Abstract This paper addresses the generation of binary 2-separating codes and the study of the code rates that can be achieved in practice. In the case of binary 2-separating codes, there exist lower and upper theoretical bounds in the rates that can be achieved. The generation of 2-separating codes has been studied from a theoretical point of view, but, as far as we know, it has not been tackled from a practical point of view. In this paper, we consider and analyze two different generation algorithms. Both algorithms were implemented in CUDA and executed in GPUs, for the sake of efficiency. The first algorithm is inspired by the Moser–Tardos algorithm, which is based on the Local Lovász Lemma. This algorithm has a strong theoretical appeal; codes obtained through this first algorithm can be shown to match the best known lower bound. To generate codes with rates as large as possible, a second algorithm has been implemented. The rates achieved are larger than those achieved with the first algorithm, but they still are very far from the theoretical upper bound. The results obtained suggest that the theoretical upper bound can probably be improved.

The affine projection (AP) algorithm enhances the performance of gradient-based adaptive algorithms when dealing with colored reference signals, which is typically the case with filtered-X type algorithms. This enhancement is achieved by using various delayed versions of the reference signal data vector, which are appropriately orthogonalized and normalized to optimize convergence performance. The number of these vectors, known as the projection order of the AP, increases the computational requirements, mainly due to the calculation of a matrix inversion whose dimensions are proportional to this projection order. When used in distributed systems, the AP algorithm typically requires each acoustic node in the system to compute the complete matrix inversion, even though they only need a specific set of data (a subblock) from it. This means that the AP does not offer much advantage in terms of computational savings when used in distributed collaborative networks. To address this issue, an approximate version of the filtered-X affine projection (FXAP) algorithm is introduced in this work. This approximate version avoids the matrix inversion computation in each iteration using a precalculated inverse matrix. This strategy provides computational savings and enables easy distribution of the algorithm. Additionally, a variable step-size approach is proposed to mitigate the deviation caused by a precalculated matrix, which provides good performance, high robustness, and cost-effective distribution.

This paper addresses the assessment of the stability of distributed active noise control (ANC) systems, which are designed to cancel acoustic noise at given points in space. These systems distribute the control task across several simple acoustic nodes that generate the control signals by filtering a noise reference signal. The coefficients of each node filter are iteratively calculated by the filtered-X LMS algorithm. The nodes remain stable when the adaptive filters computed in each node converge to finite values. However, the acoustic coupling among nodes can cause instability (i.e., divergence). Collaboration among nodes is required to avoid this phenomenon. It is shown that the properties of the system are summarized in a system matrix and that the system remains stable when the real parts of all of the eigenvalues of this system matrix are positive. However, computation of all of the eigenvalues is computationally expensive. In this paper, we propose a fast method for checking the positiveness of the real parts of the system matrix eigenvalues. It is shown that the proposed method is faster than the direct calculation of eigenvalues and it assesses the stability/instability of the ANC systems without any false stability outcomes and more accurately than existing alternatives.

The choice of a suitable convergence step that allows the fast convergence of the filtered-x LMS algorithm in practical scenarios is usually carried out by trial and error, since the theoretical developments provide only indicative values. The particularity of the filtered-x structure, which adds a delay between the output of the adaptive filter and the error signal and colors the reference signal, increases the inaccuracy of the theoretical models. Furthermore, the use of band-limited reference signals is beyond the scope of most theoretical studies, which focus on the cases of full-band reference signals, making it difficult to extrapolate these models to band-limited signals. In this paper, we propose a low-cost and meaningful method for selecting the convergence step that is well tuned in most practical cases. It can be used regardless of the type of the reference signal, the system delays, and the nature of the filter required in the filtered-x structure. Numerical simulations are performed to validate the effectiveness of the proposed approach.

Multichannel Active Noise Control (ANC) headrest systems have usually been designed with the objective of creating quiet areas at the passenger positions within the cabin of a public transport. Due to the high computational demands of dealing with multiple loudspeakers and multiple microphones by using a single centralized processor, and the convenience of a scalable system, a distributed implementation may be advisable. On the other hand, the addition of the remote microphone (RM) technique to the ANC headrest systems has recently allowed the creation of local zones of quiet at unachievable placements for the error sensors. This technique allows the quiet zone to be shifted to a desired location away from the physical sensor. However, to our knowledge, the implementation of an ANC headrest system with virtual microphones over a distributed acoustic sensor network has not been addressed. In this work, a distributed version of the multiple-error FxLMS (MEFxLMS) algorithm considering the RM method (RM-DMEFxLMS) is proposed by using an alternative formulation of the RM method. Through a set of simulations, it is found that on a non-constrained communication network, the proposed algorithm presents the same performance of its centralized version and provides a scalable and more versatile ANC system.

