7.1.1 Input Impedance and Matching

Input impedance of the antenna (Z_a) is defined as the impedance presented by the antenna at its terminals as shown in Figure 7.1. It is a complex number and is equal to the ratio between input voltage (V_in) and current (I_in) at its terminals. Mathematically,

(7.1)

Where R_a and X_a is the frequency dependent antenna resistance and reactance, respectively. The antenna resistance, R_a, consists of two components: radiation resistance (R_r) that accounts for the resistance of the antenna dissipating the power and causing radiation of equal amount and loss resistance (R_L) from the conductor and dielectric losses. Values of 50 and 75 Ω are typically used for the characteristic impedance (Z_o) of RF test equipment, connectors and cables for the sake of standardization. The input impedance of the antennas is, therefore, required to carry the same value in practical designs.

The antenna acts just as a load to a transmission line from the circuit point of view making impedance matching an utmost necessity in order to minimize reflections and maximize power transmission. Reflection coefficient (S₁₁), voltage standing wave ratio (VSWR) and return loss (RL), as a function of frequency, are used to assess the impedance matching of the antenna.

• Reflection coefficient:
  (7.2)
• Return loss:
  (7.3)
• VSWR:
  (7.4)

Commonly, an antenna is required to exhibit a reflection coefficient of < −10 dB or VSWR of < 2. These values correspond to a 11.07% of reflected power and 0.51 dB of transmission loss [1]. For mobile phone antennas, a reflection coefficient of < −6 dB or VSWR of < 3 is also usually accepted.

7.1.2 Bandwidth

Impedance bandwidth of the antenna can be defined as the frequency range over which 90% of the incident power is delivered to the antenna corresponding to the reflection coefficient value of < −10 dB and VSWR < 2:1. The absolute impedance bandwidth of the antenna is calculated as the difference between upper and lower frequencies at which these criteria are met as illustrated in Figure 7.2. Alternatively, the fractional impedance bandwidth is calculated as the percentage of the difference between the upper and lower frequency divided by the centre frequency of bandwidth, as follows:

(7.5)

7.1.3 Radiation Pattern

The radiation pattern is a graphical representation of the radiation properties of an antenna as a function of spatial coordinates. It is a plot of the radiated field or power with respect to the angle at a fixed distance in the farfield region of the antenna. For an electrically small antenna with a size D, the farfield distance r can be calculated as:

(7.6)

Where λ represents the wavelength.

Spherical coordinates are typically used in antenna measurements. The 3D radiation pattern efficiently illustrates the radiated field distribution as a function of angle θ and ϕ as shown in Figure 7.3. However, measurement of 3D pattern requires sophisticated equipment. Therefore, the 2D radiation patterns in the elevation plane measuring θ with a fixed ϕ at 0^o azimuth plane measuring θ with a fixed ϕ at 90^o are the most useful, as illustrated in Figure 7.4.

The radiation pattern provides very useful information about the antenna operation. A scalar radiation pattern of an antenna is illustrated in Figure 7.5 [2]. The major features of an antennas’s radiation pattern include:

• Major lobe: The angular region containing the direction of maximum radiation. For a symmetrical main beam, central direction is termed the boresight of an antenna.
• Minor lobes: Any lobe apart from the main lobe.
• Back lobe: A radiation lobe that is directly opposite to the main lobe.
• Null: Angle at which the radiation pattern is zero.
• Half‐power beamwidth (HPBW): The angle subtended by the half‐power points of the main beam, also called 3 dB beamwidth.

7.1.4 Directivity and Gain

Directivity (D) is a quantitative measure of the ability of the antenna to concentrate radiated power in a particular direction. It is the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions [3] and can be calculated as:

(7.7)

where P_rad is the total radiated power and U is the radiation intensity per unit solid angle.

Gain (G) is defined as the ratio of the radiation intensity in a given direction from the antenna to the total input power accepted by the antenna divided by 4π. If the direction is not specified, the direction of maximum radiation is implied. It is expressed relative to a lossless isotropic and expressed in terms of dBi. Mathematically, it can be written as:

(7.8)

where P_in is the total input power accepted by the antenna and U is the radiation intensity per unit solid angle. Gain does not include mismatch losses.

7.1.5 Efficiency

Total antenna efficiency defines the losses taking place during the process of converting the input power to the radiated power.

(7.9)

where η_radiation is the radiation efficiency and η_mismatch is the mismatch efficiency.

