time domain measurements like dispersion and group delay become significant in addition to conventional frequency domain characteristics. Furthermore, the development of future UWB-MIMO communication systems brings more challenges for the antenna design. MIMO antennas are required to be characterized for mutual coupling, correlation and diversity gain. However, a detailed study on characterization of MIMO antennas for UWB is among the current hot topics of research. Also, the design of UWB-MIMO antenna system is always confronted with the same constraints like cost, size, ease of fabrication and integration with other circuits as in the case of single antenna design. Having the specific parameters used essentially for the analysis of UWB and MIMO antennas, the current research orientations with a state of the art are now detailed.
