View source for Engineering:Carrier interferometry

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'''Carrier Interferometry''' '''(CI)''' is a [[Spread spectrum|spread spectrum]] scheme designed to be used in an [[Orthogonal frequency-division multiplexing|Orthogonal Frequency-Division Multiplexing]] (OFDM) communication system for [[Engineering:Multiplexing|multiplexing]] and multiple access, enabling the system to support multiple users at the same time over the same frequency band.

Like [[Engineering:Multi-carrier code-division multiple access|MC-CDMA]], CI-OFDM spreads each data symbol in the frequency domain. That is, each data symbol is carried over multiple OFDM subcarriers. But unlike MC-CDMA, which uses binary-phase [[Hadamard code|Hadamard]] codes (code values of 0 or 180 degrees) or binary pseudonoise, CI codes are complex-valued [[Orthogonality|orthogonal]] codes. In the simplest case, CI code values are coefficients of a [[Discrete Fourier transform (general)|discrete Fourier transform]] (DFT) matrix. Each row or column of the DFT matrix provides an orthogonal CI spreading code which spreads a data symbol. Spreading is achieved by multiplying a vector of data symbols by the DFT matrix to produce a vector of coded data symbols, then each coded data symbol is mapped to an OFDM subcarrier via an input bin of an inverse [[Fast Fourier transform|fast Fourier transform]] (IFFT). A block of contiguous subcarriers may be selected, or to achieve better frequency diversity, non-contiguous subcarriers distributed over a wide frequency band can be used. A guard interval, such as a cyclic prefix (CP), is added to the baseband CI-OFDM signal before the signal is processed by a radio front-end to convert it to an RF signal, which is then transmitted by an antenna.

A significant advantage of CI-OFDM over other OFDM techniques is that CI spreading shapes the time-domain characteristics of the transmitted waveform. Thus, CI-OFDM signals have a much lower peak-to-average-power ratio (PAPR), or [[Crest factor|crest factor]], compared to other types of OFDM.<ref>{{Cite book|edition = 2002|title = Multi-Carrier Technologies for Wireless Communication|publisher = Springer|date = 2001-11-30|location = Stanford, Calif|isbn = 9780804725071}}</ref> This greatly improves power efficiency and reduces the cost of power amplifiers used in the radio transmitter.

A CI-OFDM receiver removes the cyclic prefix from a received CI-OFDM transmission and performs OFDM demodulation with a DFT (e.g., an FFT) typically used in OFDM receivers. The CI-spread symbol values are collected from their respective subcarriers in an inverse-mapping process and may be equalized to compensate for multipath fading or processed for [[Spatial multiplexing|spatial demultiplexing]]. The CI de-spreader performs an inverse-DFT on the spread symbols to recover the original data symbols.
[[File:CI Transceiver copy.jpg|alt=CI-OFDM Transmitter and Receiver|thumb|CI-OFDM Transmitter and Receiver]]
Since CI coding can shape the time-domain characteristics of the transmitted waveform, it can be used to synthesize various waveforms, such as [[Direct-sequence spread spectrum|direct-sequence spread spectrum]]<ref>{{Cite book |doi = 10.1109/VTC.2001.957194 |isbn = 978-0-7803-7005-0|chapter = Ultra wideband DS-CDMA via innovations in chip shaping|title = IEEE 54th Vehicular Technology Conference. VTC Fall 2001. Proceedings (Cat. No.01CH37211)|volume = 4|pages = 2470–2474|year = 2001|last1 = Zhiqiang Wu|last2 = Nassar|first2 = C.|last3 = Shattil|first3 = S.| s2cid=28052623 }}</ref> and [[Engineering:Frequency-shift keying|frequency shift key]]<ref>{{Cite book |doi = 10.1109/ETS.2001.979440 |isbn = 978-0-7803-7161-3|chapter = Enhanced Bluetooth and IEEE 802.11 (FH) via multi-carrier implementation of the physical layer|title = 2001 IEEE Emerging Technologies Symposium on Broad ''Band'' Communications for the Internet Era. Symposium Digest (Cat. No.01EX508)|pages = 129–133|year = 2001|last1 = Natarajan|first1 = B.|last2 = Nassar|first2 = C.R.|last3 = Shattil|first3 = S.| s2cid=16077120 }}</ref> [4] signals. The advantage is that the receiver can select time-domain or frequency-domain [[Equalization (communications)|equalization]] based on how much scattering occurs in the transmission channel. For rich scattering environments, frequency-domain equalization using FFTs requires less computation than conventional time-domain equalization and performs substantially better.