Radiation efficiency takes into account the conduction and dielectric losses of the antenna. It can be calculated as:

(7.10)

Comparing Equations 7.7, 7.8 and 7.10 enables us to relate the antenna gain with the directivity as follows:

(7.11)

Mismatch efficiency is also termed as reflection efficiency. It accounts for the power loss due to impedance mismatch and can be expressed as the ratio of the input power accepted by the antenna and the power supplied by the source (P_s):

(7.12)

Ideally, the feed line is required to have a perfect match with the antenna so no reflections take place making S₁₁ equal zero and results in a 100% matching efficiency. However, it is practically not possible due to material limitations.

7.1.6 Polarization

A radio wave propagating over a long distance takes the form of a plane wave. A typical plane electromagnetic wave has in‐phase electric and magnetic fields of constant amplitude. They are orthogonal to each other as well as to the direction of propagation, z, as illustrated in Figure 7.6.

Polarization can be described as the property of the electromagnetic waves that defines the directional variation of electric field vector E. The electric field vector of the wave propagating in the z direction can be expressed as:

(7.13)

where A and B represent the amplitudes of the electric field components in the x and y directions, respectively.

There are three possibilities for polarization of the electromagnetic wave. A wave having A = 0 or B = 0 carries a linear polarization. If A = B, the wave becomes circularly polarized. If A ≠ 0 and B ≠ 0 and A ≠ B, the wave tends to have elliptical polarization.

Circular and elliptical polarizations can be classified as Right Hand Polarization (RHP) and Left Hand Polarization (LHP). An RHP wave is defined as if the right hand thumb points to the direction of propagation, while the fingers curl along the direction of electric field vector rotation. An LHP wave is defined as if the left thumb points in direction of propagation while the fingers curl along the direction of electric field vector rotation. The three possible scenarios of wave polarization are shown in Figure 7.7.

The ratio of amplitudes A to B is called the axial ratio and is used to describe the purity of circular polarization. It is unity (0 dB) for a perfect circular polarized wave.

(7.14)

The antenna polarization is the same as the polarization of its radiating wave. Mixed polarization may be found in many antennas since it has to meet many requirements. Moreover, some applications may also require a pure linearly polarized or circularly polarized antenna; for example, most mobile phone antennas are not purely linearly polarized as they are used to receive signals with mixed polarization. However, the polarization of the antenna needs to be matched with the incoming electromagnetic wave in order to achieve the maximum efficiency of the whole system.

7.2.1 Frequency Bands

Spectrum is a big topic in LTE deployment at the moment. Over 40 frequency bands of operation have been defined in the 3GPP standard to support LTE network deployments. The International Telecommunication Union (ITU), based on the decisions reached at the World Radio Conference, allocates these frequencies. It has been up to the network operators and the regional/national telecommunications authorities to determine what frequencies will be used in practice in each nation.

Some estimates suggest a future in which LTE is deployed in many of the supported bands, possibly enabled by software‐defined radio devices that can easily switch between bands. However, for the time being, most networks and devices are constrained by RF limitations to a limited number of bands.

The frequency bands allocated by the World Radio Conference for LTE are presented in Table 7.1. Some of which have been recently assigned, such as the 2.6 GHz IMT by the ITU to support the so‐called Digital Dividend bands due to the availability from the global switch from analogue to digital television. The LTE standard defines a large number of frequency bands to allow global deployment in a variety of different spectra. This is designed to be bandwidth agnostic, permitting channel bandwidths ranging from 1.4 to 20 MHz [6].

In LTE, there is the paired spectrum that is the Frequency Division Duplex (FDD) mode and the unpaired spectrum that is the Time Division Duplex (TDD) mode. The FDD has both the downlink (DL) and uplink (UL) transmitted simultaneously on different frequencies while the TDD has the downlink and uplink transmitted at different time using the same frequency band. Mostly, the DL uses a higher frequency than UL but in Bands 13, 14, 20 and 24 the UL uses higher frequency than the DL. LTE frequency bands can be categorized into two groups; those that provide coverage and those that provide capacity. In terms of coverage, lower frequencies are needed for their propagation characteristics that accommodate larger cell sizes and better building penetration for indoor coverage. For the capacity, higher frequencies are used; they tend to include wider spectra and less spectrum fragmentation between different network operators.

To provide a comprehensive nationwide coverage, the network operator needs to use the lower frequency band, for example 700 MHz for broad coverage at a moderate data rate, and a higher frequency band, for example 2600 MHz for capacity/high data rates in a dense urban area where small cell sizes and indoor relays can be utilized. The data rate of LTE must be able to achieve peak download at 100 Mbps and peak upload of 50 Mbps. Many mobile operators are now inculcating multiple frequency bands from the LTE for effective service. In the Samsung A3 released in 2016, the LTE (FDD) Bands 20, 5, 8, 3, 1 and 7 and LTE (TDD) Band 40, LTE (Data) CAT 4 were introduced.

