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

Annals of the Institute of Statistical Mathematics

For the emerging 5G millimeter-wave communications, the nonlinearity is inevitable due to RF power amplifiers of the enormous bandwidth operating in extremely high frequency, which, in collusion with frequency-selective propagations, may pose great challenges to signal detections. In contrast to classical schemes, which calibrate nonlinear distortions in transmitters, we suggest a nonlinear equalization algorithm, with which the multipath channel and unknown symbols contaminated by nonlinear distortions and multipath interferences are estimated in receiver-ends. Attributed to the nonlinearity and marginal integration, the involved posterior density is analytically intractable and, unfortunately, most existing linear equalization schemes may become invalid. To solve this problem, the Monte-Carlo sequential importance sampling based particle filtering is suggested, and the non-analytical distribution is approximated numerically by a group of random measures with the evolving probability-mass. By applying the Taylor's series expansion technique, a local-linearization observation model is further constructed to facilitate the practical design of a sequential detector. Thus, the unknown symbols are detected recursively as new observations arrive. Simulation results validate the proposed joint detection scheme. By excluding transmitting pre-distortion of high complexity, the presented algorithm is specially designed for the receiver-end, which provides a promising framework to nonlinear equalization and signal detection in millimeter-wave communications.

https://www.researchgate.net/profile/Haijun_Zhang7/publication/273887008_A_Bayesian_Approach_for_Nonlinear_Equalization_and_Signal_Detection_in_Millimeter-wave_Communications/links/550fab2e0cf2ac2905aed04f.pdf

A Bayesian Approach for Nonlinear Equalization and Signal Detection in Millimeter-Wave Communications

We discuss approximate maximum-likelihood methods for blind identification and deconvolution. These algorithms are based on particle approximation versions of the expectation-maximization (EM) algorithm. We consider three different methods which differ in the way the posterior distribution of the symbols is computed. The first algorithm is a particle approximation method of the fixed-interval smoothing. The two-filter smoothing and the novel joined-two-filter smoothing involve an additional backward-information filter. Because the state space is finite, it is furthermore possible at each step to consider all the offsprings of any given particle. It is then required to construct a novel particle swarm by selecting, among all these offsprings, particle positions and computing appropriate weights. We propose here a novel unbiased selection scheme, which minimizes the expected loss with respect to general distance functions. We compare these smoothing algorithms and selection schemes in a Monte Carlo experiment. We show a significant performance increase compared to the expectation maximization Viterbi algorithm (EMVA), a fixed-lag smoothing algorithm and the Block constant modulus algorithm (CMA).

On Approximate Maximum-Likelihood Methods for Blind Identification: How to Cope With the Curse of Dimensionality

In previous papers, we introduced two modified "Bussgang" algorithms (MBAs) for blind-channel equalization based on Bayesian iterative estimation of the source sequence. They were developed in order to reduce the computational complexity of the original "Bussgang" algorithm as well as to make it more flexible by introducing a kind of source adaptivity. However, the previous work relied on some heuristic findings, validated by a series of computer-based experiments. The aim of this paper is to present a theoretical investigation of some particular aspects of the adapting equations, namely, the steady-state conditions, in order to ameliorate the performances of the MBAs and to better explain their numerical behavior.

Analysis of modified "Bussgang" algorithms (MBAs) for channel equalization

We analyze the problem of joint channel-data estimation in fast fading channels. We propose a hybrid structure which associates the Kalman filter and particle filtering, respectively, for the channel and data estimation. We compare this solution with the classical reduced complexity methods. We show that the application of particle filtering to the discrete state space of the data leads to an approach similar to the T algorithm. Hence, this method cannot improve the trade-off between performance and computational complexity of the classical solutions. We conclude that it is preferable to use particle filtering for the joint estimation of discrete and continuous parameters.

/pdf/on-particle-filtering-for-digital-communications-432u8s0tx1.pdf

On particle filtering for digital communications

Instead of the per-survivor processing (PSP) detector which is the state-of-the-art solution for the joint data channel estimation in fast fading channels, a new reduced complexity maximum likelihood sequence detector (MLSD) based on the particle filtering technique is proposed It is shown that the particle detector offers a better trade-off between performance and computational complexity, compared to a reduced complexity PSP detector based on the decision-feedback sequence estimation (DFSE) algorithm Moreover, the computational complexity of this new detector is adapted according to the signal-to-noise ratio

/pdf/joint-data-channel-estimation-using-the-particle-filtering-42rq752t0y.pdf

Joint data-channel estimation using the particle filtering on multipath fading channels

For a given computational complexity, the Viterbi algorithm applied on the discrete representation of the state space provided by a standard particle filtering, outperforms the particle filtering. However, the computational complexity of the Viterbi algorithm is still high. We propose to use the M and T algorithms in order to reduce the computational complexity of the Viterbi algorithm and we show that these algorithms enable a reduction of the number of particles by up to 20%, practically without loss of performance with respect to the Viterbi algorithm.

/pdf/trellis-based-search-of-the-maximum-a-posteriori-sequence-32yb5f5s2z.pdf

Trellis-based search of the maximum a posteriori sequence using particle filtering

Instead of reduced-state decision-feedback sequence estimation (DFSE) equalization which is the state-of-the-art solution for the complexity reduction of the full-state Viterbi decoder over a multipath fading channel, we propose a new reduced complexity maximum likelihood sequence detector (MLSD) based on the particle filtering technique. The computational complexity of this new detector is adapted according to the signal-to-noise ratio. Compared to the DFSE detector the particle detector offers a better trade-off between performance and computational complexity.

/pdf/mlse-receiver-using-the-particle-filtering-over-a-multipath-38xdut7vy2.pdf

MLSE receiver using the particle filtering over a multipath fading channel

In this paper, we propose to use the particle filtering methods in order to estimate jointly the data and the channel coefficients in fast fading conditions. We compare the obtained reduced complexity maximum likelihood detector with the state-of-the-art solution represented by the per-survivor processing (PSP) detector. We show that the proposed particle detector (PD) presents a better trade-off between performance and computational complexity than the reduced complexity PSP detector. Moreover, we observe that the computational complexity of the PD is adapted according to the signal-to-noise ratio.

https://www.irisa.fr/aspi/hmm-stic/isis/bertozzi/GdR-dec02-env.pdf

H. Vu-Thien

Papers

On particle filtering for digital communications

Joint data-channel estimation using the particle filtering on multipath fading channels

Trellis-based search of the maximum a posteriori sequence using particle filtering

MLSE receiver using the particle filtering over a multipath fading channel

Particle filtering for joint data-channel estimation in fast fading channels