Markus V. S. Lima

Sparsity-Aware Data-Selective Adaptive Filters

We propose two adaptive filtering algorithms that combine sparsity-promoting schemes with data-selection mechanisms. Sparsity is promoted via some well-known nonconvex approximations to the l0 norm in order to increase convergence speed of the algorithms when dealing with sparse/compressible signals. These approximations circumvent some difficulties of working with the l0 norm, thus allowing the development of online data-selective algorithms. Data selection is implemented based on set-membership filtering, which yields robustness against noise and reduced computational burden. The proposed algorithms are analyzed in order to set properly their parameters to guarantee stability. In addition, we characterize their updating processes from a geometrical viewpoint. Simulation results show that the proposed algorithms outperform the state-of-the-art algorithms designed to exploit sparsity.

Affine projection algorithms for sparse system identification

We propose two versions of affine projection (AP) algorithms tailored for sparse system identification (SSI). Contrary to most adaptive filtering algorithms devised for SSI, which are based on the l1 norm, the proposed algorithms rely on homotopic l0 norm minimization, which has proven to yield better results in some practical contexts. The first proposal is obtained by direct minimization of the AP cost function with a penalty function based on the l0 norm of the coefficient vector, whereas the second algorithm is a simplified version of the first proposal. Simulation results are presented in order to evaluate the performance of the proposed algorithms considering three different homotopies to the l0 norm as well as competing algorithms.

Steady-State MSE Performance of the Set-Membership Affine Projection Algorithm

The set-membership affine projection (SM-AP) algorithm has many desirable characteristics such as fast convergence speed, low power consumption due to data-selective updates, and low misadjustment. The main reason hindering the widespread use of the SM-AP algorithm is the lack of analytical results related to its steady-state performance. In order to bridge this gap, this paper presents an analysis of the steady-state mean square error (MSE) of a general form of the SM-AP algorithm. The proposed analysis results in closed-form expressions for the excess MSE and misadjustment of the SM-AP algorithm, which are also applicable to many other algorithms. This work also provides guidelines for the analysis of the whole family of SM-AP algorithms. The analysis relies on the energy conservation method and has the attractive feature of not assuming a specific model for the input signal. In addition, the choice of the upper bound for the error of the SM-AP algorithm is addressed for the first time. Simulation results corroborate the accuracy of the proposed analysis.

Steady-state analysis of the set-membership affine projection algorithm

Among the adaptive filtering algorithms the set-membership affine projection (SM-AP) algorithm has the attractive feature of not trading off misadjustment with convergence speed. This paper presents an analysis of the steady-state mean-square error (MSE) of the SM-AP algorithm. Our analysis relies on the energy conservation method and does not assume a specific probability distribution for the input vector. Moreover, since the SM-AP algorithm with a fixed-modulus error-based constraint vector generalizes some important algorithms, such as the SM normalized least-mean-square (SM-NLMS) algorithm, the results can be directly applied to these algorithms. Simulation results confirm the accuracy of our analysis.

Stability and MSE analyses of affine projection algorithms for sparse system identification

We analyze two algorithms, viz. the affine projection algorithm for sparse system identification (APA-SSI) and the quasi APA-SSI (QAPA-SSI), regarding their stability and steady-state mean-squared error (MSE). These algorithms exploit the sparsity of the involved signals through an approximation of the l0 norm. Such approach yields faster convergence and reduced steady-state MSE, as compared to algorithms that do not take the sparse nature of the signals into account. In addition, modeling sparsity via such approximation has been consistently verified to be superior to the widely used l1 norm in several scenarios. In this paper, we show how to properly set the parameters of the two aforementioned algorithms in order to guarantee convergence, and we derive closed-form theoretical expressions for their steady-state MSE. A key conclusion from the proposed analysis is that the MSE of these two algorithms is a monotonically decreasing function of the sparsity degree. Simulation results are used to validate the theoretical findings.

A Volumetric SRP with Refinement Step for Sound Source Localization

This paper proposes an efficient method based on the steered-response power (SRP) technique for sound source localization using microphone arrays: the volumetric SRP (VSRP). As compared to the SRP, by deploying a sparser volumetric grid, the V-SRP achieves a significant reduction of the computational complexity without sacrificing the accuracy of the location estimates. By appending a fine search step to the VSRP, its refined version (RV-SRP) improves on the compromise between complexity and accuracy. Experiments conducted in both simulatedand real-data scenarios demonstrate the benefits of the proposed approaches. Specifically, the RV-SRP is shown to outperform the SRP in accuracy at a computational cost of about ten times lower.This letter proposes an efficient method based on the steered-response power (SRP) technique for sound source localization using microphone arrays: the refined volumetric SRP (RV-SRP). By deploying a sparser volumetric grid, the RV-SRP achieves a significant reduction of the computational complexity without sacrificing the accuracy of location estimates. In addition, a refinement step improves on the compromise between complexity and accuracy. Experiments conducted in both simulated- and real-data scenarios show that the RV-SRP outperforms state-of-the-art methods in accuracy with lower computational cost.

Open-source physical-layer simulator for LTE systems

This article describes a physical-layer simulator for both uplink and downlink connections of LTE systems, whose performances are assessed by simulating standardized environments. The simulator is compliant with Release 9 of LTE standard and it is publicly available for educational purposes, allowing students and researchers to test the performance of Signal Processing and Digital Communications techniques in an easy-to-use MATLAB framework. Users may benefit from implemented features such as channel estimation using different demodulation reference signals, channel coding, equalization, multiple access schemes in which multiple cells are employed, as well as diversity, spatial multiplexing, and beamforming transmissions. As an example, we evaluate the impact on the performance of an uplink connection due to inaccuracy in channel estimation and multi-user interference. In addition, we include the evaluation of using diversity and spatial multiplexing transmissions on downlink connections.

On the steady-state MSE performance of the set-membership NLMS algorithm

The aim of this paper is to investigate the steady-state mean square error (MSE) performance of the set-membership (SM) normalized least-mean-square (NLMS) algorithm. Until recently there was no analysis tool available for the SM-NLMS algorithm, mainly due to its inherent nonlinear selective update which requires more involved mathematical treatment. The few recent available works invoke some unrealistic assumptions in order to simplify the problem. This paper investigates the validity of these assumptions and their influence in the accuracy of the resulting relations. Some simulation results are included in order to verify how reliable and accurate are the discussed analysis methods of the SM-NLMS algorithm.

A simple set-membership affine projection algorithm for sparse system modeling

In this paper, we derive two algorithms, namely the Simple Set-Membership Affine Projection (S-SM-AP) and the improved S-SM-AP (IS-SM-AP), in order to exploit the sparsity of an unknown system while focusing on having low computational complexity. To achieve this goal, the proposed algorithms apply a discard function on the weight vector to disregard the coefficients close to zero during the update process. In addition, the IS-SM-AP algorithm reduces the overall number of computations required by the adaptive filter even further by replacing small coefficients with zero. Simulation results show similar performance when comparing the proposed algorithm with some existing state-of-the-art sparsity-aware algorithms while the proposed algorithms require lower computational complexity.

Semi-blind data-selective equalizers for QAM

This paper proposes a new semi-blind data-selective affine-projection algorithm for channel equalization considering that the transmitted symbols belong to an M-QAM constellation. The main novelties of this algorithm are the combination of the affine-projection (AP) and set-membership (SM) concepts with the formulation of an error measure that is related to a square region (in the complex plane) centered at an element of the constellation. Simulations show that the proposed algorithm tracks slow channel variations as fast as a supervised algorithm, requiring less updates and keeping good BER performance.