# Experimental Analysis of Concentrated versus Distributed Massive MIMO in an Indoor Cell at 3.5 GHz

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Channel Characterization Methodology

_{f}sub-carriers, which correspond to the measured tones.

**y**[k] is a column vector with M elements corresponding to the k-th sub-carrier;

**G**[k] is the channel matrix of order M × Q, in which each one of its columns corresponds with the narrowband channel of the q-th user

**g**

_{q}[k] of order M × 1;

**s**[k] (Q × 1) is the vector representing the signals vector transmitted from the UTs and normalized in such a way that $E\left\{{\Vert s\Vert}^{2}\right\}=1$, where E{.} represents the mean or expected value; and

**n**[k] is a complex Gaussian noise vector with independent and identically distributed (i.i.d.) unit variance elements. Finally, the SNR represents the mean signal to noise ratio at the receiver.

**G**is obtained from the matrix of the raw channel measurements (

**G**

^{raw}) by means of:

**J**is a diagonal matrix of order Q × Q. Different normalizations can be considered, provided they verify (2), which guarantees the conservation of the total transmitted power. Following the proposal and the nomenclature in [23], we consider two normalizations that we will denote as normalization 1 (N1) and normalization 2 (N2).

**J**is a diagonal matrix of order Q × Q, whose elements (j

_{qq}) are given by

**J**take different values so that all the columns in

**G**are normalized to one; consequently, the power imbalance between the channels corresponding to each UT is eliminated, although the channel variations between antennas within the receiver array and frequency tones are maintained. The resulting normalized matrix,

**G**, can be interpreted as that associated with a system in which an ideal power control is performed. In this case, the total available power transmitted by the users is not distributed equally, but each UT is assigned the necessary power so that all UTs reach the BS with the same mean power.

**J**are equal and thus, the operation in (3) is equivalent to multiplying the matrix by a scalar:

**G**is defined by the relationship:

**G**

^{H}

**G**matrix, i.e., the square of the q-th singular value of the

**G**matrix.

**V**and expressed as

_{f}frequency tones. The JFI takes values between 1/Q and 1, so that the value 1 corresponds to the maximum fairness among the SE values of the active UTs.

## 3. Indoor Channel Measurements

#### 3.1. The Indoor Environment

_{Rx}for the center of the scanning area, and centered in the lower-widest half of the corridor. Furthermore, concerning the D-mMIMO VA arrangement, it consists of 64 antennas placed at the ceiling board at a height h

_{Rx}, uniformly spaced Δl, and distributed over two linear trajectories, T1 and T2, which are located at both sides of the columns and linearly shifted from each other Δl/2.

_{2}, UT

_{6}, and UT

_{8}(though strictly the UT

_{6}is under NLOS conditions for most of the D-mMIMO VA positions), and the rest are under NLOS conditions, i.e., UT

_{1}, UTs

_{3-5}, and UT

_{7}. In this case, the Tx antenna is placed at a height h

_{Tx}. The summary of the main parameters for both C-mMIMO and D-mMIMO virtual arrays, including those concerning the UTs, is presented in Table 1.

#### 3.2. Measurement Setups

_{21}(f) scattering parameter that corresponds with the complex channel transfer function, H(f).

_{21}-trace is acquired and, from the post-processing of the traces, a complete characterization of the indoor channel established between that Tx, i.e., an UT, and the Rx VA, i.e., the virtual array at the BS, can be carried out. Concerning the D-mMIMO measurement time, and in spite of the fact that the trace acquisition from the VNA takes less than 15 s per Rx position, the manual movement of the Rx antenna increases the overall measurement time for every UT position up to around one hour on average.

#### 3.3. Measurement Settings

_{21}-trace, N

_{f}= 12,801 frequency tones, Δf = 31.25 kHz uniformly spaced in the 400 MHz band have been considered; close to 30 kHz, one of the OFDM sub-carrier spacings was adopted in 5G New Radio (NR)-based air interface. The frequency resolution Δf leads to a maximum observable distance of 9.6 km (stated as c

_{0}/Δf, in which c

_{0}represents the speed of light), so the multipath contributions are properly considered.

_{21}measured takes into account the joint effect of both channel and antennas, which represents the radio channel [30].

## 4. Results

#### 4.1. Distributed and Collocated Massive MIMO Sum Capacity

**G**

^{raw}has been normalized considering the two normalization methods presented in (4) and (5), i.e., N1 and N2. Moreover, a typical SNR value of 10 dB has been considered to calculate the capacity.

