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<title>Space–time code</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Space–time code</span></span>

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<p>A <b>space–time code</b> (<b>STC</b>) is a method employed to improve the reliability of data <a href="Transmission_(telecommunications)" class="mw-redirect" title="Transmission (telecommunications)">transmission</a> in <a href="Wireless" title="Wireless">wireless communication systems</a> using multiple transmit <a href="Antenna_(radio)" title="Antenna (radio)">antennas</a>. STCs rely on transmitting multiple, <a href="Redundancy_(information_theory)" title="Redundancy (information theory)">redundant</a> copies of a data stream to the <a href="Receiver_(radio)" class="mw-redirect" title="Receiver (radio)">receiver</a> in the hope that at least some of them may survive the <a href="Transmission_medium" title="Transmission medium">physical path</a> between transmission and reception in a good enough state to allow reliable decoding.

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<div class="mw-heading mw-heading2"><h2 id="Types">Types</h2></div>

<p>Space time codes may be split into two main types:

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<ul><li><a href="Space%E2%80%93time_trellis_code" title="Space–time trellis code">Space–time trellis codes</a> (STTCs)<sup id="cite_ref-construction_1-0" class="reference"><a href="#cite_note-construction-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> distribute a <a href="Convolutional_code" title="Convolutional code">trellis code</a> over multiple antennas and multiple time-slots and provide both coding gain and <a href="Diversity_reception" class="mw-redirect" title="Diversity reception">diversity gain</a>.</li>

<li><a href="Space%E2%80%93time_block_code" title="Space–time block code">Space–time block codes</a> (STBCs)<sup id="cite_ref-alamouti_2-0" class="reference"><a href="#cite_note-alamouti-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-orthog_3-0" class="reference"><a href="#cite_note-orthog-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> act on a block of data at once (similarly to <a href="Block_code" title="Block code">block codes</a>) and also provide <a href="Diversity_reception" class="mw-redirect" title="Diversity reception">diversity gain</a> but doesn't provide coding gain.</li>

<li>Space–time line codes (STLCs)<sup id="cite_ref-STLC_4-0" class="reference"><a href="#cite_note-STLC-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and STBCs are symmetric with respect to the transmit-and-receive processes, like a <a href="Maximal-ratio_combining" title="Maximal-ratio combining">maximum-ratio combining</a> (MRC) and maximum-ratio transmission (MRT). The STLC scheme provides full <a href="Diversity_reception" class="mw-redirect" title="Diversity reception">diversity gain</a> even when there is no full channel state information (CSI) at the receiver.</li></ul>

<p>STC may be further subdivided according to whether the receiver knows the <a href="Channel_(communications)" class="mw-redirect" title="Channel (communications)">channel</a> impairments. In coherent STC, the receiver knows the channel impairments through training or some other form of estimation. These codes have been studied more widely, and <a href="Division_algebra" title="Division algebra">division algebras</a><sup id="cite_ref-divalg_5-0" class="reference"><a href="#cite_note-divalg-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> over number fields have now become the standard tool for constructing such codes.

</p><p>In <a href="Noncoherent_STC" title="Noncoherent STC">noncoherent STC</a> the receiver does not know the channel impairments but knows the statistics of the channel.<sup id="cite_ref-hm_6-0" class="reference"><a href="#cite_note-hm-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> In <a href="Differential_space%E2%80%93time_code" title="Differential space–time code">differential space–time codes</a> neither the channel nor the statistics of the channel are available.<sup id="cite_ref-jsac_7-0" class="reference"><a href="#cite_note-jsac-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

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<ul><li><a href="Diversity_scheme" title="Diversity scheme">Diversity scheme</a> – the concept from which STC arose.</li>

<li><a href="MIMO" title="MIMO">MIMO</a> – the term for wireless communication systems employing multiple antennas at both a transmitter and a receiver.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFVahid_TarokhNambi_SeshadriA._R._Calderbank1998" class="citation journal cs1">Vahid Tarokh; Nambi Seshadri & A. R. Calderbank (March 1998). "Space–time codes for high data rate wireless communication: Performance analysis and code construction". <i>IEEE Transactions on Information Theory</i>. <b>44</b> (2): <span class="nowrap">744–</span>765. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.4293">10.1.1.112.4293</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F18.661517">10.1109/18.661517</a>.</cite></span>

