Giovanni Del Galdo

Analytical Performance Assessment of Multi-Dimensional Matrix- and Tensor-Based ESPRIT-Type Algorithms

In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal subspace obtained via an SVD of the noisy observation matrix. We extend these results in a number of aspects. Firstly, we demonstrate that an explicit first-order expansion of the Higher-Order SVD (HOSVD)-based subspace estimate can be derived. Secondly, we show how to obtain explicit first-order expansions of the estimation error of arbitrary ESPRIT-type algorithms and provide the expressions for R-D Standard ESPRIT, R-D Unitary ESPRIT, R-D Standard Tensor-ESPRIT, as well as R-D Unitary Tensor-ESPRIT. Thirdly, we derive closed-form expressions for the mean square error (MSE) and show that they only depend on the second-order moments of the noise. Hence, to apply this framework we only need the noise to be zero mean and possess finite second order moments. Additional assumptions such as Gaussianity or circular symmetry are not needed.

Signal-to-reverberant ratio estimation based on the complex spatial coherence between omnidirectional microphones

The signal-to-reverberant ratio (SRR) is an important parameter in several applications such as speech enhancement, dereverberation, and parametric spatial audio coding. In this contribution, an SRR estimator is derived from the direction-of-arrival dependent complex spatial coherence function computed via two omnidirectional microphones. It is shown that by employing a computationally inexpensive DOA estimator, the proposed SRR estimator outperforms existing approaches.

On the spatial coherence in mixed sound fields and its application to signal-to-diffuse ratio estimation

Many applications in spatial sound recording and processing model the sound scene as a sum of directional and diffuse sound components. The power ratio between both components, i.e., the signal-to-diffuse ratio (SDR), represents an important measure for algorithms which aim at performing robustly in reverberant environments. This contribution discusses the SDR estimation from the spatial coherence between two arbitrary first-order directional microphones. First, the spatial coherence is expressed as function of the SDR. For most microphone setups, the spatial coherence is a complex function where both the absolute value and phase contain relevant information on the SDR. Secondly, the SDR estimator is derived from the spatial coherence function. The estimator is discussed for different practical microphone setups including coincident setups of arbitrary first-order directional microphones and spaced setups of identical first-order directional microphones. An unbiased SDR estimation requires noiseless coherence estimates as well as information on the direction-of-arrival of the directional sound, which usually has to be estimated. Nevertheless, measurement results verify that the proposed estimator is applicable in practice and provides accurate results.

Spatial filtering using directional audio coding parameters

Directional audio coding (DirAC) is a recent method for spatial audio processing, based on a perceptually motivated representation of spatial sound. Due to its efficiency, DirAC has already been proposed for spatial audio teleconferencing scenarios. Modern hands-free communication systems usually include beamforming techniques to improve speech intelligibility by suppressing diffuse background noise and interfering sources. In this paper, we propose a novel spatial filtering method which can be integrated into the DirAC spatial codec. It uses a spectral weighting of the recorded audio signal, where the design of the corresponding spatial filter transfer function is based on the DirAC parameters, i. e., direction-of-arrival and diffuseness of the sound field. Simulation results show that compared to a standard beamformer the novel technique offers significantly higher interference attenuation, while introducing similar distortion of the desired signal.

The diffuse sound field in energetic analysis

Measuring the degree of diffuseness of a sound field is crucial in many modern parametric spatial audio techniques. In these applications, intensity-based diffuseness estimators are particularly convenient, as the sound intensity can also be used to obtain, e.g., the direction of arrival of the sound. This contribution reviews different diffuseness estimators comparing them under the conditions found in practice, i.e., with arrays of noisy microphones and with the expectation operators substituted by finite temporal averages. The estimators show a similar performance, however, each with specific advantages and disadvantages depending on the scenario. Furthermore, the paper derives an estimator and highlights the possibility of using spatial averaging to improve the temporal resolution of the estimates.