**g**

_{q}. With this normalization, it can be observed in Figure 4 that the C-mMIMO channel presents a sum capacity with a median value 3 bit/s/Hz below the i.i.d. Rayleigh channel. This reduction can be explained by means of the CDF of the ICN presented in Figure 5, showing for this case the lowest ICN median value, around 0.07, which is associated with a low orthogonality between at least two sub-channels. Conversely, for the D-mMIMO channel, the sum capacity is very close to that of the reference channel. The widespread spatial distribution of the antennas on the BS side provides very different channels between each UT and each one of the BS antennas; thus, the elements in the

**G**matrix present a different and independent fading. The effect of this macro diversity over the orthogonality between the user sub-channels is confirmed through the analysis of the ICN performance shown in Figure 5, which is close to that of the i.i.d. Rayleigh channel.

**G**, in particular in the C-mMIMO channel, where the imbalance is higher than for the D-mMIMO case.

_{2}, UT

_{6}, and UT

_{8}for C-mMIMO and UT

_{2}and UT

_{8}for D-mMIMO) and lower than 1 for the rest of UTs, those under NLOS conditions. In fact, it is in these NLOS situations where the D-mMIMO channel, with gains from 0.4 to 0.8, outperforms C-mMIMO, which presents very low gains, in the range of 0.01–0.07. These gains are higher in the D-mMIMO channel thanks to the widespread distribution of the BS elements which, in general, reduces the propagation losses and makes them more uniform for all the UTs, i.e., it reduces the power imbalance. Thus, although D-mMIMO with N2 does not introduce any power control, its distributed architecture tends to receive at the BS a similar average power from all the UTs.

#### 4.2. Distributed and Collocated Massive MIMO Spectral Efficiency

**G**matrices. Thus, the ICN, which quantifies the degree of ill conditioning of the

**G**matrix, is also a good indicator of the amplification degree of the noise level. The previous section already showed that the C-mMIMO channel matrix is ill conditioned with an ICN median value much lower than 1, ICN = 0.06, which contrasts with the median ICN value of 0.29 obtained for the D-mMIMO channel, as shown in Figure 5. Therefore, this degree of ill conditioning is responsible not only for the lower capacity values, but also for the higher degradation of the SE in the C-mMIMO channel compared to the D-mMIMO one.

_{7-8}), in which the C-mMIMO channel reaches its best SE values and almost equals that achieved by the D-mMIMO one.

_{3}) to 8.2 bit/s/Hz (UT

_{8}), according to the results given in Table 4. These values contrast with those associated with the D-mMIMO channel shown in Figure 10b, which are concentrated in a narrower range, between 5 (UT

_{5}) and 7.4 (UT

_{8}) bit/s/Hz. Jain’s Fairness Index quantifies this great variability in the C-mMIMO channel between UT locations, leading to a JFI of 0.57, compared with JFI = 0.98 when considering the D-mMIMO channel.

_{6}and UT

_{8}. However, at NLOS locations, the SE suffers a high degradation. However, the D-mMIMO channel performs very well in both cases, with UTs under LOS and NLOS conditions. In LOS locations, the SE is slightly lower than in C-mMIMO channels. However, in general, in the NLOS situations, the distributed architecture involves lower propagation losses; thus, significantly higher SE values can be achieved. In fact, the performance of D-mMIMO is similar to that of the C-mMIMO channel at LOS locations, as it occurs with UT

_{2}and UT

_{6}.

## 5. Conclusions

**G**matrices, as is the case of the concentrated channel versus the distributed one, as confirmed from the observation of the measured ICN performance.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Top view of the indoor office environment: (

**a**) General overview of the measurement environment; (

**b**) Zoom of the central part of the floor considered in the experimental analysis, including positions for both UTs and receiver trajectories.

**Figure 2.**Schematic of the concentrated massive multiple-input multiple-output (C-mMIMO) channel sounder: (

**a**) Detail of the measurement setup; (

**b**) Block diagram of the channel sounding system.

**Figure 3.**Schematic of the distributed massive multiple-input multiple-output (D-mMIMO) channel sounder: (

**a**) Detail of the measurement setup; (

**b**) Block diagram of the channel sounding system.

**Figure 4.**CDF of the sum capacity considering concentrated and distributed MIMO systems, along with the normalizations N1 and N2. The i.i.d. Rayleigh channel result is included as a reference.

**Figure 5.**CDF of the Inverse Condition Number for C-mMIMO and D-mMIMO channels, along with the two normalizations, N1 and N2. The i.i.d. Rayleigh channel result is included as a reference.

**Figure 6.**Expected value, $E\left\{{\Vert {g}_{q}\Vert}^{2}\right\}$, considering concentrated and distributed MIMO systems, along with N1 and N2 normalizations.

**Figure 7.**CDF comparing the sum spectral efficiency and sum capacity for both C-mMIMO and D-mMIMO channels when considering the N1 normalization.

**Figure 8.**CDF of the spectral efficiency for every UT, comparing both (

**a**) C-mMIMO and (

**b**) D-mMIMO systems, when the N1 normalization is applied.

**Figure 9.**CDF comparing the sum spectral efficiency and sum capacity for both C-mMIMO and D-mMIMO channels when considering the N2 normalization.

