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This paper proposes an efficient algorithm for robust sensor placement with the purpose of recovering a source signal from noisy measurements. To model uncertainty on the spatially-variant sensors gain and on the spatially correlated noise, we assume that both are realizations of Gaussian processes. Since the signal to noise ratio (SNR) is also uncertain in this context, to achieve a robust signal extraction, we propose a new placement criterion based on the maximization of the probability that the SNR exceeds a given threshold. This criterion can be easily evaluated using the Gaussian process assumption. Moreover, to reduce the computational complexity of the joint maximization of the criterion with respect to all sensor positions, we suggest a sequential maximization approach, where the sensor positions are chosen one at a time. Finally, we present numerical results showing the superior robustness of the proposed approach when compared to standard sensor placement criteria aimed at interpolating the spatial gain and to a recently proposed criterion aimed at maximizing the average SNR. [ABSTRACT FROM AUTHOR]

The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows the Gaussian distribution. However, the real world distribution of assets return is usually asymmetric and heavy-tailed, which is far from being a Gaussian distribution. The asymmetry and the heavy-tailedness are characterized by the third and fourth central moments, i.e., skewness and kurtosis, respectively. Higher skewness and lower kurtosis are preferred to reduce the probability of extreme losses. However, incorporating high-order moments in the portfolio design is very difficult due to their non-convexity and rapidly increasing computational cost with the dimension. In this paper, we propose a very efficient and convergence-provable algorithm framework based on the successive convex approximation (SCA) algorithm to solve high-order portfolios. The efficiency of the proposed algorithm framework is demonstrated by the numerical experiments. [ABSTRACT FROM AUTHOR]

While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper presents a new (stochastic) distributed algorithm with Nesterov momentum for accelerated optimization of non-convex and non-smooth problems. Theoretically, we show that the proposed algorithm can achieve an $\epsilon$ -stationary solution under a constant step size with $\mathcal {O}(1/\epsilon ^2)$ computation complexity and $\mathcal {O}(1/\epsilon)$ communication complexity when the epigraph of the non-smooth term is a polyhedral set. When compared to the existing gradient tracking based methods, the proposed algorithm has the same order of computation complexity but lower order of communication complexity. To the best of our knowledge, the presented result is the first stochastic algorithm with the $\mathcal {O}(1/\epsilon)$ communication complexity for non-convex and non-smooth problems. Numerical experiments for a distributed non-convex regression problem and a deep neural network based classification problem are presented to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP’ SE matches perfectly the exact MMSE predicted by the replica method, which is well-known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMP's computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems. [ABSTRACT FROM AUTHOR]

In this paper we consider maximum-likelihood (ML) MIMO detection under one-bit quantized observations and binary symbol constellations. This problem is motivated by the recent interest in adopting coarse quantization in massive MIMO systems—as an effective way to scale down the hardware complexity and energy consumption. Classical MIMO detection techniques consider unquantized observations, and many of them are not applicable to the one-bit MIMO case. We develop a new non-convex optimization algorithm for the one-bit ML MIMO detection problem, using a strategy called homotopy optimization. The idea is to transform the ML problem into a sequence of approximate problems, from easy (convex) to hard (close to ML), and with each problem being a gradual modification of its previous. Then, our attempt is to iteratively trace the solution path of these approximate problems. This homotopy algorithm is well suited to the application of deep unfolding, a recently popular approach for turning certain model-based algorithms into data-driven, and performance enhanced, ones. While our initial focus is on one-bit MIMO detection, the proposed technique also applies naturally to the classical unquantized MIMO detection. We performed extensive simulations and show that the proposed homotopy algorithms, both non-deep and deep, have satisfactory bit-error probability performance compared to many state-of-the-art algorithms. Also, the deep homotopy algorithm has attractively low computational complexity. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation is a classical topic in source localization. Notably, a reliable grid-free sparse representation algorithm, called FRI (finite rate of innovation) algorithm, was proposed to recover the finite number of Dirac pulses from a stream of 1D temporal samples, which also offers a efficient solution to the DOA estimation problem. Typically, FRI method assumes uniform sampling with single snapshot. However, the actual situation is richer and more diverse. Motivated by the requests of practical applications (e.g. array deployment, algorithm run-speed, etc.), a generic FRI method is proposed to tackle the more general case in practice, i.e. non-uniform sampling with multiple snapshots. Instead of annihilating the measured sensor data, a model-fitting method is used to robustly retrieve the sparse representation (i.e. DOAs and associated amplitudes) of the 1D samples. We demonstrate that our algorithm can handle challenging DOA tasks with high-resolution, which we validate in various conditions, such as multiple coherent sources, insufficient signal snapshots, low signal-to-noise ratio (SNR), etc. Moreover, we show that the computational complexity of our algorithm mainly scales with the number of sources and varies very slowly with the number of samples and snapshots, which meets the needs of a wider range of practical applications. [ABSTRACT FROM AUTHOR]

The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multitarget tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a Second-Order PHD (SO-PHD) filter, propagating the second-order moment (i.e., variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modeling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. This paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multiobject filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters. [ABSTRACT FROM PUBLISHER]

