It has previously been shown that a reverberation chamber can conveniently be used to measure ergodic multiple-input multiple-output (MIMO) capacity for over-the-air (OTA) tests. However, the MIMO channel in the reverberation chamber has not been fully studied before. In this paper, the spatial correlation of the MIMO channel in the chamber is studied by comparing the measured channel with two popular MIMO channel models. It is shown that the models can accurately predict the ergodic MIMO capacity of the channel in the reverberation chamber, but not the outage capacity (especially at high signal-to-noise regime). It is verified that the capacity estimation error is due to the fact that the measured MIMO channel in the chamber does not satisfy multivariate normality (MVN), which causes the capacity error increases additively with MIMO size and multiplicatively with signal-to-noise (SNR).

Multiple-input multiple-output (MIMO) systems have drawn considerable popularity, over the past decade, due to their performance-enhancement capability in multipath environments [

The aim of this paper is to study the measured channel in the chamber by comparing it with two well-known channel models, (i.e., Kronecker model and full-correlation model [

This work is of particular interest for OTA characterization of MIMO terminals in reverberation chambers, because it helps to understand the channel conditions under which the passive and/or active MIMO measurements have been conducted in the chamber.

It has been shown that the ergodic MIMO capacity of a multiantenna system can be easily determined based on the reverberation chamber measurement [

Drawing of the Bluetest RC with two mechanical plate stirrers, platform, three wall antennas, and six-monopole array.

In order to calibrate out the long-term fading, or attenuation, in the chamber (so that only short-term fading came into play) [

The resulting channel matrix

Assume that the receiver has perfect channel state information and that transmitted power is equally allocated among transmitting antenna elements, the ergodic MIMO capacity can be computed from the measured channel matrices by [

Wireless channel that can be assumed as wide-sense stationary uncorrelated scattering (WSSUS) [

Note that different fading-type environments can be emulated involving reverberation chamber. Holloway [

Assume a single-user narrow band MIMO system, consisting of

A general, so-called, full-correlation channel model is given by [

The Kronecker model assumes separable

From Section

The full channel covariance matrix is estimated from

Kronecker correlation error as a function of receive monopole number with the three wall antennas fixed as transmit antenna.

From Figure

Comparison of the Kronecker model and full-correlation model against reverberation chamber measurement of

Comparison of the Kronecker model and full-correlation model against reverberation chamber measurement of

Figure

Figure

It is shown that the Kronecker model has the same performance as the full-correlation model because that multibounce rich scattering property of the chamber makes the correlations at transmit and receive sides separable [

The good agreement between the Kronecker model and the other two advanced models means that, unlike in real-life multipath environments, the discrepancy of capacity of the Kronecker model with the measured one in the reverberation chamber is not due to the Kronecker structure. Instead, it is probably because the entries of the measured MIMO channel matrix are not jointly Gaussian (or normal). It has been found that the Henze-Zirkeler’s test [

Let

Applying the Henze-Zirkeler’s test to the measured channel matrices, it is found that every subchannel coefficient of

Number of wall antennas: 1 | Number of wall antennas: 2 | Number of wall antennas: 3 | |
---|---|---|---|

Number of Monopoles: 1 | 0.850 | 0.196 | 0.000 |

Number of Monopoles: 2 | 0.657 | 0.060 | 0.000 |

Number of Monopoles: 3 | 0.370 | 0.000 | 0.000 |

Number of Monopoles: 4 | 0.230 | 0.000 | 0.000 |

Number of Monopoles: 5 | 0.066 | 0.000 | 0.000 |

Number of Monopoles: 6 | 0.020 | 0.000 | 0.000 |

It is found that the channels with large MIMO sizes show strong non-MVN and that channels with MIMO small size (e.g.,

Due to the non-MVN of

Note that the non-MVN may not be the main contribution for channel model errors for real-life multipath environments, where the full-correlation model can outperform the Kronecker model. The equal performance of all the models for the reverberation chamber measurement is because of the multibounce rich scattering property of the chamber, as discussed in Section

In this paper, the MIMO channel in a reverberation chamber is studied by comparing the measurements with different channel models. It is found that both models have the same performance in terms of capacity estimation for the reverberation chamber measurements and that all of them can well predict the ergodic capacity up to six antenna elements with only slight overestimation at high-SNR regime. However, the models fail to predict the CDFs of the capacities for more than three antenna elements, especially at high SNR regime. The reason for this is because of the non-MVN of the MIMO channel in the chamber. Since all the models involves i.i.d. complex Gaussian channel, there will be modeling errors due to the non-MVN of the measured channel. And the channel modeling errors will additively increase with MIMO size and multiplicatively increase with SNR, for MIMO capacity estimations. The equal performance of the Kronecker model and the full-correlation model (for reverberation chamber measurements) implies that the correlations at transmit and receive sides can be treated separately. This is actually very desirable, since it allows characterizing the performance of a MIMO terminal independently (without the effect of the other MIMO side) by doing an OTA test in the chamber, which in turn allows fair comparisons of different MIMO terminals.

This work has been supported by The Swedish Governmental Agency for Innovation Systems (VINNOVA) within the VINN Excellence Center Chase. The author would like to thank Dr. Li Yang and the anonymous reviewers for their helpful comments to increase the quality of this paper.