# Full-Azimuth Beam Steering MIMO Antenna Arranged in a Daisy Chain Array Structure

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- (1)
- Anticipated changes in received power when the position of the car changes relative to the incident waves.
- (2)
- Increase in spatial fading correlation between the array branches due to the narrow APS.
- (3)
- Changes in both the received power and correlation, which may be encountered at the same time, as the car moves in different directions relative to the incident waves.
- (4)
- A possible increase or decrease in the MIMO channel capacity caused by (1), (2), or (3).

- (A)
- (B)
- Development of radiation pattern steering capability to achieve a large signal-to-noise power ratio (SNR) that can direct the peak radiation toward the communication target.
- (C)
- Realization of low correlation between the MIMO channels established by the orthogonal relationship between the array alignment and the incident waves over the full azimuth.
- (D)
- Development of an angle of arrival (AOA) estimation antenna that obtains bearing information from radio waves incident on the MIMO antenna, using an RF-based interferometric monopulse technique with reduced hardware complexity.

## 2. New Concept of a Large-Scale MIMO Antenna

## 3. Daisy Chain 32 × 32 Multiple-Input Multiple-Output (MIMO) Antenna

_{1}and d

_{2}denote the distance between Elements #2 and #3, and Elements #1 and #4, respectively. E

_{0}signifies the amplitude of the electric field, and j indicates the complex unit. Using these parameters, the excitation conditions for the four subarrays to establish an in-phase state for the formation of a beam toward the communication target are described in Section 5.

## 4. Formulation of Monte Carlo Simulation

_{c}clusters, each of which comprises M uncorrelated waves, forming K

_{m}scatterers surrounding N MS antennas. Thus, the M uncorrelated waves are subject to an independent and identically distributed (i.i.d) complex Gaussian process. Furthermore, the correlation characteristics of the BS and MS sides are taken to be independent of each other, based on the Kronecker assumption [24]. MS antennas are assumed to be surrounded by K

_{m}scatterers, created by Q

_{c}clusters. The K

_{m}scatterers belonging to the q-th cluster are Gaussian distributed in azimuth in two-dimensional coordinates. Figure 6b depicts the coordinates of the k-th scatterer, in which the MS is moving toward the azimuth direction, ϕ

_{v}. Using the above-mentioned channel modeling, we carried out a Monte Carlo simulation according to the following procedure:

#### 4.1. Step 1: Generation of K_{m}-Path

_{q}is the azimuth angle of the mean of the incident wave, σ

_{q}is the standard deviation of the power spectrum, and XPR is the cross-polarization power ratio, given as the propagation parameter, and is assumed to be the average value [25]. The channel responses of the signals for a particular snapshot of fading are generated using random numbers, which ensures orthogonality between subchannels for the purpose of ideal MIMO transmission with a full-rank channel matrix.

#### 4.2. Step 2: Generation of Polarization and Summation of All Clusters

_{θn}(π/2, ϕ

^{q}

_{k,m}) and E

_{ϕn}(π/2, ϕ

^{q}

_{k,m}) are the complex electric field directivities of the n-th antenna element in the xy-plane for the θ and ϕ components, respectively, which are defined at the origin of the coordinates. h

^{q}

_{k,m}represents the equivalent amplitude of the incident waves and can be set to an arbitrary value; thus, it is assumed to have unity amplitude. XPR is the cross-polarization power ratio. The phases of the vertical and horizontal polarization components, φ

^{q}

_{Vk,m}and φ

^{q}

_{Hk,m}, are independent of each other, and are uniformly distributed from 0 to 2π. For each path, the two polarization components are combined with reference to the schematic diagram shown in Figure 7b, as the complex sum of the vertical and horizontal components, and we have

#### 4.3. Step 3: Generation of the Resultant Channel Response

_{v}, as shown in Figure 6b. This scheme is applied repeatedly to generate the following channel response matrix at the s-th snapshot

_{1}and h

_{2}represent the two distinct channel responses in the matrix of Equation (8), and <X> denotes the ensemble average of X where Y* represents the complex conjugate of Y. Using this definition, the absolute value of the complex correlation coefficient can be obtained from

_{a}in Equation (10) is used as a general description of the correlation behavior of the MIMO antenna performance throughout this paper, as mentioned in Section 5.