Generalized Spatial Modulation (GSM) is a recent Multiple-Input Multiple-Output (MIMO) scheme, which achieves high spectral and energy efficiencies. Specifically, soft-output detectors have a key role in achieving the highest coding gain when an error-correcting code (ECC) is used. Nowadays, soft-output Maximum Likelihood (ML) detection in MIMO-GSM systems leads to a computational complexity that is unfeasible for real applications; however, it is important to develop low-complexity decoding algorithms that provide a reasonable computational simulation time in order to make a performance benchmark available in MIMO-GSM systems. This paper presents three algorithms that achieve ML performance. In the first algorithm, different strategies are implemented, such as a preprocessing sorting step in order to avoid an exhaustive search. In addition, clipping of the extrinsic log-likelihood ratios (LLRs) can be incorporating to this algorithm to give a lower cost version. The other two proposed algorithms can only be used with clipping and the results show a significant saving in computational cost. Furthermore clipping allows a wide-trade-off between performance and complexity by only adjusting the clipping parameter.

In this work we propose a multi-channel active noise equalizer (ANE) that can deal with multi-frequency noise signals and assigns simultaneously different equalization gains to each frequency component at each monitoring sensor. For this purpose, we state a pseudo-error noise signal for each sensor of the ANE, which has to be cancelled out in order to get the desired equalization profiles. Firstly the optimal analytic solution for the ANE filters in the case of single-frequency noise is provided, and an adaptive algorithm based on the Least Mean Squared (LMS) is proposed for the same case. We also show that this adaptive strategy reaches the theoretical solution in steady state. Secondly, we state an equivalent approach for the case of multi-frequency noise based on two alternatives: a common pseudo-error signal at each sensor for all frequencies, and a different pseudo-error signal at each sensor for each frequency. The analytic and adaptive solutions for the ANE control filters have been developed for both pseudo-error alternatives. Finally, the ability of the proposed ANE to achieve simultaneously different user-selected noise profiles in different locations has been validated by their transfer functions and simulations.

Abstract Generalized Spatial Modulation is a recently developed technique that is designed to enhance the efficiency of transmissions in MIMO Systems. However, the procedure for correctly retrieving the sent signal at the receiving end is quite demanding. Specifically, the computation of the maximum likelihood solution is computationally very expensive. In this paper, we propose a parallel method for the computation of the maximum likelihood solution using the parallel computing library OpenMP. The proposed parallel algorithm computes the maximum likelihood solution faster than the sequential version, and substantially reduces the worst-case computing times.

This work presents a wireless acoustic sensor network (WASN) that monitors urban environments by recognizing a given set of sound events or classes. The nodes of the WASN are Raspberry Pi devices that not only record the ambient sound, but also detect and recognize different sound events. All the signal processing tasks, from the recording to the classification carried out by a convolutional neural network (CNN), are run on Raspberry Pi devices. Due to the low cost of the proposed acoustic nodes, the system exhibits a very high potential scalability. Regarding the underlying WASN, it has been designed according to the open standard FIWARE, thus the whole system can be deployed without the need of proprietary software. Regarding the performance of the sound classifier, the proposed WASN achieves similar accuracy compared to other WASNs that make use of cloud computing. However, the proposed WASN significantly minimizes the network traffic since it does not exchange audio signals, but only contextual information in form of labels. On the other hand, most of the time the class reported by the WASN nodes is the “background” soundscape, which usually contains no event of interest. This is the case when monitoring the soundscape of big avenues, where four events have been identified: “traffic”, “siren”, “horn” and “noisy vehicles”, being the “traffic” class associated to the background soundscape. In this paper, the use of a simple pre-detection stage prior to the CNN classification is proposed, with the aim of saving computation and power consumption at the nodes. The pre-detection stage is able to differentiate the other three relevant sounds from the “traffic” and activates the classifier only when some of these three events is likely occurring. The proposed pre-detection stage has been validated through data recorded in the city of Valencia (Spain), achieving a reduction of the Raspberry Pi CPU’s usage by a factor of six.