The antenna element needs to be designed such that it can support the device’s operation in the required frequency band. If more than one frequency band is being used by the LTE device, multiple antennas resonating at different frequencies can be used. However, this method becomes trivial when strict size limitations are needed to be adhered with. Use of advanced solutions such as multiband, multimode or reconfigurable antennas turn into a more practical approach in such scenarios [9, 10]. These antennas are discussed in detail in Chapters 8, 9 and 10.

7.2.2 Form Factor and Size Limitation

The sizes of antennas range from micro‐miniature to gigantic. A general proportionality between the antenna size and the wavelength at the resonant frequency exists. An antenna appreciably less than a half wavelength is termed electrically small. As the size of average handheld wireless devices continues to reduce, the space for installing the antenna on the PCB is really limited.

A major technical challenge in the LTE antenna design comes from the limitation of the size and shape of antennas and their integration with other electronic components particularly in portable devices. To tackle this challenge, the antenna designers have to exploit novel solutions that not only meet the size limitations but also offer acceptable impedance matching and radiation characteristics such as space‐saving PIFAs (planar inverted‐F antennas).

7.2.3 Impedance Matching, Directivity, Gain and Efficiency

The LTE antennas are typically designed to have a return loss of better than 10 dB. This corresponds to a VSWR of 2:1 and a reflected power of 11%. In the case of mobile phone applications, a 6 dB return loss or 3:1 VSWR with 25% of the reflected power is also considered acceptable. It is a relatively high level of reflection that reflects the difficulty of achieving a good match over a number of frequency bands with an electrically small antenna.

Often the device aesthetic design takes the priority over electrical considerations to appease the end user. There is no theoretical upper limit on the LTE antenna’s directivity, but it again depends on the intended application. For handset and portable LTE antennas, it is assumed that the small antenna’s directivity is limited by the small dipole and monopole directivities of 1.8 and 4.8 dB, respectively [11].

Practically, the antenna gain has limitations due to the issues related to minimizing the losses within the impedance matching network, achieving maximum radiation efficiency with suitable choice of conductor dimensions and dielectric materials and reducing radiation levels in undesired directions.

While matching the antenna impedance mitigates mismatch loss, there are ohmic loses due to specific implementation of a matching network. These losses reduce the radiation efficiency of the antenna, but ideally they are less than the mismatch losses. The antenna radiation efficiency is generally required to be greater than 50%. It often includes the mismatch loss while occasionally it reflects a figure averaged over each frequency band and depends on the particular requirements of the manufacturer [10].

These requirements may change depending on the usage and mechanical design, especially when a particular design of an LTE device is specified. In this case, the overall efficiency requirement may be relaxed in order to accomplish the bandwidth, which is a strong function of the size of the printed circuit board’s ground plane size.

7.2.4 Directionality

Most portable LTE devices operate in a cluttered environment such as city streets and indoors where the transmitted electromagnetic waves reach the receiving terminal through multipath by going through reflections, refractions and scattering, as illustrated in Figure 7.8. This means that the signal could be arriving at the LTE device from a multitude of different directions and direction‐of‐arrival (DoA) cannot be defined. This scenario requires an antenna with an omni‐directional pattern enabling it to receive the signal from any of these directions and establish the communication link. However, such antennas usually offer limited gain values.

In scenarios where the direction of the incoming radio signal is known, for example a fixed receiving terminal or LOS links, directional antenna solutions improving the radiation in the desired direction and suppressing signals at unwanted angles become practically more viable. These antennas also offer high gain values and low interference to the neighbouring devices. An antenna designer, therefore, has to select the antenna element that suits the intended application best, given the application scenario.

7.2.5 Polarization

In many wireless communications systems where the communications link may be established through multipath, some randomness in the antenna’s polarization properties may be desirable. Ideally, the LTE antennas should have a uniform radiation pattern over an entire upper hemisphere to receive the incoming communications signal efficiently. A good rejection of cross polarization is also required to avoid multipath interference [12, 13]. However, these requirements are difficult to fulfil in portable devices, especially smart phones that are required to allow maximum mobility of the user and flexibility of use with multiple functions such as Wi‐Fi, Bluetooth, digital camera, mobile TV and navigation [14].

