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This paper introduces Bayes risk (expected loss) as a criterion for linear equalization. Since the probability of error is equal to the Bayes risk (BR) for a particular binary loss function, this work is a natural generalization of previous works on minimum probability of error (PE) equalizers. Adaptive equalization algorithms are developed that minimize the BR. Like the minimum PE equalizers, the BR algorithms have low computational complexity which is comparable to that of the LMS algorithm. The advantage of the BR criterion is that the loss function can be specified in a manner that accelerates adaptive equalizer convergence relative to the minimum PE adaptive algorithm as illustrated in simulation examples. Besides introducing a new criterion, this paper provides another independent contribution to the field of PE minimizing equalization. While most prior works focus on M-ary QAM type modulations with rectangular decision regions, this paper uses upper bounds on the probabilities of certain events to yield tractable mathematics that apply to two-dimensional constellations with arbitrarily shaped decision regions. The resulting adaptive algorithm use the full information available in the phase of the error signal, whereas previous algorithms use a quantized version of this error phase. [ABSTRACT FROM AUTHOR]

Recently, a novel maximum-likelihood sequence estimation (MLSE) equalizer was reported that avoids the explicit estimation of the channel impulse response. Instead, it is based on the fact that the (noise-free) channel outputs, needed by the Viterbi algorithm, coincide with the points around which the received (noisy) samples are clustered and can thus be estimated directly with the aid of a supervised clustering method. Moreover, this is achieved in a computationally efficient manner that exploits the channel linearity and the symmetries underlying the transmitted signal constellation. The resulting computational savings over the conventional MLSE equalization scheme are significant even in the case of relatively short channels where MLSE equalization is practically applicable. It was demonstrated, via simulations, that the performance of this algorithm is close to that using a least-squares (LS) channel estimator, although its computational complexity is even lower than that of the least-mean squares (LMS)-trained MLSE equalizer. This paper investigates the relationship of the center estimation (CE) part of the proposed equalizer with the LS method. It is proved that, when using LS with the training sequence employed by CE, the two methods lead to the same solution. However, when LS is trained with random data, it outperforms CE, with the performance difference being proportional to the channel length. A modified CE method, called MCE, is thus developed, that attains the performance of LS with perfectly random data, while still being much simpler computationally than classical LS estimation. Through the results of this paper, CE is confirmed as a method- ology that combines high performance, simplicity, and low computational cost, as required in a practical equalization task. An alternative, algebraic viewpoint on the CE method is also provided. [ABSTRACT FROM AUTHOR]

This paper proposes low-complexity constrained affine-projection (CAP) algorithms. The algorithms are suitable for linearly constrained filtering problems often encountered in communications systems. The CAP algorithms derived in this paper trade convergence speed and computational complexity in the same way as the conventional afilne-projection (AP) algorithm. In addition, data-selective versions of the CAP algorithm are derived based on the concept of set-membership filtering. The set-membership constrained affine-projection (SM-CAP) algorithms include several constraint sets in order to construct a space of feasible solutions for the coefficient updates. The SM-CAP algorithms include a data-dependent step size that provides fast convergence and low mean-squared error. The paper also discusses important aspects of convergence and stability of constrained normalized adaptation algorithms and shows that normalization may introduce bias in the final solution. [ABSTRACT FROM AUTHOR]

This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple "beams" directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail so-called Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DP-based scheme proposed by Tu and Blum. We also propose another user-selection method of he same computational complexity based on simple zero-forcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum's scheme and, thus, offers an attractive alternative to DP-based schemes. [ABSTRACT FROM AUTHOR]

We study the problem of power efficient multiuser beamforming transmission for both uplink and downlink. The base station is equipped with multiple antennas, whereas the mobile units have single antennas. In the uplink, interference is canced by successive decoding. in the downlink, ideal "dirty paper" precoding is assumed. The design goal is to minimize the total transmit power while maintaining individual SINR constraints. In the uplink, the optimization problem is solved by a recursive formula with low computational complexity. The downlink problem is solved by exploiting the duality between uplink and downlink; thus, the uplink solution carries over to the downlink. In the second part of the paper, we show how the solution can be applied to the problem of rate balancing in Gaussian multiuser channels. We propose a strategy for throughput-wise optimal transmission for broadcast and multiple access channels under a sum power constraint. Finally, we show that single-user transmission achieves the sum capacity in the low-SNR regime. We completely characterize the SNR-range where single-user transmission is optimal. [ABSTRACT FROM AUTHOR]

