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As antennas are inherently included recommended in Over-The-Air (OTA) testing, it is important to also consider realistic channel models for the multiple-input multiple-output (MIMO) device performance evaluation. This paper aims to emulate realistic multi-Path propagation channels in terms of angles of arrivals (AoA) and cross-polarization ratio (XPR) with Rayleigh fading, inside an anechoic chamber, for antenna diversity measurements. In this purpose, a practical multi-probe anechoic chamber measurement system (MPAC) with 24 probe antennas (SATIMO SG24) has been used. However, the actual configuration of this system is not able to reproduce realistic channels. Therefore, a new method based on the control of the SG24 probes has been developed. At first time, this method has been validated numerically through the comparison of simulated and analytical AoA probability density distributions. At the second time, the performance of an antenna diversity system inside the SG24 has been performed in terms of the correlation coefficient and diversity gain (DG) using an antenna reference system. Simulated and measurements results have shown a good agreement.

Generally, the multiple antennas configuration has been adopted in wireless communication systems in order to improve the capacity of data transmission and mitigate the effects of multipath fading. Due to constraints on the physical dimensions of the wireless terminals, the distances between the multiple antennas are usually small. These distances induce a high mutual coupling between the antennas [

Recently, many methodologies Multiple-Input Multiple-Output (MIMO) Over The Air (OTA) have been discussed in 3GPP and COST2100 [

In this paper, we present a new test method, considerably, less complex than other emulators proposed in the literature, in terms of cost-effectiveness. It consists to replace the channel emulator by a switch in order to generate a realistic Rayleigh channel in terms of AoA and XPR, based on the ignition probabilities of emitting antennas. This method allows evaluating the performance of antenna diversity systems. Two types of propagation models, such as Uniform and selective in terms of AoA, are used for OTA testing in terms of correlation coefficient and diversity gain (DG). These parameters have been computed from the signals received at the different branches of the antenna systems.

An illustration of the MPAC measurement system developed for this contribution is shown in

generate multi-path environments free from undesired reflection inside the chamber and unwanted external interferences, an antenna array for emulating realistic channel models around a device under test (DUT) and a switch related to the emitting antennas.

In this work, the SATIMO SG24 measurement system [

A Nakagami channel is obtained when the DUT is placed at the probes center during the control. And, that is due to the same amplitude and the same shift phase values introduced on the different received paths, where the Euclidean distances between the emitting antennas and the DUT are equals. As the material configuration of the SG24 is not able to modify the amplitude and the shift phase of the paths for generating a multi-path channel with Rayleigh fading, a solution consists to displace the DUT horizontally has been proposed.

This method consists in generating a desired multipath propagation channel in terms of angles of arrivals (AoA) at a DUT. It is based on the ignition probabilities of probes, used in emitting way, of the SG24 measurement system.

In this method, we consider that at each rotation step of the device under test (centered or displaced) a new group of probes is created artificially. So, after a U turn of the DUT an artificial spherical probes distribution is obtained as illustrated in

The SATIMO SG24 has a finite number of probes distributed discretely on an arch. Therefore, in this method the space surrounding the device under test is decomposed in many cells in azimuth (φ) and elevation (θ) by a discretization step of k˚ (

In this method we compute the ignition probabilities of each probe to manage the angles of arrivals (AoA) at the DUT in order to obtain a desired multi-path propagation channel. These probabilities are obtained using the law of total probability [

We consider here that the probes number of the artificial sphere equal to J and the cells number equal to M. So, the probability to illuminate the cell number 1 is computed from the equation as listed below:

P ( c e l l 1 ) = P ( θ 1 , φ 1 ) = P ( c e l l 1 | p r o b e 1 ) ∗ P ( p r o b e 1 ) + ⋯ + P ( c e l l 1 | p r o b e j ) ∗ P ( p r o b e j ) + ⋯ + P ( c e l l 1 | p r o b e J ) ∗ P ( p r o b e J ) (1)

where,

P ( c e l l 1 | p r o b e j ) is the probability that the cell number 1 is illuminated given the probe number j is switched on and the others are switched off.

P ( p r o b e j ) is the ignition probability of the probe number j.

The procedure of the cell number 1 is repeated for all the cells. The obtained equations of all the cells can be written in matrix form as illustrated in (2).

A = [ P c e l l 1 ⋮ P c e l l m ⋮ P c e l l M ] = [ P ( θ 1 , φ 1 ) ⋮ P ( θ m , φ m ) ⋮ P ( θ M , φ M ) ] = H ⋅ B = H ⋅ [ P ( P r o b e 1 ) ⋮ P ( P r o b e j ) ⋮ P ( P r o b e J ) ] (2)

With:

H = [ P ( c e l l 1 | P r o b e 1 ) ⋯ P ( c e l l 1 | P r o b e j ) ⋯ P ( c e l l 1 | P r o b e J ) ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ P ( c e l l m | P r o b e j ) ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ P ( c e l l M | P r o b e 1 ) ⋮ ⋮ ⋮ P ( c e l l M | P r o b e J ) ] (3)

The angles of arrival of a given cell ( θ m , φ m ) are computed for every cell as illustrated in (4).

θ m = θ m min + k ∘ / 2 φ m = φ m min + k ∘ / 2 (4)

where, θ m min , φ m min are the minimum AoA of a given cell in elevation and in azimuth respectively. And, k is the discretization step of cells.

