**3. Practical phased array antenna design for indoor positioning**

The indoor localization and positioning system depend considerably on the phased array antenna structure. The structure as well as parameters of phased array antenna such as array geometry, element spacing, and feed network needs to be carefully defined. For indoor positioning, we only care about the location of users and ignore altitude information, hence a linear array structure with 2D scanning can fully meet this requirement. Other architectures such as planar array, circular array, and spherical array are also options, but they make the system much more complex and cumbersome. With a straightforward beam steering principle, the uniform amplitude and spacing linear array is chosen.

incoming waves at output ports. Therefore, if output ports of power divider are highly isolated to each other, the reflected waves will not affect other ports.

element resistor at the end. To analyze this circuit, the "even-odd" mode analysis

*The Wilkinson power divider: (a) microstrip line configuration, (b) equivalent transmission line circuit [22].*

quarter-wave transmission lines with impedance of ffiffi

*Directivity as a function of the element spacing of linear array antenna [21].*

*Beamforming Phased Array Antenna toward Indoor Positioning Applications*

*DOI: http://dx.doi.org/10.5772/intechopen.93133*

**Figure 5.**

**Figure 6.**

**103**

Power divider is a passive component to split the input signal into two or more lower power output signals. Power dividers usually provide in-phase output signals with both equal power division ratio (3 dB) and unequal power division ratios. As described in [22], T-junction and Wilkinson are two kinds of most popular power dividers. While the T-junction dividers have some disadvantages related to impedance matching, power loss or isolation, the Wilkinson Power Divider (WPD) can simultaneously solve these problems. The WPD appears lossless when the output ports are matched. The structure of WPD, shown in **Figure 6**, comprises two

2

<sup>p</sup> *<sup>Z</sup>*<sup>0</sup> and a 2*Z*<sup>0</sup> lumped-

Regarding the element spacing of linear array antenna system, it should be a suitable value in order to limit the mutual coupling, avoid grating lobes, and increase the directivity. As mentioned in Section 2, to reduce the adverse effects of mutual coupling, element spacing should be from 0.33λ to 0.5λ. With respect to the usage, the antenna system is aimed to be located at the corner of the room and the user will move inside the room, yielding the main beam angle from 45 to 45°. Thus, from Eq. (3), the element spacing is chosen to be less than 0.58λ to prevent the appearance of grating lobes when scanning main beam angle from 45 to 45°. In [21], Rabinovich and Alexandrov show the relationship between directivity and element spacing of array antenna (**Figure 5**). When element spacing *d* is less than wavelength λ, the directivity is proportional to *d*/λ. To sum up, the element spacing equals to half wavelength in my antenna system. Finally, with advantages compared to serial feed and butler matrix, the parallel feed network is selected for this beamforming phased array.

### **3.1 Power divider**

A parallel feed network is composed of power dividers and phase shifters. The incident wave is split to multiple ports through power dividers. With design of uniform amplitude and spacing linear array, the power should be equally split to each output port. If the phases of outgoing waves are identical, the compensation of phase will not be required. In microwave, reducing the loss enables more power to feed into antennas, which increases the transmission range. Finally, the mismatch in microwave circuits causes the reflection waves, which can play another role as

*Beamforming Phased Array Antenna toward Indoor Positioning Applications DOI: http://dx.doi.org/10.5772/intechopen.93133*

**Figure 5.** *Directivity as a function of the element spacing of linear array antenna [21].*

incoming waves at output ports. Therefore, if output ports of power divider are highly isolated to each other, the reflected waves will not affect other ports.