Grant-free random access is a promising protocol to support massive access in beyond fifth-generation (B5G) cellular Internet-of-Things (IoT) with sporadic traffic. Specifically, in each coherence interval, the base station (BS) performs joint activity detection and channel estimation (JADCE) before data transmission. Due to the deployment of a large-scale antennas array and the existence of a huge number of IoT devices, JADCE usually has high computational complexity and needs long pilot sequences. To solve these challenges, this paper proposes a dimension reduction method, which projects the original device state matrix to a low-dimensional space by exploiting its sparse and low-rank structure. Then, we develop an optimized design framework with a coupled full column rank constraint for JADCE to reduce the size of the search space. However, the resulting problem is non-convex and highly intractable, for which the conventional convex relaxation approaches are inapplicable. To this end, we propose a logarithmic smoothing method for the non-smoothed objective function and transform the interested matrix to a positive semidefinite matrix, followed by giving a Riemannian trust-region algorithm to solve the problem in complex field. Simulation results show that the proposed algorithm is efficient to a large-scale JADCE problem and requires shorter pilot sequences than the state-of-art algorithms which only exploit the sparsity of device state matrix. [ABSTRACT FROM AUTHOR]

In recent years, the sources localization has noticed an increase in research conducted on the problem of mixed far-field sources (FFSs) and near-field sources (NFSs). The main assumption of the existing researches is that the signals should be uncorrelated. Therefore, they cannot be used for multipath environments. The present paper provides a method called components separation algorithm (CSA) for the localization of multiple mixed FFSs and NFSs, including uncorrelated, lowly correlated and coherent signals. Firstly, by constructing one special cumulant matrix, and using a MUSIC-based technique, the noncoherent DOA vector (NDOAV) is extracted. By constructing another special cumulant matrix, and with respect to NDOAV, an estimate of the range, as well as a signal classification is obtained for noncoherent sources. Then, by estimating their kurtosis, the noncoherent component and consequently the coherent one of the second cumulant matrix is obtained. Finally, by introducing a novel approach based on squaring, projection, spatial smoothing, array interpolation transform and coherent component restoring, the parameters of coherent signals in each coherent group are estimated separately. The CSA prevents severe loss of the aperture. Furthermore, it does not require any pairing. The simulation results validate its satisfactory performance in terms of estimation accuracy, resolution, computational complexity, reasonable classification, and also its robustness against lowly correlated sources. [ABSTRACT FROM AUTHOR]

In this paper, we develop a kernel adaptive filter for quaternion data, using stochastic information gradient (SIG) cost function based on the information theoretic learning (ITL) approach. The new algorithm (QKSIG) is useful for quaternion-based kernel applications of nonlinear filtering. Adaptive filtering in quaterion domain intrinsically incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input. We apply generalized Hamilton-real (GHR) calculus that is applicable to quaternion Hilbert space for evaluating the cost function gradient. The QKSIG algorithm minimizes Shannon's entropy of the error between the filter output and desired response and minimizes the divergence between the joint densities of input-desired and input-output pairs. The SIG technique reduces the computational complexity of the error entropy estimation. Here, ITL with SIG approach is applied to quaternion adaptive filtering for three different reasons. First, it reduces the algorithm computational complexity compared to our previous work quaternion kernel minimum error entropy algorithm (QKMEE). Second, it improves the filtering performance by considering the coupling within the dimensions of the quaternion input. Third, it performs better in biased or non-Gaussian signal and noise environments due to ITL approach. We present convergence analysis and steady-state performance analysis results of the new algorithm (QKSIG). Simulation results are used to show the behavior of the new algorithm QKSIG in quaternion non-Gaussian signal and noise environments compared to the existing ones such as quadruple real-valued kernel stochastic information gradient (KSIG) and quaternion kernel LMS (QKLMS) algorithms. [ABSTRACT FROM AUTHOR]

Classification with a sparsity constraint on the solution plays a central role in many high dimensional signal processing applications. In some cases, the features can be grouped together, so that entire subsets of features can be selected or discarded. In many applications, however, this can be too restrictive. In this paper, we are interested in a less restrictive form of structured sparse feature selection: We assume that while features can be grouped according to some notion of similarity, not all features in a group need be selected for the task at hand. The Sparse Group Lasso (SGL) was proposed to solve problems of this form. The main contributions of this paper are a new procedure called Sparse Overlapping Group (SOG) lasso, an extension to the SGL to overlapping groups and theoretical sample complexity bounds for the same. We establish model selection error bounds that specializes to many other cases. We experimentally validate our proposed method on both real and toy datasets. [ABSTRACT FROM AUTHOR]

