Jayesh H. Kotecha

Gaussian particle filtering

Sequential Bayesian estimation for nonlinear dynamic state-space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations. This paper introduces a new filter called the Gaussian particle filter. It is based on the particle filtering concept, and it approximates the posterior distributions by single Gaussians, similar to Gaussian filters like the extended Kalman filter and its variants. It is shown that under the Gaussianity assumption, the Gaussian particle filter is asymptotically optimal in the number of particles and, hence, has much-improved performance and versatility over other Gaussian filters, especially when nontrivial nonlinearities are present. Simulation results are presented to demonstrate the versatility and improved performance of the Gaussian particle filter over conventional Gaussian filters and the lower complexity than known particle filters.

Gaussian sum particle filtering

We use the Gaussian particle filter to build several types of Gaussian sum particle filters. These filters approximate the filtering and predictive distributions by weighted Gaussian mixtures and are basically banks of Gaussian particle filters. Then, we extend the use of Gaussian particle filters and Gaussian sum particle filters to dynamic state space (DSS) models with non-Gaussian noise. With non-Gaussian noise approximated by Gaussian mixtures, the non-Gaussian noise models are approximated by banks of Gaussian noise models, and Gaussian mixture filters are developed using algorithms developed for Gaussian noise DSS models. As a result, problems involving heavy-tailed densities can be conveniently addressed. Simulations are presented to exhibit the application of the framework developed herein, and the performance of the algorithms is examined.

Transmit signal design for optimal estimation of correlated MIMO channels

We address optimal estimation of correlated multiple-input multiple-output (MIMO) channels using pilot signals, assuming knowledge of the second-order channel statistics at the transmitter. Assuming a block fading channel model and minimum mean square error (MMSE) estimation at the receiver, we design the transmitted signal to optimize two criteria: MMSE and the conditional mutual information between the MIMO channel and the received signal. Our analysis is based on the recently proposed virtual channel representation, which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in the correlated channel. However, our design framework is applicable to more general channel models, which include known channel models, such as the transmit and receive correlated model, as special cases. We show that optimal signaling is in a block form, where the block length depends on the signal-to-noise ratio (SNR) as well as the channel correlation matrix. The block signal corresponds to transmitting beams in successive symbol intervals along fixed virtual transmit angles, whose powers are determined by (nonidentical) water filling solutions based on the optimization criteria. Our analysis shows that these water filling solutions identify exactly which virtual transmit angles are important for channel estimation. In particular, at low SNR, the block length reduces to one, and all the power is transmitted on the beam corresponding to the strongest transmit angle, whereas at high SNR, the block length has a maximum length equal to the number of active virtual transmit angles, and the power is assigned equally to all active transmit angles. Consequently, from a channel estimation viewpoint, a faster fading rate can be tolerated at low SNRs relative to higher SNRs.

Distributed multitarget classification in wireless sensor networks

We study distributed strategies for classification of multiple targets in a wireless sensor network. The maximum number of targets is known a priori but the actual number of distinct targets present in any given event is assumed unknown. The target signals are modeled as zero-mean Gaussian processes with distinct temporal power spectral densities, and it is assumed that the noise-corrupted node measurements are spatially independent. The proposed classifiers have a simple distributed architecture: local hard decisions from each node are communicated over noisy links to a manager node which optimally fuses them to make the final decision. A natural strategy for local hard decisions is to use the optimal local classifier. A key problem with the optimal local classifier is that the number of hypotheses increases exponentially with the maximum number of targets. We propose two suboptimal (mixture density and Gaussian) local classifiers that are based on a natural but coarser repartitioning of the hypothesis space, resulting in linear complexity with the number of targets. We show that exponentially decreasing probability of error with the number of nodes can be guaranteed with an arbitrarily small but nonvanishing communication power per node. Numerical results based on real data demonstrate the remarkable practical advantage of decision fusion: an acceptably small probability of error can be attained by fusing a moderate number of unreliable local decisions. Furthermore, the performance of the suboptimal mixture density classifier is comparable to that of the optimal local classifier, making it an attractive choice in practice.

Why Does the Kronecker Model Result in Misleading Capacity Estimates

Many recent works that study the performance of multiple-input-multiple-output (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigenbases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this paper, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigenbases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low-and the high-SNR extremes: 1) sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the low- SNR extreme, and 2) nonregularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the high-SNR extreme.

