Franz Hlawatsch

Linear and quadratic time-frequency signal representations

A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided.<<ETX>>

Frame-theoretic analysis of oversampled filter banks

We provide a frame-theoretic analysis of oversampled finite impulse response (FIR) and infinite impulse response (FIR) uniform filter banks (FBs). Our analysis is based on a new relationship between the FBs polyphase matrices and the frame operator corresponding to an FB. For a given oversampled analysis FB, we present a parameterization of all synthesis FBs providing perfect reconstruction. We find necessary and sufficient conditions for an oversampled FB to provide a frame expansion. A new frame-theoretic procedure for the design of paraunitary FBs from given nonparaunitary FBs is formulated. We show that the frame bounds of an FB can be obtained by an eigen-analysis of the polyphase matrices. The relevance of the frame bounds as a characterization of important numerical properties of an FB is assessed by means of a stochastic sensitivity analysis. We consider special cases in which the calculation of the frame bounds and synthesis filters is simplified. Finally, simulation results are presented.

A compressed sensing technique for OFDM channel estimation in mobile environments: Exploiting channel sparsity for reducing pilots

We consider the estimation of doubly selective wireless channels within pulse-shaping multicarrier systems (which include OFDM systems as a special case). A new channel estimation technique using the recent methodology of compressed sensing (CS) is proposed. CS-based channel estimation exploits a channels delay-Doppler sparsity to reduce the number of pilots and, hence, increase spectral efficiency. Simulation results demonstrate a significant reduction of the number of pilots relative to least-squares channel estimation.

Compressive Estimation of Doubly Selective Channels in Multicarrier Systems: Leakage Effects and Sparsity-Enhancing Processing

We consider the application of compressed sensing (CS) to the estimation of doubly selective channels within pulse-shaping multicarrier systems (which include orthogonal frequency-division multiplexing (OFDM) systems as a special case). By exploiting sparsity in the delay-Doppler domain, CS-based channel estimation allows for an increase in spectral efficiency through a reduction of the number of pilot symbols. For combating leakage effects that limit the delay-Doppler sparsity, we propose a sparsity-enhancing basis expansion and a method for optimizing the basis with or without prior statistical information about the channel. We also present an alternative CS-based channel estimator for (potentially) strongly time-frequency dispersive channels, which is capable of estimating the ¿off-diagonal¿ channel coefficients characterizing intersymbol and intercarrier interference (ISI/ICI). For this estimator, we propose a basis construction combining Fourier (exponential) and prolate spheroidal sequences. Simulation results assess the performance gains achieved by the proposed sparsity-enhancing processing techniques and by explicit estimation of ISI/ICI channel coefficients.

Distributed particle filtering in agent networks: A survey, classification, and comparison

Distributed particle filter (DPF) algorithms are sequential state estimation algorithms that are executed by a set of agents. Some or all of the agents perform local particle filtering and interact with other agents to calculate a global state estimate. DPF algorithms are attractive for large-scale, nonlinear, and non-Gaussian distributed estimation problems that often occur in applications involving agent networks (ANs). In this article, we present a survey, classification, and comparison of various DPF approaches and algorithms available to date. Our emphasis is on decentralized ANs that do not include a central processing or control unit.

Likelihood Consensus and Its Application to Distributed Particle Filtering

We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task-based on the past and current measurements of all sensors-using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This “likelihood consensus” method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem.

Oversampled cosine modulated filter banks with perfect reconstruction

Oversampled filter banks (FBs) offer more design freedom and better noise immunity than critically sampled FBs. Due to the increased computational complexity caused by oversampling, oversampled FBs allowing an efficient implementation, such as cosine modulated filter banks (CMFBs), are of particular interest. So far, only critically sampled CMFBs have been considered. In this paper, we introduce oversampled CMFBs with perfect reconstruction (PR). Extending a classification of CMFBs recently proposed by Gopinath, we consider two types of oversampled CMFBs with PR. One of these types allows linear phase filters in all channels, and comprises CMFBs recently introduced by Lin and Vaidyanathan as well as Wilson-type CMFBs. For both types of oversampled CMFBs, we formulate PR conditions in the time, frequency, and polyphase domains. It is shown that any PR CMFB corresponds to a PR DFT FB with twice the oversampling factor and that (under a specific condition) the same PR prototype can be used for both CMFB types. We also show that the frame-theoretic properties of a CMFB and of the corresponding DFT FB are closely related. In particular, it is demonstrated that the minimum-norm synthesis prototype in an oversampled PR CMFB equals that in the corresponding DFT FB. Finally, we briefly address design methods and the efficient DCT/DST-based implementation of oversampled CMFBs.

Noise reduction in oversampled filter banks using predictive quantization

We introduce two methods for quantization noise reduction in oversampled filter banks. These methods are based on predictive quantization (noise shaping or linear prediction). It is demonstrated that oversampled noise shaping or linear predictive subband coders are well suited for subband coding applications where, for technological or other reasons, low-resolution quantizers have to be used. In this case, oversampling combined with noise shaping or linear prediction improves the effective resolution of the subband coder at the expense of increased rate. Simulation results are provided to assess the achievable quantization noise reduction and resolution enhancement, and to investigate the rate-distortion properties of the proposed methods.

Pulse-shaping OFDM/BFDM systems for time-varying channels: ISI/ICI analysis, optimal pulse design, and efficient implementation

This paper considers practically relevant aspects and advantages of pulse-shaping orthogonal/biorthogonal frequency division multiplexing (OFDM/BFDM) systems. We analyze the intersymbol/intercarrier interference (ISI/ICI) in such systems when they operate over time-varying channels. Two methods for an ISI/ICI-minimizing pulse design are proposed, and efficient FFT-based modulator and demodulator implementations are presented. Simulations show that for fast time-varying channels, optimized BFDM systems can outperform conventional OFDM systems with respect to ISI/ICI.

Analysis, Optimization, and Implementation of Low-Interference Wireless Multicarrier Systems

This paper considers pulse-shaping multicarrier (MC) systems that transmit over doubly dispersive fading channels. We provide exact and approximate expressions for the intersymbol and intercarrier interference occurring, in such systems. This analysis reveals that the time and frequency concentration of the transmit and receive pulses is of paramount importance for low interference. We prove the (nonobvious) existence of such jointly concentrated pulse pairs by adapting recent mathematical results on Weyl-Heisenberg frames to the MC context. Furthermore, pulse optimization procedures are proposed that aim at low interference and capitalize on the design freedom existing for redundant MC systems. Finally, we present efficient FFT-based modulator and demodulator implementations. Our numerical results demonstrate that for realistic system and channel parameters, optimized pulse-shaping MC systems can outperform conventional cyclic-prefix OFDM systems