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<li id="cite_note-alamouti-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-alamouti_2-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFS.M._Alamouti1998" class="citation journal cs1">S.M. Alamouti (October 1998). "A simple transmit diversity technique for wireless communications". <i>IEEE Journal on Selected Areas in Communications</i>. <b>16</b> (8): <span class="nowrap">1451–</span>1458. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F49.730453">10.1109/49.730453</a>.</cite></span>

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<li id="cite_note-orthog-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-orthog_3-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFVahid_TarokhHamid_JafarkhaniA._R._Calderbank1999" class="citation journal cs1">Vahid Tarokh; Hamid Jafarkhani & A. R. Calderbank (July 1999). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091229160912/http://www.mast.queensu.ca/~math800/W03/papers/TrkhJafarkCldb_IT99.pdf">"Space–time block codes from orthogonal designs"</a> <span class="cs1-format">(PDF)</span>. <i><a href="IEEE_Transactions_on_Information_Theory" title="IEEE Transactions on Information Theory">IEEE Transactions on Information Theory</a></i>. <b>45</b> (5): <span class="nowrap">1456–</span>1467. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.4537">10.1.1.138.4537</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F18.771146">10.1109/18.771146</a>. Archived from <a rel="nofollow" class="external text" href="http://www.mast.queensu.ca/~math800/W03/papers/TrkhJafarkCldb_IT99.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2009-12-29.</cite></span>

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<li id="cite_note-STLC-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-STLC_4-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFJingon_Joung2017" class="citation journal cs1">Jingon Joung (November 2017). <a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FACCESS.2017.2777528">"Space–Time Line Code"</a>. <i><a href="IEEE_Access" title="IEEE Access">IEEE Access</a></i>. <b>6</b>: <span class="nowrap">1023–</span>1041. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FACCESS.2017.2777528">10.1109/ACCESS.2017.2777528</a></span>.</cite></span>

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<li id="cite_note-divalg-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-divalg_5-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFB.A._SethuramanB._Sundar_RajanV._Shashidhar2003" class="citation journal cs1">B.A. Sethuraman; B. Sundar Rajan & V. Shashidhar (October 2003). "Full-diversity, high-rate space-time block codes from division algebras". <i>IEEE Transactions on Information Theory</i>. <b>49</b> (10): <span class="nowrap">2596–</span>2616. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Ftit.2003.817831">10.1109/tit.2003.817831</a>.</cite></span>

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<li id="cite_note-hm-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-hm_6-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFMarzetta,_T.L.Hochwald,_B.M.1999" class="citation journal cs1">Marzetta, T.L. & Hochwald, B.M. (January 1999). "Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading". <i>IEEE Transactions on Information Theory</i>. <b>45</b> (1): <span class="nowrap">139–</span>157. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.4611">10.1.1.134.4611</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F18.746779">10.1109/18.746779</a>.</cite></span>

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<li id="cite_note-jsac-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-jsac_7-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFV._Tarokh_and_H._Jafarkhani2000" class="citation journal cs1">V. Tarokh and <a href="Hamid_Jafarkhani" title="Hamid Jafarkhani">H. Jafarkhani</a> (July 2000). "A Differential Detection Scheme for Transmit Diversity". <i>IEEE Journal on Selected Areas in Communications</i>. <b>18</b> (7): <span class="nowrap">1169–</span>1174. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.421.8007">10.1.1.421.8007</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F49.857917">10.1109/49.857917</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1507749">1507749</a>.</cite></span>

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<div class="mw-heading mw-heading2"><h2 id="General_references">General references</h2></div>

<ul><li>Louay M.A. Jalloul and Sam. P. Alex, "Evaluation Methodology and Performance of an IEEE 802.16e System", Presented to the IEEE Communications and Signal Processing Society, Orange County Joint Chapter (ComSig), December 7, 2006. Available at: <a rel="nofollow" class="external free" href="http://chapters.comsoc.org/comsig/meet.html">http://chapters.comsoc.org/comsig/meet.html</a></li>

<li>Sam P. Alex and Louay M.A. Jalloul, "Performance Evaluation of MIMO in IEEE802.16e/WiMAX", IEEE Journal of Selected Topics in Signal Processing, VOL. 2, NO. 2, April, 2008.</li></ul></div><div><div class="zim-footer">

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