Interference alignment with asymmetric complex signaling

Syed A. Jafar, Viveck Cadambe, Chenwei Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

It has been conjectured that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom (DoF) regardless of the number of users. While several examples are known of constant channels that achieve more than 1 DoF, these special cases only span a subset of measure zero. In other words, for almost all channel coefficient values, it is not known if more than 1 DoF is achievable. In this paper, we settle this conjecture in the negative. We show that at least 1.2 DoF are achievable for all values of complex channel coefficients except for a subset of measure zero. To establish the achievability of 1.2 DoF we introduce the novel idea of asymmetric complex signaling - i.e., the inputs are chosen to be complex but not circularly symmetric. It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric. In addition, with this idea, we also show that 4/3 DoF can be achieved for 2 user X channel with constant, complex channel coefficients.

Original languageEnglish (US)
Title of host publication2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Pages991-996
Number of pages6
DOIs
StatePublished - Dec 1 2009
Event2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States
Duration: Sep 30 2009Oct 2 2009

Publication series

Name2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

Other

Other2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
CountryUnited States
CityMonticello, IL
Period9/30/0910/2/09

Fingerprint

interference
broadcast
Values

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Control and Systems Engineering
  • Communication

Cite this

Jafar, S. A., Cadambe, V., & Wang, C. (2009). Interference alignment with asymmetric complex signaling. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 (pp. 991-996). [5394885] (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). https://doi.org/10.1109/ALLERTON.2009.5394885
Jafar, Syed A. ; Cadambe, Viveck ; Wang, Chenwei. / Interference alignment with asymmetric complex signaling. 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009. 2009. pp. 991-996 (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009).
@inproceedings{b45786597d774b6bbd9555ffee3ad6c0,
title = "Interference alignment with asymmetric complex signaling",
abstract = "It has been conjectured that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom (DoF) regardless of the number of users. While several examples are known of constant channels that achieve more than 1 DoF, these special cases only span a subset of measure zero. In other words, for almost all channel coefficient values, it is not known if more than 1 DoF is achievable. In this paper, we settle this conjecture in the negative. We show that at least 1.2 DoF are achievable for all values of complex channel coefficients except for a subset of measure zero. To establish the achievability of 1.2 DoF we introduce the novel idea of asymmetric complex signaling - i.e., the inputs are chosen to be complex but not circularly symmetric. It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric. In addition, with this idea, we also show that 4/3 DoF can be achieved for 2 user X channel with constant, complex channel coefficients.",
author = "Jafar, {Syed A.} and Viveck Cadambe and Chenwei Wang",
year = "2009",
month = "12",
day = "1",
doi = "10.1109/ALLERTON.2009.5394885",
language = "English (US)",
isbn = "9781424458714",
series = "2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009",
pages = "991--996",
booktitle = "2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009",

}

Jafar, SA, Cadambe, V & Wang, C 2009, Interference alignment with asymmetric complex signaling. in 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009., 5394885, 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, pp. 991-996, 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, Monticello, IL, United States, 9/30/09. https://doi.org/10.1109/ALLERTON.2009.5394885

Interference alignment with asymmetric complex signaling. / Jafar, Syed A.; Cadambe, Viveck; Wang, Chenwei.

2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009. 2009. p. 991-996 5394885 (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Interference alignment with asymmetric complex signaling

AU - Jafar, Syed A.

AU - Cadambe, Viveck

AU - Wang, Chenwei

PY - 2009/12/1

Y1 - 2009/12/1

N2 - It has been conjectured that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom (DoF) regardless of the number of users. While several examples are known of constant channels that achieve more than 1 DoF, these special cases only span a subset of measure zero. In other words, for almost all channel coefficient values, it is not known if more than 1 DoF is achievable. In this paper, we settle this conjecture in the negative. We show that at least 1.2 DoF are achievable for all values of complex channel coefficients except for a subset of measure zero. To establish the achievability of 1.2 DoF we introduce the novel idea of asymmetric complex signaling - i.e., the inputs are chosen to be complex but not circularly symmetric. It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric. In addition, with this idea, we also show that 4/3 DoF can be achieved for 2 user X channel with constant, complex channel coefficients.

AB - It has been conjectured that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom (DoF) regardless of the number of users. While several examples are known of constant channels that achieve more than 1 DoF, these special cases only span a subset of measure zero. In other words, for almost all channel coefficient values, it is not known if more than 1 DoF is achievable. In this paper, we settle this conjecture in the negative. We show that at least 1.2 DoF are achievable for all values of complex channel coefficients except for a subset of measure zero. To establish the achievability of 1.2 DoF we introduce the novel idea of asymmetric complex signaling - i.e., the inputs are chosen to be complex but not circularly symmetric. It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric. In addition, with this idea, we also show that 4/3 DoF can be achieved for 2 user X channel with constant, complex channel coefficients.

UR - http://www.scopus.com/inward/record.url?scp=77949608177&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949608177&partnerID=8YFLogxK

U2 - 10.1109/ALLERTON.2009.5394885

DO - 10.1109/ALLERTON.2009.5394885

M3 - Conference contribution

AN - SCOPUS:77949608177

SN - 9781424458714

T3 - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

SP - 991

EP - 996

BT - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

ER -

Jafar SA, Cadambe V, Wang C. Interference alignment with asymmetric complex signaling. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009. 2009. p. 991-996. 5394885. (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). https://doi.org/10.1109/ALLERTON.2009.5394885