==History of CI==
CI was introduced by Steve Shattil, a scientist at Idris Communications, in U.S. Pat. No. 5,955,992,<ref>[http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US5955992 US 5955992], "Frequency-shifted feedback cavity used as a phased array antenna controller and carrier interference multiple access spread-spectrum transmitter"</ref> filed February 12, 1998, and in the first of many papers<ref>{{Cite book |doi = 10.1109/ETWCS.1999.897312 |isbn = 978-0-7803-5554-5|chapter = Introduction of carrier interference to spread spectrum multiple access|title = 1999 IEEE Emerging Technologies Symposium. Wireless Communications and Systems (IEEE Cat. No.99EX297)|pages = 4.1–4.5|year = 1999|last1 = Nassar|first1 = C.R.|last2 = Natarajan|first2 = B.|last3 = Shattil|first3 = S.|hdl = 2097/4274| s2cid=37339498 }}</ref> in April, 1999. The concept was inspired by optical [[Physics:Mode-locking|mode-locking]] 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 [[Physics:Spectral interferometry|spectral interferometry]] 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.<ref>[http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=WO9941871 WO9941871], "Multiple Access System and Method"</ref> CI in [[Physics:Fiber-optic communication|optical fiber communications]] and [[MIMO]] is described in US 7076168.<ref>[http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7076168 US 7076168], "Method and apparatus for using multicarrier interferometry to enhance optical fiber communications"</ref> US 6331837<ref>[http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US6331837 US 6331837], "Spatial interferometry multiplexing in wireless communications"</ref> describes spatial demultiplexing using multicarrier signals that eliminates the need for multiple receiver antennas. CI coding of reference signals is disclosed in US 7430257.<ref>[http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7430257 US 7430257], "Multicarrier sub-layer for direct sequence channel and multiple-access coding"</ref> The use of CI for linear network coding and onion coding is disclosed in US 20080095121<ref>[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 US 20080095121], "Carrier interferometry networks"</ref> 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 [[Engineering:Phased array|phased array]]s, 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 cyclic delay diversity.<ref>{{Cite journal |doi = 10.1109/JCN.2000.6596766 |title = Smart antenna spatial sweeping for combined directionality and transmit diversity |journal = Journal of Communications and Networks |volume = 2 |issue = 4 |pages = 325–330 |year = 2000 |last1 = Zekavat |first1 = Seyed Alireza |last2 = Nassar |first2 = Carl R. |last3 = Shattil |first3 = Steve |s2cid = 18877233 }}</ref><ref>{{Cite book |doi = 10.1109/ICC.2002.996954 |isbn = 978-0-7803-7400-3|chapter = Merging DS-CDMA (With CI chip shapes) and oscillating-beam smart antenna arrays: Exploiting transmit diversity, frequency diversity and directionality|title = 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333)|volume = 2|pages = 742–747|year = 2002|last1 = Zekavat|first1 = S.A.|last2 = Nassar|first2 = C.R.|last3 = Shattil|first3 = S.| s2cid=33663974 }}</ref><ref>{{Cite book  |doi = 10.1109/RAWCON.1999.810968 |isbn = 978-0-7803-5454-8|chapter = Array control systems for multicarrier protocols using a frequency-shifted feedback cavity|title = RAWCON 99. 1999 IEEE Radio and Wireless Conference (Cat. No.99EX292)|pages = 215–218|year = 1999|last1 = Shattil|first1 = S.|last2 = Nassar|first2 = C.R.| s2cid=108425375 }}</ref> Combinations of CI coding with MIMO precoding have been studied,<ref>{{Cite book |doi = 10.1109/GLOCOM.2003.1258360 |isbn = 978-0-7803-7974-9|chapter = High-Performance MIMO-OFDM via Carrier Interferometry|title = GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489)|volume = 2|pages = 853–857|year = 2003|last1 = Barbosa|first1 = P.R.|last2 = Zhiqiang Wu|last3 = Nassar|first3 = C.R.| s2cid=20747953 }}</ref> and the idea of using CI in MIMO pre-coded [[Distributed antenna system|distributed antenna system]]s with central coordination was first disclosed in a provisional patent application in 2001.<ref>US Pat. Appl. 60286850, “Method and apparatus for using Carrier Interferometry to process multi-carrier signals”</ref> CI-based [[Software-defined radio|software-defined radio]] (SDR) that implemented four different protocol stacks was developed at Idris in 2000 and described in US 7418043.<ref>[http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7418043 US 7418043], "Software adaptable high performance multicarrier transmission protocol"</ref>

