We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of sparse common support (SCS) channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.

We propose an algorithm (SCS-FRI) to estimate multipath channels with Sparse Common Support (SCS) based on Finite Rate of Innovation (FRI) sampling. In this setup, theoretical lower-bounds are derived, and simulation in a Rayleigh fading environment shows that SCS-FRI gets very close to these bounds. We show how to apply SCS-FRI to OFDM and CDMA downlinks. Recovery of a sparse common support is, among other, especially relevant for channel estimation in a multiple output system or beam-forming from multiple input. The present algorithm is based on a multi-output extension of the Cadzow denoising/annihilating filter method.

In sensor networks and communication systems, one is often confronted with sampling multiple sparse signals having a common support set. Multipath channels in a multiple-input multiple-output (MIMO) wireless communication setting is an interesting example where one generally needs to perform channel estimation for each transmit-receive antenna pair. MIMO multipath channels are usually (approximately) sparse and satisfy the common-support property whenever the distances between the antennas are small compared to the distance the electromagnetic wave can travel in the time corresponding to the inverse bandwidth of the communication system. This assumption is satisfied by small and medium bandwidth communication systems like OFDM and CDMA. This leads us to extend the finite rate of innovation sampling and reconstruction scheme to the sparse common-support scenario (SCS-FRI), in which input signals contain Diracs with common locations but arbitrary weights. The goal is to efficiently reconstruct the input signals from a set of uniform samples, making use of the common-support property to improve robustness. We first find the best theoretical performance for the SCS-FRI setup by de riving the Cramér-Rao lower bound. Our results show that for a set of well-separated Diracs, it is the total energy of the Diracs at each common position which determines the bound. We then propose a multichannel reconstruction algorithm and compare its performance with the Cramér-Rao lower bound. Numerical results clearly demonstrate the effectiveness of our proposed sampling and reconstruction scheme in low SNR regimes.

Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based on the set of test results obtained for each pool. In a classical noiseless group testing setup, it is assumed that the sampling procedure is fully known to the reconstruction algorithm, in the sense that the existence of a defective member in a pool results in the test outcome of that pool to be positive. However, this may not be always a valid assumption in some cases of interest. In particular, we consider the case where the defective items in a pool can become independently inactive with a certain probability. Hence, one may obtain a negative test result in a pool despite containing some defective items. As a result, any sampling and reconstruction method should be able to cope with two different types of uncertainty, i.e., the unknown set of defective items and the partially unknown, probabilistic testing procedure. In this work, motivated by the application of detecting infected people in viral epidemics, we design nonadaptive sampling procedures that allow successful identification of the defective items through a set of probabilistic tests. Our design requires only a small number of tests to single out the defective items. In particular, for a population of size N and at most K defective items with activation probability p, our results show that M = O(K2log (N/K)/p3) tests is sufficient if the sampling procedure should work for all possible sets of defective items, while M = O(K log (N)/p3) tests is enough to be successful for any single set of defective items. Moreover, we show that the defective members can be recovered using a simple reconstruction algorithm with complexity of O(MN).

We consider the task of recovering correlated vectors at a central decoder based on fixed linear measurements obtained by distributed sensors. A general formulation of the problem is proposed, under both a universal and an almost sure reconstruction requirement. We then study a specific correlation model which involves a filter that is sparse in the time domain. While this sparsity assumption does not allow reducing the description cost in the universal case, we show that large gains can be achieved in the almost sure scenario by means of a novel distributed scheme based on annihilating filters. The robustness of the proposed method is also investigated.

Compressed sensing (CS) deals with the reconstruction of sparse signals from a small number of linear measurements. One of the main challenges in CS is to find the support of a sparse signal from a set of noisy observations. In the CS literature, several information-theoretic bounds on the scaling law of the required number of measurements for exact support recovery have been derived, where the focus is mainly on random measurement matrices. In this paper, we investigate the support recovery problem from an estimation theory point of view, where no specific assumption is made on the underlying measurement matrix. By using the Hammersley-Chapman-Robbins (HCR) bound, we derive a fundamental lower bound on the performance of any unbiased estimator which provides necessary conditions for reliable ¿2-norm support recovery. We then analyze the optimal decoder to provide conditions under which the HCR bound is achievable. This leads to a set of sufficient conditions for reliable ¿2-norm support recovery.

Consider a scenario where a distributed signal is sparse and is acquired by various sensors that see different versions. Thus, we have a set of sparse signals with both some common parts, and some variations. The question is how to acquire such signals and how to reconstruct them perfectly (noiseless case) or approximately (noisy case). We propose an extension of the annihilating filter method [3] to this distributed scenario. We model the inter-relation between the sparse signals by introducing three joint sparse models. For each model, we propose sensing and reconstruction algorithms that reduce the number of measurements below the limit for the single sensor scenario and results in power and bandwidth reduction in the system. In the noiseless scenario, we are close to the minimum number of measurements possible for the perfect reconstruction while by taking more measurements, we introduce redundancy in the system to effectively mitigate the noise. Simulation results justify the applicability of the approach.