4. Array optimization based on integrated antenna array

It is important to combine the integrated antenna array and the array optimization algorithm. We assume that the integrated antenna array is utilized as a transmit system, and then the channel capacity of the MIMO system may be described as

$$\mathbf{C} = \mathbb{E}\left\{ \log \det \left( \mathbf{I}\_{N\_r} + \frac{\text{SNR}}{N\_t} \mathbf{H} \mathbf{W} \mathbf{W}^\dagger \mathbf{H}^\dagger \right) \right\}, \tag{17}$$

The channel capacity of the 16-port integrated antenna is described in Figure 10. It is found that the channel capacity of 16-port integrated antenna achieves channel

We consider the four-port integrated antenna, which was proposed in Section 3 as the array element of the integrated antenna array. We assume that all antenna arrays have Nt ¼ 16 antenna elements and that the receive system has ideal channel condition which means R<sup>H</sup><sup>r</sup> ¼ INr . We verify the performance of the integrated antenna array compared to two reference arrays as shown in Figure 11. The reference arrays are mono-polarization (MPOL) and dual-polarization (DPOL) antenna arrays. The MPOL and DPOL antenna arrays have array elements which are composed of mono-polarization dipole and dual-polarization dipoles, respectively. Then, MPOL, DPOL and integrated antenna arrays have Bt ¼ 1, 2 and 4 and Lt ¼ 16, 8 and 4, respectively. Here, we consider a channel model describing an

The channel capacities of the integrated MPOL and DPOL antenna arrays are illustrated in Figure 12. Although the integrated antenna array occupies smaller size than the others, the integrated antenna array has higher channel capacity than the MPOL and DPOL antenna arrays. It means that the multiple radiation patterns of various antenna elements for the integrated antenna may enhance the channel

To optimize an integrated antenna array in wireless communication area, we study the mathematical optimization of the integrated antenna array. Under assumption of W ¼ I, we can derive an optimization problem given by

capacity without increasing antenna space to utilize spatial gain.

capacity close to that of the ideal 16-port antenna.

Array Pattern Based on Integrated Antenna DOI: http://dx.doi.org/10.5772/intechopen.81087

4.2 Performance of integrated antenna array

urban macro-cell environment [20].

4.3 Further works

Figure 10.

79

Channel capacity of practical 16-port integrated antenna.

where SNR is signal-to-noise ratio and W is a precoding matrix [19]. To simplify the optimization problem, we consider that the receive system has ideal channel condition, which means R<sup>H</sup><sup>r</sup> ¼ I. From (4) and (13), the MIMO channel H is given by <sup>H</sup> <sup>¼</sup> <sup>H</sup>wR<sup>1</sup>=<sup>2</sup> <sup>H</sup><sup>t</sup> , where <sup>R</sup><sup>H</sup><sup>t</sup> <sup>¼</sup> <sup>T</sup> †R<sup>M</sup> <sup>t</sup> <sup>T</sup> . There are three variables <sup>R</sup><sup>M</sup> <sup>t</sup> , T and W in (17). We can control <sup>T</sup> and <sup>W</sup> according to <sup>R</sup><sup>M</sup> <sup>t</sup> which is given by the channel environment.

However, T and W have different characteristics. First, T is determined by the structure of the integrated antenna array, while W can be changed in real time. Second, T is dependent on the specification of the integrated antenna such as antenna space, required bandwidth and the number of antenna elements. W is dependent on the specification of RF chains such as resolutions of phase shifter and attenuator. Lastly, it is not clear to implement a specific integrated antenna according to an arbitrary T .

Therefore, it is necessary to optimize the T and W with different constraints. We study the optimization of W under practical T .

#### 4.1 Performance of integrated antenna

In order to show the possibility of the integrated antenna in wireless communication area, we verify the performance of the integrated antenna by optimizing W under fixed T given by the practical 16-port and 4-port integrated antennas in the previous section.

There are various objective functions for optimization of W, such as maximizations of spectral and energy efficiency and minimizations of interference and side lobe level [12]. Here, we consider an objective function as a maximization of spectral efficiency expressed by

$$f = \max\_{\text{Tr}\left\{\mathbf{W}\mathbf{W}^\dagger\right\} = \mathbf{N}\_t} \mathbf{C}.\tag{18}$$

To obtain the optimum value of W, we apply a singular value decomposition (SVD) precoding method into the integrated antenna array [19]. This SVD precoding method provides the precoding matrix W ¼ v1⋯vNr ½ �, where <sup>U</sup>SV† <sup>¼</sup> svdð Þ <sup>H</sup> and <sup>V</sup> <sup>¼</sup> <sup>v</sup>1⋯vNt ½ �.