==Mathematical description==
In spread-OFDM, spreading is performed across orthogonal subcarriers to produce a transmit signal expressed by
'''x''' = '''F'''<sup>−1</sup>'''Sb'''
where '''F'''<sup>−1</sup> 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'''<sup>−1</sup>'''Sb''',
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'''<sup>−1</sup>'''Λ'''<sub>H</sub>'''FF'''<sup>−1</sup>'''Sb'''

 = '''F'''<sup>−1</sup>'''Λ'''<sub>H</sub>'''Sb'''

where the relationship '''H''' = '''F'''<sup>−1</sup>'''Λ'''<sub>H</sub>'''F''' is from the definition of a circulant matrix, and '''Λ'''<sub>H</sub> 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''' = '''Λ'''<sub>H</sub>'''Sb'''.

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'''<sup>−1</sup>'''Λ'''<sub>H</sub>'''FF'''<sup>−1</sup>('''Λ'''<sub>C</sub>'''F''')'''b''',

where '''S''' = '''Λ'''<sub>C</sub>'''F''', and '''C''' is a circulant matrix defined by '''C''' = '''F'''<sup>−1</sup>'''Λ'''<sub>C</sub>'''F''', where '''Λ'''<sub>C</sub> is the circulant's diagonal matrix. Thus, the received signal, '''r''', can be written as

'''r''' = '''F'''<sup>−1</sup>'''Λ'''<sub>H</sub>'''Λ'''<sub>C</sub>'''Fb''' = '''F'''<sup>−1</sup>'''Λ'''<sub>C</sub>'''Λ'''<sub>H</sub>'''Fb''',

and the signal '''y''' after the receiver's DFT is '''y''' = '''Λ'''<sub>C</sub>'''Λ'''<sub>H</sub>'''Fb'''

The spreading matrix '''S''' can include a pre-equalization diagonal matrix (e.g., '''Λ'''<sub>C</sub> = '''Λ'''<sub>H</sub><sup>−1</sup> 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., '''Λ'''<sub>C</sub> = '''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 '''Λ'''<sub>C</sub>.

==Useful properties==
# Low PAPR ([[Crest factor|Crest Factor]])
# Low sensitivity to non-linear distortion
# Low sensitivity to [[Carrier frequency offset|carrier-frequency offset]]
# Robustness to deep fades (spectral nulls)

==See also==
* [[Subcarrier multiplexing]]
* [[Engineering:Multi-carrier code-division multiple access|MC-CDMA]]
* [[Orthogonal frequency-division multiplexing|OFDM]]

==References==
{{Reflist}}

[[Category:Channel access methods]]

{{Sourceattribution|Carrier interferometry}}