#### 4.4. Step 4: Evaluation of the Channel Capacity

**U**and

_{s}**V**

_{s}are the singular vectors of the receiving (mobile station) and transmitting (base station) antennas, respectively.

**D**represents the singular values, where λ

_{s}_{i}denotes the eigenvalue of the i-th subchannel for spatial multiplexing transmission in the MIMO system. Using these eigenvalues, the instantaneous channel capacity and its average value are finally evaluated by

## 5. Theoretical Investigation

#### 5.1. Design of 4 × 4 MIMO Antenna

_{1}shown in Figure 3b) was a quarter-wavelength at 2 GHz. In this case, the directivity of Subarray1 is expected to have a cardioid radiation pattern in the absence of mutual electromagnetic coupling between antenna elements.

_{1}= λ/4. Furthermore, the received signal from Element #2 is delayed by ϕ

_{p}= π/2 using a phase shifter. The total received signal, E

_{t}, is given by summing the received signals from Elements #2 and #3 using a signal combiner, and calculated from the equation

_{a}denotes the amplitude of excitation of each element. Using this circuit topology shown in Figure 8a, an actual signal processing unit was fabricated, as described in Section 6 (see Figure 18a).

_{2}and w

_{3}) and the phase shift value (τ

_{2}) are optimized by Equation (18) using the two electric field directivities (E

_{2}and E

_{3}) of the angle of the incident wave (ϕ) when the antenna elements are excited individually.

_{2}and P

_{3}are the input power at the feed point of Elements #2 and #3, respectively. The phase of one element shifts to an in-phase state with respect to the other element at the angle of the incident wave in consideration of the mutual electromagnetic coupling. The weight functions are determined in such a way that the gain in the communication direction of the combined radiation pattern yields the maximum value. In Subarray2, the same procedure is applied to optimize the radiation pattern. In Section 6, we will introduce a microwave circuit for realizing weight functions in an experimental way (see Figure 18a).

#### 5.2. Performance Evaluation of 32 × 32 MIMO Antenna

_{1}for the cluster1 in Figure 7a) is set to 30°. The SNR of the incident wave is set to 30 dB.

#### 5.3. Antenna–Propagation Mutual Interactions

_{a}in Equation (10). Note that we obtained the correlation coefficient in such a way that the average operation is performed with respect to all 32 incident waves. As described in Figure 6, and Equations (3) and (4) in Section 4, the incident waves from the base station are assumed to be plane waves, i.e., far-field assumption, and thus the channel model does not include the effects of the distance between the base and mobile stations on the correlation.

## 6. Experimental Verification

#### 6.1. Impedance and Radiation Measurements

_{1}and w

_{4}) using a double-sided printed circuit board with a thickness of 1 mm and a relative permittivity of 4.2 (FR4). The phase shift of the received signal for each element was realized using different lengths of microstrip transmission lines. The 30° phase difference between #1 and #4 is equivalent to a difference in length of 7.6 mm. The phase difference of the produced network was 34°, indicating that the phase difference was achieved. Furthermore, to get the correct weight function, the difference in power loss between the microstrip lines, which was 0.21 dB, was considered.

_{1}= 1.0 and w

_{4}= 0.38 for Subarray2, as listed in Table 1, the received signal of #4 had to be synthesized by attenuating 8.40 dB compared to that of #1. Since the power loss for #4 due to the microstrip line was 0.21 dB larger than that for #1, a power loss of 8.19 dB had to be realized by the attenuator. 0 dB and 8 dB attenuators were connected to the terminals of #1 and #4 of the fabricated microwave circuit, respectively. The 0 dB attenuator was used for realizing the retention of the phase of the received signals of #1 and #4. Hence, the difference in the received power between #1 and #4 was 8.50 dB, indicating that the weight function had been achieved.