Acoustic sensor networks (ASNs) are an effective solution to implement active noise control (ANC) systems by using distributed adaptive algorithms. On one hand, ASNs provide scalable systems where the signal processing load is distributed among the network nodes. On the other hand, their noise reduction performance is comparable to that of their respective centralized processing systems. In this sense, the distributed multiple error filtered-x least mean squares (DMEFxLMS) adaptive algorithm has shown to obtain the same performance than its centralized counterpart as long as there are no communications constraints in the underlying ASN. Regarding affine projection (AP) adaptive algorithms, some distributed approaches that are approximated versions of the multichannel filtered-x affine projection (MFxAP) algorithm have been previously proposed. These AP algorithms can efficiently share the processing load among the nodes, but at the expense of worsening their convergence properties. In this paper we develop the exact distributed multichannel filtered-x AP (EFxAP) algorithm, which obtains the same solution as that of the MFxAP algorithm as long as there are no communications constraints in the underlying ASN. In the EFxAP algorithm each node can compute a part or the entire inverse matrix needed by the centralized MFxAP algorithm. Thus, we propose three different strategies that obtain significant computational saving: 1) Gauss Elimination, 2) block LU factorization, and 3) matrix inversion lemma. As a result, each node computes only between 25% - 60% of the number of multiplications required by the direct inversion of the matrix. Regarding the performance in transient and steady states, the EFxAP exhibits the fastest convergence and the highest noise level reduction for any size of the acoustic network and any projection order of the AP algorithm compared to the DMEFxLMS and two previously reported distributed AP algorithms.

Generalized Spatial Modulation (GSM) is a trans-mission technique used in wireless communications in which only part of the transmitter antennas are activated during each time signaling period. A low complexity Sphere Decoding (SD) algorithm to achieve maximum likelihood (ML) detection has recently been proposed by using subproblem partitions, sorting preprocessing and radius updating. However, the ordering method has a serious limitation when the number of activated antennas is equal to the number of received antennas. Therefore, alternative sorting methods are studied in the present paper. In addition, the computational cost of the ML algorithm can be high when the system sizes increases. In this paper a suboptimal version is proposed where only the first L SD subproblems are carried out. The results show that the proposed algorithm achieves near optimal performance at lower computational cost than ML algorithms.

Personal Sound Zones (PSZ) systems aim to render independent sound signals to multiple listeners within a room by using arrays of loudspeakers. One of the algorithms used to provide PSZ is Weighted Pressure Matching (wPM), which computes the filters required to render a desired response in the listening zones while reducing the acoustic energy arriving to the quiet zones. This algorithm can be formulated in time and frequency domains. In general, the time-domain formulation (wPM-TD) can obtain good performance with shorter filters and delays than the frequency-domain formulation (wPM-FD). However, wPM-TD requires higher computation for obtaining the optimal filters. In this article, we propose a novel approach to the wPM algorithm named Weighted Pressure Matching with Subband Decomposition (wPM-SD), which formulates an independent time-domain optimization problem for each of the subbands of a Generalized Discrete Fourier Transform (GDFT) filter bank. Solving the optimization independently for each subband has two main advantages: 1) lower computational complexity than wPM-TD to compute the optimal filters; 2) higher versatility than the classic wPM algorithms, as it allows different configurations (sets of loudspeakers, filter lengths, etc.) in each subband. Moreover, filtering the input signals with a GDFT filter bank (as in wPM-SD) requires lower computational effort than broadband filtering (as in wPM-TD and wPM-FD), which is beneficial for practical PSZ systems. We present experimental evaluations showing that wPM-SD offers very similar performance to wPM-TD. In addition, two cases where the versatility of wPM-SD is beneficial for a PSZ system are presented and experimentally validated.

This paper focus on the implementation of an active noise control system over a network of distributed nodes acoustically coupled. We have considered the distributed Multiple Error filtered-x Least Mean Square (DMEFxLMS) algorithm that allows collaboration between nodes following an incremental strategy. To reduce the computational network requirements, an alternative strategy which brings together only the acoustically coupled nodes has been used. However, a rule to define the subsets of nodes that are required to collaborate is needed. A collaborative condition based on the analysis in the frequency domain of the eigenvalues of the acoustic path matrix is proposed. Results demonstrate the ability of the introduced method to define the subsets of nodes that collaborate.