Partial updating of LMS filter coefficients is an effective method for reducing computational load and power consumption in adaptive filter implementations. This paper presents an analysis of convergence of the class of Sequential Partial Update LMS algorithms (S-LMS) under various assumptions and shows that divergence can be prevented by scheduling coefficient updates at random, which we call the Stochastic Partial Update LMS algorithm (SPU-LMS). Specifically, under the standard independence assumptions, for wide sense stationary signals, the SSLMS algorithm converges in the mean if the step-size parameter μ is in the convergent range of ordinary LMS. Relaxing the independence assumption, it is shown that S-LMS and LMS algorithms have the same sufficient conditions for exponential stability. However, there exist nonstationary signals for which the existing algorithms, S-LMS included, are unstable and do not converge for any value of μ. On the other hand, under broad conditions, the SPU-LMS algorithm remains stable for nonstationary signals. Expressions for convergence rate and steady-state mean-square error of SPU.LMS are derived. The theoretical results of this paper are validated and compared by simulation through numerical examples. [ABSTRACT FROM AUTHOR]

Most adaptive filtering algorithms couple performance with complexity. Over the last 15 years, a class of algorithms, termed "affine projection" algorithms, have given system designers the capability to tradeoff performance with complexity. By changing parameters and the size/scale of data used to update the coefficients of an adaptive filter but without fundamentally changing the algorithm structure, a system designer can radically change the performance of the adaptive algorithm. This paper discusses low-complexity data reusing algorithms that are closely related to affine projection algorithms. This paper presents various low-complexity and highly flexible schemes for improving convergence rates of adaptive algorithms that utilize data reusing strategies. All of these schemes are unified by a row. projection framework in existence for more than 65 years. This framework leads to the classification of all data reusing and affine projection methods for adaptive filtering into two categories: the Kaczmarz and Cimmino methods. Simulation and convergence analysis results are presented for these methods under a number of conditions. They are compared in terms of convergence rate performance and computational complexity. [ABSTRACT FROM AUTHOR]

As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple “correct” indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K>1), provided that the sensing matrix satisfies the RIP with \deltaNK<{{\sqrt{N}}\over{\sqrt{K}+3\sqrt{N}}}. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to \ell1-minimization technique with fast processing speed and competitive computational complexity. [ABSTRACT FROM PUBLISHER]

Recently, the problem of optimal spectral balancing (OSB) for digital subscriber lines (DSL) with constrained transmit power has been solved using Lagrange's dual optimization technique and a weighted sum rate maximization (WSRM) approach. In many cases, the total power constraint is not binding. Although, this means a huge computational complexity reduction, the algorithm fails to reach certain points on the rate region (RR). In this paper, an in-depth analytical view of the WSRM approach is provided, and it is shown that when the RR is not strictly convex, the WSRM approach fails to reach certain points on the RR. Moreover, using N-dimensional geometry, a novel iterative facet dividing algorithm (IFDA) capable of reaching any point on the RR is proposed. Analytical and simulation results show that our technique is much more reliable and considerably faster than current algorithms. Moreover, it can be used for a wide range of problems which use WSRM approach, including OSB in the general case. [ABSTRACT FROM AUTHOR]

Iteratively reweighted least-squares (IRLS) algorithms have been successfully used in compressive sensing to reconstruct sparse signals from incomplete linear measurements taken in nonsparse domains. The underlying optimization problem corresponds to finding the vector that solves the ℓp, minimization while explaining the measurements, and IRLS allows to easily control the used value of p, with effect on the number of required measurements. In this paper, we propose a weighting strategy in the reconstruction method based on IRLS in order to add prior information on the support of the sparse domain. Our simulation results show that the use of prior knowledge about positions of at least some of the nonzero coefficients in the sparse domain leads to a reduction in the number of linear measurements required for unambiguous reconstruction. This reduction occurs for all values of p, so that a further reduction can be achieved by decreasing p and using prior information. The proposed weighting scheme also reduces the computational complexity with respect to the IRLS with no prior information, both in terms of number of iterations and computation time. [ABSTRACT FROM AUTHOR]

