This letter deals with the application of the expectation propagation (EP) algorithm to turbo equalization. The EP has been successfully applied to obtain either a better approximation at the output of the equalizer or at the output of the channel decoder to better initialize the Gaussian prior used by the equalizer. In this letter we combine both trends to propose a novel double EP-based equalizer that is able to decrease the number of iterations needed, reducing the computational complexity. This novel equalizer is presented in three different implementations: a block design that exploits the whole vector of observations, a Wiener filter-type approach that just uses the observations within a predefined window and a Kalman smoothing filter-type approach that emulates the BCJR behavior. Finally, we include some experimental results to compare the three different implementations and to illustrate their improvements with respect to other EP-based proposals in the literature.

In this paper we propose a novel turbo equalizer based on the expectation propagation (EP) algorithm. Optimal equalization is computationally unfeasible when high-order modulations and/or large memory channels are used. In these scenarios, low-cost and suboptimal equalizers, such as those based on the linear minimum mean square error (LMMSE), are commonly used. The LMMSE-based equalizer can be efficiently implemented with a Kalman smoother (KS), i.e., a forward and backward Kalman filtering whose predictions are merged in a posterior smoothing step. Recently, it was shown that applying EP at the forward and backward stages of a KS equalizer could significantly improve its performance. In this paper, we investigate applying EP at the smoothing level instead. Also, we propose some further modifications to better exploit the information coming from the channel decoder in turbo equalization schemes. Overall, we remarkably reduce the computational complexity while highly improving the performance in terms of bit error rate.

We propose a novel filter-type equalizer to improve the solution of the linear minimum-mean squared-error (LMMSE) turbo equalizer, with computational complexity constrained to be quadratic in the filter length. When high-order modulations and/or large memory channels are used, the optimal BCJR equalizer is unavailable, due to its computational complexity. In this scenario, the filter-type LMMSE turbo equalization exhibits a good performance compared to other approximations. In this paper, we show that this solution can be significantly improved by using expectation propagation (EP) in the estimation of the a posteriori probabilities. First, it yields a more accurate estimation of the extrinsic distribution to be sent to the channel decoder. Second, compared to other solutions based on EP, the computational complexity of the proposed solution is constrained to be quadratic in the length of the finite impulse response. In addition, we review the previous EP-based turbo equalization implementations. Instead of considering default uniform priors, we exploit the outputs of the decoder. Some simulation results are included to show that this new EP-based filter remarkably outperforms the turbo approach of the previous versions of the EP algorithm and also improves the LMMSE solution, with and without turbo equalization.

In localization tasks, one typically assumes a statistical model of the observations, where the model quantifies the observations by exploiting interrelationships based on geometry. These models might incorporate unknown parameters that, in general, are functions of space. In this article, we propose a crowd sensing method for estimating a spatial field of a quantity (e.g., ranging biases due to line-of-sight/non-line-of-sight or path-loss parameter) allowing for improved indoor localization. Our method takes advantage of the information provided by various users that navigate the area of interest. The proposed learning approach is based on Gaussian processes and its computational cost does not increase with the number of measurements. We present numerical results that show how the proposed method estimates a spatial field of biases and how these estimates lead to much improved performance in estimation of user positions.

In probabilistic equalization of channels with intersymbol interference, the BCJR algorithm and its approximations become intractable for high-order modulations, even for moderate channel dispersions. In this paper, we introduce a novel soft equalizer to approximate the symbol a posteriori probabilities (APP), where the expectation propagation (EP) algorithm is used to provide an accurate estimation. This new soft equalizer is presented as a block solution, denoted as block-EP (BEP), where the structure of the matrices involved is exploited to reduce the complexity order to O(LN2), i.e., linear in the length of the channel, L, and quadratic in the frame length, N. The solution is presented in complex-valued formulation within a turbo equalization scheme. This algorithm can be cast as a linear minimum-mean-squared-error (LMMSE) turbo equalization with double feedback architecture, where constellations being discrete is a restriction exploited by the EP that provides a first refinement of the APP. In the experiments included, the BEP exhibits a robust performance, regardless of the channel response, with gains in the range 1.5-5 dB compared with the LMMSE equalization.

In this paper, we face the soft equalization of channels with inter-symbol interference for large constellation sizes, M. In this scenario, the optimal BCJR solution and most of their approximations are intractable, as the number of states they track grows fast with M. We present a probabilistic equalizer to approximate the posterior distributions of the transmitted symbols using the expectation propagation (EP) algorithm. The solution is presented as a recursive sliding window approach to ensure that the computational complexity is linear with the length of the frame. The estimations can be further improved with a forward-backward approach. This novel soft equalizer, denoted as smoothing EP (SEP), is also tested as a turbo equalizer, with a low-density parity-check (LDPC) channel decoder. The extensive results reported reveal remarkably good behavior of the SEP. In low dimensional cases, the bit error rate (BER) curves after decoding are closer than 1 dB from those of the BJCR, robust to the channel response. For large M, the SEP exhibits gains in the range of 3-5 dB compared to the linear minimum mean square error algorithm.

This letter presents a novel time-of-arrival (TOA) blind estimation technique for ultra wideband energy detection receivers with reduced complexity. The proposed method is blind in the sense that it does not exploit any information about channel or noise power. This new approach is based on a set of approximations of the exact likelihood function (ELF) of the observed energy. Even though these approximations achieve an important reduction of complexity, the shape of the new approximated function is accurate enough compared to the ELF. Application of a threshold to the differential of the approximated log-likelihood function completes the procedure. Simulations show that the performance of the proposed method in terms of the cumulative distribution function of the estimation error approaches that of a method based on the ELF and a genie-aided algorithm with perfect knowledge of the optimal threshold.

This paper deals with a wireless indoor positioning problem in which the location of a tag is estimated from range measurements taken by fixed beacons. The measurements may be affected by non-line-of-sight (NLOS) errors that must be mitigated. We discuss a maximum likelihood (ML) positioning technique that assumes a realistic model for the range errors and a signature database providing information on the propagation conditions at every hypothesized tag spot. The database can be gathered from knowledge of the service area infrastructure and through pre-measurements. It is given in the form of a map indicating, at any node of a close-mesh grid, the nature (LOS/NLOS) of the link between that node and each beacon. The performance of the positioning algorithm is assessed by simulation and is compared with other methods available in literature. The results show that the proposed technique provides significant improvements and is robust against mismatches between true and assumed values of the parameters in the range error model. Comparisons with the Cramer-Rao Bound are made.

This paper deals with a novel energy-detection receiver for ultra-wideband systems operating in dense multi-path environments. For binary PPM modulation we propose a detection scheme that operates on signal energy measurements taken on small fractions (bins) of the symbol period. Assuming that the fractional energies of the channel response over those bins can be estimated in some way, we look for the decision strategy that minimizes the error probability. This leads us to a receiver structure that generalizes the conventional energy- detection scheme. The new strategy turns out to be superior to the conventional strategy and its performance is found to improve as the bin size decreases. A simple method is proposed to estimate the fractional energies of the channel response exploiting a training sequence. The impact of the estimation errors on the receiver performance is shown to be marginal.

This paper deals with energy detection receivers for ultra-wideband systems operating in a dense multipath environment. For binary PPM modulation we propose a novel detection scheme that exploits some information on the channel energy-delay profile. We show that the BER performance of this detector is superior to that of a conventional scheme operating with no knowledge of the channel response. A simple method for estimating the channel delay profile is discussed and it is shown that the impact of the estimation errors on the receiver performance is negligible.