Thushara D. Abhayapala

Reproduction of a plane-wave sound field using an array of loudspeakers

Reproduction of a sound field is a fundamental problem in acoustic signal processing. In this paper, we use a spherical harmonics analysis to derive performance bounds on how well an array of loudspeakers can recreate a three-dimensional (3-D) plane-wave sound field within a spherical region of space. Specifically, we develop a relationship between the number of loudspeakers, the size of the reproduction sphere, the frequency range, and the desired accuracy. We also provide analogous results for the special case of reproduction of a two-dimensional (2-D) sound field. Results are verified through computer simulations.

Theory and design of high order sound field microphones using spherical microphone array

A major problem in sound field reconstruction systems is how to record the higher order (> 1) harmonic components of a given sound field. Spherical harmonics analysis is used to establish theory and design of a higher order recording system, which comprises an array of small microphones arranged in a spherical configuration and associated signal processing. This result has implications to the advancement of future sound field reconstruction systems. An example of a third order system for operation over a 10∶1 frequency range of 340 Hz to 3.4 kHz is given.

Intrinsic Limits of Dimensionality and Richness in Random Multipath Fields

We study the dimensions or degrees of freedom of farfield multipath that is observed in a limited, source-free region of space. The multipath fields are studied as solutions to the wave equation in an infinite-dimensional vector space. We prove two universal upper bounds on the truncation error of fixed and random multipath fields. A direct consequence of the derived bounds is that both fixed and random multipath fields have an effective finite dimension. For circular and spherical spatial regions, we show that this finite dimension is proportional to the radius and area of the region, respectively. We use the Karhunen-Loegraveve (KL) expansion of random multipath fields to quantify the notion of multipath richness. The multipath richness is defined as the number of significant eigenvalues in the KL expansion that achieve 99% of the total multipath energy. We establish a lower bound on the largest eigenvalue. This lower bound quantifies, to some extent, the well-known reduction of multipath richness with reducing the angular power spread of multipath angular power spectrum

Theory and design of sound field reproduction in reverberant rooms

With the recent emergence of surround sound technology, renewed interest has been shown in the problem of sound field reproduction. However, in practical acoustical environments, the performance of sound reproduction techniques are significantly degraded by reverberation. In this paper, we develop a method of sound field reproduction for reverberant environments. The key to this method is an efficient parametrization of the acoustic transfer function over a region of space. Using this parametrization, a practical method has been provided for determining the transfer function between each loudspeaker and every point in the reproduction region. Through several simulation examples, the reverberant field designs have been shown to yield a reproduction accuracy as good as conventional free-field designs, and better than multipoint least squares designs when loudspeaker numbers are limited. The successful reproduction of sound over a wide frequency range has also been demonstrated. This approach reveals the appropriate choices for fundamental design parameters.

Spatial correlation for general distributions of scatterers

The well-known results of the spatial correlation function for two-dimensional and three-dimensional diffuse fields of narrowband signals are generalized to the case of general distributions of scatterers. A method is presented that allows closed-form expressions for the correlation function to be obtained for arbitrary scattering distribution functions. These closed-form expressions are derived for a variety of commonly used scattering distribution functions.

On dimensionality of multipath fields: Spatial extent and richness

We establish that an arbitrary narrowband multi path field in any circular region in two dimensional space has an intrinsic functional dimensionality of (πe) R/λ ≈ 8.54 R/λ. that scales only linearly with radius R/λ. in wavelengths. This result implies there is no such thing as an arbitrarily complicated multi path field. That is, a field generated by any number of nearfield and farfield, specular and diffuse multipath reflections is no more complicated than a field generated by a limited number plane waves. As such, there are limits on how rich multipath can be. This result has significant implications including means: i) to determine a parsimonious parameterization for arbitrary multipath fields, ii) of synthesizing arbitrary multi path fields with arbitrarily located nearfield or farfield, spatially discrete or continuous sources. We give examples of multipath field analysis and synthesis.

Broadband nearfield beamforming using a radial beampattern transformation

This paper presents a new method of designing a beamformer having a desired nearfield broadband beampattern. The methodology uses the spherical harmonic solution to the wave equation to transform the desired nearfield beampattern to an equivalent farfield beampattern. A farfield beamformer is then designed for a transformed farfield beampattern that, if achieved, gives the desired nearfield pattern exactly. Salient features of the new method are as follows. (i) The nearfield patterns can be achieved for all angles, not just the primary look direction. (ii) There is no theoretical restriction on the bandwidth. (iii) General array geometries may be used. As an illustration, we apply the method to the problem of producing a practical array design that achieves a nearfield beampattern that is frequency invariant over an octave bandwidth, where at the lowest frequency, the array-source separation is three wavelengths.

Theory and Design of Soundfield Reproduction Using Continuous Loudspeaker Concept

Reproduction of a soundfield is a fundamental problem in acoustic signal processing. A common approach is to use an array of loudspeakers to reproduce the desired field where the least-squares method is used to calculate the loudspeaker weights. However, the least-squares method involves matrix inversion which may lead to errors if the matrix is poorly conditioned. In this paper, we use the concept of theoretical continuous loudspeaker on a circle to derive the discrete loudspeaker aperture functions by avoiding matrix inversion. In addition, the aperture function obtained through continuous loudspeaker method reveals the underlying structure of the solution as a function of the desired soundfield, the loudspeaker positions, and the frequency. This concept can also be applied for the 3-D soundfield reproduction using spherical harmonics analysis with a spherical array. Results are verified through computer simulations.

Introducing Space into MIMO Capacity Calculations

The large spectral efficiencies promised for multiple-input multiple-output (MIMO) wireless fading channels are derived under certain conditions which do not fully take into account the spatial aspects of the channel. Spatial correlation, due to limited angular spread or insufficient antenna spacing, significantly reduces the performance of MIMO systems. In this paper we explore the effects of spatially selective channels on the capacity of MIMO systems via a new capacity expression which is more general and realistic than previous expressions. By including spatial information we derive a closed-form expression for ergodic capacity which uses the physics of signal propagation combined with the statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and leads to valuable insights into the factors determining capacity for a wide range of scattering models.

Spatial Multizone Soundfield Reproduction: Theory and Design

Spatial multizone soundfield reproduction over an extended region of open space is a complex and challenging problem in acoustic signal processing. In this paper, we provide a framework to recreate 2-D spatial multizone soundfields using a single array of loudspeakers which encompasses all spatial regions of interest. The reproduction is based on the derivation of an equivalent global soundfield consisting of a number of individual multizone soundfields. This is achieved by using spatial harmonic coefficients translation between coordinate systems. A multizone soundfield reproduction problem is then reduced to the reproduction over the entire region. An important advantage of this approach is the full use of the available dimensionality of the soundfield. This paper provides quantitative performances of a 2-D multizone system and reveals some fundamental limits on 2-D multizone soundfield reproduction. The extensions of the multizone soundfield reproduction design in reverberant rooms are also included.