In this paper, we consider a diffusion network with the objective of minimizing a cost function at each node by a global optimizer, assumed to be K-sparse, by utilizing diffusion based collaboration among the nodes. In the proposed algorithm termed as DiffstoHT here, in each iteration, first a stochastic gradient based update is calculated followed by K level hard thresholding at each node. The resulting estimates are then shared with the neighbors of the node by means of diffusion and subsequently a weighted linear combination of the incoming estimates is taken followed by 2K level hard thresholding. Next, each node carries out certain gradient descent iterations sequentially, restricted to the 2K-sized support obtained from previous stage. Lastly, another K level hard thresholding is performed by each node, completing one iteration. The proposed DiffStoHT algorithm is particularly useful for large scale problems where full gradient calculation is expensive. Theoretical analysis of the proposed DiffStoHT algorithm is carried out using the restricted positive definite Hessian (RPDH) property of the cost functions and sufficient conditions for recovery are derived. Simulations suggest that the proposed algorithm is not only faster than existing diffusion based methods, but it is also capable of outperforming them in terms of probability of recovery.

This paper presents a unified treatment to hard thresholding based compressed sensing recovery algorithms. For this, it modifies the cost function by a power series in$\mathbf {A}\mathbf {A}^{H}$where$\mathbf {A}$is the so-called sensing matrix. For appropriate choice of the power series coefficients, the proposed treatment not only leads to various existing hard thresholding based recovery algorithms, but, more importantly, it enables one to develop new algorithms belonging to this category. The paper also presents a convergence analysis of the proposed method and derives convergence guarantees in terms of the restricted isometry constant (RIC) of the sensing matrix. It is seen that in case of some of the well known hard thresholding based algorithms, the proposed convergence analysis results in wider ranges of algorithm parameters and faster convergence than suggested by existing analyses. Some new, power series based hard thresholding algorithms are also proposed and their recovery performance studied via simulation.

In this paper, we propose a Hard Thresholding (HT) based robust algorithm for large scale Multiple Measurement Vectors (MMV) problem in Compressed Sensing. The proposed MStoLIHT algorithm is based upon Stochastic Gradient Descent (SGD) and employs the Lorentzian norm of residual as the underlying cost function which provides robustness against impulsive errors in the measurements. Each iteration of the MStoLIHT algorithm consists of multiple subiterations. At each iteration, only a block of rows of the sensing matrix is used for carrying out the update, and at each subiteration, only few of the columns of the estimated data matrix are updated based on the SGD and the HT strategies. At the end of subiterations, another HT operation is performed ensuring the row sparsity in the estimated data matrix. Extensive numerical simulations are carried out, which indicate that by updating the data matrix in blocks of columns followed by HT operation, the performance in terms of probability of support recovery is improved when compared to its deterministic counterpart. It is further observed that the MStoLIHT algorithm outperforms other existing algorithms for the MMV problem in literature.

In this paper, we first present a stochastic gradient based robust algorithm for recovering a sparse signal from compressed measurements corrupted by impulsive noise for large problems where calculation of the full gradient is expensive. This stochastic gradient based strategy is then modified and applied to diffusion based distributed compressed sensing. In the proposed algorithm, a proxy to the actual gradient is found and hard thresholding based updates are carried out. The proposed algorithm uses Lorentzian norm of the residual as the cost function, making it robust against impulsive noise. It is observed through simulations that the proposed algorithm is able to outperform existing stochastic gradient based algorithms and is able to provide at par recovery performance to that of other robust deterministic algorithms currently available in literature for distributed compressed sensing.

