Recent developments have demonstrated that particle filtering is an emerging and powerful methodology, using Monte Carlo methods, for sequential signal processing with a wide range of applications in science and engineering. It has captured the attention of many researchers in various communities, including those of signal processing, statistics and econometrics. Based on the concept of sequential importance sampling and the use of Bayesian theory, particle filtering is particularly useful in dealing with difficult nonlinear and non-Gaussian problems. The underlying principle of the methodology is the approximation of relevant distributions with random measures composed of particles (samples from the space of the unknowns) and their associated weights. First, we present a brief review of particle filtering theory; and then we show how it can be used for resolving many problems in wireless communications. We demonstrate its application to blind equalization, blind detection over flat fading channels, multiuser detection, and estimation and detection of space-time codes in fading channels.

Particle filtering

The emerging massive/large-scale multiple-input multiple-output (LS-MIMO) systems that rely on very large antenna arrays have become a hot topic of wireless communications. Compared to multi-antenna aided systems being built at the time of this writing, such as the long-term evolution (LTE) based fourth generation (4G) mobile communication system which allows for up to eight antenna elements at the base station (BS), the LS-MIMO system entails an unprecedented number of antennas, say 100 or more, at the BS. The huge leap in the number of BS antennas opens the door to a new research field in communication theory, propagation and electronics, where random matrix theory begins to play a dominant role. Interestingly, LS-MIMOs also constitute a perfect example of one of the key philosophical principles of the Hegelian Dialectics, namely, that “quantitative change leads to qualitative change.” In this treatise, we provide a recital on the historic heritages and novel challenges facing LS-MIMOs from a detection perspective. First, we highlight the fundamentals of MIMO detection, including the nature of co-channel interference (CCI), the generality of the MIMO detection problem, the received signal models of both linear memoryless MIMO channels and dispersive MIMO channels exhibiting memory, as well as the complex-valued versus real-valued MIMO system models. Then, an extensive review of the representative MIMO detection methods conceived during the past 50 years (1965–2015) is presented, and relevant insights as well as lessons are inferred for the sake of designing complexity-scalable MIMO detection algorithms that are potentially applicable to LS-MIMO systems. Furthermore, we divide the LS-MIMO systems into two types, and elaborate on the distinct detection strategies suitable for each of them. The type-I LS-MIMO corresponds to the case where the number of active users is much smaller than the number of BS antennas, which is currently the mainstream definition of LS-MIMO. The type-II LS-MIMO corresponds to the case where the number of active users is comparable to the number of BS antennas. Finally, we discuss the applicability of existing MIMO detection algorithms in LS-MIMO systems, and review some of the recent advances in LS-MIMO detection.

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Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs

Spherical microphone arrays have been recently studied for sound-field recordings, beamforming, and sound-field analysis which use spherical harmonics in the design. Although the microphone arrays and the associated algorithms were presented, no comprehensive theoretical analysis of performance was provided. This work presents a spherical-harmonics-based design and analysis framework for spherical microphone arrays. In particular, alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations. The analysis framework can also provide a useful guide for the design and analysis of more general spherical microphone arrays which do not use spherical harmonics explicitly.

Analysis and design of spherical microphone arrays

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.

/pdf/three-dimensional-surround-sound-systems-based-on-spherical-gts6rffrmw.pdf

Three-Dimensional Surround Sound Systems Based on Spherical Harmonics

Speech enhancement and separation are core problems in audio signal processing, with commercial applications in devices as diverse as mobile phones, conference call systems, hands-free systems, or hearing aids. In addition, they are crucial preprocessing steps for noise-robust automatic speech and speaker recognition. Many devices now have two to eight microphones. The enhancement and separation capabilities offered by these multichannel interfaces are usually greater than those of single-channel interfaces. Research in speech enhancement and separation has followed two convergent paths, starting with microphone array processing and blind source separation, respectively. These communities are now strongly interrelated and routinely borrow ideas from each other. Yet, a comprehensive overview of the common foundations and the differences between these approaches is lacking at present. In this paper, we propose to fill this gap by analyzing a large number of established and recent techniques according to four transverse axes: 1 the acoustic impulse response model, 2 the spatial filter design criterion, 3 the parameter estimation algorithm, and 4 optional postfiltering. We conclude this overview paper by providing a list of software and data resources and by discussing perspectives and future trends in the field.

/pdf/a-consolidated-perspective-on-multimicrophone-speech-qnbaqxmtvq.pdf

A Consolidated Perspective on Multimicrophone Speech Enhancement and Source Separation

Traditional acoustic source localization algorithms attempt to find the current location of the acoustic source using data collected at an array of sensors at the current time only. In the presence of strong multipath, these traditional algorithms often erroneously locate a multipath reflection rather than the true source location. A recently proposed approach that appears promising in overcoming this drawback of traditional algorithms, is a state-space approach using particle filtering. In this paper we formulate a general framework for tracking an acoustic source using particle filters. We discuss four specific algorithms that fit within this framework, and demonstrate their performance using both simulated reverberant data and data recorded in a moderately reverberant office room (with a measured reverberation time of 0.39 s). The results indicate that the proposed family of algorithms are able to accurately track a moving source in a moderately reverberant room.

/pdf/particle-filtering-algorithms-for-tracking-an-acoustic-3t94732ge2.pdf

Particle filtering algorithms for tracking an acoustic source in a reverberant environment

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.

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

The theory and design of a broadband array of sensors with a frequency invariant far‐field beam pattern over an arbitrarily wide design bandwidth is presented. The frequency invariant beam pattern property is defined in terms of a continuously distributed sensor, and the problem of designing a practical sensor array is then treated as an approximation to this continuous sensor using a discrete set of filtered broadband omnidirectional array elements. The design methodology is suitable for one‐, two‐, and three‐dimensional sensor arrays; it imposes no restrictions on the desired aperture distribution (beam shape), and can cope with arbitrarily wide bandwidths. An important consequence of the results is that the frequency response of the filter applied to the output of each sensor can be factored into two components: One component is related to a slice of the desired aperture distribution, and the other is sensor independent. The results also indicate that the locations of the sensors are not a crucial design consideration, although it is shown that nonuniform spacings simultaneously avoid spatial aliasing and minimize the number of sensors. An example design which covers a 10:1 frequency range (which is suitable for speech acquisition using a microphone array) illustrates the utility of the method. Finally, the theory is generalized to cover a parameterized class of arrays in which the frequency dependence of the beam pattern can be controlled in a continuous manner from a classical single‐frequency design to a frequency invariant design.

Theory and design of broadband sensor arrays with frequency invariant far‐field beam patterns

Traditional acoustic source localization uses a two-step procedure requiring intermediate time-delay estimates from pairs of microphones. An alternative single-step approach is proposed in this paper in which particle filtering is used to estimate the source location through steered beamforming. This scheme is especially attractive in speech enhancement applications, where the localization estimates are typically used to steer a beamformer at a later stage. Simulation results show that the algorithm is robust to reverberation, and is able to accurately follow the source trajectory.

Particle filter beamforming for acoustic source localization in a reverberant environment

A parallel detection method is proposed for use in the context of uncoded multiple antenna communication. The method does not require power reordering and helps reduce the system delay at the cost of higher computational complexity. The scheme also shows marked improvement in performance over the classical scheme.

D.B. Ward

Papers

Particle filtering algorithms for tracking an acoustic source in a reverberant environment

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

Theory and design of broadband sensor arrays with frequency invariant far‐field beam patterns

Particle filter beamforming for acoustic source localization in a reverberant environment

Parallel multistage detection for multiple antenna wireless systems