#### 6.2. Over-the-Air Testing

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**A big challenge toward 100 Gbps channel capacity. (

**A**) A family of daisy chain MIMO antennas. (

**B**) History of the development.

**Figure 3.**Beam steering MIMO antenna arranged in a daisy chain array structure. (

**a**) The whole structure of a 32 × 32 MIMO system. (

**b**) 4 × 4 MIMO system.

**Figure 4.**Combinations of the subarrays. (

**a**) Combination1. (

**b**) Combination2. (

**c**) Combination3. (

**d**) Combination4.

**Figure 6.**Channel model used for performing the Monte Carlo simulation. (

**a**) Cluster channel model of M × N MIMO. (

**b**) Coordinates of the k-th scatterer.

**Figure 7.**Incident wave model for the Monte Carlo simulation. (

**a**) Gaussian incident wave in azimuth. (

**b**) Two polarization components.

**Figure 8.**Principle of the cardioid radiation pattern created by two isotropic point sources. (

**a**) Configuration of the array. (

**b**) Cardioid radiation pattern.

**Figure 10.**Radiation pattern of Subarray2 when the 4 × 4 MIMO antenna is used. (

**a**) ϕ = 0 deg (Combination1). (

**b**) ϕ = 45 deg (Combination2). (

**c**) ϕ = 90 deg (Combination3). (

**d**) ϕ = 135 deg (Combination4).

**Figure 11.**Radiation patterns of Subarray2 and Subarray18 when the 32 × 32 MIMO antenna is used. (

**a**) Subarray2. (

**b**) Subarray18.

**Figure 16.**Channel gain and correlation characteristics of each subarray. (

**a**) Channel gain. (

**b**) Correlation.

**Figure 18.**Radiation pattern measurement setup of a 4 × 4 MIMO array in an anechoic chamber. (

**a**) Fabricated microwave circuit. (

**b**) Prototype of a 4 × 4 MIMO array.

**Figure 21.**OTA testing of a 32 × 32 daisy chain MIMO antenna. (

**a**) Two-dimensional fading emulator. (

**b**) External view.

**Figure 24.**Channel gain and correlation of a 32 × 32 MIMO array measured by OTA testing. (

**a**) Channel gain. (

**b**) Correlation.

Frontward for Incident Wave | Backward for Incident Wave | |
---|---|---|

Subarray1 | #2 1 V, −160° | #3 0.72 V, 0° |

Subarray2 | #1 1 V, −330° | #4 0.38 V, 0° |

Subarray3 | #8 1 V, −330° | #5 0.38 V, 0° |

Subarray4 | #7 1 V, −160° | #6 0.72 V, 0° |

Frequency | 2000 MHz |

Number of elements (M, N) | M = N = 32 |

Number of clusters (Q_{c}) | 1 |

Number of scatterers (K_{m}) | 30 |

Initial phase for scatterers | Random |

Traveling distance (d) (dependent on angular spread) | 1000λ for σ = 10° 100λ for σ = 100° |

Number of samples (S) | 5000 |

Sampling interval (Δd = d/S) (dependent on angular spread) | 0.2λ for σ = 10° 0.02λ for σ = 100° |

Moving direction (ϕ_{V}) | 5° |

XPR | 50 dB (Vertical Pol.) |

Antenna element | Half-wavelength dipole |

Method of EM analysis | Method of moments |

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## Share and Cite

**MDPI and ACS Style**

Honda, K.; Fukushima, T.; Ogawa, K.
Full-Azimuth Beam Steering MIMO Antenna Arranged in a Daisy Chain Array Structure. *Micromachines* **2020**, *11*, 871.
https://doi.org/10.3390/mi11090871

**AMA Style**

Honda K, Fukushima T, Ogawa K.
Full-Azimuth Beam Steering MIMO Antenna Arranged in a Daisy Chain Array Structure. *Micromachines*. 2020; 11(9):871.
https://doi.org/10.3390/mi11090871

**Chicago/Turabian Style**

Honda, Kazuhiro, Taiki Fukushima, and Koichi Ogawa.
2020. "Full-Azimuth Beam Steering MIMO Antenna Arranged in a Daisy Chain Array Structure" *Micromachines* 11, no. 9: 871.
https://doi.org/10.3390/mi11090871