Random Access Protocols with Collision Resolution in a Noncoherent Setting

Wireless systems are increasingly used for Machine-Type Communication (MTC), where the users sporadically send very short messages. In such a setting, the overhead imposed by channel estimation is substantial, thereby demanding noncoherent communication. In this paper we consider a noncoherent setup in which users randomly access the medium to send short messages to a common receiver. We propose a transmission scheme based on Gabor frames, where each user has a dedicated codebook of M possible codewords, while the codebook simultaneously serves as an ID for the user. The scheme is used as a basis for a simple protocol for collision resolution.Comment: 5 pages, 3 figures; EDIT: A version of this work has been submitted for publication in the IEEE Wireless Communication Letters Journa

Frame Coherence and Sparse Signal Processing

The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate whether an arbitrary matrix, or frame, is suitable for sensing sparse signals. To this end, the present paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first provide several examples of frames that have small spectral norm, worst-case coherence, and average coherence. Next, we present a new lower bound on worst-case coherence and compare it to the Welch bound. Later, we propose an algorithm that decreases the average coherence of a frame without changing its spectral norm or worst-case coherence. Finally, we use worst-case and average coherence, as opposed to the Restricted Isometry Property, to garner near-optimal probabilistic guarantees on both sparse signal detection and reconstruction in the presence of noise. This contrasts with recent results that only guarantee noiseless signal recovery from arbitrary frames, and which further assume independence across the nonzero entries of the signal---in a sense, requiring small average coherence replaces the need for such an assumption

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

Compressed Neighbour Discovery using Sparse Kerdock Matrices

We study the network-wide neighbour discovery problem in wireless networks in which each node in a network must discovery the network interface addresses (NIAs) of its neighbours. We work within the rapid on-off division duplex framework proposed by Guo and Zhang (2010) in which all nodes are assigned different on-off signatures which allow them listen to the transmissions of neighbouring nodes during their off slots, leading to a compressed sensing problem at each node with a collapsed codebook determined by a given node's transmission signature. We propose sparse Kerdock matrices as codebooks for the neighbour discovery problem. These matrices share the same row space as certain Delsarte-Goethals frames based upon Reed Muller codes, whilst at the same time being extremely sparse. We present numerical experiments using two different compressed sensing recovery algorithms, One Step Thresholding (OST) and Normalised Iterative Hard Thresholding (NIHT). For both algorithms, a higher proportion of neighbours are successfully identified using sparse Kerdock matrices compared to codebooks based on Reed Muller codes with random erasures as proposed by Zhang and Guo (2011). We argue that the improvement is due to the better interference cancellation properties of sparse Kerdock matrices when collapsed according to a given node's transmission signature. We show by explicit calculation that the coherence of the collapsed codebooks resulting from sparse Kerdock matrices remains near-optimal