Compressive Demodulation of Mutually Interfering Signals

Multi-User Detection is fundamental not only to cellular wireless communication but also to Radio-Frequency Identification (RFID) technology that supports supply chain management. The challenge of Multi-user Detection (MUD) is that of demodulating mutually interfering signals, and the two biggest impediments are the asynchronous character of random access and the lack of channel state information. Given that at any time instant the number of active users is typically small, the promise of Compressive Sensing (CS) is the demodulation of sparse superpositions of signature waveforms from very few measurements. This paper begins by unifying two front-end architectures proposed for MUD by showing that both lead to the same discrete signal model. Algorithms are presented for coherent and noncoherent detection that are based on iterative matching pursuit. Noncoherent detection is all that is needed in the application to RFID technology where it is only the identity of the active users that is required. The coherent detector is also able to recover the transmitted symbols. It is shown that compressive demodulation requires $\mathcal{O}(K\log N(\tau+1))$ samples to recover $K$ active users whereas standard MUD requires $N(\tau+1)$ samples to process $N$ total users with a maximal delay $\tau$. Performance guarantees are derived for both coherent and noncoherent detection that are identical in the way they scale with number of active users. The power profile of the active users is shown to be less important than the SNR of the weakest user. Gabor frames and Kerdock codes are proposed as signature waveforms and numerical examples demonstrate the superior performance of Kerdock codes - the same probability of error with less than half the samples.Comment: submitted for journal publicatio

Coherence-Based Performance Guarantees of Orthogonal Matching Pursuit

In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two variants of OMP either with known sparsity level or with a stopping rule are analyzed. It is shown that if the measurement matrix $X\in\mathbb{C}^{n\times p}$ satisfies the strong coherence property, then with $n\gtrsim\mathcal{O}(k\log p)$, OMP will recover a $k$-sparse signal with high probability. In particular, the performance guarantees obtained here separate the properties required of the measurement matrix from the properties required of the signal, which depends critically on the minimum signal to noise ratio rather than the power profiles of the signal. We also provide performance guarantees for partial support recovery. Comparisons are given with other performance guarantees for OMP using worst-case analysis and the sorted one step thresholding algorithm.Comment: appeared at 2012 Allerton conferenc

Random Access in C-RAN for User Activity Detection with Limited-Capacity Fronthaul

Cloud-Radio Access Network (C-RAN) is characterized by a hierarchical structure in which the baseband processing functionalities of remote radio heads (RRHs) are implemented by means of cloud computing at a Central Unit (CU). A key limitation of C-RANs is given by the capacity constraints of the fronthaul links connecting RRHs to the CU. In this letter, the impact of this architectural constraint is investigated for the fundamental functions of random access and active User Equipment (UE) identification in the presence of a potentially massive number of UEs. In particular, the standard C-RAN approach based on quantize-and-forward and centralized detection is compared to a scheme based on an alternative CU-RRH functional split that enables local detection. Both techniques leverage Bayesian sparse detection. Numerical results illustrate the relative merits of the two schemes as a function of the system parameters.Comment: 6 pages, 3 figures, under revision in IEEE Signal Processing Letter