Power divider is a passive component to split the input signal into two or more lower power output signals. Power dividers usually provide in-phase output signals with both equal power division ratio (3 dB) and unequal power division ratios. As described in [22], T-junction and Wilkinson are two kinds of most popular power dividers. While the T-junction dividers have some disadvantages related to impedance matching, power loss or isolation, the Wilkinson Power Divider (WPD) can simultaneously solve these problems. The WPD appears lossless when the output ports are matched. The structure of WPD, shown in **Figure 6**, comprises two quarter-wave transmission lines with impedance of ffiffi 2 <sup>p</sup> *<sup>Z</sup>*<sup>0</sup> and a 2*Z*<sup>0</sup> lumpedelement resistor at the end. To analyze this circuit, the "even-odd" mode analysis

**Figure 6.**

*The Wilkinson power divider: (a) microstrip line configuration, (b) equivalent transmission line circuit [22].*

gain also enables to compensate the loss on phase shifter, of which loss value is not

*Advanced Radio Frequency Antennas for Modern Communication and Medical Systems*

Butler matrix is also an approach usually studied in phased array antennas [17–19]. The Butler matrix is a type of beamforming network and first described by Jesse Butler and Ralph Lowe in [20]. It has *N* inputs and *N* outputs; with *N* is usually 4, 8, and 16. One input signal fed from one of input ports goes through components of Butler matrix like couplers, phase shifters, crossovers in order to create phase difference of wave at N output ports, which combines with antenna elements to create beams with different predefined directions, as shown in **Figure 4**. Because beam direction is predefined, this system is also considered as a switched beam system. Nevertheless, there are two main drawbacks when using Butler matrix. First of all, the complexity and dimension significantly increase when *N* increases. That is why Butler matrix network is hardly designed with the number of input ports of 16 or more. Secondly, the number of beams is limited. With N inputs, this system can only create *N* beams with different directions, hence it is not suitable to

**3. Practical phased array antenna design for indoor positioning**

The indoor localization and positioning system depend considerably on the phased array antenna structure. The structure as well as parameters of phased array antenna such as array geometry, element spacing, and feed network needs to be carefully defined. For indoor positioning, we only care about the location of users and ignore altitude information, hence a linear array structure with 2D scanning can fully meet this requirement. Other architectures such as planar array, circular array, and spherical array are also options, but they make the system much more complex and cumbersome. With a straightforward beam steering principle, the uniform

Regarding the element spacing of linear array antenna system, it should be a suitable value in order to limit the mutual coupling, avoid grating lobes, and increase the directivity. As mentioned in Section 2, to reduce the adverse effects of mutual coupling, element spacing should be from 0.33λ to 0.5λ. With respect to the usage, the antenna system is aimed to be located at the corner of the room and the user will move inside the room, yielding the main beam angle from 45 to 45°. Thus, from Eq. (3), the element spacing is chosen to be less than 0.58λ to prevent the appearance of grating lobes when scanning main beam angle from 45 to 45°. In [21], Rabinovich and Alexandrov show the relationship between directivity and element spacing of array antenna (**Figure 5**). When element spacing *d* is less than wavelength λ, the directivity is proportional to *d*/λ. To sum up, the element spacing equals to half wavelength in my antenna system. Finally, with advantages compared to serial feed and butler matrix, the parallel feed network is selected for this

A parallel feed network is composed of power dividers and phase shifters. The incident wave is split to multiple ports through power dividers. With design of uniform amplitude and spacing linear array, the power should be equally split to each output port. If the phases of outgoing waves are identical, the compensation of phase will not be required. In microwave, reducing the loss enables more power to feed into antennas, which increases the transmission range. Finally, the mismatch in microwave circuits causes the reflection waves, which can play another role as

provide beams with high resolution scan angle.

amplitude and spacing linear array is chosen.

beamforming phased array.

**3.1 Power divider**

**102**

small.

technique is often used, and the scattering matrix calculation is represented in [22]. Finally, the scattering matrix of WPD is:

$$\mathbf{S} = \frac{-\mathbf{1}}{\sqrt{2}} \begin{bmatrix} \mathbf{0} & j & j \\ j & \mathbf{0} & \mathbf{0} \\ j & \mathbf{0} & \mathbf{0} \end{bmatrix} \tag{4}$$

lines in a three-stage structure. The 50 Ω transmission lines allow to arbitrarily adjust distances between output ports in order to satisfy the dimension of phase shifters and