In the common scenarios of cluttered environments including indoors and on city streets, Line‐of‐Sight (LOS) signals arriving at the mobile device are weak while the reflected signals may have arbitrary polarizations. Moreover, mobile phones are rarely used in a fixed position and orientation of the antenna is not strictly defined. Furthermore, the antenna suffers from electromagnetic absorptions and shielding of clear sky view in hand‐held positions. Establishing a quick communications link is, therefore, a difficult task in such devices. Use of wide‐beam linearly polarized LTE antennas could help to address the uncertainty of antenna orientation, blockage of LOS signal and clear sky view, as well as losses due to user’s body. Hence, linearly polarized antennas are a preferred choice for mobile terminals as they give better performance compared to the circular and elliptical antennas [15]. Fixed terminals, such as access points, however, can make use of omni‐directional or directional radiation patterns with a choice of circular polarization or linear polarization depending on the location of the access point and intended coverage area. Therefore, antenna designers have to adhere to the required polarization requirements when designing the antenna.

7.2.6 Human Body Effects and Specific Absorption Rate (SAR)

The human body is an inherent part of portable LTE applications. Electromagnetic distortions caused by lossy human body tissues is an important issue to deal with. Performance of the antennas operating in close proximity to the human user is degraded due to losses caused by varying electric properties of human tissues resulting in distortion in radiation pattern, reduction in radiation efficiency and de‐tuning of input impedance [16–19]. The antenna designers have to consider the potential electromagnetic interaction of the LTE antennas with the human user and its aftermaths in order to ensure overall system reliability and robustness.

Moreover, the fears for the safety of the human user have resulted in standardization of maximum levels of expositions of human tissues to electromagnetic radiations emitted by the portable antennas defined in terms of Specific Absorption Rate (SAR) [20–23].

The SAR is used as a figure of merit to define the level of safety of human body exposure to the electromagnetic devices including antennas. Average absorption of RF energy over a volume is termed volume‐averaged SAR and can be calculated as follows:

(7.15)

where σ is conductivity of the tissue in S/m, ρ is mass density of the tissue in kg/m³ and E is total RMS electric field strength in V/m.

Different standardization bodies use certain SAR limits for wireless devices to ensure the safety of the user in terms of maximum absorption in a 1 or 10 g cube anywhere in a given volume, termed the spatial‐peak SAR. The US and a number of other countries follow The Federal Communications Commission’s (FCC) recommended SAR limit of 1.6 W/kg for a 1 g volume‐averaged SAR. European countries have adopted an SAR limit of 2 W/kg for 10 g volume averaged SAR as recommended by the International Commission on Non‐Ionising Radiation Protection (ICNIRP) and The Institute of Electrical and Electronics Engineers (IEEE). The FCC limit is more stringent because it is volume‐averaged over a smaller amount of tissue. The whole body averaged SAR limit is 0.08 W/kg for both the FCC and ICNIRP/IEEE [20, 21, 24].

LTE devices, especially phone and laptop manufacturers, are required to ensure that their devices comply with these objective limits for safe exposure of users. The antenna designers have to test their designs against these levels and make sure that they are not posing any health hazards.

7.2.7 Multiple Input Multiple Output (MIMO)

Multiple Input Multiple Output (MIMO) antennas are another consideration for LTE systems that require high data rates, improved system capacity and wider coverage. The MIMO approach makes use of spatial diversity and requires two or more antennas at both the transmission and reception side as depicted in Figure 7.9 [25].

By using multiple antennas along with some complex digital signal processing, MIMO enables the system to set up multiple data streams on the same channel. It results in an increased data capacity of the channel. MIMO operation requires that the transmissions from each antenna are uniquely identifiable enabling each receiver to determine what combination of transmissions it has received. This identification can be achieved using pilot signals employing orthogonal patterns for each antenna. Although MIMO enables high data rates and improved spectral efficiency, it adds to system complexity in terms of hardware and processing.

There are a number of challenges in designing antennas for an LTE MIMO system, including antenna matching, isolation between the antenna elements, cross‐correlation and interactions with other electronic components on the device. A number of techniques are proposed by the researchers to deal with these issues such as placing the antenna elements at half a wavelength apart, using branch line hybrid with passive inductors and capacitors to decouple the antenna ports and using orthogonally polarized elements for port isolation [26–28].

Along with MIMO, beamforming and diversity approaches are also recommended to improve signal robustness and the LTE system capacity [25]. Beam‐forming exploits correlation such that the radiation pattern from a transmitter is directed towards the receiver. It is achieved by utilizing time delays to a calibrated phased array of antennas. The effectiveness of beamforming varies with the number of antennas. Gain improvement is small with just two antennas but considerable gain enhancements are possible with four antennas. Diversity is achieved by utilizing multiple antennas spaced or polarized appropriately in order to provide protection against fading.

These issues are further addressed in the following chapters by exploring the suitability of various antenna types to LTE solutions.