Carrier interferometry

<h2 id="history-of-ci">History of CI</h2>
CI was introduced by Steve Shattil, a scientist at Idris Communications, in U.S. Pat. No. 5,955,992,<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a> filed February 12, 1998, and in the first of many papers<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> in April, 1999. The concept was inspired by optical <a href="/facts/Mode-locking/7p9MjBjT">mode-locking</a> in which frequency-domain synthesis using a resonant cavity produces desired time-domain features in the transmitted optical signal. In radio systems, users share the same subcarriers, but use different orthogonal CI codes to achieve Carrier Interference Multiple Access (CIMA) via <a href="/facts/Spectral_interferometry/VlwWeo2q">spectral interferometry</a> mechanisms.
Many applications of CI principles were published in dozens of subsequent patent filings, conference papers, and journal articles. CI in frequency-hopped OFDM is described in the international patent application WO 9941871.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> CI in <a href="/facts/Fiber-optic_communication/dc6S0Hg5">optical fiber communications</a> and <a href="/facts/MIMO/1EXPB7Vl">MIMO</a> is described in US 7076168.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> US 6331837<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> describes spatial demultiplexing using multicarrier signals that eliminates the need for multiple receiver antennas. CI coding of reference signals is disclosed in US 7430257.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> The use of CI for linear network coding and onion coding is disclosed in US 20080095121<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> in which random linear codes based on the natural multipath channel are used to encode transmitted signals routed by nodes in a multi-hop peer-to-peer network.
The similarity between antenna array processing and CI processing was recognized since the earliest work in CI. When CI is combined with <a href="/facts/Phased_array/5wvA9WLV">phased arrays</a>, the continuous phase change between subcarriers causes the array's beam pattern to scan in space, which achieves transmit diversity and represents an early form of <a href="/facts/Cyclic_delay_diversity/eY33yfC7">cyclic delay diversity</a>.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a><a class="footnote-ref" id="fnref:12" href="#fn:12">12</a><a class="footnote-ref" id="fnref:13" href="#fn:13">13</a> Combinations of CI coding with MIMO precoding have been studied,<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a> and the idea of using CI in MIMO pre-coded <a href="/facts/Distributed_antenna_system/pj9SGWYb">distributed antenna systems</a> with central coordination was first disclosed in a provisional patent application in 2001.<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a> CI-based <a href="/facts/Software-defined_radio/k7qLq1mu">software-defined radio</a> (SDR) that implemented four different protocol stacks was developed at Idris in 2000 and described in US 7418043.<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a>

<h2 id="mathematical-description">Mathematical description</h2>
In spread-OFDM, spreading is performed across orthogonal subcarriers to produce a transmit signal expressed by
x = F−1Sb
where F−1 is an inverse DFT, S is a spread-OFDM code matrix, and b is a data symbol vector. The inverse DFT typically employs an over-sampling factor, so its dimension is KxN (where K > N is the number of time-domain samples per OFDM symbol block), whereas the dimension of the spread-OFDM code matrix is NxN.
At the receiver, the received spread-OFDM signal is expressed by
r = HF−1Sb,
where H represents a channel matrix. Since the use of a cyclic prefix in OFDM changes the Toeplitz-like channel matrix into a circulant matrix, the received signal is represented by
r = F−1ΛHFF−1Sb

= F−1ΛHSb

where the relationship H = F−1ΛHF is from the definition of a circulant matrix, and ΛH is a diagonal matrix whose diagonal elements correspond to the first column of the circulant channel matrix H. The receiver employs a DFT (as is typical in OFDM) to produce
y = ΛHSb.
In the trivial case, S = I, where I is the identity matrix, gives regular OFDM without spreading.
The received signal can also be expressed as:
r = F−1ΛHFF−1(ΛCF)b,
where S = ΛCF, and C is a circulant matrix defined by C = F−1ΛCF, where ΛC is the circulant's diagonal matrix. Thus, the received signal, r, can be written as
r = F−1ΛHΛCFb = F−1ΛCΛHFb,
and the signal y after the receiver's DFT is y = ΛCΛHFb
The spreading matrix S can include a pre-equalization diagonal matrix (e.g., ΛC = ΛH−1 in the case of zero-forcing), or equalization can be performed at the receiver between the DFT (OFDM demodulator) and the inverse-DFT (CI de-spreader).
In the simplest case of CI-OFDM, the spreading matrix is S = F (i.e., ΛC = I, so the CI spreading matrix is just the NxN DFT matrix). Since OFDM's over-sampled DFT is KxN, with K>N, the basic CI spreading matrix performs like a sinc pulse-shaping filter which maps each data symbol to a cyclically shifted and orthogonally positioned pulse formed from a superposition of OFDM subcarriers. Other versions of CI can produce alternative pulse shapes by selecting different diagonal matrices ΛC.