Finally, the ignition probabilities of the SG24 probes are obtained in resolving the system of linear equations mentioned in (2) according to the QR factorization method with column pivoting.

In order to validate the developed method numerically, two propagations models are used. The first model is characterized by a uniform distribution of the AoA in elevation and azimuth with a XPR equal to 0 dB. The second model is defined as selective in terms of AoA where it is characterized by a Gaussian distribution in elevation ( θ ¯ = 0 ∘ , σ θ = 20 ∘ ) and in azimuth ( φ ¯ = 180 ∘ , σ φ = 20 ∘ ) with a XPR equal to 3 dB.

On the other hand, these models are also adopted in this paper with the purpose of evaluating the performance of an antenna diversity system using an antenna reference system.

In order to generate a multi-path propagation channel with Rayleigh Fading, the DUT has been displaced of 0.7 meters from the arch center, where the Euclidian distances between probes and antennas are different. The DUT has been rotated from 0˚ to 175˚ at 5˚ step in azimuth and from −7˚ to 7˚ at 1˚ step in elevation. In addition, at each position of the DUT 500 samples have been captured for statistical needs.

As the AoA estimation of the received paths on the DUT is impossible to be achieved using the SG24 system, a program based on the ray tracing method that models this system has been developed. The numerical validation of the developed method is done through the comparison between the analytical and simulated probability density distribution of the angles of arrivals (AoA). A discretization step of 18˚ has been computed in order to illuminate all cells. In

After validating the developed method numerically, the performances of an antenna diversity system will be evaluated through the ray tracing program and measurements using the SATIMO SG24 system.

In this paragraph, we characterize an antenna diversity system at a frequency of 3.5 GHZ using the propagation models mentioned previously in the section 3. The reference antenna (

Analytical distribution | Simulated distribution | |
---|---|---|

Uniform model | ||

Selective model |

In these measurements (

In post processing, the received signals at each position of the antenna systems in elevation have been summed. This procedure has been performed in order to represent a 3D multi-path propagation channel. The obtained signals at each branch of the diversity system are used to evaluate its performance in terms of the correlation coefficient and DG using the signal collected by the reference antenna system.

In this section, the propagation models mentioned in the paragraph 3 are used to evaluate the performances of the antenna diversity system in terms of correlation coefficient and diversity gain (DG) using an antenna reference system. The correlation coefficient is computed through the signals collected on the antenna diversity branches [

As mentioned before, the angles of arrivals in this model are uniform in elevation and in azimuth, and the XPR is equal to 0 dB. Measurements and simulations have been done. In order to validate the diversity measurements using this model, measurements have been performed also in a reverberation chamber [

The obtained fading amplitude distribution of the normalized received signal (power = 0 dB) using the SATIMO SG24, depicted in

The correlation coefficient has been computed as illustrated in

In the previous figures, we see that the CDF’s of the received signals show a good agreement with the theoretical Rayleigh distribution. However, we denote that there is a small difference between these CDF’s. It is due to the radiation patterns of the antennas systems.

A consolidated summary of the different simulated and measurement diversity parameters is depicted in

Envelope Correlation coefficient | DG at 1% probability (dB)/ EGC | DG at 1% probability (dB)/MRC | |
---|---|---|---|

Simulations | 1.6 × 10^{−1} | 11 | 11.5 |

SG24 measurements | 6 × 10^{−3} | 11 | 11.5 |

RC measurements | 8.8 × 10^{−2} | 11 | 11.5 |

Using this model, we have proved also that the emulated environment is characterized by Rayleigh fading as illustrated in

The CDF curves have been computed in order to deduce the diversity gains as depicted in

The previous figures show that the CDF’s of the signals received by the reference system and the branch 1 (Antenna 1) of diversity system have a good similarity with the theoretical Rayleigh distribution. However, the CDF of the signal collected by the branch 2 (Antenna 2) is different due to the sensitivity of the radiation patterns using a selective model in terms of AoA.

The simulated and measured diversity parameters have been shown in

Envelope correlation coefficient | DG at 1% probability (dB)/EGC | DG at 1% probability (dB)/MRC | |
---|---|---|---|

Simulation | 23 × 10^{−2} | 6.5 | 7 |

SG24 measurements | 28 × 10^{−2} | 7.5 | 8 |

In this paper, realistic multi-path propagation channels in terms of angles of arrivals (AoA) and cross polarization ratio (XPR) with Rayleigh fading have been emulated with the purpose of diversity measurements using the SATIMO SG24 measurement system. Two propagation models such as Uniform and selective in terms of AoA have been used. The performances of a diversity system, using these models, have been evaluated in terms of correlation coefficient and diversity gain using an antenna reference system. Simulation and measurement results have shown a good agreement.

The future work of this paper consists on one hand, in evaluating the performance of diversity antennas systems in realistic environment using MPAC such as out-door and in-door propagation channel models in order to save time and equipments in comparison with measurements on the land. And, on the other hand, taking into account the delay spread on the interfering rays, in order to assess the overall MIMO performances including the antennas characteristics and the RF transmitter.

The authors declare no conflicts of interest regarding the publication of this paper.

Choumane, A., El Sayed Ahmad, A. and Khoder, K. (2020) Emulation of Realistic Multi-Path Propagation Channels inside an Anechoic Chamber for Antenna Diversity Measurements. Wireless Engineering and Technology, 11, 1-12. https://doi.org/10.4236/wet.2020.111001