A sparsity detection framework for on-off random access channels

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

doi:10.1117/12.824127

4 September 2009 A sparsity detection framework for on-off random access channels

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

Proceedings Volume 7446, Wavelets XIII; 744607 (2009) https://doi.org/10.1117/12.824127
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

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(symbol)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.

Citation Download Citation

Alyson K. Fletcher, Sundeep Rangan, and Vivek K. Goyal "A sparsity detection framework for on-off random access channels", Proc. SPIE 7446, Wavelets XIII, 744607 (4 September 2009); https://doi.org/10.1117/12.824127

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