Service provided by fading MIMO channels: a deterministic perspective. Issue 17 (22nd October 2012)

• Record Type: Journal Article
• Authors: Dong, Yunquan; Fan, Pingyi; Letaief, Khaled Ben
• Is Part Of: Wireless communications and mobile computing. Volume 14:Issue 17(2014)
• Page Start: 1647
• Page End: 1656
• Publication Date: 2012-10-22
• Subjects: Wireless communication systems -- Periodicals; Mobile communication systems -- Periodicals; 621.38205
• DOI: 10.1002/wcm.2309
• Languages: English
• ISSNs: 1530-8669

Abstract

<abstract abstract-type="main" id="wcm2309-abs-0001"> <title>ABSTRACT</title> <p>In this paper, we study the channel service process of a multiple‐input multiple‐output (MIMO) system over an independent and identically distributed (<italic>i.i.d</italic>.) fading channel. One key problem of communication over fading MIMO channels is <italic>what kind of service the MIMO channel can provide</italic>. In this paper, this problem is investigated in terms of channel service process. Assuming that the channel state information is available at the receiver, the channel service process <italic>S</italic>(<italic>t</italic>) is defined as the integral of the instantaneous channel capacity over a time interval of length <italic>t</italic>, which specifies the service provided by the channel during the period. Using the characteristic function approach and the infinitely divisible law, it is proved that the channel service process <italic>S</italic>(<italic>t</italic>) is a deterministic linear function of time <italic>t</italic>, other than any curve form or a stochastic process. Specifically, <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1fdjvhb2" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:15308669:media:wcm2309:wcm2309-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi><mml:mrow><mml:mo class="MathClass-open">(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo class="MathClass-close">)</mml:mo></mml:mrow><mml:mo class="MathClass-rel">=</mml:mo><mml:msubsup><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>mimo</mml:mi></mml:mrow><mml:mrow><mml:mo class="MathClass-bin">*</mml:mo></mml:mrow></mml:msubsup><mml:mo class="MathClass-bin">⋅</mml:mo><mml:mi>t</mml:mi></mml:math></alternatives></inline-formula>, where <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1fdjvh8z" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:15308669:media:wcm2309:wcm2309-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>mimo</mml:mi></mml:mrow><mml:mrow><mml:mo class="MathClass-bin">*</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula> is a constant equal to the corresponding ergodic capacity. This result has two implications: (i) <italic>i.i.d</italic>. fading MIMO channels can support a constant rate traffic stream of rate <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1fdjvh6v" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:15308669:media:wcm2309:wcm2309-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>mimo</mml:mi></mml:mrow><mml:mrow><mml:mo class="MathClass-bin">*</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula> without higher layer transmission delay; (ii) the ergodic capacity is the actual transmission capacity of the fading channel, other than only a statistical average value. Copyright © 2012 John Wiley & Sons, Ltd.</p> </abstract>