Large Multi-User Multiple-Input Multiple-Output (MU-MIMO) system is considered as a potential technique to serve a high number of users simultaneously increasing the achievable data rates. By large we mean a large number of transmit antennas (Nt) at the base station (BS) and a large number of downlink user's terminals (UTs). In large MU-MIMO systems, the complexity of precoding algorithms becomes a bottleneck. In this work, we propose a low complexity precoder scheme with two steps. In the proposed scheme the UTs are classified into B blocks. Thereby, in the first step, the interference between block users block is mitigated using a Block Diagonalization (BD) method. In the second step, the interference between users belonging to the same block is palliated employing a more complex precoding. Simulation results show that the proposed scheme can achieve suitable performance while offering lower computational complexity than a nonlinear precoding.

Wave field synthesis (WFS) is a multichannel audio reproduction method, of a considerable computational cost that renders an accurate spatial sound field using a large number of loudspeakers to emulate virtual sound sources. The moving of sound source locations can be improved by using fractional delay filters, and room reflections can be compensated by using an inverse filter bank that corrects the room effects at selected points within the listening area. However, both the fractional delay filters and the room compensation filters further increase the computational requirements of the WFS system. This paper analyzes the performance of a WFS system composed of 96 loudspeakers which integrates both strategies. In order to deal with the large computational complexity, we explore the use of a graphics processing unit (GPU) as a massive signal co-processor to increase the capabilities of the WFS system. The performance of the method as well as the benefits of the GPU acceleration are demonstrated by considering different sizes of room compensation filters and fractional delay filters of order 9. The results show that a 96-speaker WFS system that is efficiently implemented on a state-of-art GPU can synthesize the movements of 94 sound sources in real time and, at the same time, can manage 9216 room compensation filters having more than 4000 coefficients each.

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.

A new algorithm called SUMIS-BO is proposed for soft-output MIMO detection. This method is a meaningful improvement of the "Subspace Marginalization with Interference Suppression" (SUMIS) algorithm. It exhibits good performance with reduced complexity and has been evaluated and compared in terms of performance and efficiency with the SUMIS algorithm using different system parameters. Results show that the performance of the SUMIS-BO is similar to the SUMIS algorithm, however its efficiency is improved. The new algorithm is far more efficient than SUMIS, especially with large systems.

In Multiple-Input Multiple-Output (MIMO) schemes, the high computational complexity of soft optimal detection algorithms can make these algorithms impractical for real systems, especially when the number of antennas and modulation orders increase. In this paper, we present a modification on Repeated Tree Search (RTS) strategy, reducing the complexity by using Box- Optimization (BO) method combined with the Zero Forcing (ZF) algorithm. The proposed soft input soft output algorithm presents lower complexity than already proposed optimal algorithms, however it loses the optimal behavior. The proposed suboptimal soft detector exhibits a scalable tradeoff between complexity and performance.

Summary Multiple‐input multiple‐output (MIMO) systems have attracted considerable attention in wireless communications because they offer a significant increase in data throughput and link coverage without additional bandwidth requirement or increased transmit power. The price that has to be paid is the increased complexity of hardware components and algorithms. The sphere detector (SD) algorithm solves the problem of maximum likelihood (ML) detection for MIMO channels by significantly reducing the search space of possible solutions. The main drawback of the SD algorithm is in its sequential nature, consequently, running it on massively parallel architectures (MPAs) is very inefficient. In order to overcome the drawbacks of the SD algorithm, a new parallel sphere detector (PSD) algorithm is proposed. It implements a novel hybrid tree search method, where the algorithm parallelism is assured by the efficient combination of depth‐first search and breadth‐first search algorithms. A path metric‐based parallel sorting is employed at each intermediate stage. The PSD algorithm is able to adjust its memory requirements and extent of parallelism to fit a wide range of parallel architectures. Mapping details for MPAs are proposed by giving the details of thread dependent, highly parallel building blocks of the algorithm. Based on the building blocks proposed, a mapping to general‐purpose graphics processing unit is provided, and its performance is evaluated. In order to achieve high‐throughput, several levels of parallelism are introduced, and different scheduling strategies are considered. Copyright © 2015 John Wiley & Sons, Ltd.

