Kronecker Model

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Ernst Bonek - One of the best experts on this subject based on the ideXlab platform.

  • A Novel Stochastic MIMO Channel Model and Its Physical Interpretation
    2020
    Co-Authors: Werner Weichselberger, Ernst Bonek
    Abstract:

    We present a novel stochastic channel Model for multiple-input multiple-output (MIMO) wireless radio channels. In contrast to state of the art stochastic MIMO channel Models, we do not divide the spatial correlation properties of the channel into separate contributions from transmitter and receiver. We rather Model the joint correlation properties by describing the average coupling between the eigenmodes of the two link ends. The structure of this coupling is shown to be crucial for the spatial properties of a MIMO channel. We discuss the mathematical elements of the Model from a radio propagation point of view, and explain the physical restrictions on the MIMO setup imposed by the Model. A comparison to the more restrictive but popular ‘KroneckerModel is provided. Finally, we show that our Model is capable of correctly predicting the mutual information of measured indoor MIMO channels.

  • Experimental Study of MIMO Channel Statistics and Capacity via Virtual Channel Representation
    2020
    Co-Authors: Yan Zhou, Markus Herdin, Akbar M. Sayeed, Ernst Bonek
    Abstract:

    This work presents an experimental study of MIMO channel statistics and capacity via the recently proposed virtual channel representation, which describes the channel by a finite number of fixed virtual transmit/receive angles and delays. Our results confirm two important implications of virtual path partitioning: the virtual coefficients are approximately uncorrelated, and there exist fundamental angle-delay dependencies which limit the degrees of freedom in MIMO channels. The virtual channel power matrix reflects the distribution of channel power in angle-delay domain, quantifies the spatial-frequency correlation of actual channel coefficients, and also provides an intuitive explanation of the impact of scattering environments on capacity. The Modeling accuracy of the popular Kronecker Model, as well as the recently proposed eigenbeam Model, is compared to the virtual channel Model. The results indicate that both the virtual and eigenbeam Models achieve good prediction accuracy, because they can Model nonseparable 2D angular spectrum, while the Kronecker Model results in larger prediction error due to the restrictive structure.

  • On the practical use of analytical MIMO channel Models
    2005 IEEE Antennas and Propagation Society International Symposium, 2005
    Co-Authors: C. Oestges, H. Ozcelik, Ernst Bonek
    Abstract:

    The practical use of so-called analytical Models for representing measured and simulated narrowband MIMO channels is discussed with respect to several metrics. Four analytical Models are compared (the Kronecker Model, the Weichselberger Model, the virtual channel representation, and the diagonal-decorrelation Model) using several performance metrics. The investigation is based upon indoor experimental results at 5.2 GHz as well as geometry-based statistical propagation Models.

  • Experimental validation of analytical MIMO channel Models
    Elektrotechnik Und Informationstechnik, 2005
    Co-Authors: Ernst Bonek
    Abstract:

    The promise of multiple-input multiple-output systems (MIMO) to overcome the radio bottleneck in high-speed data transmission requires detailed Models of the spatio-temporal MIMO channel to come true. In this paper, popular MIMO channel Models are compared with two independent measurement campaigns at 2 and 5 GHz by using four different, mostly novel performance figures (or metrics). Each of these metrics describes one or more different aspects of MIMO, such as multiplexing gain, spatial diversity, or beamforming. Of the Models investigated, the Weichselberger Model performs overall best, whereas the Kronecker Model should be used only for limited antenna numbers, such as 2 × 2, and “the virtual channel representation” only for very large antenna numbers.

  • What Makes a Good MIMO Channel Model?
    2005
    Co-Authors: Huseyin Ozcelik, Nicolai Czink, Ernst Bonek
    Abstract:

    Using different meaningful measures of quality, this paper investigates the accuracy of analytical MIMO channel Models. Different metrics should be applied if the underlying MIMO channel supports predominantly beamforming, spatial multiplexing or diversity. The number of envisaged antennas plays an important role. By comparing the results of an extensive indoor measurement campaign at 5.2 GHz, we find the following main conclusions: (i) The recently developed Weichselberger Model predicts capacity for any antenna number and represents diversity best of all three Models, but still not satisfactorily. (ii) Except for 2 × 2 MIMO systems the Kronecker Model fails to predict capacity, joint angular power spectrum, and diversity. (iii) The virtual channel representation should only be used for Modeling the joint angular power spectrum for very large antenna numbers. The answer to the question given in the title: The appropriate Model has to be chosen according to the considered application

Evgeny A. Mavrychev - One of the best experts on this subject based on the ideXlab platform.

Francois Chin - One of the best experts on this subject based on the ideXlab platform.

  • WCNC - Kronecker Modelling for Correlated Shadowing in UWB MIMO Channels
    2007 IEEE Wireless Communications and Networking Conference, 2007
    Co-Authors: Xiaoming Peng, Francois Chin
    Abstract:

    The shadowing in ultra wideband (UWB) channels may degrade the system performance significantly. Although UWB multipath channels exhibit high resolution in space and time. The large scale shadow fading were moderately correlated based on UWB indoor channel measurement. In this paper, a new Modelling method for correlated shadowing with log-normal distribution in UWB multiple-input multiple-output (MIMO) channels is proposed based on the Kronecker Model and IEEE 802.15.3a channel Model recommendation. Moreover, antenna selection technique with low hardware complexity is proposed for a UWB system with multiple receive or transmit antennas to mitigate its channel shadowing effect. The BER performance for orthogonal frequency division multiplexing (OFDM) UWB system with power based antenna selection is evaluated. Antenna selection technique is shown to be effective in mitigating the correlated shadow fading.

