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We describe a simple multiple-input/multiple-output (MIMO) channel measurement system for acquiring indoor MIMO channel responses. Four configurations of the polarization diversity antenna, referred to as

The multiple-input/multiple-output (MIMO) system proposed by Foschini [

Recently, many researchers have examined multiple polarizations for an MIMO antenna system. Andrews et al. [

On the other hand, one way of reducing the level of correlation between antenna elements is to provide sufficient interelement spacing. However, for the practical application of MIMO systems to a wireless local area network, the spacing between adjacent antenna elements cannot be too large. Given this constraint, the most probable solution is a dense MIMO array with nonnegligible correlation. In addition, the use of polarization diversity may be a solution for obtaining a more compact antenna array layout since another diversity dimension can be provided to the MIMO radio channel. Therefore, modeling the polarization diversity technique is an interesting topic of study in MIMO radio channels, and it necessitates the construction of realistic MIMO radio channel models featuring both space and polarization diversity [

Dissimilar channel environments and different incoming wave angular distributions result in a distinct spatial correlation among antenna array elements, which are the main parameters that affect MIMO channel characteristics [

The validation of the model is supported by measurement results. Using two measurement setups having several transmitting and receiving elements, four polarization schemes have been investigated in several different LOS and NLOS rooms as indoor environments. The parameters of the MIMO model are extracted from the measurement data and fed to the model to compare simulation results with the measurement results.

In this paper, we propose an analysis method, which utilizes a correlation coefficient for both transmission and reception and the average receiving power, to calculate the MIMO channel capacity in polarization systems. In addition, we derive the optimal received-power matrix for both additive white Gaussian noise (AWGN) and multipath fading channels. Furthermore, measurement results show that the proposed analysis method outperforms traditional method in polarization systems.

The remainder of this paper is organized as follows. In Section

MIMO measurements with an

MIMO measurement system.

To measure the response of the single-input/single-output (SISO) channel, a two-port vector network analyzer is used. Both

Parameters of measurement.

Central frequency | 2.4 GHz |
---|---|

Frequency span | 500 MHz |

Number of frequency points | 801 |

Antenna type | 2.4 GHz omniantenna |

No. of transmit antennas | 3 |

No. of receive antennas | 3 |

The measurement sites are located in Electrical Engineering Building II at the National Taiwan University campus. Two dissimilar environments are selected for their different characteristics. Figure ^{2} area to obtain channel responses for sixteen positions. As a result, we obtain a total of 128 MIMO channel matrices at the end of the experiment. Figure

The experimental layout for indoor LOS environment.

The experimental layout for indoor NLOS environment.

For both environments, a large number of receiving locations are used to gather more statistical information for the environment. In addition, to remove the effect of attenuation or loss resulting from equipment, we calibrate the data by dividing the measured frequency response by that measured for 1-m

In this study, we investigate different polarization configurations: vertical (V), horizontal (H), and slanting (Y) polarizations (angle of slant =

Four antenna configurations which are denoted as (a)

Photos of the four different polarization combinations denoted as (a)

In this section, we analyze the measurement results obtained for the MIMO radio channels used in narrowband systems. Although our measurement system is wideband, we only use data in the frequency range 2.35–2.45 GHz, corresponding to 161 frequency points in the central region, because the antenna possesses a narrowband operational bandwidth. Thus, our discussion deals with narrowband analysis. Moreover, to analyze the capacity and eigenvalue of the measured data, we first need to normalize the data. For each location, let

We discuss the relationship between polarization and channel capacity. The method for normalizing the

The normalization method is different for the

In analyzing the capacity of an MIMO system,

For a fixed channel realization, the channel capacity has the following constraints:

To investigate the characteristics of

The columns of

Therefore, the channel capacity is affected not only by the maximal value of

If a channel has a low condition number, then its correlation is low, its diversity is high, and thus its capacity is high. The channel is then said to be “well conditioned.” Otherwise, the channel is referred to as being “ill conditioned” [

We modify the method of analysis of channel capacity for different polarization schemes. A different polarization configuration has a different received power owing to cross-polarization. Therefore, we consider the effect of the cross-polarization ratio (XPR) in different polarization schemes. Moreover, the use of the XPR for polarization antenna systems has been previously studied.

The XPR is defined as the ratio of the copolarized average received power to the cross-polarized average received power. The XPR has been used in the capacity analysis of different polarization combinations [

To obtain XPRs for different polarization cases, we normalize the

For a measured MIMO channel matrix

Our experiment focuses on indoor measurements. We intend to gain a deeper understanding of the effects of different polarizations from our experimental results.

The first and the second MIMO scenario performances are illustrated in terms of the cumulative distribution functions (CDFs) of their eigenvalues, as shown in Figures

The plots of CDF versus eigenvalues when the polarization system employing (a)

The plots of CDF versus eigenvalues when the polarization system employing (a)

Let us consider the channel correlation matrices listed in Tables

Correlation matrix for different polarization schemes in LOS environment.

Correlation matrix for different polarization schemes in NLOS environment.

We also examine the correlation for direct path power which defines the first path in time domain among the subchannels in the four polarization schemes. As shown in Tables

Correlation matrix of direct path power analysis for different polarization schemes in LOS environment.

Correlation matrix of direct path power analysis for different polarization schemes in NLOS environment.

Normalized power for different polarization schemes in indoor LOS environment.

Normalized power for different polarization schemes in indoor NLOS environment.

Average normalized power for various polarization schemes.

Measurement types | Polarization schemes | |||

LOS | 1 | 0.73 | 0.46 | 0.19 |

NLOS | 1 | 0.66 | 0.65 | 0.27 |

We now present results from the analysis of the measurement data in CDFs. The channel capacities of the four polarization schemes obtained from measurement and simulation analyses are, respectively, shown as straight and dotted lines in Figure

The plots of CDF versus capacities obtained by measurement analysis (solid line), proposed simulation analysis (dotted line) for dissimilar polarization systems in indoor LOS environment.

The plots of CDF versus capacities obtained by measurement analysis (solid line), proposed simulation analysis (dotted line) for dissimilar polarization systems in indoor NLOS environment.

By observing the CDF of capacity analysis under different conditions, it is found that the simulation analysis method, which makes use of (

For the NLOS condition, as shown in Figure

We introduced the concept of the MIMO system and factors that determined the channel capacity, including eigenvalues and correlation coefficients. We studied the effect of space and polarization diversity on the MIMO system in detail. Furthermore, we designed a series of experiments to determine the correlation between antenna polarization and the channel characteristics. From measurement data, the channel capacity and correlation coefficient were used for explaining the effects of various polarization schemes in the MIMO channels. Moreover, the concepts of normalizing the received power and the polarization effect were described in modifying the numerical analysis of the polarized channel capacity. In addition, we found that the performance of an MIMO system exploiting a copolarized antenna combination can be described simply using spatial correlation properties, but when adopting a cross-polarized antenna combination, both the isolation and correlation properties were needed to fully describe the system performance. Consequently, we found and verified the proposed algorithm of (

This work was supported by the National Science Council, Taiwan, under the Grant of NSC95-2219-E-002-003 and NSC97-2218-E027-007.