In this paper, we present two heavy ball based hard thresholding algorithms aimed at recovering jointly sparse signals in multiple measurement vector (MMV) scenario, arising in compressed sensing. The proposed Simultaneous Heavy Ball based Iterative Hard Thresholding (SHBIHT) and Simultaneous Heavy Ball based Hard Thresholding Pursuit (SHBHTP) algorithms use heavy ball based acceleration technique, which uses the current estimate as well as the previous estimate in the gradient based update. By exploiting the MMV structure, we use a weighted momentum rather than a common momentum for each of the signals. In the first algorithm, hard thresholding is carried out on the gradient based update whereas the other algorithm requires solving a least squares problem (pursuit step) on top of the hard thresholded update. Theoretical analysis is carried out using the Restricted Isometry Property (RIP) and sufficient conditions for convergence are derived. It is observed through simulations that the proposed heavy ball based algorithms for MMV problem provide computational advantage in terms of total time required for convergence while performing at-par with existing algorithms in terms of recovery performance.

In this paper, we present two robust, thresholding based distributed algorithms for recovering a sparse signal from compressed measurements. These algorithms use Lorentzian norm as the cost function which has been observed to give robustness against heavy tailed noise, e.g., impulsive noise. The first algorithm named Diffusion based Lorentzian Iterative Hard Thresholding (DLIHT) requires only gradient information whereas the second algorithm named Diffusion based Lorentzian Hard Thresholding Pursuit(DLHTP) requires solving a linear system, on top of the gradient based update. It is observed through simulations that for moderate corruptions, DLHTP converges faster than DLIHT to similar steady state error value. However, for higher levels of corruptions, DLIHT leads to much less steady state error than offered by DLHTP.

Multitask diffusion strategies are useful to estimate node-specific, or, multiple parameter vectors over a distributed network by exploiting inter-cluster and intra-cluster cooperation. During cooperation, all nodes transmit their intermediate estimates to their neighboring nodes, resulting in high energy consumption. In this paper, we propose a clustered multitask diffusion affine projection algorithm by transmitting only a subset of the entries of the intermediate estimate vectors among the neighboring nodes. The proposed algorithm, namely, clustered multitask partial diffusion affine projection algorithm provides a trade-off between the estimation performance and the required communication cost. Important results on convergence (in mean and mean square) of the proposed strategy are presented. Numerical simulations reveal that even though the estimation performance deteriorates somewhat as the number of coefficients transmitted to the neighboring nodes decreases, the degradation can be compensated to a large extent by a proportional increase in the magnitude of the regularization strength among the clusters.

Logic Encryption has emerged to be a promising solution to the ever-increasing problem of IP piracy and counterfeiting. The state-of-the-art logic encryption techniques fail to offer adequate protection to the designs, equipped with Design-for-Testability (DfT) infrastructure. In this paper, we propose a new logic encryption strategy which prevents scan-chain guided circuit partitioning attack by introducing circular dependency among all the keys irrespective of their locations. Leveraging the circular dependency, the proposed method can also thwart path sensitization, logic cone based, and SAT attacks without adopting any complex key-gate placement algorithms.

In this paper, we first derive closed form expressions for the steady state mean and mean square deviations (MSD) of an l0-RLS adaptive filter. The latter is seen to depend on the sparsity promoting parameter (which is denoted by `β'), and the dependence is seen to be a function of the signal to noise ratio (SNR). Since the optimum value of β, for which the steady state MSD is minimized, is a function of the SNR, it is difficult to choose a suitable β when the SNR is time-varying, or, can not be known a priori. To circumvent this problem, this paper presents a new convex combination based l0-RLS adaptive filter for identifying a sparse system under variable SNR. The proposed scheme combines M number of differently parameterized l0-RLS adaptive filters, each having a parameter value (β) suitable for a specific SNR. The combining coefficients are updated so that the best filter in terms of optimum or near optimum β is chosen. Simulation results establish excellent robustness of the proposed method against variable SNR.

