### Abstract

In this paper, we consider the downlink of a cognitive radio network where a cognitive base station serves multiple cognitive users on the same frequency band as a group of primary transceivers. The cognitive base station uses an orthogonal scheduling scheme (TDMA/FDMA) to serve its users. For this purpose, the base station is interested in acquiring an estimate of the interference (from the primary network) power at each of its cognitive receivers as a measure of channel quality. This can be surely achieved if we allow for the feedback (from the cognitive receivers to the cognitive base station) bandwidth to scale linearly in the number of cognitive receivers, but in densely populated networks, the cost of such an acquisition might be too high. This leads us to the question of whether we can do better in terms of bandwidth efficiency. We observe that in many scenarios - that are common in practice - where the primary network exhibits sparse changes in transmit powers from one scheduling instant to the next, it is possible to acquire this interference state with only a logarithmic scaling in feedback bandwidth. More specifically, in cognitive networks where the channels are solely determined by the positions of nodes, we can use compressed sensing to recover the interference state. In addition to being a first application of compressed sensing in the domain of limited feedback, to the best of our knowledge, this paper makes a key mathematical contribution concerning the favourable sensing properties of path-loss matrices that are composed of nonzero mean, dependent random entries. Finally, we numerically study the robustness properties of the least absolute shrinkage and selection operator (LASSO), a popular recovery algorithm, under two error models through simulations. The first model considers a varying amount of error added to all entries of the sensing matrix. The second one, a more adversarial model, considers a large amount of error added to only a fraction of the entries of the sensing matrix that are chosen uniformly at random. Simulation results establish that the LASSO recovery algorithm is robust to imperfect channel knowledge.

Original language | English (US) |
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Title of host publication | 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 |

Pages | 1090-1097 |

Number of pages | 8 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 - Monticello, IL, United States Duration: Sep 29 2010 → Oct 1 2010 |

### Other

Other | 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 |
---|---|

Country | United States |

City | Monticello, IL |

Period | 9/29/10 → 10/1/10 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Control and Systems Engineering

### Cite this

*2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010*(pp. 1090-1097). [5707031] https://doi.org/10.1109/ALLERTON.2010.5707031

**Limited feedback for cognitive radio networks using compressed sensing.** / Ganapathy, Harish; Caramanis, Constantine; Ying, Lei.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010.*, 5707031, pp. 1090-1097, 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010, Monticello, IL, United States, 9/29/10. https://doi.org/10.1109/ALLERTON.2010.5707031

}

TY - GEN

T1 - Limited feedback for cognitive radio networks using compressed sensing

AU - Ganapathy, Harish

AU - Caramanis, Constantine

AU - Ying, Lei

PY - 2010

Y1 - 2010

N2 - In this paper, we consider the downlink of a cognitive radio network where a cognitive base station serves multiple cognitive users on the same frequency band as a group of primary transceivers. The cognitive base station uses an orthogonal scheduling scheme (TDMA/FDMA) to serve its users. For this purpose, the base station is interested in acquiring an estimate of the interference (from the primary network) power at each of its cognitive receivers as a measure of channel quality. This can be surely achieved if we allow for the feedback (from the cognitive receivers to the cognitive base station) bandwidth to scale linearly in the number of cognitive receivers, but in densely populated networks, the cost of such an acquisition might be too high. This leads us to the question of whether we can do better in terms of bandwidth efficiency. We observe that in many scenarios - that are common in practice - where the primary network exhibits sparse changes in transmit powers from one scheduling instant to the next, it is possible to acquire this interference state with only a logarithmic scaling in feedback bandwidth. More specifically, in cognitive networks where the channels are solely determined by the positions of nodes, we can use compressed sensing to recover the interference state. In addition to being a first application of compressed sensing in the domain of limited feedback, to the best of our knowledge, this paper makes a key mathematical contribution concerning the favourable sensing properties of path-loss matrices that are composed of nonzero mean, dependent random entries. Finally, we numerically study the robustness properties of the least absolute shrinkage and selection operator (LASSO), a popular recovery algorithm, under two error models through simulations. The first model considers a varying amount of error added to all entries of the sensing matrix. The second one, a more adversarial model, considers a large amount of error added to only a fraction of the entries of the sensing matrix that are chosen uniformly at random. Simulation results establish that the LASSO recovery algorithm is robust to imperfect channel knowledge.

AB - In this paper, we consider the downlink of a cognitive radio network where a cognitive base station serves multiple cognitive users on the same frequency band as a group of primary transceivers. The cognitive base station uses an orthogonal scheduling scheme (TDMA/FDMA) to serve its users. For this purpose, the base station is interested in acquiring an estimate of the interference (from the primary network) power at each of its cognitive receivers as a measure of channel quality. This can be surely achieved if we allow for the feedback (from the cognitive receivers to the cognitive base station) bandwidth to scale linearly in the number of cognitive receivers, but in densely populated networks, the cost of such an acquisition might be too high. This leads us to the question of whether we can do better in terms of bandwidth efficiency. We observe that in many scenarios - that are common in practice - where the primary network exhibits sparse changes in transmit powers from one scheduling instant to the next, it is possible to acquire this interference state with only a logarithmic scaling in feedback bandwidth. More specifically, in cognitive networks where the channels are solely determined by the positions of nodes, we can use compressed sensing to recover the interference state. In addition to being a first application of compressed sensing in the domain of limited feedback, to the best of our knowledge, this paper makes a key mathematical contribution concerning the favourable sensing properties of path-loss matrices that are composed of nonzero mean, dependent random entries. Finally, we numerically study the robustness properties of the least absolute shrinkage and selection operator (LASSO), a popular recovery algorithm, under two error models through simulations. The first model considers a varying amount of error added to all entries of the sensing matrix. The second one, a more adversarial model, considers a large amount of error added to only a fraction of the entries of the sensing matrix that are chosen uniformly at random. Simulation results establish that the LASSO recovery algorithm is robust to imperfect channel knowledge.

UR - http://www.scopus.com/inward/record.url?scp=79952407676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952407676&partnerID=8YFLogxK

U2 - 10.1109/ALLERTON.2010.5707031

DO - 10.1109/ALLERTON.2010.5707031

M3 - Conference contribution

AN - SCOPUS:79952407676

SN - 9781424482146

SP - 1090

EP - 1097

BT - 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010

ER -