In a multisensor target tracking system, observations produced by sensors typically arrive at a central processor out of sequence. There have been some update algorithms for single out-of-sequence measurement (OOSM). In this paper, we consider optimal centralized update algorithms with multiple asynchronous (different lag time) OOSMs. First, we generalize the optimal update algorithm with single one-step-lag OOSM in [Y. Bar-Shalom, "Update With Out-of-Sequence Measurements in Tracking: Exact Solution," IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, vol. 38, pp. 769-778, July 2002] to optimal centralized update algorithm with multiple one-step-lag OOSMs. Then, based on best linear unbiased estimation, we present an optimal centralized update algorithm with multiple arbitrary-step-lag OOSMs. Finally, two suboptimal centralized update algorithms are proposed to reduce the computational complexity. A numerical example shows that performances of two suboptimal centralized algorithms are close to that of the optimal centralized update algorithm. [ABSTRACT FROM AUTHOR]

Abstract-Adaptive filters of significant order, requiring high computational complexity, are necessary in many applications such as acoustic echo cancellation and wideband active noise control. Successful approaches to lessen the computational complexity of such filters are subband methods, and partial updating schemes where only a part of the filter is updated at each instant. To avoid the time delay introduced by the subband-splitting, delayless structures which reconstructs a fullband filter, producing delayless output, from the adaptive subband filters have been proposed. This paper proposes a delayless subband adaptive filter partial updating scheme, where the general idea is to only update the most misadjusted subband filter(s). Analysis in terms of mean square deviation is presented and shows that the fullband filter convergence speed is significantly increased, even for flat spectrum signals, as compared to traditional periodic subband filter update with the same computational complexity. Echo cancellation simulations with an artificial system to verify the analysis, using both flat spectrum signals and speech, is also presented, as well as offline calculations using signals from a real system. [ABSTRACT FROM AUTHOR]

In this paper, we derive a novel implementation of some very computationally demanding matched filter-bank-based spectral estimators, namely the amplitude and phase estimator (APES), the amplitude spectrum Capon (ASC) estimator, and the power spectrum Capon (PSC) estimator. Filter-bank-based spectral estimation methods that adopt data-dependent filter banks can provide spectra characterized by a significantly improved resolution compared to classical approaches. However, the computational complexity of the currently available implementation algorithms, is extremely high. A novel technique is introduced that provides efficient algorithms for the computation of the APES, ASC, and PSC spectra. The proposed method is based on suitable displacement representations of all pertinent data matrices, that are subsequently utilized for the computation of the associated complex valued polynomials. The computational complexity of the proposed algorithms is lower than all relevant existing methods [ABSTRACT FROM AUTHOR]

Prefilters are generally applied to the discrete multi-wavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit offered by DMWT, it is important to have the pre-filter designed appropriately so as to preserve the important properties of multiwavelets. To this end, we have recently shown that it is possible to have the prefilter designed to be maximally decimated, yet preserve the linear phase and orthogonal properties as well as the approximation power of multiwavelets. However, such design requires the point of symmetry of each channel of the prefilter to match with the scaling functions of the target multiwavelet system. It can be very difficult to find a compatible filter bank structure; and in some cases, such filter structure simply does not exist, e.g., for multiwavelets of multiplicity 2. In this paper, we suggest a new DMWT structure in which the prefilter is combined with the first stage of DMWT. The advantage of the new structure is twofold. First, since the prefiltering stage is embedded into DMWT, the computational complexity can be greatly reduced. Experimental results show that an over 20% saving in arithmetic operations can be achieved comparing with the traditional DMWT realizations. Second, the new structure provides additional design freedom that allows the resulting prefilters to be maximally decimated, orthogonal and symmetric even for multiwavelets of low multiplicity. We evaluated the new DMWT structure in terms of computational complexity, energy compaction ratio as well as the compression performance when applying to a VQ based image coding system. Satisfactory results are obtained in all cases comparing with the traditional approaches. [ABSTRACT FROM AUTHOR]