In parallel feed network, the main role of phase shifter is to create the phase

reconfigure a beam shape. Three characteristics are required for this phase shifter. Firstly, it must be capable of shifting phase of waves in full 360° range in order to meet all of the demands of the phase difference in phased array antenna system. Secondly, continuously shifting makes it possible to create any phase, which enables steering main beam with high resolution. Finally, with a uniform amplitude and spacing linear array, when power divider equally splits power to output ports, a phase shifter with low insertion loss variation is very important. Without this property, our linear array should be treated as a non-uniform amplitude linear

Depending on the required output, phase shifters are classified into analog phase shifter and digital phase shifter. Digital phase shifters with semiconductor components such as PIN diode and FET switch predefined states to provide predetermined phase shift. The phase shift, generated by this type, has high accuracy. However, structure of this type will become cumbersome to meet high-resolution demands. With high resolution, the number of predefined states increases, resulting in the expansion of the number of switching elements as well as size of controller for them. Meanwhile, analog phase shifter with the use of varactors or Schottky diodes can continuously change the phase shift. These diodes have capacitance depending on the bias voltage, for this reason, they can be used as electrically variable capacitor in tuned circuit accordingly. By shifting the phase continuously, this type can provide high-resolution phase shift without changing its hardware structure. However, less accuracy and relatively narrow bandwidth are drawbacks of this type. On implementing a microwave phase shifter,

There exist four types of phase shifters, as shown in **Figure 9**. One of the digital phase shifter, the switched-line one, adopts delay lines and switching elements to

The phase shift depends only on transmission line length; therefore, it is very stable over time and temperature. A basic schematic of switched line phase shifter is shown in **Figure 9a**. The second type, switched network phase shifter (**Figure 9b**), is similar to switched line phase shifter but delay lines are replaced by networks composed of inductors and capacitors. The dimension of this type does not change as much as switched line phase shifter, besides this type is suitable for low frequency design. Loaded line phase shifters (**Figure 9c**) are loaded with a shunt reactance that is electrically shortened or lengthen by PIN diode or FET in order to get the desired phase shift. This type has advantages of simplicity and low insertion loss for phase shift less than 45°. However, for larger values of phase shift, high sensitivity is required in order to increase insertion loss. Therefore, this type is only suitable for phase shift less than 45°. Reflection type phase shifter comprises a 3-dB hybrid couple and two tunable loads, as shown in **Figure 9d**. By selecting the appropriate load, this type can shift more than 360° continuously and has low insertion loss, like in [24–26]. From requirement of phase shifter, it is obvious that reflection type phase shifter with full 360° and continuous phase shift is the most

difference of waves coming to the antennas in order to scan a beam or to

array, which is more complex in beam steering principle.

these disadvantages must be enhanced for better performance.

appropriate choice for this phased array antenna system.

generate time delay differences.

**105**

element spacing between antennas in phased array antenna system.

*Beamforming Phased Array Antenna toward Indoor Positioning Applications*

**3.2 Phase shifter**

*3.2.1 Phase shifter theoretical calculation*

*DOI: http://dx.doi.org/10.5772/intechopen.93133*

We can see that the power from input port is split into two output ports without power loss on transmission line, there is no reflection wave from output ports and output ports are completely isolated. With advantages of WPD over T-junction dividers, the WPD is utilized as the power divider for feed network of antenna array. In [22], professor Pozar introduced the N-way WPD (**Figure 7**) in which the transmission line has impedance depending on the number of output ports. This circuit can be matched at all ports, with isolation between all ports. The drawback of this structure is to use crossovers for the resistors for *N* ≥3, which makes fabrication difficult in planar form. The WPD is arranged in cascade structure for low loss and better isolation, shown in **Figure 8**. Two-way WPD is connected together by 50 Ω transmission

**Figure 7.** *An N-way, equal-split Wilkinson power divider [22].*

**Figure 8.** *The eight-way equal-split Wilkinson power divider [23].*

lines in a three-stage structure. The 50 Ω transmission lines allow to arbitrarily adjust distances between output ports in order to satisfy the dimension of phase shifters and element spacing between antennas in phased array antenna system.