In the audio signal processing field, multiple IIR filters are required in many applications. As an example, equalizing a Wave Field Synthesis system requires massive filter processing in real time. Graphics Processing Units (GPUs) are well known for their potential in highly parallel data processing. Up to now, the use of the GPUs for implementing IIR filters has not been clearly tackled in audio processing because of its feedback loop that prevents its total parallelization. However, using the Parallel form of IIR filters, this feedback is reduced, since every single sample is computed in a parallel way. This paper analyzes the performance of multiple IIR filters using GPUs and compares it with a powerful multi-core computer. The proposed GPU implementation can run up to 1256 concurrent IIR filters of order 256th in real time, which means 321,536 total filter order, with a latency time of 0.72 ms (sampling frequency of 44.1 kHz). This demonstrates that GPUs are well suited for computing massive IIR filtering.

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.

Multichannel adaptive equalization (AE) systems require high computational capacity, which constraints their practical implementation. Graphics Processing Units (GPUs) are well known due to their potential for highly parallel data processing. Although the GPUs seem to be suitable platforms for multichannel scenarios, an efficient use of parallel computation in the adaptive filtering context is not straightforward due to the feedback loops. This paper presents a GPU implementation of a multichannel AE system based on the filtered-x LMS algorithm working over a real-time prototype. Details of the parallelization of the algorithm are given. Experimental results are presented to validate and computationally analyze the real-time performance of the AE GPU implementation. Results show the usefulness of GPUs to develop versatile, scalable and low cost multichannel AE systems.

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.

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.

Adaptive filtering schemes exhibit a compromise between convergence speed and steady-state mean square error. Trying to overcome this trade-off, convex combination of adaptive filters have been recently developed for system identification achieving better performance than traditional approaches. The purpose of this work is to apply the convex combination strategy to single-channel and multichannel active noise control systems. In these systems it is necessary to take into account the secondary path between the adaptive filter output and the error sensor and the possible unavailability of the disturbance signal, which depends on the filtering scheme considered. Even though this strategy involves a higher computational burden than the classic adaptive filters, it exhibits a good performance in terms of convergence speed and steady-state mean square error.

Fast parallel processing capability of general purpose Graphic Processing Units (GPU) can be exploited to accelerate the precoding calculation needed in spatially multiplexed wireless communication systems. In this paper, a GPU-based implementation of the well-known multiuser Tomlinson-Harashima precoding (THP) scheme combined with a lattice-reduction (LR) stage is presented. The proposed approach allows the LR stage to be switched off when user requirements are achieved by using only THP. Moreover, our GPU implementation provides scalability in the number of sub-carriers per symbol, which is a key factor in LTE and 4G wireless standards. Simulation results show that the GPU-based THP implementation performs up to 7 times faster than its CPU-equivalent whereas the LR stage implementation only achieves a speedup of 3. Despite the fact that the LR cannot be as efficiently parallelized as the THP, a speedup of nearly 6 is achieved when both are combined.

Crosstalk cancellation is one of the main applications in multichannel acoustic signal processing. This field has experienced a major development in recent years because of the in crease in the number of sound sources used in playback applications available to users. Developing these applications re quires high computing capabilities because of its high number of operations. Graphics Processor Unit (GPU), a high parallel commodity programmable co-processors, offer the possibility of parallelizing these operations. This allows to obtain the results in a much shorter time and also to free up CPU resources which can be used for other tasks. One important aspect lies in the possibility to overlap the data transfer from CPU to GPU and vice versa with the computation, in order to carry out real-time applications. Thus, this work focuses on two main points: to describe an efficient implementation of a crosstalk cancellation on GPU and to incorporate it into a real-time application.

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.

Tree search detection algorithms can provide Maximum-Likelihood detection over Gaussian MIMO channels with lower complexity than the exhaustive search. Furthermore, the performance of MIMO detectors is highly influenced by the channel matrix condition number. In this paper, the impact of the 2-norm condition number in data detection is exploited in order to decrease the complexity of already proposed algorithms. A suboptimal tree search method called K-Best is combined with a channel matrix condition number estimator and a threshold selection method. This approach leads to a variable-breadth K-Best detector with predictable average performance and suitable for hardware implementation. The results show that the proposed scheme has lower complexity, i.e. it is less power consuming, than a fixed K-Best detector of similar performance.