We design an efficient robust multi-group multicast beamforming scheme for massive multiple-input multiple-output (MIMO) systems. Assuming only estimates of the channel covariance matrices are available at the base station with a bounded error, we formulate the robust quality-of-service (QoS) problem, which is to minimize the transmit power subject to the worst-case minimum signal-to-interference-plus-noise-ratio (SINR) guarantee. We directly solve the worst-case SINR problem and convert the robust QoS constraint into a number of non-convex constraints. Based on the recent convergence result of the alternating direction method of multipliers (ADMM) for non-convex problems, we develop an ADMM-based fast algorithm to directly tackle the reformulated non-convex problem with a convergence guarantee. The algorithm contains two layers of ADMM procedures. We design the outer-layer ADMM to decompose the problem into three convex subproblems and solve them alternatingly. We further develop an inner-layer consensus-ADMM-based algorithm to efficiently solve one subproblem. By exploring each subproblem structure and developing the special optimization techniques, we obtain closed-form or semi-closed-form solutions to each subproblem. These results lead to a fast iterative algorithm, which is guaranteed to converge to a stationary point of the original robust QoS problem. Simulation shows that our proposed algorithm provides a favorable performance compared with existing alternative methods with magnitudes of computational complexity reduction. [ABSTRACT FROM AUTHOR]

This paper develops a novel algorithm, termed SPARse Truncated Amplitude flow (SPARTA), to reconstruct a sparse signal from a small number of magnitude-only measurements. It deals with what is also known as sparse phase retrieval (PR), which is NP-hard in general and emerges in many science and engineering applications. Upon formulating sparse PR as an amplitude-based nonconvex optimization task, SPARTA works iteratively in two stages: In stage one, the support of the underlying sparse signal is recovered using an analytically well-justified rule, and subsequently a sparse orthogonality-promoting initialization is obtained via power iterations restricted on the support; and in the second stage, the initialization is successively refined by means of hard thresholding based gradient-type iterations. SPARTA is a simple yet effective, scalable, and fast sparse PR solver. On the theoretical side, for any n-dimensional k-sparse (k ≪ n) signal x with minimum (in modulus) nonzero entries on the order of (1/√k)||x||2, SPARTA recovers the signal exactly (up to a global unimodular constant) from about k2 log n random Gaussian measurements with high probability. Furthermore, SPARTA incurs computational complexity on the order of k2 n log n with total runtime proportional to the time required to read the data, which improves upon the state of the art by at least a factor of k. Finally, SPARTA is robust against additive noise of bounded support. Extensive numerical tests corroborate markedly improved recovery performance and speedups of SPARTA relative to existing alternatives. [ABSTRACT FROM AUTHOR]

Based on the minimum noise subspace (MNS) method previously introduced in the context of blind channel identification, generalized minimum noise subspace (GMNS) is proposed in this paper for array processing that generalizes MNS with respect to the availability of only a fixed number of parallel computing units. Different batch and adaptive algorithms are then introduced for fast and parallel computation of signal (principal) and noise (minor) subspaces. The computational complexity of GMNS and its related estimation accuracy are investigated by simulated experiments and a real-life experiment in radio astronomy. It is shown that GMNS represents an excellent tradeoff between the computational gain and the subspace estimation accuracy, as compared to several standard subspace methods. [ABSTRACT FROM PUBLISHER]

In this paper, a computationally efficient algorithm for Bayesian joint change point detection (CPD) in multiple time series is presented. The data generation model includes a number of change configurations (CC), each affecting a unique subset of the time series, which introduces correlation between the positions of change points (CPs) in the monitored time series. The inference objective is to identify joint changes and the associated CC. The algorithm consists of two stages: First, a univariate CPD algorithm is applied separately to each of the involved time series. The outcomes of this step are maximum a posteriori (MAP) detected CPs and posterior distributions of CPs conditioned on the MAP CPs. These outcomes are used in combination to approximate the posterior for the CCs. In the second algorithm stage, dynamic programming is used to find the maxima of this approximate CC posterior. The algorithm is applied to synthetic data, and it is shown to be both significantly faster and more accurate compared to a previously proposed algorithm designed to solve similar problems. Also, the initial algorithm is extended with steps from the maximization–maximization algorithm, which allows the hyperparameters of the data generation model to be estimated jointly with the CCs, and we show that these estimates coincide with estimates obtained from a Markov chain Monte Carlo algorithm. [ABSTRACT FROM AUTHOR]

This paper considers the reconstruction of a discrete-valued random vector from possibly underdetermined linear measurements using sum-of-absolute-value (SOAV) optimization. The proposed algorithm, referred to as discreteness-aware approximate message passing (DAMP), is based on the idea of approximate message passing (AMP), which has been originally proposed for compressed sensing. The DAMP algorithm has low computational complexity and its performance in the large system limit can be predicted analytically via state evolution framework, where we provide a condition for the exact reconstruction with DAMP in the noise-free case. From the analysis, we also propose a method to determine the parameters of the SOAV optimization. Moreover, based on the state evolution, we provide Bayes optimal DAMP, which has the minimum mean-square-error at each iteration of the algorithm. Simulation results show that the DAMP algorithms can reconstruct the discrete-valued vector from underdetermined linear measurements and the empirical performance agrees with our theoretical results in large-scale systems. When the problem size is not large enough, the SOAV optimization with the proposed parameters can achieve better performance than the DAMP algorithms for high signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

