A sparsity detection framework for on-off random access channels

Alyson K. Fletcher, Sundeep Rangan, Vivek K. Goyal

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

Abstract

This paper considers a simple on-off random multiple access channel, where n users communicate simultaneously to a single receiver over m degrees of freedom. Each user transmits with probability λ, where typically λn < m ≪ n, and the receiver must detect which users transmitted. We show that when the codebook has i.i.d. Gaussian entries, detecting which users transmitted is mathematically equivalent to a certain sparsity detection problem considered in compressed sensing. Using recent sparsity results, we derive upper and lower bounds on the capacities of these channels. We show that common sparsity detection algorithms, such as lasso and orthogonal matching pursuit (OMP), can be used as tractable multiuser detection schemes and have significantly better performance than single-user detection. These methods do achieve some near-far resistance but-at high signal-to-noise ratios (SNRs)-may achieve capacities far below optimal maximum likelihood detection. We then present a new algorithm, called sequential OMP, that illustrates that iterative detection combined with power ordering or power shaping can significantly improve the high SNR performance. Sequential OMP is analogous to successive interference cancellation in the classic multiple access channel. Our results thereby provide insight into the roles of power control and multiuser detection on random-access signaling.

Original languageEnglish (US)
Title of host publicationWavelets XIII
Volume7446
DOIs
StatePublished - 2009
EventWavelets XIII - San Diego, CA, United States
Duration: Aug 2 2009Aug 4 2009

Other

OtherWavelets XIII
CountryUnited States
CitySan Diego, CA
Period8/2/098/4/09

Fingerprint

random access
Multiuser detection
Random Access
Sparsity
Signal to noise ratio
Matching Pursuit
Compressed sensing
Multiuser Detection
Multiple Access Channel
Power control
Maximum likelihood
multiple access
Receiver
Iterative Detection
Maximum Likelihood Detection
Successive Interference Cancellation
Lasso
Compressed Sensing
Sequential Algorithm
Codebook

Keywords

  • Compressed sensing
  • Convex optimization
  • Lasso
  • Maximum likelihood estimation
  • Multiple access channel
  • Multiuser detection
  • Orthogonalmatching pursuit
  • Power control
  • Random matrices
  • Single-user detection
  • Sparsity
  • Thresholding

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Fletcher, A. K., Rangan, S., & Goyal, V. K. (2009). A sparsity detection framework for on-off random access channels. In Wavelets XIII (Vol. 7446). [744607] https://doi.org/10.1117/12.824127

A sparsity detection framework for on-off random access channels. / Fletcher, Alyson K.; Rangan, Sundeep; Goyal, Vivek K.

Wavelets XIII. Vol. 7446 2009. 744607.

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

Fletcher, AK, Rangan, S & Goyal, VK 2009, A sparsity detection framework for on-off random access channels. in Wavelets XIII. vol. 7446, 744607, Wavelets XIII, San Diego, CA, United States, 8/2/09. https://doi.org/10.1117/12.824127
Fletcher, Alyson K. ; Rangan, Sundeep ; Goyal, Vivek K. / A sparsity detection framework for on-off random access channels. Wavelets XIII. Vol. 7446 2009.
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