This paper provides an analysis of the steady-state behavior of the filtered-x affine projection algorithm (FXAP). This efficient affine projection (AP) algorithm for active noise control (ANC) applications is based on the filtered-x scheme, unlike most AP algorithms based on the more computationally demanding modified filtered-x scheme. This study depends on energy conservation arguments and does not require an specific signal distribution. The theoretical expressions derived for the mean square error (MSE) allowed to accurately predict the steady-state performance of the FXAP for meaningful practical cases. Simulation results of a single-channel ANC system validate the analysis and the theoretical expressions derived.

In recent years, affine projection algorithms have been proposed for adaptive system applications as an efficient alternative to the slow convergence speed of least mean square (LMS)-type algorithms. Whereas much attention has been focused on the development of efficient versions of affine projection algorithms for echo cancellation applications, the similar adaptive problem presented by active noise control (ANC) systems has not been studied so deeply. This paper is focused on the necessity to reduce even more the computational complexity of affine projection algorithms for real-time ANC applications. We present some alternative efficient versions of existing affine projection algorithms that do not significantly degrade performance in practice. Furthermore, while in the ANC context the commonly used affine projection algorithm is based on the modified filtered-x structure, an efficient affine projection algorithm based on the (nonmodified) conventional filtered-x structure, as well as efficient methods to reduce its computational burden, are discussed throughout this paper. Although the modified filtered-x scheme exhibits better convergence speed than the conventional filtered-x structure and allows recovery of all the signals needed in the affine projection algorithm for ANC, the conventional filtered-x scheme provides a significant computational saving, avoiding the additional filtering needed by the modified filtered-x structure. In this paper, it is shown that the proposed efficient versions of affine projection algorithms based on the conventional filtered-x structure show good performance, comparable to the performance exhibited by the efficient approaches of modified filtered-x affine projection algorithms, and also achieve meaningful computational savings. Experimental results are presented to validate the use of the algorithms introduced in the paper for practical applications.

The problem of designing joint power control and optimal beamforming (JPCOB) algorithms for the downlink of a coordinated multi-cell WCDMA system is considered throughout this paper. In this case, the JPCOB design is formulated as the problem of minimizing the total transmitted power in the coordinated multi-cell system, subject to a certain quality of service requirement for each user. In this paper, the performance of two JPCOB algorithms based on different beamforming approaches is compared over the coordinated multi-cell system. The first one, obtains local beamformers by means of the well-known virtual uplink-downlink duality. In contrast, the second algorithm implements multi-base beamformers, taking into account match filter equalizers at the receivers. Moreover, realistic system parameters, such as per-base station power constraints or the asynchronous nature of the signals arriving at the receivers, are taken into account. Simulation results show that the algorithm based on multi-base beamforming presents attractive properties, such as an inherent multi-base scheduling technique or a decreasing total transmitted power as the degree of coordination between base stations is increased.

An efficient version of the affine projection (AP) algorithm, which is called FXAP-AC throughout the paper, is presented. This algorithm uses the filtered-x structure instead of the modified structure which is required for the implementation of the AP algorithm when the desired signal is not available, for instance in active noise control (ANC) applications. The conventional AP algorithm for ANC, which is based on the modified structure (MFXAP), provides good performance. However the filtered-x structure is advisable for practical cases since it achieves a meaningful computational saving avoiding the additional filtering needed by the modified structure without significantly affect the performance in practice. In this paper, an efficient computation of coefficient update is developed for the FXAP resulting in the FXAP-AC. This low-cost strategy already proposed in the conventional AP algorithm can be suitably combined with others previously reported to achieve very fast and robust FXAP algorithms. Experimental results validate the use of the proposed algorithm for practical applications

An algorithmic variant of the conventional active noise equalizer (ANE), which independently controls some given frequencies of the primary signal, has been developed and extended to the multichannel case. The modified version of the ANE is named common-error multiple-frequency ANE. A detailed analysis of both multichannel equalizers has been carried out. From a convergence analysis in the frequency-domain, the significance of transducer locations in the behavior of a practical system can be predicted through the matrix of secondary path responses at each frequency. The ANEs steady-state transfer functions from the primary input signal to the noise output have also been developed and compared for different parameter settings and for accurate and inaccurate secondary path estimation. Furthermore, the multichannel extension of both equalizers has been implemented in a real-time active system inside a listening room for multifrequency noise. Useful-size zones of equalization have been binaurally measured by using a head and torso simulator. It was found that the common-error multiple-frequency ANE performs better than the conventional equalizer because it achieves a saving in computational complexity and has smaller overshoot. It can also be implemented in a real controller more easily than the conventional ANE and without showing meaningful differences in the practical results provided.