This paper proposes a low complexity n-dimensional (nD) FastICA algorithm and architecture by introducing the concept of coordinate rotation where n\geq 2. The proposed algorithm can merge the two key steps of conventional FastICA—preprocessing and update and is therefore capable of reducing the hardware complexity of the conventional FastICA significantly as demonstrated in this paper. Hardware implementation can further be simplified due to the recursive nature of the proposed algorithm where the same 2D hardware module can be used as the fundamental core to implement nD architecture. Together with the algorithm formulation, its functionality is also validated and hardware complexity is analyzed and compared with the conventional nD FastICA. [ABSTRACT FROM PUBLISHER]

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters in an online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaptation of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz 63 system. [ABSTRACT FROM PUBLISHER]

BigBand is a technique for wideband spectrum sensing (WSS) that can capture gigahertz of sparse spectrum in real time by using shifted multiple channels without sampling the signal at GS/s. In this paper, we focus on enforcing BigBand with the proposed improved algorithm, namely, AD-BigBand, for efficient and robust computation. AD-BigBand converts the nonlinear process (locating frequency and computing the spectrum value) of sparse WSS into two steps of solving linear equations. In particular, we define an r -degree frequency locator polynomial to rapidly locate nonzero frequencies. The computing complexity of the proposed method decreases from O(K{\log ^2}K ({{{n\log K} \over K}})^{\log K}) of shifted sampling based BigBand to O(K{\log ^2}K)$, where the $K$-sparse signals of bandwitdth $n$ are subsampled with arithmetic time-shifted sensing channels. We implement AD-BigBand on a commercial four-channel acquisition card. Experimental results show that AD-BigBand improves the WSS capabilities and exhibits higher processing speed and lower error spectrum construction rate than BigBand, especially in the case of relative low signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

Conventional direction-of-arrival (DOA) estimation methods are sensitive to outlier measurements. Therefore, their performance may degrade substantially in the presence of impulsive noise. In this paper, we address the problem of DOA estimation in additive outliers from the perspective of sparse Bayesian learning (SBL). A Bayes-optimal algorithm is devised for robust DOA estimation, which can achieve excellent performance in terms of resolution and accuracy. To reduce the computational complexity of the SBL scheme, a fast alternating algorithm is also developed. New grid-refining procedures are further introduced into these two proposed algorithms to efficiently fix the off-grid gap. As our solutions do not require the prior knowledge of the number of sources and can resolve highly correlated or coherent sources, it is expected that they have higher applicability. Simulation results verify the outlier-robust performance of the SBL approach. [ABSTRACT FROM AUTHOR]

This paper examines the mean-square error performance of diffusion stochastic algorithms under a generalized coordinate-descent scheme. In this setting, the adaptation step by each agent is limited to a random subset of the coordinates of its stochastic gradient vector. The selection of coordinates varies randomly from iteration to iteration and from agent to agent across the network. Such schemes are useful in reducing computational complexity at each iteration in power-intensive large data applications. They are also useful in modeling situations where some partial gradient information may be missing at random. Interestingly, the results show that the steady-state performance of the learning strategy is not always degraded, while the convergence rate suffers some degradation. The results provide yet another indication of the resilience and robustness of adaptive distributed strategies. [ABSTRACT FROM AUTHOR]

In multiple-input multiple-output radar, to localize a target and estimate its reflection coefficient, a given cost function is usually optimized over a grid of points. The performance of such algorithms is directly affected by the grid resolution. Increasing the number of grid points enhances the resolution of the estimator but also increases its computational complexity exponentially. In this paper, two reduced complexity algorithms are derived based on Capon and amplitude and phase estimation (APES) to estimate the reflection coefficient, angular location, and Doppler shift of multiple moving targets. By exploiting the structure of the terms, the cost function is brought into a form that allows us to apply the two-dimensional fast Fourier transform (2D-FFT) and reduce the computational complexity of estimation. Using low resolution 2D-FFT, the proposed algorithm identifies suboptimal estimates and feeds them as initial points to the derived Newton gradient algorithm. In contrast to the grid-based search algorithms, the proposed algorithm can optimally estimate on- and off-the-grid targets in very low computational complexity. A new APES cost function with better estimation performance is also discussed. Generalized expressions of the Cramér–Rao lower bound are derived to assess the performance of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper considers the coherent integration problem for a maneuvering target with complex motions, where the velocity, acceleration, and jerk result in respectively the first-order range migration (FRM), second-order range migration (SRM), and third-order range migration (TRM) within the coherent pulse interval. A new coherent integration algorithm based on generalized keystone transform (KT) and second-order dechirp process is proposed, which employs the third-order KT, six-order KT, second-order KT, and fold factor searching to correct the TRM, SRM, and FRM, respectively. The range migration change during each step and computational complexity are also theoretically analyzed. Compared with the generalized Radon Fourier transform (GRFT) algorithm, the presented method can avoid the blind speed sidelobe (BSSL) and acquire close integration performance but with much lower computational cost. Simulations are provided to demonstrate the effectiveness. Finally, a generalized method, named generalized KT and generalized dechirp process (GKTGDP), is also introduced for the maneuvering target with arbitrary high-order range migration. [ABSTRACT FROM PUBLISHER]

