Performance of Hierarchical Sparse Detectors for Massive MTC

Recently, a new class of so-called \emph{hierarchical thresholding algorithms} was introduced to optimally exploit the sparsity structure in joint user activity and channel detection problems. In this paper, we take a closer look at the user detection performance of such algorithms under noise and relate its performance to the classical block correlation detector with orthogonal signatures. More specifically, we derive a lower bound for the diversity order which, under suitable choice of the signatures, equals that of the block correlation detector. Surprisingly, in specific parameter settings non-orthogonal pilots, i.e. pilots where (cyclically) shifted versions interfere with each other, outperform the block correlation detector. Altogether, we show that, in wide parameter regimes, the hierarchical thresholding detectors behave like the classical correlator with improved detection performance but operate with much less required pilot subcarriers. We provide mathematically rigorous and easy to handle formulas for numerical evaluations and system design. Finally, we evaluate our findings with numerical examples and show that, in a practical parameter setting, a classical pilot channel can accommodate up to three advanced pilot channels with the same performance.Comment: 15 pages, 12 figure

Compressed Sensing Channel Estimation for OFDM with non-Gaussian Multipath Gains

This paper analyzes the impact of non-Gaussian multipath component (MPC) amplitude distributions on the performance of Compressed Sensing (CS) channel estimators for OFDM systems. The number of dominant MPCs that any CS algorithm needs to estimate in order to accurately represent the channel is characterized. This number relates to a Compressibility Index (CI) of the channel that depends on the fourth moment of the MPC amplitude distribution. A connection between the Mean Squared Error (MSE) of any CS estimation algorithm and the MPC amplitude distribution fourth moment is revealed that shows a smaller number of MPCs is needed to well-estimate channels when these components have large fourth moment amplitude gains. The analytical results are validated via simulations for channels with lognormal MPCs such as the NYU mmWave channel model. These simulations show that when the MPC amplitude distribution has a high fourth moment, the well known CS algorithm of Orthogonal Matching Pursuit performs almost identically to the Basis Pursuit De-Noising algorithm with a much lower computational cost.Comment: Published in IEEE Transactions on Wireless Communications. arXiv admin note: text overlap with arXiv:1812.0723