Maria de Diego

Evolutionary and variable step size strategies for multichannel filtered-x affine projection algorithms

This study is focused on the necessity to improve the performance of the affine projection (AP) algorithm for active noise control (ANC) applications. The proposed algorithms are evaluated regarding their steady-state behaviour, their convergence speed and their computational complexity. To this end, different strategies recently applied to the AP for channel identification are proposed for multichannel ANC. These strategies are based either on a variable step size, an evolving projection order, or the combination of both strategies. The developed efficient versions of the AP algorithm use the modified filtered-x structure, which exhibits faster convergence than other filtering schemes. Simulation results show that the proposed approaches exhibit better performance than the conventional AP algorithm and represent a meaningful choice for practical multichannel ANC applications.

An affine projection algorithm with variable step size and projection order

It is known that the performance of adaptive algorithms is constrained by their computational cost. Thus, affine projection adaptive algorithms achieve higher convergence speed when the projection order increases, which is at the expense of a higher computational cost. However, regardless of computational cost, a high projection order also leads to higher final error at steady state. For this reason it seems advisable to reduce the computational cost of the algorithm when high convergence speed is not needed (steady state) and to maintain or increase this cost only when the algorithm is in transient state to encourage rapid transit to the permanent regime. The adaptive order affine projection algorithm presented here addresses this subject. This algorithm adapts its projection order and step size depending on its convergence state by simple and meaningful rules. Thus it achieves good convergence behavior at every convergence state and very low computational cost at steady state.

GPU implementation of multichannel adaptive algorithms for local active noise control

Multichannel active noise control (ANC) systems are commonly based on adaptive signal processing algorithms that require high computational capacity, which constrains their practical implementation. Graphics Processing Units (GPUs) are well known for their potential for highly parallel data processing. Therefore, GPUs seem to be a suitable platform for multichannel scenarios. However, efficient use of parallel computation in the adaptive filtering context is not straightforward due to the feedback loops. This paper compares two GPU implementations of a multichannel feedforward local ANC system working as a real-time prototype. Both GPU implementations are based on the filtered-x Least Mean Square algorithms; one is based on the conventional filtered-x scheme and the other is based on the modified filtered-x scheme. Details regarding the parallelization of the algorithms are given. Finally, experimental results are presented to compare the performance of both multichannel ANC GPU implementations. The results show the usefulness of many-core devices for developing versatile, scalable, and low-cost multichannel ANC systems.

Transient Analysis of the Conventional Filtered-x Affine Projection Algorithm for Active Noise Control

Affine projection (AP) algorithms have been proposed in recent years for use in active noise control systems. This is due to their potential high convergence speed along with their robustness and moderate computational cost. However, these algorithms can exhibit an excessive computational cost for high projection orders (just when higher convergence speed is achieved). Thus, computationally efficient versions of these algorithms have been proposed. For the particular case of the AP algorithms applied to active noise control, the use of the conventional filtered-x structure instead of the commonly used modified filtered-x method can be understood as an efficient strategy, since it needs fewer operations to update the adaptive filter coefficients. However, the use of this structure implies different algorithm behavior for the following two reasons: the signals needed in the coefficient updates do not correspond exactly to the AP algorithm and this structure introduces a delay between the update of the adaptive filter coefficients and its effect on the noise signal. In practice, this dual effect mainly affects convergence of the algorithms in the transient regime. This correspondence presents a mathematical model so that the transient behavior of the conventional filtered-x AP algorithm can be predicted from the reference signal statistics and algorithm parameters.

The frequency partitioned block modified filtered-x NLMS with orthogonal correction factors for multichannel Active Noise Control

The Normalized Least Mean Square (NLMS) algorithm with a filtered-x structure (FxNLMS) is a widely used adaptive algorithm for Active Noise Control (ANC) due to its simplicity and ease of implementation. One of the major drawbacks is its slow convergence. A modified filtered-x structure (MFxNLMS) can be used to moderately improve the speed of convergence, but it does not offer a huge improvement. A greater increase in the speed of convergence can be obtained by using the MFxNLMS algorithm with orthogonal correction factors (M-OCF), but the usage of orthogonal correction factors also increases the computational complexity and limits the usage of the M-OCF in massive real-time applications. However, Graphics Processing Units (GPUs) are well known for their potential for highly parallel data processing. Therefore, GPUs seem to be a suitable platform to ameliorate this computational drawback. In this paper, we propose to derive the M-OCF algorithm to a partitioned block-based version in the frequency domain (FPM-OCF) for multichannel ANC systems in order to better exploit the parallel capabilities of the GPUs. The results show improvements in the convergence rate of the FPM-OCF algorithm in comparison to other NLMS-type algorithms and the usefulness of GPU devices for developing versatile, scalable, and low-cost multichannel ANC systems.

Control Effort Strategies for Acoustically Coupled Distributed Acoustic Nodes

This paper considers the effect of effort constraints on the behavior of an active noise control (ANC) system over a distributed network composed of acoustic nodes. A distributed implementation can be desirable in order to provide more flexible, versatile, and scalable ANC systems. In this regard, the distributed version of the multiple error filtered-x least mean square (DMEFxLMS) algorithm that allows collaboration between nodes has shown excellent properties. However, practical constraints need to be considered since, in real scenarios, the acoustic nodes are equipped with power constrained actuators. If these constraints are not considered within the adaptive algorithm, the control signals may increase and saturate the hardware devices, causing system instability. To avoid this drawback, a control effort weighting can be considered in the cost function of the distributed algorithm at each node. Therefore, a control effort strategy over the output signals at each node is used to keep them under a given threshold and ensuring the distributed ANC system stability. Experimental results show that, assuming ideal network communications, the proposed distributed algorithm achieves the same performance as the leaky centralized ANC system. A performance evaluation of several versions of the leaky DMEFxLMS algorithm in realistic scenarios is also included.