Multichannel adaptive affine projection algorithms (multichannel AP) are currently under development for multichannel audio applications, mainly for transaural audio reproduction. These algorithms present several advantages for real time systems such as moderate computational cost, good stability, and adjustable convergence speed. However the basic version of the AP algorithm needs to be optimized to be used on digital signal processors working on real time. Thus several variants of AP and its fast version (FAP) have been developed. Regarding its computational cost and real time implementation, an N /spl times/ N inverse matrix have to be calculated in each algorithm iteration, being N the affine projection order. This paper presents a comparison between several versions of the AP algorithm for real time multichannel audio and proposes a series of recommendations, such as the initialization parameters, to use the variants of the AP algorithm in multichannel sound.

joint power control and optimal beamforming (JPCOB) algorithms have been proposed in the literature as promising solutions to increase the capacity of wireless multimedia networks. A new development of one of such JPCOB techniques is presented in this paper, whose main feature is the possibility of downlink cooperative transmission between all the base stations involved. Some practical applications under adverse conditions of deep fading are discussed, and different realistic scenarios have been simulated in order to analyze the new algorithm performance. Finally, some interesting conclusions are stated.

A novel approach to the widespread problem of evaluating the “quality” of noise of a car engine is presented. Traditionally some psychoacoustic parameters of the sound are calculated and used to generate a certain Noise Quality Index (NQI) according to a previous jury assessment. Once the NQI is validated, new noise recordings can be evaluated and automobile engineers can estimate how the perceived quality varies as engine working conditions change. In this paper we relate well-known psychoacoustic features - which usually contribute to generate the NQI - to Time-Frequency (TF) characteristics of diesel noise, in order to find relations between both kinds of parameters. These relations could help engine designers to predict the noise quality just analysing the spectral changes of the noise waveform. Some promising results are showed involving a diesel engine belonging to the luxury class of an European car manufacturer.

This work is a preliminary study which focuses on subjective improvements of vehicle interior noise by using active noise control techniques. A local active noise control system has been mounted inside a room in order to reduce synthesized and real engine noise in the area around the headrest of a typical car seat. Recordings before and after cancellation have been made using a head acoustics mannequin positioned in the seat with two calibrated microphones at the ear-canals. Two methods were used to evaluate the comfort improvements achieved by active noise control. First, a prediction model of comfort based on four psychoacoustic descriptors (loudness, roughness, sharpness and tonality) was applied. Secondly, the subjective evaluation of controlled signals was carried out by means of a jury test. The reduction of noise levels does not necessarily reduce the annoyance of car engine noise that depends on spectral characteristics of noise.

The condition number of the matrix of electro-acoustic head-related transfer functions (HRTF) in a two-channel sound reproduction system has been used as a measure of robustness of the Atal-Schroeder (1962) crosstalk canceler. A comparative study has been made using results produced by computer simulations and HRTFs measured in an anechoic chamber by means of a dummy head. It has been found that acoustic scattering by the head has a very important and beneficial influence on robustness, specially for large loudspeaker separations. For narrow loudspeaker separations of less than about 40 degrees it is found that crosstalk cancellation exhibits a large variation of alternating very low and very high robustness. Also, simulations and measurements have been made of the natural channel separation under the same conditions. Scattering by the head is seen to provide a good level of natural channel separation at high frequencies and large loudspeaker angles. At low frequencies or small loudspeaker angles natural channel separation is poor.

The reproduction of three-dimensional (3-D) sound (either from binaural recordings or virtual source synthesis) through loudspeakers, also known as transauralization, adds difficulties to the traditional method using headphones: the cross-talk effect between speakers and the listener's ears must be taken into account. The common way of removing this distortion consists of placing a filter bank before reproduction through the loudspeakers, but these crosstalk cancellers are notoriously nonrobust to slight movements of the head. Recent theoretical works studied the influence of loudspeaker positions relating to robustness of the system. This paper presents a series of experiments that validate the theory and add new ideas for the design of crosstalk cancellers.