<h2 id="useful-properties">Useful properties</h2>
<ol><li>Low PAPR (<a href="/facts/Crest_factor/blwdPwdU">Crest Factor</a>)</li>
<li>Low sensitivity to non-linear distortion</li>
<li>Low sensitivity to <a href="/facts/Carrier_frequency_offset/CJ8TH8nA">carrier-frequency offset</a></li>
<li>Robustness to deep fades (spectral nulls)</li></ol>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Subcarrier_multiplexing/tYT1KzML">Subcarrier multiplexing</a></li>
<li><a href="/facts/Multi-carrier_code-division_multiple_access/UbxvJLy1">MC-CDMA</a></li>
<li><a href="/facts/Orthogonal_frequency-division_multiplexing/YhPkx5ql">OFDM</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Multi-Carrier Technologies for Wireless Communication (2002 ed.). Stanford, Calif: Springer. 2001-11-30. ISBN 9780804725071. <a href="9780804725071" target="_blank">9780804725071</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Zhiqiang Wu; Nassar, C.; Shattil, S. (2001). "Ultra wideband DS-CDMA via innovations in chip shaping". IEEE 54th Vehicular Technology Conference. VTC Fall 2001. Proceedings (Cat. No.01CH37211). Vol. 4. pp. 2470–2474. doi:10.1109/VTC.2001.957194. ISBN 978-0-7803-7005-0. S2CID 28052623. <a href="978-0-7803-7005-0" target="_blank">978-0-7803-7005-0</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Natarajan, B.; Nassar, C.R.; Shattil, S. (2001). "Enhanced Bluetooth and IEEE 802.11 (FH) via multi-carrier implementation of the physical layer". 2001 IEEE Emerging Technologies Symposium on Broad Band Communications for the Internet Era. Symposium Digest (Cat. No.01EX508). pp. 129–133. doi:10.1109/ETS.2001.979440. ISBN 978-0-7803-7161-3. S2CID 16077120. <a href="978-0-7803-7161-3" target="_blank">978-0-7803-7161-3</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">US 5955992, "Frequency-shifted feedback cavity used as a phased array antenna controller and carrier interference multiple access spread-spectrum transmitter" <a href="http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US5955992" target="_blank">http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US5955992</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Nassar, C.R.; Natarajan, B.; Shattil, S. (1999). "Introduction of carrier interference to spread spectrum multiple access". 1999 IEEE Emerging Technologies Symposium. Wireless Communications and Systems (IEEE Cat. No.99EX297). pp. 4.1 – 4.5. doi:10.1109/ETWCS.1999.897312. hdl:2097/4274. ISBN 978-0-7803-5554-5. S2CID 37339498. <a href="978-0-7803-5554-5" target="_blank">978-0-7803-5554-5</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">WO9941871, "Multiple Access System and Method" <a href="http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=WO9941871" target="_blank">http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=WO9941871</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">US 7076168, "Method and apparatus for using multicarrier interferometry to enhance optical fiber communications" <a href="http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7076168" target="_blank">http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7076168</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">US 6331837, "Spatial interferometry multiplexing in wireless communications" <a href="http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US6331837" target="_blank">http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US6331837</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">US 7430257, "Multicarrier sub-layer for direct sequence channel and multiple-access coding" <a href="http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7430257" target="_blank">http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7430257</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">US 20080095121, "Carrier interferometry networks" <a href="http://worldwide.espacenet.com/publicationDetails/biblio?FT=D&date=20080424&DB=worldwide.espacenet.com&locale=en_EP&CC=US&NR=2008095121A1&KC=A1&ND=4" target="_blank">http://worldwide.espacenet.com/publicationDetails/biblio?FT=D&date=20080424&DB=worldwide.espacenet.com&locale=en_EP&CC=US&NR=2008095121A1&KC=A1&ND=4</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Zekavat, Seyed Alireza; Nassar, Carl R.; Shattil, Steve (2000). "Smart antenna spatial sweeping for combined directionality and transmit diversity". Journal of Communications and Networks. 2 (4): 325–330. doi:10.1109/JCN.2000.6596766. S2CID 18877233. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Zekavat, S.A.; Nassar, C.R.; Shattil, S. (2002). "Merging DS-CDMA (With CI chip shapes) and oscillating-beam smart antenna arrays: Exploiting transmit diversity, frequency diversity and directionality". 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333). Vol. 2. pp. 742–747. doi:10.1109/ICC.2002.996954. ISBN 978-0-7803-7400-3. S2CID 33663974. <a href="978-0-7803-7400-3" target="_blank">978-0-7803-7400-3</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Shattil, S.; Nassar, C.R. (1999). "Array control systems for multicarrier protocols using a frequency-shifted feedback cavity". RAWCON 99. 1999 IEEE Radio and Wireless Conference (Cat. No.99EX292). pp. 215–218. doi:10.1109/RAWCON.1999.810968. ISBN 978-0-7803-5454-8. S2CID 108425375. <a href="978-0-7803-5454-8" target="_blank">978-0-7803-5454-8</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Barbosa, P.R.; Zhiqiang Wu; Nassar, C.R. (2003). "High-Performance MIMO-OFDM via Carrier Interferometry". GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489). Vol. 2. pp. 853–857. doi:10.1109/GLOCOM.2003.1258360. ISBN 978-0-7803-7974-9. S2CID 20747953. <a href="978-0-7803-7974-9" target="_blank">978-0-7803-7974-9</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">US Pat. Appl. 60286850, “Method and apparatus for using Carrier Interferometry to process multi-carrier signals” <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">US 7418043, "Software adaptable high performance multicarrier transmission protocol" <a href="http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7418043" target="_blank">http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7418043</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
</ol>

Carrier interferometry open-in-new

Carrier interferometry