Adaptive Filtered-x Algorithms for Room Equalization Based on Block-Based Combination Schemes

Room equalization has become essential for sound reproduction systems to provide the listener with the desired acoustical sensation. Recently, adaptive filters have been proposed as an effective tool in the core of these systems. In this context, this paper introduces different novel schemes based on the combination of adaptive filters idea: a versatile and flexible approach that permits obtaining adaptive schemes combining the capabilities of several independent adaptive filters. In this way, we have investigated the advantages of a scheme called combination of block-based adaptive filters which allows a blockwise combination splitting the adaptive filters into nonoverlapping blocks. This idea was previously applied to the plant identification problem, but has to be properly modified to obtain a suitable behavior in the equalization application. Moreover, we propose a scheme with the aim of further improving the equalization performance using the a priori knowledge of the energy distribution of the optimal inverse filter, where the block filters are chosen to fit with the coefficients energy distribution. Furthermore, the biased block-based filter is also introduced as a particular case of the combination scheme, especially suited for low signal-to-noise ratios (SNRs) or sparse scenarios. Although the combined schemes can be employed with any kind of adaptive filter, we employ the filtered-x improved proportionate normalized least mean square algorithm as basis of the proposed algorithms, allowing to introduce a novel combination scheme based on partitioned block schemes where different blocks of the adaptive filter use different parameter settings. Several experiments are included to evaluate the proposed algorithms in terms of convergence speed and steady-state behavior for different degrees of sparseness and SNRs.

Nonlinear filtered-X second-order adaptive volterra filters for listening-room compensation

The presence of nonlinearities as well as reverberation effects severely degrades the audio quality in sound reproduction systems. In this context, many adaptive strategies have been developed to compensate for room effects. However, when nonlinear distortion becomes significant, room equalization requires the introduction of suitable solutions to tackle this problem. Linearization of loudspeakers has been deeply investigated but its combination with room equalization systems may not be so straightforward, mainly when the nonlinearities present memory. In this paper, the nonlinear system has been modeled as a Volterra filter that represents the loudspeaker tandemly connected to a linear filter that corresponds to the electroacoustic path including the enclosure and the microphone setup. Based on this structure, we introduce a nonlinear filtered-x second-order adaptive Volterra filter that uses the virtual path concept to preprocess the audio signals. Simulation results validate the performance of the new approach.

Channel Quantization Based on the Statistical Characterization of Spatially Correlated Fading

Multiuser multiple-input-multiple-output (MU-MIMO) techniques, such as scheduling and precoding, have shown to improve the spectral efficiency of wireless communication systems. However, these techniques require an accurate knowledge of the channel of the different users at the transmitter. In frequency-division duplex (FDD) systems, this information has to be provided by the different users, motivating the research of efficient limited feedback schemes. This paper presents a novel statistical characterization of the spatial multiple-input-single-output (MISO) channel. In this characterization, one antenna is selected as the reference, and the channel fading experienced from this antenna is also considered to be the reference. The conditional probability density functions (CPDFs) of the envelope and phase of the channel fading coefficients from the rest of the antennas (denoted as nonreference channel fading and nonreference antennas) are obtained given the reference one. Based on this statistical characterization, this paper proposes a channel quantization scheme that individually quantizes the channel fading coefficient of each transmit antenna that is seen by each user. The envelope and phase of the reference channel fading are quantized considering a Rayleigh distribution and a uniform distribution, respectively. The nonreference channel fading coefficients are quantized according to their respective CPDFs, which in turn depend on the spatial correlation between each channel fading and the reference channel fading. Numerical simulations have been carried out to compare the performance of the proposed conditional quantization (CQ) scheme with a polar quantization (PQ) and with a quantization based on the Karhunen-Loève (KL) transform. PQ does not consider spatial correlation, CQ needs one spatial correlation coefficient per nonreference antenna, and the KL scheme makes use of the full spatial correlation matrix. The results show that CQ achieves a lower quantization mean square error (MSE) than the other two schemes in highly and moderately correlated environments. When the spatial channel model (SCM) is considered, the proposed scheme allows the spatial correlation to be successfully exploited in arrays with N = 4 and N = 8 transmit antennas for antenna separations that are lower than d= 1.3λ and d=0.75λ, respectively.

STEADY-STATE ANALYSIS OF BIASED FILTERED-X ALGORITHMS FOR ADAPTIVE ROOM EQUALIZATION

This paper provides an analysis of the steady-state behavior of two biased adaptive algorithms recently introduced for listening room compensation, the biased filtered-x normalized least mean squares (Fx-BNLMS) and the biased filtered-x improved proportionate NLMS (Fx-BIPNLMS). We give theoretical results that show that the biased algorithms can outperform the unbiased ones in terms of the mean square error, especially in low signal-to-noise ratio (SNR) scenarios. Moreover, for impulse responses exhibiting high sparse-ness, the improved proportionate algorithms achieve faster convergence than the standard NLMS. Thereby, the advantages of the Fx-BIPNLMS algorithm are justified theoretically in terms of the excess mean square error. Simulation results show that there is a relatively good match between theory and practice, especially for low μ values.