This paper presents a new maximum likelihood (ML) symbol detection algorithm for multiple-input multiple-output (MIMO) systems. To achieve the ML performance with low complexity, we search the integer points corresponding to symbol vectors in increasing order of the distance from the unconstrained least-squares solution. For each integer point, we test if it is the ML solution, and continue the integer point search until one of searched points is determined to be the ML solution. We present an efficient iterative search strategy, which is based on the shortest path algorithm for a graph. The simulation results show that the proposed algorithm has the lower complexity compared to the sphere decoding for channel matrices having low condition numbers. For further complexity reduction, we propose to use scaling, lattice-reduction, and regularization techniques. By applying these techniques, the computational complexity of proposed algorithm is reduced significantly when the channel matrix has a high condition number. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient adaptive realization of the Wiener model for the identification of complex-valued nonlinear systems. Using a two-dimensional simplicial canonical piecewise linear filter for the complex-valued nonlinear mapping, we derive a realization of the Wiener model requiring fewer parameters than previous approaches. An adaptive implementation of the proposed Wiener model is derived, and local convergence analysis for the updating algorithm is presented. The tradeoff between computational complexity and modeling performance is discussed. Simulations of a system identification example show that the proposed algorithm can provide similar or better performance than other approaches in terms of computational complexity, convergence speed, and final mean-squared error (MSE). [ABSTRACT FROM AUTHOR]

This paper describes a transform coding technique based on M-channel perfect reconstruction filter banks with a nonlinear phase. In contrast with linear-phase filter banks, the nonlinearity provides an extra degree of freedom that can be used to design a more efficient transform. We present new lattice structures of paraunitary and perfect reconstruction (biorthogonal) filter banks, which can be implemented with a lower computational complexity and/or represented by a few free parameters, through the decomposition of the lattice blocks and the displacement across the delay block. We further discuss a smooth extension method for nonlinear-phase filter banks to obtain a nonexpansive transform. The promise of our proposed approaches is demonstrated through several design examples, extended signals and compression results. [ABSTRACT FROM AUTHOR]

In this paper, a robust watermarking algorithm using balanced multiwavelet transform is proposed. The latter transform achieves simultaneous orthogonality and symmetry without requiring any input prefiltering. Therefore, considerable reduction in computational complexity is possible, making this transform a good candidate for real-time watermarking implementations such as audio broadcast monitoring and DVD video watermarking. The embedding scheme is image adaptive using a modified version of a well-established perceptual model. Therefore, the strength of the embedded watermark is controlled according to the local properties of the host image. This has been achieved by the proposed perceptual model, which is only dependent on the image activity and is not dependent on the multifilter sets used, unlike those developed for scalar wavelets. This adaptivity is a key factor for achieving the imperceptibility requirement often encountered in watermarking applications. In addition, the watermark embedding scheme is based on the principles of spread-spectrum communications to achieve higher watermark robustness. The optimal bounds for the embedding capacity are derived using a statistical model for balanced multiwavelet coefficients of the host image. The statistical model is based on a generalized Gaussian distribution. Limits of data hiding capacity clearly show that balanced multiwavelets provide higher watermarking rates. This increase could also be exploited as a side channel for embedding watermark synchronization recovery data. Finally, the analytical expressions are contrasted with experimental results where the robustness of the proposed watermarking system is evaluated against standard watermarking attacks. [ABSTRACT FROM AUTHOR]

The FastICA or fixed-point algorithm is one of the most successful algorithms for linear independent component analysis (ICA) in terms of accuracy and computational complexity. Two versions of the algorithm are available in literature and software: a one-unit (deflation) algorithm and a symmetric algorithm. The main result of this paper are analytic closed-form expressions that characterize the separating ability of both versions of the algorithm in a local sense, assuming a ‘good’ initialization of the algorithms and long data records. Based on the analysis, it is possible to combine the advantages of the symmetric and one-unit version algorithms and predict their performance. To validate the analysis, a simple check of saddle points of the cost function is proposed that allows to find a global minimum of the cost function in almost 100% simulation runs. Second, the Cramér-Rao lower bound for linear ICA is derived as an algorithm independent limit of the achievable separation quality. The FastICA algorithm is shown to approach this limit in certain scenarios. Extensive computer simulations supporting the theoretical findings are included. [ABSTRACT FROM AUTHOR]

