Abstract—The design of a pilot symbol for orthogonal frequency- division multiplexing packet detection and synchronization is presented. Algorithms are described for packet detection and for synchronization using maximum likelihood estimation of channel frequency offset, phase offset for coherent detection, and subsample timing offset. The efficacy of the detection and synchronization algorithms is demonstrated experimentally. A performance analysis of these algorithms appears in a companion paper.
Abstract—We consider a cognitive radio system with N secondary user (SU) pairs and a pair of primary users (PU). The SU power allocation problem is formulated as a capacity maximisation problem under PU and SU quality of service and SU peak power constraints. The problem is formulated as a geometric program, solved for both low- and high- signal-tointerference- and-noise ratio (SINR) regimes. We present a novel method of detecting and removing infeasible SU quality of service constraints from the SU power allocation problem that results in considerably improved SU performance. Capacity cumulative distribution functions for Rayleigh fading channels are produced.
Abstract—Spectrum sharing systems such as cognitive radios must both strive to avoid interference and be tolerant to interference. While pilot symbol assisted systems have previously been shown to have detection and synchronization adversely affected by narrowband interference, the impact of wideband interference has received little attention. This paper shows both analytically and by computer simulation that wideband interference prevents correct pilot symbol assisted detection and synchronization for SIRs of 0 dB and less. An asymptotically optimal detector is derived for pilot symbols in the presence of Gaussian distributed wideband interference. Simulation results are presented to demonstrate that robust detection can be achieved for SIRs as low as −60 dB using a low complexity implementation for a typical OFDM system.
Abstract—We consider a cognitive radio (CR) relay network consisting of a cognitive source, a cognitive destination and a number of cognitive relay nodes that share spectrum with a primary transmitter and receiver. Due to poor channel conditions, the cognitive source is unable to communicate directly with the cognitive destination and hence employs the cognitive relays for assistance. We assume that the CR has a very loose cooperation with the primary network and therefore, only partial channel state information is available. Under these assumptions, we propose a new statistically robust CR cooperative relay beamformer where either the total relay transmit power or the cognitive destination signal-to-interference-and-noise ratio (SINR) is optimised subject to primary receiver outage probability constraint. We formulate the robust total relay power and the cognitive destination SINR optimisation problems as a convex second order cone program and a convex feasibility problem, respectively, that provide near optimum results. We also present efficient iterative algorithms that provide the optimum results.
Abstract—A performance analysis of algorithms for maximum likelihood estimation of channel parameters for orthogonal frequency-division multiplexing packet detection and synchronization is presented. The detection and synchronization algorithms, which are based on the use of a pilot symbol, are described in a companion paper. The performance analyses concentrate on operation in additive white Gaussian noise channels, and the accuracy of these analyses are demonstrated using experimental and simulation data. Methods to extend these analyses to frequency flat multipath fading channels are presented.
Abstract - Sound reproduction systems using open arrays of loudspeakers in rooms suffer from degradations due to room reflections. These reflections can be reduced using pre-compensation of the loudspeaker signals, but this requires calibration of the array in the room, and is processor-intensive. This paper examines 3D sound reproduction systems using spherical arrays of fixed-directivity loudspeakers which reduce the sound field radiated outside the array. A generalized form of the simple source formulation and a mode-matching solution are derived for the required loudspeaker weights. The exterior field is derived and expressions for the exterior power and direct to reverberant ratio are derived. The theoretical results and simulations confirm that minimum interference occurs for loudspeakers which have hyper-cardioid polar responses.
Abstract - Successful recording of large spatial soundfields is a prevailing challenge in acoustic signal processing due to the enormous numbers of microphones required. This paper presents the design and analysis of an array of higher order microphones that uses 2D wavefield translation to provide a mode matching solution to the height invariant recording problem. It is shown that the use of Mth order microphones significantly reduces the number of microphone units by a factor of 1/(2M+1) at the expense of increased complexity at each microphone unit. Robustness of the proposed array is also analyzed based on the condition number of the translation matrix while discussing array configurations that result in low condition numbers. The white-noise gain (WNG) of the array is then derived to verify that improved WNG can be achieved when the translation matrix is well conditioned. Furthermore, the array’s performance is studied for interior soundfield recording as well as exterior soundfield recording using appropriate simulation examples.
Abstract - Higher order sound sources of Nth order can radiate sound with 2N+1 orthogonal radiation patterns, which can be represented as phase modes or, equivalently, amplitude modes. This paper shows that each phase mode response produces a spiral wave front with a different spiral rate, and therefore a different direction of arrival of sound. Hence, for a given receiver position a higher order source is equivalent to a linear array of 2N+1 monopole sources. This interpretation suggests performance similar to a circular array of higher order sources can be produced by an array of sources, each of which consists of a line array having monopoles at the apparent source locations of the corresponding phase modes. Simulations of higher order arrays and arrays of equivalent line sources are presented. It is shown that the interior fields produced by the two arrays are essentially the same, but that the exterior fields differ because the higher order sources produces different equivalent source locations for field positions outside the array. This work provides an explanation of the fact that an array of L Nth order sources can reproduce sound fields whose accuracy approaches the performance of (2N+1)L monopoles.
