Orhan Ocal

Source localization and tracking in non-convex rooms

We consider the estimation of the acoustic source position in a known room from recordings by a microphone array. We propose an algorithm that does not require the room to be convex, nor a line-of-sight path between the microphone array and the source to be present. Times of arrival of early echoes are exploited through the image source model, thereby transforming the indoor localization problem to a problem of localizing multiple sources in the free-field. The localized virtual sources are mirrored into the room using the image source method in the reverse direction. Further, we propose an optimization-based algorithm for improving the estimate of the source position. The algorithm minimizes a cost function derived from the geometry of the localization problem. We apply the designed optimization algorithm to track a moving source, and show through numerical simulations that it improves the tracking accuracy when compared with the naïve approach.

Compressed sensing of streaming data

We introduce a recursive scheme for performing Compressed Sensing (CS) on streaming data and analyze, both analytically and experimentally, the computational complexity and estimation error. The approach consists of sampling the input stream recursively via overlapping windowing and making use of the previous measurement in obtaining the next one. The signal estimate from the previous window is utilized in order to achieve faster convergence in an iterative optimization algorithm to decode the new window. To remove the bias of the estimator a two-step estimation procedure is proposed comprising support set detection and signal amplitude estimation. Estimation accuracy is enhanced by averaging estimates obtained from overlapping windows. The proposed method is shown to have asymptotic computational complexity O(nm3/2), where n is the window length, and m is the number of samples. The variance of normalized estimation error is shown to asymptotically go to 0 if k = O(n1-∈) as n increases. The simulation results show speed up of at least ten times with respect to applying traditional CS on a stream of data while obtaining significantly lower reconstruction error under mild conditions on the signal magnitudes and the noise level.

Collaborative randomized beamforming for phased array radio interferometers

The Square Kilometre Array (SKA) will form the largest radio telescope ever built and such a huge instrument in the desert poses enormous engineering and logistic challenges. Algorithmic and architectural breakthroughs are needed. Data is collected and processed in groups of antennas before transport for central processing. This processing includes beamforming, primarily so as to reduce the amount of data sent. The principal existing technique points to a region of interest independently of the sky model and how the other stations beam-form. We propose a new collaborative beamforming algorithm in order to maximize information captured at the stations (thus reducing the amount of data transported). The method increases the diversity in measurements through randomized beamforming. We demonstrate through numerical simulation the effectiveness of the method. In particular, we show that randomized beamforming can achieve the same image quality while producing 40% less data when compared to the prevailing method matched beamforming.

Density evolution on a class of smeared random graphs

We introduce a new ensemble of random bipartite graphs, which we term the ‘smearing ensemble’, where each left node is connected to some number of consecutive right nodes. Such graphs arise naturally in recovering sparse wavelet coefficients when signal acquisition is in the Fourier domain, such as in magnetic resonance imaging (MRI). Graphs from this ensemble exhibit small, structured cycles with high probability, rendering current techniques for determining iterative decoding thresholds inapplicable. In this paper, we develop a theoretical platform to analyze and evaluate the power of smearing-based structure. Despite the existence of these small cycles, we derive exact density evolution recurrences for iterative decoding on graphs with smear-length two. Furthermore, we give lower bounds on the performance of a much larger class from the smearing ensemble, and provide numerical experiments showing tight agreement between empirical thresholds and those determined by our bounds. We additionally detail a system architecture to recover sparse wavelet representations in the MRI setting, and show that K-sparse 1-stage Haar wavelet coefficients of an n-dimensional signal can be recovered using 2.63K Fourier domain samples asymptotically using O(K log K) operations.

A sparse-graph-coded filter bank approach to minimum-rate spectrum-blind sampling

Sampling of bandlimited signals whose frequency support is unknown is called spectrum-blind sampling. It has attracted considerable attention due to its potential for sampling much lower than the Nyquist rate. The minimum rate for spectrum-blind sampling has been established as twice the measure of the frequency support. We study this sampling problem and propose a novel sampling framework by leveraging tools from modern coding theory. Our approach is based on subsampling the outputs of a carefully designed sparse-graph-codedfilter bank. The key idea is to exploit, rather than avoid, the aliasing artifacts induced by subsampling, which introduces linear mixing of spectral components in the form of parity constraints for sparse-graph codes. Under the proposed sampling scheme, signal reconstruction becomes equivalent to the peeling decoding of sparse-graph codes in erasure channels. As a result, we can simultaneously approach the minimum sampling rate, while also having a computational cost that is linear in the number of samples. We support our theoretical findings through numerical experiments.

Parameter estimation from samples of stationary complex Gaussian processes

Sampling stationary, circularly-symmetric complex Gaussian stochastic process models from multiple sensors arise in array signal processing, including applications in direction of arrival estimation and radio astronomy. The goal is to take narrow-band filtered samples so as to estimate process parameters as accurately as possible. We derive analytical results on the estimation variance of the parameters as a function of the number of samples, the sampling rate, and the filter, under two different statistical estimators. The first is a standard sample variance estimator. The second, a generalization, is a maximum-likelihood estimator, useful when samples are correlated. The explicit relationships between estimation performance and filter autocorrelation can be used to improve process parameter estimation when sampling at higher than Nyquist. Additionally, they have potential application in filter optimization.