In this paper, we first propose an efficient algorithm for computing one-dimensional (1-D) discrete cosine transform (DCT) for a signal block, given its two adjacent sub blocks in the DCT domain and then introduce several algorithms for the fast computation of multidimensional (m-D) DCT with size N1 × N2 ×…× Nm given 2m subblocks of DCT coefficients with size N1/2 × N2/2 ×… × Nm/2, where Ni(i=1,2,ߪ,m) are powers of 2. Obviously, the row-column method, which employs the most efficient algorithms along each dimension, reduces the computational complexity considerably, compared with the traditional method, which employs only the one-dimensional (1-D) fast DCT and inverse DCT (IDCT) algorithms. However, when m & 2, the traditional method, which employs the most efficient multidimensional DCT/IDCT algorithms, has lower computational complexity than the row-column method. Besides, we propose a direct method by dividing the data into 2m parts for independent fast computation, in which only two steps of r-dimensional (r = 1,2,…, m) IDCT and additional multiplications and additions are required. If all the dimensional sizes are the same, the number of multiplications required for the direct method is only (2m - 1)/m2m-1 times of that required for the row-column method, and if N & 22m-1, the computational efficiency of the direct method is surely superior to that of the traditional method, which employs the most efficient multidimensional DCT/DCT algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces a fast implementation of the power iteration method for subspace tracking, based on an approximation that is less restrictive than the well-known projection approximation. This algorithm, referred to as the fast approximated power iteration (API) method, guarantees the orthonormality of the subspace weighting matrix at each iteration. Moreover, it out-performs many subspace trackers related to the power iteration method, such as PAST, NIC, NP3, and OPAST, while having the same computational complexity. The API method is designed for both exponential windows and sliding windows. Our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations. [ABSTRACT FROM AUTHOR]

It is usually assumed that all state metric values are necessary in the maximum a posteriori (MAP) algorithm in order to compute the a posteriori probability (APP) values. This paper extends the mathematical derivation of the original MAP algorithm and shows that the log likelihood values can be computed using only partial state metric values. By processing N stages in a trellis concurrently, the proposed algorithm results in savings in the required memory size and leads to a power efficient implementation of the MAP algorithm in channel decoding. The computational complexity analysis for the proposed algorithm is presented. Especially for the N = 2 case, we show that the proposed algorithm halves the memory requirement without increasing the computational complexity. [ABSTRACT FROM AUTHOR]

Recently, a generalized noise reduction scheme has been proposed, called the Spatially Preprocessed, Speech Distortion Weighted, Multichannel Wiener Filter (SP-SDW-MWF). It encompasses the Generalized Sidelobe Canceller (GSC) and a multichannel Wiener filtering technique as extreme cases. Compared with the widely studied GSC with Quadratic Inequality Constraint (QICuGSC), the SP-SDW-MWF achieves a better noise reduction performance for a given maximum speech distortion level. In this paper, we develop a low-cost, stochastic gradient implementation of the SP-SDW-MWE To speed up convergence and reduce computational complexity, the algorithm is implemented in the frequency domain. Experimental results with a behind-the-ear hearing aid show that the proposed frequency-domain stochastic gradient algorithm preserves the benefit of the exact SP-SDW-MWF over the QIC-GSC, while its computational cost is comparable to the least mean square-based scaled projection algorithm for QIC-GSC. [ABSTRACT FROM AUTHOR]

In this paper, we present a new design method of infinite impulse response (IIR) digital filters with quasi-equiripple absolute error in the complex domain. This method is based on solving a least squares solution iteratively. At each iteration, the desired response for the least squares approximation is transformed to have equiripple error. This algorithm is efficient because there is no need for any initial value or complex optimization algorithm. By this method, a quasi-equiripple solution is obtained very quickly with less computational complexity. Moreover, by multiplying an arbitrary weighting function on the desired responses of passband and stopband, respectively, the error at the passband and stopband can be controlled. Finally, we show some examples to validate the proposed method. [ABSTRACT FROM AUTHOR]

Time-frequency distributions (TFDs) are bilinear transforms of the signal and, as such, suffer from a high computational complexity. Previous work has shown that one can decompose any TFD in Cohen's class into a weighted sum of spectrograms. This is accomplished by decomposing the kernel of the distribution in terms of an orthogonal set of windows. In this paper, we introduce a mathematical framework for kernel decomposition such that the windows in the decomposition algorithm are not arbitrary and that the resulting decomposition provides a fast algorithm to compute TFDs. Using the centrosymmetric structure of the time-frequency kernels, we introduce a decomposition algorithm such that any TFD associated with a bounded kernel can be written as a weighted sum of cross-spectrograms. The decomposition for several different discrete-time kernels are given, and the performance of the approximation algorithm is illustrated for different types of signals. [ABSTRACT FROM AUTHOR]