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]

Decimation and interpolation are very common multirate signal processing operations. Conventional decimation or interpolation technique using polyphase filters has the advantage that for a given transition-band sharpness, the filter's computational complexity decreases with increasing interpolation or decimation factor. Nevertheless, if the transition band of the decimation or interpolation filter is very sharp, the complexity of the filter may still be very high. The complexity of a very sharp filter may be reduced using the frequency-response masking (FRM) technique. However, as shown in this paper, for a given transition-band sharpness, the computational complexity of the classical FRM method does not reduce as rapidly as the increase in decimation or interpolation factor. In this paper, we present a novel variant of the FRM technique for interpolation or decimation application. In this new variant, the computational complexity reduces as rapidly as the interpolation or decimation factor increases. The reduction in computational complexity increases with decreasing transition width. Over an order of magnitude reduction in computational complexity is achieved when compared with conventional polyphase approach in a particular example presented in this paper. [ABSTRACT FROM AUTHOR]

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective channel matrices. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a Partial Interference Alignment and Interference Detection (PIAID) design for K-user quasi-static MIMO interference channels with discrete constellation inputs. Each transmitter has M antennas and transmits L independent data streams to the desired receiver with N receive antennas. We focus on the case where not all K-1 interfering transmitters can be aligned at every receiver. As a result, there will be residual interference at each receiver that cannot be aligned. Each receiver detects and cancels the residual interference based on the constellation map. However, there is a window of unfavorable interference profile at the receiver for Interference Detection (ID). In this paper, we propose a low complexity Partial Interference Alignment scheme in which we dynamically select the user set for IA so as to create a favorable interference profile for ID at each receiver. We first derive the average symbol error rate (SER) by taking into account of the non-Guassian residual interference due to discrete constellation. Using graph theory, we then devise a low complexity user set selection algorithm for the PIAID scheme, which minimizes the asymptotically tight bound for the average end-to-end SER performance. Moreover, we substantially simplify interference detection at the receiver using Semi-Definite Relaxation (SDR) techniques. It is shown that the SER performance of the proposed PIAID scheme has significant gain compared with various conventional baseline solutions. [ABSTRACT FROM PUBLISHER]

Achieving the boundary of the capacity region in the multiple-input multiple-output (MIMO) broadcast channel requires the use of dirty paper coding (DPC). As practical nearly optimum implementations of DPC are computationally complex, purely linear approaches are often used instead. However, in this case, the problem of maximizing a weighted sum rate constitutes a nonconvex and, in most cases, also a combinatorial optimization problem. In this paper, we present two heuristic nearly optimum algorithms with reduced computational complexity. For this purpose, a lower bound for the weighted sum rate under linear zero-forcing constraints is used. Based on this bound, both greedy algorithms successively allocate data streams to users. In each step, the user is determined that is given an additional data stream such that the increase in weighted sum rate becomes maximum. Thereby, the data stream allocations and filters obtained in the previous steps are kept fixed and only the filter corresponding to the additional data stream is optimized. The first algorithm determines the receive and transmit filters directly in the downlink. The other algorithm operates in the dual uplink, from which the downlink transmit and receive filters can be obtained via the general rate duality leading to nonzero-forcing in the downlink. Simulation results reveal marginal performance losses compared to more complex algorithms. [ABSTRACT FROM AUTHOR]

Very often, random signals are modeled as autoregressive moving-average (ARMA) processes in engineering and scientific applications. The acquisition of the second-order statistics or the calculation of the autocorrelation function for an ARMA process is very important in those applications. In this paper, we discuss two kinds of ARMA-autocorrelation computation approaches, namely the recursive approach and the direct approach. To overcome the problems of memory usage and computational burden, we design a new ARMA-autocorrelation calculation algorithm which belongs to the direct approach. Our novel algorithm originates from the partial fractional decomposition for the rational trigonometric functions and the associated definite integrals. For comparison, we also provide the theoretical analysis of computational complexity for our new scheme and the conventional recursion-based algorithm. From our studies, it can be shown that our new ARMA-autocorrelation calculation method is more efficient than the conventional algorithm when the underlying autocorrelation function is long or the corresponding power spectrum possesses the narrowband characteristics. On the other hand, the conventional algorithm is more efficient than our new algorithm when the model orders of the ARMA process are large' and the underlying autocorrelation function is short (the corresponding power spectrum is wideband). Since our proposed new scheme involves the root-finding of a polynomial, the effect, of the error-tolerance in solving polynomials on the induced complexity is also discussed in this paper. [ABSTRACT FROM AUTHOR]

The paper presents two formulations of causal cubic splines with equidistant knots. Both are based on a causal direct B-spline filter with parallel or cascade implementation. In either implementation, the causal part of the impulse response is realized with an efficient infinite-impulse-response (HR) structure, while only the anticausal part is approximated with a finite-order finite-impulse-response (FIR) filter. Resulting cubic coefficients are computed from the causal B-spline coefficients by using a third-order output FIR filter with either single-input multiple-output (SIMO) or multiple-input multiple-output (MIMO) structure, depending on the chosen formulation of the cubic spline. The paper demonstrates and proves that the properties of the resulting causal splines are quite different, whether they are based on a more popular B-spline formulation, or a bit neglected tridiagonal matrix formulation. It is shown that the proposed low-complexity but accurate causal interpolators can be realized for many practical applications with the delay of only a few samples. [ABSTRACT FROM AUTHOR]