**Figure 10.**CDF of the spectral efficiency for every UT, comparing both (

**a**) C-mMIMO and (

**b**) D-mMIMO systems, when the N2 normalization is applied.

**Table 1.**Parameters for the arrangement of concentrated massive multiple-input multiple-output (C-mMIMO), distributed massive multiple-input multiple-output (D-mMIMO), and user terminals (UTs).

C-mMIMO | VA size (y × z) | 8 × 8 |

VA inter-element separation at 3.5 GHz, Δy = Δz (mm/λ) | 50/0.58 | |

VA total scanning area (m^{2}) | 0.1225 | |

Height at the center of the scanning area, h_{Rx} (m) | 2.52 | |

D-mMIMO | Number of antennas (T1 + T2) | 64 |

T1 and T2 inter-element separation at 3.5 GHz, Δl (mm/λ) | 600/7 | |

Longitudinal shift between T1 and T2 (mm) | 300 | |

Trajectory length, T1 = T2 (m) | 18.60 | |

Height of the Rx antenna, h_{Rx} (m) | 2.98 | |

UTs | Height of the Tx antenna, h_{Tx} (m) | 1.40 |

Frequency range (GHz) | 3.3–3.7 |

Frequency tones, N_{f} | 12,801 |

Frequency resolution, Δf (kHz) | 31.25 |

VNA power at Port 1 (dBm) | 7 |

VNA IF bandwidth (kHz) | 3 |

Averaging factor (number of S traces) | 3 |

Dwell time (μs) | 1 |

Signal to noise ratio observed at any UT position (dB) | >35 |

**Table 3.**Representative values of the spectral efficiency obtained for 10 and 50% outage, considering both mMIMO systems and the N1 normalization. Values expressed in bit/s/Hz.

UT Index | SE (10%) | SE (50%) | ||
---|---|---|---|---|

C-mMIMO | D-mMIMO | C-mMIMO | D-mMIMO | |

1 | 4.6 | 5.6 | 5.2 | 6.2 |

2 | 4.3 | 5.8 | 5.0 | 6.0 |

3 | 4.2 | 5.7 | 5.1 | 6.1 |

4 | 4.9 | 5.8 | 5.4 | 6.2 |

5 | 4.7 | 5.9 | 5.4 | 6.2 |

6 | 4.7 | 5.8 | 5.3 | 6.2 |

7 | 5.2 | 5.6 | 5.7 | 6.0 |

8 | 5.8 | 5.9 | 6.2 | 6.2 |

Sum SE | 41.1 | 47.5 | 43.2 | 49.1 |

**Table 4.**Representative values of the spectral efficiency obtained for 10 and 50% outage, considering both mMIMO systems and the N2 normalization. Values expressed in bit/s/Hz.

UT Index | SE (10%) | SE (50%) | ||
---|---|---|---|---|

C-mMIMO | D-mMIMO | C-mMIMO | D-mMIMO | |

1 | 0.4 | 4.1 | 0.6 | 4.7 |

2 | 4.6 | 6.9 | 5.3 | 7.2 |

3 | 0.3 | 5.0 | 0.5 | 5.4 |

4 | 0.6 | 4.8 | 0.7 | 5.3 |

5 | 1.1 | 4.8 | 1.5 | 5.0 |

6 | 5.9 | 5.4 | 6.5 | 5.8 |

7 | 1.9 | 5.2 | 2.3 | 5.7 |

8 | 7.8 | 7.1 | 8.2 | 7.4 |

Sum SE | 24.36 | 44.85 | 25.81 | 46.42 |

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**MDPI and ACS Style**

Pérez, J.R.; Fernández, Ó.; Valle, L.; Bedoui, A.; Et-tolba, M.; Torres, R.P. Experimental Analysis of Concentrated versus Distributed Massive MIMO in an Indoor Cell at 3.5 GHz. *Electronics* **2021**, *10*, 1646.
https://doi.org/10.3390/electronics10141646

**AMA Style**

Pérez JR, Fernández Ó, Valle L, Bedoui A, Et-tolba M, Torres RP. Experimental Analysis of Concentrated versus Distributed Massive MIMO in an Indoor Cell at 3.5 GHz. *Electronics*. 2021; 10(14):1646.
https://doi.org/10.3390/electronics10141646

**Chicago/Turabian Style**

Pérez, Jesús R., Óscar Fernández, Luis Valle, Abla Bedoui, Mohamed Et-tolba, and Rafael P. Torres. 2021. "Experimental Analysis of Concentrated versus Distributed Massive MIMO in an Indoor Cell at 3.5 GHz" *Electronics* 10, no. 14: 1646.
https://doi.org/10.3390/electronics10141646