Capacity of space-time wireless channels: a physical perspective

Existing results on MIMO channel capacity assume a rich scattering environment in which the channel power scales quadratically with the number of antennas, resulting in linear capacity scaling with the number of antennas. However, such scaling in channel power is physically impossible indefinitely. We thus address the following fundamental question: for a given channel power scaling law, what is the best achievable capacity scaling law? For a channel power scaling, /spl rho//sub c/(N) = O(N/sup /spl gamma//), /spl gamma/ /spl isin/ (0,2], we argue that the channel capacity cannot scale faster than C(N) = O(/spl radic/(/spl rho//sub c/(N))) = O(N/sup /spl gamma//2/). Our approach is based on a family of space-time channels corresponding to different distributions of channel power in the spatial signal space dimensions. We develop the concept of an ideal MIMO channel that achieves the optimal scaling law for a given /spl rho//sub c/(N). For a given number of antennas, unlike existing results that either emphasize the low or high SNR regimes, we propose a methodology for capacity-optimal signaling at any SNR. The methodology is based on creating the ideal channel from any given physical scattering environment via adaptive-resolution array configurations.

Sequential parameter estimation of time-varying non-Gaussian autoregressive processes

Parameter estimation of time-varying non-Gaussian autoregressive processes can be a highly nonlinear problem. The problem gets even more difficult if the functional form of the time variation of the process parameters is unknown. In this paper, we address parameter estimation of such processes by particle filtering, where posterior densities are approximated by sets of samples (particles) and particle weights. These sets are updated as new measurements become available using the principle of sequential importance sampling. From the samples and their weights we can compute a wide variety of estimates of the unknowns. In absence of exact modeling of the time variation of the process parameters, we exploit the concept of forgetting factors so that recent measurements affect current estimates more than older measurements. We investigate the performance of the proposed approach on autoregressive processes whose parameters change abruptly at unknown instants and with driving noises, which are Gaussian mixtures or Laplacian processes.

Optimal signal design for estimation of correlated MIMO channels

Optimal estimation of multi-input multi-output correlated channels using pilot signals is considered, assuming knowledge of the second order channel statistics at the transmitter. Assuming a block fading channel model and minimum mean square error (MMSE) estimation at the receiver, we design the transmitted signal to optimize two criteria: MMSE and the conditional mutual information between the MIMO channel and the received signal. Our analysis is based on the recently proposed virtual channel representation for uniform linear arrays, which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in correlated channels. However, the analysis can be generalized to other known channel models. We show that optimal signaling is in block form corresponding to beams transmitted in successive time intervals along the transmit virtual angles, with powers determined by water filling arguments based on the optimization criteria. The block length depends on the channel correlation and decreases with SNR. Consequently, from a channel estimation viewpoint, a faster fading rate can be tolerated at low SNRs relative to higher SNRs.

Blind equalization for time-varying channels and multiple samples processing using particle filtering ✩

Abstract In this paper we address the problem of equalization of time-varying frequency-selective channels. We formulate the problem by modeling the frequency-selective channel by an FIR filter with time-varying tap weights whose variation is characterized by an AR process. Our approach to the problem is based on Bayesian estimation using sequential Monte Carlo filtering commonly referred to as particle filtering. This estimation method represents the target posterior distribution by a set of random discrete samples and their associated weights. In this paper, we also extend the technique of equalization using particle filtering for cases where we have multiple samples per symbol and demonstrate that significant performance improvement can be achieved by processing multiple samples. The proposed algorithm is recursive and blind for it requires no training symbols for channel estimation. However, it assumes knowledge of the variance of the additive noise and the coefficients of the AR process used to model the variation of the fading channel tap weights. The proposed scheme is highly parallelizable and hence is suitable for VLSI (very large scale integration) implementation.

Coding and diversity gain tradeoff in space-time codes for correlated MIMO channels

Most space-time codes are designed for multiantenna systems assuming the ideal i.i.d. channel model, but their performance degrades over correlated channels. This paper investigates space-time code design for correlated channels using the pair-wise error probability (PEP) criterion. It is shown that, unlike i.i.d channels, performance depends not just on the code error covariance matrix but also its interaction with the channel covariance matrix. Using the example of orthogonal space-time block codes, it is shown that linear preceding can facilitate this interaction to improve performance over correlated channels. Depending on the channel covariance matrix, it may be optimal to trade diversity for higher coding gain even at high signal-to-noise ratios (SNR), i.e. better performance is obtained by lower diversity codes by pumping more power along the dominant transmit signal space dimensions to improve coding gain. This results in reduced dimensional codes which have improved performance than codes without precoding.