Video decoding applications must often cope with highly time-varying workload demands, while meeting stringent display deadlines. Voltage/frequency scalable processors are highly attractive for video decoding on resource-constrained systems, since significant energy savings can be achieved by dynamically adapting the processor speed based on the changing workload demand. Previous works on video-related voltage scaling algorithms are often limited by the lack of a good complexity model for video and often do not explicitly consider the video quality impact of various steps involved in the decoding process. Our contribution in this paper is threefold. First, we propose a novel complexity model through offline training that explicitly considers the video source characteristics, the encoding algorithm, and platform specifics to predict execution times. Second, based on the complexity model, we propose low complexity online voltage scaling algorithms to process decoding jobs such that they meet their display deadlines with high probability. We show that on average, our queuing-based voltage scaling algorithm provides approximately 10%-15% energy savings over existing voltage scaling algorithms. Finally, we propose a joint voltage scaling and quality-aware priority scheduling algorithm that decodes jobs in order of their distortion impact, such that by setting the processor to various power levels and decoding only the jobs that contribute most to the overall quality, efficient quality, and energy tradeoffs can be achieved. We demonstrate the scalability of our algorithm in various practical decoding scenarios, where reducing the power to 25% of the original power can lead to quality degradations of less than 1.0 dB PSNR. [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]

The problem of finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In communications applications, however, the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known. Therefore, in this paper, rather than dwell on the worst-case complexity of the integer least-squares problem, we study its expected complexity, averaged over the noise and over the lattice. For the "sphere decoding" algorithm of Fincke and Pohst, we find a closed-form expression for the expected complexity, both for the infinite and finite lattice. It is demonstrated in the second part of this paper that, for a wide range of signal-to-noise ratios (SNRs) and numbers of antennas, the expected complexity is polynomial, in fact, often roughly cubic. Since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial, this suggests that maximum-likelihood decoding, which was hitherto thought to be computationally intractable, can, in fact, be implemented in real time—a result with many practical implications. [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]

The least mean squared (LMS) algorithm and its variants have been the most often used algorithms in adaptive signal processing. However the LMS algorithm suffers from a high computational complexity, especially with large filter lengths. The Fourier transform-based block normalized LMS (FBNLMS) reduces the computation count by using the discrete Fourier transform (DFT) and exploiting the fast algorithms for implementing the DFT. Even though the savings achieved with the FBNLMS over the direct-LMS implementation are significant, the computational requirements of FBNLMS are still very high, rendering many real-time applications, like audio and video estimation, infrasible. The Hartley transform-based BNLMS (HBNLMS) is found to have a computational complexity much less than, and a memory requirement almost of the same order as, that of the FBNLMS. This paper is based on the cosine and sine symmetric implementation of the discrete Hartley transform (DHT), which is the key in reducing the computational complexity of the FBNLMS by 33% asymptotically (with respect to multiplications). The parallel implementation of the discrete cosine transform (DCT) in turn can lead to more efficient implementations of the HBNLMS. [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]