Generating virtual microphone signals using geometrical information gathered by distributed arrays

Conventional recording techniques for spatial audio are limited to the fact that the spatial image obtained is always relative to the position in which the microphones have been physically placed. In many applications, however, it is desired to place the microphones outside the sound scene and yet be able to capture the sound from an arbitrary perspective. This contribution proposes a method to place a virtual microphone at an arbitrary point in space, by computing a signal perceptually similar to the one which would have been picked up if the microphone had been physically placed in the sound scene. The method relies on a parametric model of the sound field based on point-like isotropic sound sources. The required geometrical information is gathered by two or more distributed microphone arrays. Measurement results demonstrate the applicability of the proposed method and reveal its limitations.

Parametric Spatial Sound Processing: A flexible and efficient solution to sound scene acquisition, modification, and reproduction

Flexible and efficient spatial sound acquisition and subsequent processing are of paramount importance in communication and assisted listening devices such as mobile phones, hearing aids, smart TVs, and emerging wearable devices (e.g., smart watches and glasses). In application scenarios where the number of sound sources quickly varies, sources move, and nonstationary noise and reverberation are commonly encountered, it remains a challenge to capture sounds in such a way that they can be reproduced with a high and invariable sound quality. In addition, the objective in terms of what needs to be captured, and how it should be reproduced, depends on the application and on the user?s preferences. Parametric spatial sound processing has been around for two decades and provides a flexible and efficient solution to capture, code, and transmit, as well as manipulate and reproduce spatial sounds.

Deterministic Cramér-Rao Bound for Strictly Non-Circular Sources and Analytical Analysis of the Achievable Gains

Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. As a benchmark for these NC methods, we derive the closed-form deterministic R-D NC Cramér-Rao bound (NC CRB) for the multi-dimensional parameter estimation of strictly non-circular (rectilinear) signal sources in this paper. Assuming a separable centro-symmetric R-D array, we show that in some special cases, the deterministic R-D NC CRB reduces to the existing deterministic R-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved under the deterministic data assumption in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain. Our analysis is supported by extensive simulation results.

Over-the-Air Testing of Cognitive Radio Nodes in a Virtual Electromagnetic Environment

This paper provides an overview of ongoing research in over-the-air (OTA) testing for next-generation communication and data transmission devices with special consideration of cognitive radio (CR). Existing state-of-the-art techniques and their merits and limitations are discussed. We identify the requirements and issues for the OTA test in a virtual electromagnetic environment (OTAinVEE) which needs to address the more complex scenario of future networks, where interference emulation becomes a highly challenging task. A complex interference scenario arises due to the attempt to simultaneously utilize several opportunity dimensions such as frequency, time, direction (space), and polarization, in a dynamic manner in a multiuser scenario. Although MIMO-OTA testing addresses many limitations of single antenna-conducted test systems, more dimensions and parameters to be addressed in the new scenarios imply further increase in cost and complexity. Closed-loop OTA test setups for CR evaluation are discussed along with an overview of other test scenarios.

Geometry-Based Spatial Sound Acquisition Using Distributed Microphone Arrays

Traditional spatial sound acquisition aims at capturing a sound field with multiple microphones such that at the reproduction side a listener can perceive the sound image as it was at the recording location. Standard techniques for spatial sound acquisition usually use spaced omnidirectional microphones or coincident directional microphones. Alternatively, microphone arrays and spatial filters can be used to capture the sound field. From a geometric point of view, the perspective of the sound field is fixed when using such techniques. In this paper, a geometry-based spatial sound acquisition technique is proposed to compute virtual microphone signals that manifest a different perspective of the sound field. The proposed technique uses a parametric sound field model that is formulated in the time-frequency domain. It is assumed that each time-frequency instant of a microphone signal can be decomposed into one direct and one diffuse sound component. It is further assumed that the direct component is the response of a single isotropic point-like source (IPLS) of which the position is estimated for each time-frequency instant using distributed microphone arrays. Given the sound components and the position of the IPLS, it is possible to synthesize a signal that corresponds to a virtual microphone at an arbitrary position and with an arbitrary pick-up pattern.