The Sherman-Morrison Formula for the Determinant and its Application for Optimizing Quadratic Functions on Condition Sets Given by Extreme Generators

Kéri, Gerzson

doi:10.1007/978-1-4613-0295-7_9

Cited by 13 publications

(11 citation statements)

References 10 publications

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“…Comparing the algorithms of Tables II and IV and making use of (23), we see that these two techniques lead to equivalent results. In particular, using (23), it is easy to show by induction that in the th step, the parameters and in line 4 of these algorithms are related as , whereas in line 12, in Table IV results in the same value as in Table II. In summary, the proposed algorithms of Tables I and II can be interpreted as QR decomposition-based techniques applied to a correspondingly row-permuted matrix .…”

Section: Qr Decomposition-based Interpretationmentioning

confidence: 75%

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Fast Antenna Subset Selection in MIMO Systems

Gharavi-Alkhansari

Gershman

2004

IEEE Trans. Signal Process.

356

260

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Multiple antenna wireless communication systems have recently attracted significant attention due to their higher capacity and better immunity to fading as compared to systems that employ a single-sensor transceiver. Increasing the number of transmit and receive antennas enables to improve system performance at the price of higher hardware costs and computational burden. For systems with a large number of antennas, there is a strong motivation to develop techniques with reduced hardware and computational costs. An efficient approach to achieve this goal is the optimal antenna subset selection.In this paper, we propose a fast antenna selection algorithm for wireless multiple-input multiple-output (MIMO) systems. Our algorithm achieves almost the same outage capacity as the optimal selection technique while having lower computational complexity than the existing nearly optimal antenna selection methods. The optimality of the proposed technique is established in several important specific cases. A QR decomposition-based interpretation of our algorithm is provided that sheds a new light on the optimal antenna selection problem.Index Terms-Channel capacity, MIMO wireless systems, optimal antenna subset selection.

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Section: Qr Decomposition-based Interpretationmentioning

confidence: 75%

“…By this selection, is inserted in a proper position in to obtain the channel matrix . Then, using (5), we have det (7) Noting that (8) and applying the Sherman-Morrison formula for determinants [23] to (7), we obtain that …”

Section: Proposed Algorithmmentioning

confidence: 98%

Fast Antenna Subset Selection in MIMO Systems

Gharavi-Alkhansari

Gershman

2004

IEEE Trans. Signal Process.

356

260

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“…According to the Sherman-Morrison formula [11] for determinants, D n+1,m can be updated using B n+1,m as …”

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confidence: 99%

Retraction: Iterative Transmit/Receive Antenna Selection in MIMO Systems Based on Channel Capacity Analysis

Lan

LIU

Sun

et al. 2013

IEICE Trans. Commun.

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SUMMARYThis letter introduces a closed form expression for the channel capacity increase achieved by adding a new pair of transmit and receive antennas. By analyzing this expression, an iterative transmit/receive antenna selection algorithm of low computational complexity is proposed. The new algorithm has higher computational complexity than some existing algorithms, but as the results show, the performance improvement of the proposed algorithm approaching more to the optimal algorithm.

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“…(9) and applying the Sherman-Morrison formula [10] , it can be obtained that (11) where D is the main diagonal of A ,and E is the off diagonal of A . Let us assume that the channel of every receive antenna is dependent, and denote the r -th row of k H by ( ) kr n h , and the r -th column of k W by ( ) kr n w .…”

Section: Capacity Maximization Selection Algorithmmentioning

confidence: 99%

Antenna subset selection in MU large-scale MIMO systems

Zhang

Chen

2013

2013 International Conference on Wireless Communications and Signal Processing

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Using a large number of transmit and receive antennas can significantly improve system performance at the price of higher hardware costs. For a large-scale MIMO system, an efficient approach to reduce the hardware cost is antenna selection. In this paper, we propose two fast antenna selection algorithms for wireless large-scale MIMO systems. The first algorithm is aiming to maximize the downlink sum-rate at a low computation complexity. Simulation results show that the proposed algorithm achieves nearly 2 dB gain in sum-capacity than the norm based selection (NBS) algorithm and has lower computational complexity than the optimal exhaust search scheme. The second algorithm minimizes the number of selected transmit antennas while maintaining a pre-defined user rate requirement, so as to reduce the hardware cost to the extreme. The performance of the proposed scheme is verified by simulation.

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The Sherman-Morrison Formula for the Determinant and its Application for Optimizing Quadratic Functions on Condition Sets Given by Extreme Generators

Cited by 13 publications

References 10 publications

Fast Antenna Subset Selection in MIMO Systems

Fast Antenna Subset Selection in MIMO Systems

Retraction: Iterative Transmit/Receive Antenna Selection in MIMO Systems Based on Channel Capacity Analysis

Antenna subset selection in MU large-scale MIMO systems

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