  • Kronecker Modelling for correlated shadowing in UWB MIMO channels
    IEEE Wireless Communications and Networking Conference WCNC, 2007
    Co-Authors: Zhiwei Lin, Khiam Boon Png, Xiaoming Peng, Francois Chin
    Abstract:

    The shadowing in ultra wideband (UWB) channels may degrade the system performance significantly. Although UWB multipath channels exhibit high resolution in space and time. The large scale shadow fading were moderately correlated based on UWB indoor channel measurement. In this paper, a new Modelling method for correlated shadowing with log-normal distribution in UWB multiple-input multiple-output (MIMO) channels is proposed based on the Kronecker Model and IEEE 802.15.3a channel Model recommendation. Moreover, antenna selection technique with low hardware complexity is proposed for a UWB system with multiple receive or transmit antennas to mitigate its channel shadowing effect. The BER performance for orthogonal frequency division multiplexing (OFDM) UWB system with power based antenna selection is evaluated. Antenna selection technique is shown to be effective in mitigating the correlated shadow fading.

Mats Bengtsson - One of the best experts on this subject based on the ideXlab platform.

  • WCSP - On the performance of Kronecker MIMO channel Models: A semi-definite relaxation approach
    2011 International Conference on Wireless Communications and Signal Processing (WCSP), 2011
    Co-Authors: Nafiseh Shariati, Mats Bengtsson
    Abstract:

    The Kronecker Model Is a popular structure In the design and analysis of multiple-input multiple-output (MIMO) systems. Despite being criticized for unrealistic results in some cases, it mathematically facilitates the analysis of MIMO transmission schemes. In our earlier work [1], we proposed algorithms in order to determine a MIMO channel covariance matrix which is as far as possible from the Kronecker Model based on semi-definite relaxation approach. In this paper, we develop this approach for different case studies. In particular, we verify our proposed algorithms for different size of antennas. Further, as a case study for the relevance of the Kronecker assumption, numerical analysis will be carried out to evaluate the performance of optimal pilot design for Kronecker and non-Kronecker MIMO channels.

  • How Far from Kronecker can a MIMO Channel be? Does it Matter?
    17th European Wireless 2011 - Sustainable Wireless Technologies, 2011
    Co-Authors: Nafiseh Shariati, Mats Bengtsson
    Abstract:

    A common assumption in the design and analysis of many MIMO transmission schemes is the so-called Kronecker Model. This Model is often a crucial step to obtain mathematically tractable solutions, but has also been criticized for being unrealistic. In this paper, we present a numerical approach to determine a channel whose statistics is as far from being Kronecker as possible, keeping only an assumption of spatial stationarity. As a case study for the relevance of the Kronecker assumption, a numerical analysis is included of the performance of optimal pilot design for Kronecker and non-Kronecker channels. The numerical results indicate that for this particular application, the Kronecker assumption may be used in the algorithm design and provide performance that is close to optimal also for non-Kronecker channels.

  • On the performance of Kronecker MIMO channel Models: A semi-definite relaxation approach
    2011 International Conference on Wireless Communications and Signal Processing (WCSP), 2011
    Co-Authors: Nafiseh Shariati, Mats Bengtsson
    Abstract:

    The Kronecker Model is a popular structure in the design and analysis of multiple-input multiple-output (MIMO) systems. Despite being criticized for unrealistic results in some cases, it mathematically facilitates the analysis of MIMO transmission schemes. In our earlier work [1], we proposed algorithms in order to determine a MIMO channel covariance matrix which is as far as possible from the Kronecker Model based on semi-definite relaxation approach. In this paper, we develop this approach for different case studies. In particular, we verify our proposed algorithms for different size of antennas. Further, as a case study for the relevance of the Kronecker assumption, numerical analysis will be carried out to evaluate the performance of optimal pilot design for Kronecker and non-Kronecker MIMO channels.

Magnus Jansson - One of the best experts on this subject based on the ideXlab platform.

  • estimating mimo channel covariances from training data under the Kronecker Model
    Signal Processing, 2009
    Co-Authors: Karl Werner, Magnus Jansson
    Abstract:

    Many algorithms for transmission in multiple input multiple output (MIMO) communication systems rely on second order statistics of the channel realizations. The problem of estimating such second order statistics of MIMO channels, based on limited amounts of training data, is treated in this article. It is assumed that the Kronecker Model holds. This implies that the channel covariance is the Kronecker product of one covariance matrix that is associated with the array and the scattering at the transmitter and one that is associated with the receive array and the scattering at the receiver. The proposed estimator uses training data from a number of signal blocks (received during independent fades of the MIMO channel) to compute the estimate. This is in contrast to methods that assume that the channel realizations are directly available, or possible to estimate almost without error. It is also demonstrated how methods that make use of the training data indirectly via channel estimates can be biased. An estimator is derived that can, in an asymptotically optimal way, use, not only the structure implied by the Kronecker assumption, but also linear structure on the transmit- and receive covariance matrices. The performance of the proposed estimator is analyzed and numerical simulations illustrate the results and also provide insight into the small sample behaviour of the proposed method.