Gunvor Elisabeth Kirkelund

Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard constraints in the part of the factor graph corresponding to belief propagation. Finally, we demonstrate an application of our method to iterative channel estimation and decoding in an orthogonal frequency division multiplexing system.

Variational Message-Passing for Joint Channel Estimation and Decoding in MIMO-OFDM

In this contribution, a multi-user receiver for M- QAM MIMO-OFDM operating in time-varying and frequency-selective channels is derived. The proposed architecture jointly performs semi-blind estimation of the channel weights and noise inverse variance, serial interference cancellation and decoding in an iterative manner. The scheme relies on a variational message-passing approach, which enables a joint design of all these functionalities or blocks but the last one. Decoding is performed using the sum-product algorithm. This is in contrast to nowadays proposed approaches in which all these blocks are designed and optimized individually. Simulation results show that the proposed receiver outperforms in coded bit-error-rate a state-of-the- art iterative receiver of same complexity, in which all blocks are designed independently. Joint block design and, as a result, the fact that the uncertainty in the channel estimation is accounted for in the proposed receiver explain this better performance.

Shout to Secure: Physical-Layer Wireless Security with Known Interference

This paper proposes a physical-layer security scheme for wireless networks, aiming to achieve communication secrecy by making the eavesdropper incapable of decoding the secret wireless message. The considered scenario features one user within the range of two access points, API and AP2. The APs are assumed to be connected through an alternative secure (e.g. wired) connection. The goal is to secure the wireless link between the user and API. While the user transmits to API, AP2 simultaneously transmits an interfering signal, which is a priori provided to API, such that API is likely the only node capable of decoding the users entire transmission. Evaluation is done through simulation by measuring the upper bound of the information-theoretic secrecy and error performance. In the latter case it is shown that the eavesdropper experiences significantly higher error rates than the intended receiver, thus providing evidence of practical security.

Message-passing algorithms for channel estimation and decoding using approximate inference

We design iterative receiver schemes for a generic communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that combines belief propagation (BP) and the mean field (MF) approximation and includes these algorithms as special cases. We also show that the expectation propagation and expectation maximization (EM) algorithms can be embedded in the BP-MF framework with slight modifications. By applying the considered inference algorithms to our probabilistic model, we derive four different message-passing receiver schemes. Our numerical evaluation in a wireless scenario demonstrates that the receiver based on the BP-MF framework and its variant based on BP-EM yield the best compromise between performance, computational complexity and numerical stability among all candidate algorithms.

Tracking of Time-Variant Radio Propagation Paths Using Particle Filtering

In this contribution a low-complexity particle filtering algorithm is proposed to track the parameters of time-variant propagation paths in multiple-input multiple-output (MIMO) radio channels. A state-space model is used to describe the path evolution in delay, azimuth of arrival, azimuth of departure, Doppler frequency and complex amplitude dimensions. The proposed particle filter (PF) has an additional resampling step specifically designed for wideband MIMO channel sounding, where the posterior probability density functions of the path states is usually highly concentrated in the multi-dimensional state space. Preliminary investigations using measurement data show that the proposed PF can track paths stably with a small number of particles, e.g. 5 per path, even in the case where the paths are undetected by the conventional SAGE algorithm.

Merging belief propagation and the mean field approximation: A free energy approach

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph. Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example.

Parametric Modeling and Pilot-Aided Estimation of the Wireless Multipath Channel in OFDM Systems

In this paper we present a refined model of the wireless multipath channel along with a thorough analysis on the impact of spatial smoothing techniques when used for improved channel estimation. The state-of-the-art channel estimation algorithm for pilot-aided OFDM systems is robustly designed and operates without knowledge of the time-varying multipath propagation delays in the wireless channel. However, algorithms exploiting knowledge of these time-varying delay parameters can outperform the state-of-the-art solution. We demonstrate from simulations how the Unitary ESPRIT algorithm together with spatial smoothing techniques exhibit a promising potential for multipath propagation delay estimation. Furthermore, we show that the optimum smoothing parameters depend notably on the channel model assumed, specifically in terms of the dynamical behavior of the multipath delays.

Interference Cancellation Based on Divergence Minimization for MIMO-OFDM Receivers

In this paper, we present a novel iterative receiver for MIMO-OFDM systems with synchronous interferers. The receiver is derived based on the Kullback-Leibler divergence minimization framework, and combines channel estimation, interference cancellation and residual noise estimation in an iterative manner. By using both the pilot and data symbols, the channel estimator improves the accuracy of the estimates in each iteration, which leads to a more effective interference cancellation and data detection process. A performance evaluation based on Monte-Carlo simulations shows that the proposed scheme can effectively mitigate the effect of interferers, and operates very close to the single-user performance even in severe interference scenarios.

Channel Estimation Based on Divergence Minimization for OFDM Systems with Co-Channel Interference

In this paper, we present a novel approach for pilot-aided channel estimation in OFDM systems with synchronous co-channel interference. The estimator is derived based on the Kullback-Leibler divergence minimization framework. The obtained solution iteratively updates both the desired users and the interferers channels, using a combination of linear minimum mean squared-error (LMMSE) filtering and interference cancellation, avoiding the complex matrix inversions involved in the full LMMSE channel estimation approach. Estimation of the noise variance is also included in the iterative algorithm, accounting for Gaussian noise and residual interference after each iteration. The estimates of both channels are used at the equalizer to reject the interfering signal, thus mitigating the degradation due to co-channel interference. Simulation results show that the receiver using the proposed estimator performs as good as the one employing the full LMMSE estimator and very closely to a receiver having perfect knowledge of the channel coefficients.

Tracking of the multi-dimensional parameters of a target signal using particle filtering

In this contribution, a low-complexity particle filter (PF) is proposed to track the parameters of the signal reflected by a target illuminated with a digital-video-broadcast terrestrial (DVB-T) signal. The tracked parameters are the delay (time of arrival), the azimuth and elevation of arrival, the Doppler frequency, the complex amplitude of the target signal, as well as the rates of change of all but the last parameter. The proposed PF tracks these parameters based on samples of the target signal by assuming that the temporal behaviour of these parameters is governed by a multi-dimensional linear state-space model. The algorithm has an additional resampling step specifically designed to cope with the highly concentrated multi-dimensional posterior probability density function of the parameters. This step allows for tracking the parameters of the target signal with only a few particles, e.g. 50, leading to low computational complexity. Simulation results show that the PF outperforms the maximum-likelihood estimator applied to individual samples of the target signal in terms of higher accuracy and robustness. Under certain conditions usually met in reality the proposed PF can be used to track the parameters of the signals contributed by individual targets in multi-target scenarios.