In this paper, an enhanced linear minimum mean square error (LMMSE) turbo equalization scheme is proposed for multiple-input multiple-output (MIMO) communication systems with bit-interleaved coded modulation (BICM) in the time domain and multiplexing in the space domain. The proposed turbo equalization scheme outperforms the conventional LMMSE turbo equalization by adopting two new signal processing techniques. First, it performs hybrid soft interference cancellation (HSOIC) by subtracting the soft decisions of the interfering symbols, and the soft decisions are calculated by using a hybrid of the a priori information at the equalizer input and the a posteriori information at the equalizer output. Second, it employs a novel block-wise reliability-based ordering scheme such that more “reliable” symbols are detected before the less “reliable” ones to reduce error propagation in HSOIC. The symbol reliability information is based on the symbol a priori probability, as a unique byproduct of turbo detection, thus can be obtained with very small overhead. A low-complexity approximation of the enhanced MIMO LMMSE turbo equalization is also proposed to balance the tradeoff between complexity and performance. The performance of the enhanced MIMO LMMSE turbo equalization has been verified through both numerical simulations and the undersea experimental data collected in the SPACE08 experiment launched near Martha's Vineyard, Edgartown, MA, in 2008. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a wireless amplify-and-forward relay network with one relay node and multiple source-destination pairs/users and propose a pricing framework that enables the relay to set prices to maximize either its revenue or any desirable system utility. Specifically, depending on the quality of the received signals, the relay sets prices and correspondingly charges the users utilizing its resources for their transmissions. The price is determined in such a way that the relay's revenue or system utility is maximized. Given the specified price, the users competitively employ the relay node to forward their signals. We model each user as a rational player, which aims at maximizing its own net utility through power allocation, and analyze the competition among the users within the framework of noncooperative game theory. It is shown that, in the game played by the users, there always exists a unique pure Nash equilibrium point that can be achieved through distributed iterations. Next, subject to the availability of complete information about the users at the relay, we propose a low-complexity uniform pricing algorithm and an optimal differentiated pricing algorithm, in which the relay either charges the users at a suboptimal uniform price or charges different users at different prices. We also show that, by applying the differentiated pricing algorithm that enforces the users to transmit at certain power levels, any system utility can be maximized. Extensive simulations are conducted to quantify the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, low-complexity joint power assignment algorithms are developed for multi-source multi-destination relay networks where multiple sources share a common relay that forwards all received signals simultaneously to destinations. In particular, we consider the following power optimization strategies: (i) Minimization of the total transmission power of the sources and the relay under the constraint that the signal-to-interference-plus-noise ratio (SINR) requirement of each source-destination pair is satisfied, and (ii) Maximization of the minimum SINR among all source-destination pairs subject to any given total power budget. Both optimization problems involve K power variables, where K is the number of source-destination pairs in the network, and an exhaustive search is prohibitive for large K. In this work, we develop a methodology that allows us to obtain an asymptotically tight approximation of the SINR and reformulate the original optimization problems to single-variable optimization problems, which can be easily solved by numerical search of the single variable. Then, the corresponding optimal transmission power at each source and relay can be calculated directly. The proposed optimization schemes are scalable and lead to power assignment algorithms that exhibit the same optimization complexity for any number (K) of source-destination pairs in the network. Moreover, we apply the methodology that we developed to solve a related max-min SINR based optimization problem in which we determine power assignment for the sources and the relay to maximize the minimum SINR among all source-destination pairs subject to any given total power budget. Extensive numerical studies illustrate and validate our theoretical developments. [ABSTRACT FROM AUTHOR]

Discrete Fourier transforms (DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic fast Fourier transforms (CFFTs) are promising due to their low multiplicative complexities. Unfortunately, there are two issues with CFFTs: (1) they rely on efficient short cyclic convolution algorithms, which have not been sufficiently investigated in the literature and (2) they have very high additive complexities when directly implemented. To address both issues, we make three main contributions in this paper. First, for any odd prime p, we reformulate a p-point cyclic convolution as the product of a (p-1)\times (p-1) Toeplitz matrix and a vector, which has well-known efficient algorithms, leading to efficient bilinear algorithms for p-point cyclic convolutions. Second, to address the high additive complexities of CFFTs, we propose composite cyclotomic Fourier transforms (CCFTs). In comparison to previously proposed fast Fourier transforms, our CCFTs achieve lower overall complexities for moderate to long lengths and the improvement significantly increases as the length grows. Third, our efficient algorithms for p-point cyclic convolutions and CCFTs allow us to obtain longer DFTs over larger fields, e.g., the 2047-point DFT over GF(2^11) and 4095-point DFT over GF(2^12), which are first efficient DFTs of such lengths to the best of our knowledge. Finally, our CCFTs are also advantageous for hardware implementations due to their modular structure. [ABSTRACT FROM AUTHOR]

Distributed network utility maximization (NUM) has received an increasing intensity of interest over the past few years. Distributed solutions (e.g., the primal-dual gradient method) have been intensively investigated under fading channels. As such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under time-varying channels is in general unknown. In this paper, we shall investigate the convergence behavior and tracking errors of the iterative primal-dual scaled gradient algorithm (PDSGA) with dynamic scaling matrices (DSC) for solving distributive NUM problems under time-varying fading channels. We shall also study a specific application example, namely the multicommodity flow control and multicarrier power allocation problem in multihop ad hoc networks. Our analysis shows that the PDSGA converges to a limit region rather than a single point under the finite state Markov chain (FSMC) fading channels. We also show that the order of growth of the tracking errors is given by \cal O\left(\bar T/\bar N\right), where \bar T and \bar N are the update interval and the average sojourn time of the FSMC, respectively. Based on this analysis, we derive a low complexity distributive adaptation algorithm for determining the adaptive scaling matrices, which can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed dynamic scaling matrix algorithm over several baseline schemes, such as the regular primal-dual gradient algorithm. [ABSTRACT FROM AUTHOR]

Multidimensional vector cross-product has not been studied from the perspective of signal processing so far to the best of our knowledge and hence no effort has been made to develop any generalized algorithm for its hardware implementation. In this paper firstly, we identify the application domain of cross-product in signal processing and then introduce a novel recursive algorithm for generalized nD cross-product computation considering three dimensional (3D) cross-product as the fundamental operation. Subsequently a generalized scheme for architecture implementation for nD cross-product is proposed based on this algorithm. Secondly, we show that if 4D cross-product is used as the fundamental operation for formulating nD cross-product problem, then exploiting the inherent mathematical symmetry of 4D cross-product it is possible to reduce the total hardware cost of nD cross-product significantly at the architecture level (symmetry-based approach). Mathematical models for hardware complexity and operational delay have been formulated both for the generalized and symmetry-based approaches. [ABSTRACT FROM AUTHOR]