Abstract - Reproduction of a given sound field interior to a circular loudspeaker array without producing an undesirable exterior sound field is an unsolved problem over a broadband of frequencies. At low frequencies, by implementing the Kirchhoff–Helmholtz integral using a circular discrete array of line source loudspeakers, a sound field can be recreated within the array and produce no exterior sound field, provided that the loudspeakers have azimuthal polar responses with variable first-order responses which are a combination of a two-dimensional (2D) monopole and a radially oriented 2D dipole. This paper examines the performance of circular discrete arrays of line-source loudspeakers which also include a tangential dipole, providing general variable-directivity responses in azimuth. It is shown that at low frequencies, the tangential dipoles are not required, but that near and above the Nyquist frequency, the tangential dipoles can both improve the interior accuracy and reduce the exterior sound field. The additional dipoles extend the useful range of the array by around an octave.
Abstract - The practical performance of circular microphone arrays is discussed. Such arrays are useful for the analysis of room acoustics, the recording of live sound fields for surround sound reproduction, and in teleconferencing applications. They also produce low-cost performance relative to three-dimensional arrays when sound sources and loudspeaker reproduction systems are predominantly in the horizontal plane. The noise performance of circular arrays and their sensitivity to transducer variability are considered, and examples are given for the ideal first-order array. In addition, the analysis of arrays using a recently proposed downsampling technique is included.
Abstract - Sound reproduction systems using omnidirectional loudspeakers produce reflections from room surfaces which interfere with the desired sound field within the array. While active compensation systems can reduce the reverberant level, they require calibration in each room and are processor-intensive. Directional loudspeakers allow the direct to reverberant level to be improved within the array, but still produce a finite exterior field which reflects from the room surfaces. The use of variable-directivity loudspeakers allows the exterior field to be eliminated at low frequencies by implementing the Kirchhoff–Helmholtz integral equation. This paper investigates the performance of variable-directivity arrays in reducing reverberant levels and compares the results with those derived in a previous paper for fixed-directivity arrays. The results presented may have some impact on the design of commercial multi-channel systems for sound reproduction.
Abstract - The theory of recording and reproduction of three-dimensional sound fields based on spherical harmonics is reviewed and extended. Free-field, sphere, and general recording arrays are reviewed, and the mode-matching and simple source approaches to sound reproduction in anechoic environments are discussed. Both methods avoid the need for both monopole and dipole loudspeakers—as required by the Kirchhoff–Helmholtz integral. An error analysis is presented and simulation examples are given. It is also shown that the theory can be extended to sound reproduction in reverberant environments.
Abstract - Spatial sound reproduction systems aim to produce a desired sound field over a volume of space. At high frequencies, the number of loudspeakers required is prohibitive. This paper shows that the use of loudspeakers with up to Nth order directivity allows reproduction over N times the bandwidth and produces a significantly attenuated exterior sound field. If the constraint on exterior cancellation of the field is removed, reproduction is possible over approximately 2N times the bandwidth. The use of higher order loudspeakers thus allows a significant reduction in the number of loudspeaker units, at the expense of increased complexity in each unit. For completeness, results are included for the generation of an exterior field with or without cancellation of the interior field.
Abstract - The design of panning functions for surround sound systems with nonuniform loudspeaker layout is considered. It is shown that theoretical solutions exist which are interpolants for nonuniform sampling of periodic functions. However, these solutions produce large interference effects for positions far from the array center, and they are sensitive to phase and magnitude mismatches between loudspeakers. Robust solutions approximate a double complementarity property in which the weights and squared weights sum to 1 for each source angle. A least-squares method is developed for developing robust panning functions which produces a more consistent sound-field directionality than those produced by matching parameters at the origin.
Abstract - In this paper, sound field reproduction is performed in a reverberant room using higher order sources (HOSs) and a calibrating microphone array. Previously a sound field was reproduced with fixed directivity sources and the reverberation compensated for using digital filters. However by virtue of their directive properties, HOSs may be driven to not only avoid the creation of excess reverberation but also to use room reflection to contribute constructively to the desired sound field. The manner by which the loudspeakers steer the sound around the room is determined by measuring the acoustic transfer functions. The requirements on the number and order N of HOSs for accurate reproduction in a reverberant room are derived, showing a 2Nþ1-fold decrease in the number of loudspeakers in comparison to using monopole sources. HOSs are shown applicable to rooms with a rich variety of wall reflections while in an anechoic room their advantages may be lost. Performance is investigated in a room using extensions of both the diffuse field model and a more rigorous image-source simulation method, which account for the properties of the HOSs. The robustness of the proposed method is validated by introducing measurement errors.