The use of Kalman filtering techniques for multichannel inverse filter design in sound reproduction systems is presented. The method exploits the nonsymmetric Toeplitz-block structure of the actual multichannel system matrix that is used to specify the electroacoustic transmission paths. The result is a matrix of causal finite impulse response filters which best approximate a given time domain response in the least squares sense. The method presents low memory and computational requirements and its time updating properties make it suitable for real time applications in nonstationary environments. Under certain conditions the method carries out the exact multichannel system inverse as formulated by the multiple-input/output inverse filtering theorem. Some practical examples are also presented which illustrate the properties of the algorithm.

In this paper, a novel adaptive algorithm for equalization of periodic signals using active control is developed. This algorithm actively cancels out a single frequency without changing the amplitude levels at close frequencies. The algorithm performance is compared with that of an adaptive equalizer previously reported (Kuo and Ji 1995 and Kuo and Morgan 1996). Both algorithms are used for a real multichannel system in order to equalize some given frequencies of a primary signal. The local active noise control system has been used to create an equalization zone. A two channel system is used and the total pressure is controlled at two microphones. A 4100 type Bruel manikin with two calibrated microphones at the ear canals has been used to obtain sound levels in a hypothetic listener's ears. The equalization points are not only the error sensors positions but an area around them which is measured using the manikin.

A time domain recursive algorithm for multichannel inverse filter design in sound reproduction systems is presented. The method exploits the non-symmetric Toeplitz-block structure of the actual multichannel system matrix that is used to specify the electroacoustic transmission paths. The result is a matrix of causal finite impulse response filters which best approximate a given time domain response in the least squares sense. The method presents low memory and computational requirements and its time updating properties make it suitable for real time applications in non-stationary environments. A cross talk cancellation experiment is presented which illustrates the properties of the algorithm.

This paper addresses the problem of computation of inverse filters in transauralization and multichannel sound reproduction. A huge set of block Toeplitz equations must be usually solved in order to design good filters under the least squares error criterion. A practical and efficient method of main matrix construction and the solution of the set of equations are thoroughly described. An optimal implementation of the Levinson algorithm in two steps that dramatically reduces the computational cost is also presented. The algorithm uses the generalized Levinson recursion for block matrices as a first step and the Gohberg-Semencul formula as the second step. This allows to save about 75% of operations in a typical transauralization problem. A study of the performance of the algorithm in terms of computational cost compared to other algorithms is also carried out.

This paper presents a multichannel active system for the local control of sound around the headrest on the back of a seat placed inside an enclosure. The size of the zones of quiet produced makes the system practical only at relatively low frequencies. Finally, some results of cancellation for narrowband and broadband noise are presented. Two different system configurations algorithms have been tested on the adaptive controller. Both of them show similar results, but the new algorithm based on the minimization of the maximum error signal power, has shown computational saving and higher speed convergence than the multiple channel least squares algorithm.

This paper presents a new multichannel adaptive filtering algorithm for the active control of single frequency noise in acoustic systems. Most active control systems with multiple error sensors minimize the sum of the modulus squared output of these sensors. An adaptive algorithm is presented that minimizes an alternative cost function which, in the limit, is equal to the maximum of the modulus squared values of all the error sensors. The physical consequences of minimizing the maximum modulus squared output to achieve noise reduction are investigated. An analytical framework is developed that covers the steady state performance as well as the convergence properties. By means of simulations, the proposed algorithm has been applied to a linear model of a one-dimensional (1-D) acoustic system and compared with the classical least squares solutions. The proposed algorithm is also used in simulations of the control of the pressure measured at 32 microphone positions in a room using 16 loudspeakers, when the room is excited with an 88 Hz pure tone. The results of these simulations show that the observed convergence and steady-state properties agree well with the theoretical predictions. A comparison with the least squares solutions leads to the conclusion that the proposed algorithm leads to a more uniform acoustic field in the enclosure than the classical least squares algorithm.

This paper deals with multiple input multiple output systems for active control of acoustic signals. These systems are used when the acoustic field is complex and therefore a number of sensors are necessary to estimate the sound field and a number of sources to create the cancelling field. A steepest descent iterative algorithm is applied to minimise the p-norm of a vector composed by the output signals of a microphone array. The existing algorithms deal with the 2-norm of this vector. This paper describes a general framework that covers the existing systems and then it focuses on the /spl infin/-norm minimisation algorithm. The minimax algorithm based on the /spl infin/-norm minimises the output signal which has the greatest power. It is shown by means of simulations using measured data from a real room that the minimax algorithm leads to a more uniform final noise field than the existing algorithms.