In this paper, we consider the resource reciprocation among self-interested peers in peer-to-peer (P2P) networks, which is modeled as a stochastic game. Peers play the game by determining their optimal strategies for resource distributions using a Markov decision process (MDP) framework. The optimal strategies enable the peers to maximize their long-term utility. Unlike in conventional MDP frameworks, we consider heterogeneous peers that have different and limited ability to characterize their resource reciprocation with other peers. This is due to the large complexity requirements associated with their decision making processes. We analytically investigate these tradeoffs and show how to determine the optimal number of state descriptions, which maximizes each peer's average cumulative download rates given a limited time for computing the optimal strategies. We also investigate how the resource reciprocation evolves over time as peers adapt their reciprocation strategies by changing the number of state descriptions. Then, we study how resulting download rates affect their performance as well as that of the other peers with which they interact. Our simulation results quantify the tradeoffs between the number of state descriptions and the resulting utility. We also show that evolving resource reciprocation can improve the performance of peers which are simultaneously refining their state descriptions. [ABSTRACT FROM AUTHOR]

Multichannel fast QR decomposition RLS (MC-FQRD-RLS) algorithms are well known for their good numerical properties and low computational complexity. The main limitation is that they lack an explicit weight vector term, limiting themselves to problems seeking an estimate of the output error signal. This paper presents techniques which allow us to use MC-FQRD-RLS algorithms with applications that previously have required explicit knowledge of the adaptive filter weights. We first consider a multichannel system identification setup and present how to obtain, at any time, the filter weights associated with the MC-FQRD-RLS algorithm. Thereafter, we turn to problems where the filter weights are periodically updated using training data, and then used for fixed filtering of a useful data sequence, e.g., burst-trained equalizers. Finally, we consider a particular control structure, indirect learning, where a copy of the coefficient vector is filtering a different input sequence than that of the adaptive filter. Simulations are carried out for Volterra system identification, decision feedback equalization, and adaptive predistortion of high-power amplifiers. The results verify our claims that the proposed techniques achieve the same performance as the inverse QRD-RLS algorithm at a much lower computational cost. [ABSTRACT FROM AUTHOR]

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 this paper, we first propose a novel common subexpression elimination (CSE) algorithm for matrix-vector multiplications over characteristic-2 fields. As opposed to previously proposed CSE algorithms, which usually focus on complexity savings due to recurrences of subexpressions, our CSE algorithm achieves two types of complexity reductions, differential savings and recurrence savings, by taking advantage of the cancelation property of characteristic-2 fields. Using our CSE algorithm, we reduce the additive complexities of cyclotomic fast Fourier transforms (CFFTs). Using a weighted sum of the numbers of multiplications and additions as a metric, our CFFTs achieve smaller total complexities than previously proposed CFFTs and other FFTs, requiring both fewer multiplications and fewer additions in many cases. [ABSTRACT FROM AUTHOR]

This paper presents several new properties of biorthogonal cosine modulated filter banks (CMFBs) and efficient algorithms for designing CMFBs with a very large number of subbands and very long filters. For a biorthogonal CMFB, we find the periodicity and symmetry of its overall transfer function and aliasing transfer functions which can be efficiently computed based on a decimated uniform discrete Fourier transform (DFT) analysis filter bank. By exploiting gradient information and 2Mth band conditions, efficient algorithms are proposed for designing both orthogonal and biorthogonal CMFBs. In addition, an efficient matrix inversion algorithm with O(N²) complexity is also presented. Several numerical examples and comparisons with many other existing methods are included to demonstrate the design performance and efficiency of the algorithms. [ABSTRACT FROM AUTHOR]

Sign-selection uses a set of subcarrier signs to reduce the peak-to-average power ratio (PAR) of orthogonal-frequency-division multiplexing (OFDM). However, the computational complexity (worst-case) is exponential in N, the number of subcarriers. Suboptimal sign-selection algorithms, achieving different tradeoffs between the PAR reduction and complexity, have thus been developed. For example, the derandomization method achieves high PAR reduction of σ(log N) with relatively high complexity of σ(N2). On the other hand, selective mapping (SLM) and partial transmit sequences (PTS) sacrifice the achievable PAR reduction for lower complexity. In this paper, we develop two new cross-entropy (CE)-based sign-selection algorithms. Our algorithms simultaneously updates the probabilities of the signs of all subcarriers. As shown in Section II-D, the first algorithm obtains a PAR lower than the above methods with a complexity level of σ(N2). However, if the number of iterations is fixed, this algorithm obtains the same PAR reduction as derandomization, but with σ(N log N) complexity. Practical PAR reduction algorithms require that the extra cost of PAR reduction must be small. Therefore, we propose the second algorithm, which adaptively adjusts the probability of "elite" samples, and stops whenever a PAR threshold is reached. Our second algorithm achieves up to 95% complexity savings over the first (with only a 0.4-dB PAR reduction loss). The simulations confirm the complexity advantages of the proposed algorithms compared to SLM and derandomization. [ABSTRACT FROM AUTHOR]