We consider the 16-port integrated antenna as the integrated antenna without array structure. We assume that the receive system has 16 antennas and that the channel is a full-scattering environment, which has the PAS given by

$$p\_{\theta\_t}(\theta,\phi) = p\_{\phi\_t}(\theta,\phi) = \frac{1}{2\pi^2}, \theta \in [0,\pi], \phi \in [-\pi,\pi]. \tag{19}$$

## Array Pattern Based on Integrated Antenna DOI: http://dx.doi.org/10.5772/intechopen.81087

4. Array optimization based on integrated antenna array

C ¼ E log det INr þ

<sup>H</sup><sup>t</sup> , where <sup>R</sup><sup>H</sup><sup>t</sup> <sup>¼</sup> <sup>T</sup> †R<sup>M</sup> <sup>t</sup>

We can control <sup>T</sup> and <sup>W</sup> according to <sup>R</sup><sup>M</sup> <sup>t</sup>

We study the optimization of W under practical T .

4.1 Performance of integrated antenna

spectral efficiency expressed by

<sup>U</sup>SV† <sup>¼</sup> svdð Þ <sup>H</sup> and <sup>V</sup> <sup>¼</sup> <sup>v</sup>1⋯vNt ½ �.

pθt

ð Þ¼ θ; ϕ p<sup>ϕ</sup><sup>t</sup>

according to an arbitrary T .

previous section.

78

<sup>H</sup> <sup>¼</sup> <sup>H</sup>wR<sup>1</sup>=<sup>2</sup>

Array Pattern Optimization

ment.

It is important to combine the integrated antenna array and the array optimization algorithm. We assume that the integrated antenna array is utilized as a transmit system, and then the channel capacity of the MIMO system may be described as

> SNR Nt

where SNR is signal-to-noise ratio and W is a precoding matrix [19]. To simplify the optimization problem, we consider that the receive system has ideal channel condition, which means R<sup>H</sup><sup>r</sup> ¼ I. From (4) and (13), the MIMO channel H is given by

However, T and W have different characteristics. First, T is determined by the structure of the integrated antenna array, while W can be changed in real time. Second, T is dependent on the specification of the integrated antenna such as antenna space, required bandwidth and the number of antenna elements. W is dependent on the specification of RF chains such as resolutions of phase shifter and

Therefore, it is necessary to optimize the T and W with different constraints.

In order to show the possibility of the integrated antenna in wireless communication area, we verify the performance of the integrated antenna by optimizing W under fixed T given by the practical 16-port and 4-port integrated antennas in the

There are various objective functions for optimization of W, such as maximizations of spectral and energy efficiency and minimizations of interference and side lobe level [12]. Here, we consider an objective function as a maximization of

> f ¼ max Tr WW† f g¼Nt

(SVD) precoding method into the integrated antenna array [19]. This SVD precoding method provides the precoding matrix W ¼ v1⋯vNr ½ �, where

ð Þ¼ <sup>θ</sup>; <sup>ϕ</sup> <sup>1</sup>

channel is a full-scattering environment, which has the PAS given by

To obtain the optimum value of W, we apply a singular value decomposition

We consider the 16-port integrated antenna as the integrated antenna without array structure. We assume that the receive system has 16 antennas and that the

attenuator. Lastly, it is not clear to implement a specific integrated antenna

HWW†

<sup>T</sup> . There are three variables <sup>R</sup><sup>M</sup> <sup>t</sup>

H†

which is given by the channel environ-

C: (18)

<sup>2</sup>π<sup>2</sup> , <sup>θ</sup>∈½ � <sup>0</sup>; <sup>π</sup> , <sup>ϕ</sup>∈½ � �π; <sup>π</sup> : (19)

, (17)

, T and W in (17).

The channel capacity of the 16-port integrated antenna is described in Figure 10. It is found that the channel capacity of 16-port integrated antenna achieves channel capacity close to that of the ideal 16-port antenna.
