Julius Kusuma

Distributed compression in a dense microsensor network

Distributed nature of the sensor network architecture introduces unique challenges and opportunities for collaborative networked signal processing techniques that can potentially lead to significant performance gains. Many evolving low-power sensor network scenarios need to have high spatial density to enable reliable operation in the face of component node failures as well as to facilitate high spatial localization of events of interest. This induces a high level of network data redundancy, where spatially proximal sensor readings are highly correlated. We propose a new way of removing this redundancy in a completely distributed manner, i.e., without the sensors needing to talk, to one another. Our constructive framework for this problem is dubbed DISCUS (distributed source coding using syndromes) and is inspired by fundamental concepts from information theory. We review the main ideas, provide illustrations, and give the intuition behind the theory that enables this framework.We present a new domain of collaborative information communication and processing through the framework on distributed source coding. This framework enables highly effective and efficient compression across a sensor network without the need to establish inter-node communication, using well-studied and fast error-correcting coding algorithms.

Distributed compression for sensor networks

We consider the problem of efficiently transmitting sets of spatially correlated observations in a distributed sensor network without requiring inter-node communication to exploit the correlation. Specifically, we provide a construction for quantizer design given a training set, and a distributed compression scheme to efficiently relay the quantized observations to a central decoder.

Sampling with finite rate of innovation: channel and timing estimation for UWB and GPS

In this work, we consider the problem of channel estimation by using the recently developed theory for sampling of signals with a finite rate of innovation. We show a framework which allows for lower than Nyquist rate sampling applicable for timing and channel estimation of both narrowband and wideband channels. In certain cases we demonstrate performance exceeding that of algorithms using Nyquist rate sampling while working at lower sampling rates, thus saving power and computational complexity.

Low-sampling rate UWB channel characterization and synchronization

We consider the problem of low-sampling rate high-resolution channel estimation and timing for digital ultra-wideband (UWB) receivers. We extend some of our recent results in sampling of certain classes of parametric non-bandlimited signals and develop a frequency domain method for channel estimation and synchronization in ultra-wideband systems, which uses sub-Nyquist uniform sampling and well-studied computational procedures. In particular, the proposed method can be used for identification of more realistic channel models, where different propagation paths undergo different frequency-selective fading. Moreover, we show that it is possible to obtain high-resolution estimates of all relevant channel parameters by sampling a received signal below the traditional Nyquist rate. Our approach leads to faster acquisition compared to current digital solutions, allows for slower A/D converters, and potentially reduces power consumption of digital UWB receivers significantly.

Multichannel Sampling of Parametric Signals with a Successive Approximation Property

Recently the sampling theory for certain parametric signals based on rate of innovation has been extended to all sampling kernels that satisfy the Strang-Fix conditions, thus including many attractive choices with finite support. We propose a new sampling scheme in which samples are taken simultaneously at the outputs of multiple channels. This new scheme is closely related to previously known cases, but provides a successive approximation property that can be used for detecting undermodeling. We also draw connections to splines and multi-scale sampling of signals.

Sampling of communication systems with bandwidth expansion

Many communication systems are bandwidth-expanding: the transmitted signal occupies a bandwidth larger than the symbol rate. The sampling theorems of Kotelnikov, Shannon, Nyquist et al. discussed by Unser (see Proceedings of the IEEE, vol. 88, no.4, p.569-87, 2000) shows that in order to represent a bandlimited signal, it is necessary to sample at what is popularly referred to as the Shannon or Nyquist rate. However, in many systems, the required sampling rate is very high and expensive to implement. We show that it is possible to get suboptimal performance by sampling close to the symbol rate of the signal, using well-studied algorithmic components. This work is based on previous results on sampling for some classes of non-bandlimited signals. We extend these sampling results to the case when there is noise. In our exposition, we use ultra wideband (UWB) signals as an example of how our framework can be applied.

On the Accuracy and Resolution of Powersum-Based Sampling Methods

Recently, several sampling methods suitable for signals that are sums of Diracs have been proposed. Though they are implemented through different acquisition architectures, these methods all rely on estimating the parameters of a powersum series. We derive Cramer-Rao lower bounds (CRBs) for estimation of the powersum poles, which translate to the Dirac positions. We then demonstrate the efficacy of simple algorithms due to Prony and Cornell for low-order powersums and low oversampling relative to the rate of innovation. The simulated performance illustrates the possibility of superresolution reconstruction and robustness to correlation in the powersum sample noise.

Signal Parameter Estimation in the Presence of Timing Noise

We consider the problem of estimating the parameters of a signal when the sampling instances are perturbed by signal-independent timing noise. The classical techniques consider timing noise to induce a signal-independent additive white Gaussian noise term on the sample values. We reject this simplification of the problem and give alternative methodologies. For the problem of delay estimation when the pulse shape and amplitude of the signal are known, we give an iterative algorithm that shows superior performance compared to the traditional method which relies on maximizing the cross-correlation.

Malleable coding with edit-distance cost

A malleable coding scheme considers not only representation length but also ease of representation update, thereby encouraging some form of recycling to convert an old codeword into a new one. We examine the trade-off between compression efficiency and malleability cost, measured with a string edit distance that introduces a metric topology to the representation domain. We characterize the achievable rates and malleability as the solution of a subgraph isomorphism problem.

Delay Estimation in the Presence of Timing Noise

We consider the problem of delay estimation in the presence of timing noise. We introduce an iterative algorithm with superior performance compared to the traditional method of using only cross-correlation. This method can exploit statistical knowledge of the timing noise such as loop bandwidth, giving further improvement in performance.