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.

Location-aware communication systems are expected to play a pivotal part in the next generation of mobile communication networks. Therefore, there is a need to understand the localization limits in these networks, particularly, using millimeter-wave technology (mmWave). Towards that, we address the uplink and downlink localization limits in terms of 3D position and orientation error bounds for mmWave multipath channels. We also carry out a detailed analysis of the dependence of the bounds on different system parameters. Our key findings indicate that the uplink and downlink behave differently in two distinct ways. First of all, the error bounds have different scaling factors with respect to the number of antennas in the uplink and downlink. Secondly, uplink localization is sensitive to the orientation angle of the user equipment (UE), whereas downlink is not. Moreover, in the considered outdoor scenarios, the non-line-of-sight paths generally improve localization when a line-of-sight path exists. Finally, our numerical results show that mmWave systems are capable of localizing a UE with sub-meter position error, and sub-degree orientation error. communications [7], assisted living applications [8], or to support the communication robustness and effectiveness in different aspects such as resource allocation [9], beamforming [10], [11], and pilot assignment [12]. Therefore, the study of positioning in 5G mmWave systems becomes specially imperative. Due to the use of directional beamforming in mmWave, in addition to the UE position also the UE orientation plays an important role in location-aided systems.Conventionally position information is obtained by GPS, though this has several limitations.Most importantly, GPS suffers from degraded performance in outdoor rich-scattering scenarios and urban canyons, and may fail to provide a position fix for indoor scenarios. Even in good conditions, GPS positioning accuracy ranges between 1-5 meters. To address these limitations, there has been intense research on competing radio-based localization technologies. To understand the fundamental behavior of any technology, the Cramér-Rao lower bound (CRLB)[13] or related bounds can be used. The CRLB provides a lower bound on the variance of an unbiased estimator of a certain parameter. The square-root of the CRLB of the position and the orientation are termed the position error bound (PEB), and the orientation error bound (OEB), respectively. PEB and OEB can be computed indirectly by transforming the bounds of the channel parameters, namely: directions of arrival (DOA), directions of departure (DOD), and time of arrival (TOA). For conventional MIMO systems, the bounds of the 2D channel parameters are derived in [14], based on received digital signals and uniform linear arrays (ULA), while bounds are derived in [15] based on 3D channel matrix with no transmit beamforming. It was found that having more transmit and receive antennas is beneficial for estimating the DOA and DOD. In both [14], [15] beamforming was not considered. The b...

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.

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-Loeve (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 achieves 99% of the total multipath energy.We prove 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 spread of multipath angular power spectrum. We also provide a numerical algorithm to find multipath eigenvalues, which unlike the Fredholm equation method, does not require selecting quadrature points.