Compressive Sampling of Multiple Sparse Signals Having Common Support Using Finite Rate of Innovation Principles

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 deriving 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 determine

FRI Sampling With Arbitrary Kernels

This paper addresses the problem of sampling non-bandlimited signals within the Finite Rate of Innovation (FRI) setting. We had previously shown that, by using sampling kernels whose integer span contains specific exponentials (generalized Strang-Fix conditions), it is possible to devise non-iterative, fast reconstruction algorithms from very low-rate samples. Yet, the accuracy and sensitivity to noise of these algorithms is highly dependent on these exponential reproducing kernels — actually, on the exponentials that they reproduce. Hence, our first contribution here is to provide clear guidelines on how to choose the sampling kernels optimally, in such a way that the reconstruction quality is maximized in the presence of noise. The optimality of these kernels is validated by comparing with Cramér-Rao’s lower bounds (CRB). Our second contribution is to relax the exact exponential reproduction requirement. Instead, we demonstrate that arbitrary sampling kernels can reproduce the “best ” exponentials within quite a high accuracy in general, and that applying the exact FRI algorithms in this approximate context results in near-optimal reconstruction accuracy for practical noise levels. Essentially, we propose a universal extension of the FRI approach to arbitrary sampling kernels. Numerical results checked against the CRB validate the various contributions of the paper and in particular outline the ability of arbitrary sampling kernels to be used in FRI algorithms

Channel Estimation and ICI Cancelation in Vehicular Channels of OFDM Wireless Communication Systems

Orthogonal frequency division multiplexing (OFDM) scheme increases bandwidth efficiency (BE) of data transmission and eliminates inter symbol interference (ISI). As a result, it has been widely used for wideband communication systems that have been developed during the past two decades and it can be a good candidate for the emerging communication systems such as fifth generation (5G) cellular networks with high carrier frequency and communication systems of high speed vehicles such as high speed trains (HSTs) and supersonic unmanned aircraft vehicles (UAVs). However, the employment of OFDM for those upcoming systems is challenging because of high Doppler shifts. High Doppler shift makes the wideband communication channel to be both frequency selective and time selective, doubly selective (DS), causes inter carrier interference (ICI) and destroys the orthogonality between the subcarriers of OFDM signal. In order to demodulate the signal in OFDM systems and mitigate ICIs, channel state information (CSI) is required. In this work, we deal with channel estimation (CE) and ICI cancellation in DS vehicular channels. The digitized model of the DS channels can be short and dense, or long and sparse. CE methods that perform well for short and dense channels are highly inefficient for long and sparse channels. As a result, for the latter type of channels, we proposed the employment of compressed sensing (CS) based schemes for estimating the channel. In addition, we extended our CE methods for multiple input multiple output (MIMO) scenarios. We evaluated the CE accuracy and data demodulation fidelity, along with the BE and computational complexity of our methods and compared the results with the previous CE procedures in different environments. The simulation results indicate that our proposed CE methods perform considerably better than the conventional CE schemes