This paper presents a novel block based convex combination of two adaptive filters - the sparsity unaware NLMS and the sparsity aware zero-attracting NLMS (ZA-NLMS) for identifying and tracking a sparse system with variable sparsity. The proposed scheme partitions the system impulse response blockwise. As most often in practice, sparse systems exhibit sparseness in blocks, such partitioning renders inactive blocks fully or almost fully sparse and active blocks highly non-sparse. For active and inactive blocks, the proposed convex combination switches respectively to the NLMS and the ZA-NLMS based filters, with the latter not suffering any performance degradation due to zero-attraction on active taps as the inactive blocks are almost fully sparse. The combined effect of this on the overall filter is a greatly reduced steady state excess mean square error, which is also corroborated by simulation studies.

A new sparsity aware recursive least squares (RLS) algorithm is proposed for distributed learning in a diffusion network. The algorithm deploys a RLS based adaptive filter at each node which is made sparsity aware by regularizing the conventional RLS cost function with a sparsity promoting penalty. The regularization introduces certain “zero-attracting” terms in the RLS update equation which help in shrinkage of the coefficients. Each node shares its tap weight information with every other node in its neighborhood and refines its own estimate by linearly combining the incoming tap weight information from neighboring nodes by a set of pre-defined weights. Results on both first and second order convergence of the algorithm are also provided. As simulations show, the proposed scheme outperforms other existing algorithms both in terms of convergence speed and steady state excess mean square error.

The proportionate normalized least mean square (PNLMS) algorithm and its variants are by far the most popular adaptive filters that are used to identify sparse systems. The convergence speed of the PNLMS algorithm, though very high initially, however, slows down at a later stage, even becoming worse than sparsity agnostic adaptive filters like the NLMS. In this paper, we address this problem by introducing a carefully constructed l1norm (of the coefficients) penalty in the PNLMS cost function which favors sparsity. This results in certain zero attracting terms in the PNLMS weight update equation which help in the shrinkage of the coefficients, especially the inactive taps, thereby arresting the slowing down of convergence and also producing lesser steady state excess mean square error (EMSE). A rigorous convergence analysis of the proposed algorithm is presented that expresses the steady state mean square deviation of both the active and the inactive taps in terms of a zero attracting coefficient of the algorithm. The analysis reveals that further reduction of the EMSE is possible by deploying a variable step size (VSS) simultaneously with a variable zero attracting coefficient in the weight update process. Simulation results confirm superior performance of the proposed VSS zero attracting PNLMS algorithm over existing algorithms, especially in terms of having both higher convergence speed and lesser steady state EMSE simultaneously.

In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the network in order to achieve an overall network performance superior to that of the simple diffusion LMS, albeit at the cost of increased computational overhead. In this paper, we provide analytical as well as experimental results which show that the convex regularization can be selectively applied only to some chosen nodes keeping rest of the nodes sparsity agnostic, while still enjoying the same optimum behavior as can be realized by deploying the convex regularization at all the nodes. Due to the incorporation of unregularized learning at a subset of nodes, less computational cost is needed in the proposed approach. We also provide a guideline for selection of the sparsity aware nodes and a closed form expression for the optimum regularization parameter.

Diagnosis is extremely important to ramp up the yield during the integrated circuit manufacturing process. It reduces the time to market and product cost. The back bone of any diagnosis algorithm is the test set in use. In this paper, a novel method has been proposed to increase the diagnosability of a given test set. The proposed method, which takes as input a test set generated for high fault coverage, is capable of increasing the diagnostic power of the test set without affecting its fault coverage. It is able to achieve this with either no or small increase in number of patterns. The crux of the method lies in introducing test patterns having `X' bits into the test set without changing its coverage, and using a `X' bit filling algorithm to maximize its diagnostic power.

The proportionate normalized least mean square (PNLMS) algorithm and its variants are by far the most popular adaptive filters that are used to identify sparse systems. The convergence speed of the PNLMS algorithm, though very high initially, however, slows down at a later stage, even becoming worse than sparsity agnostic adaptive filters like the NLMS. In this paper, we address this problem by introducing a carefully constructed l1norm (of the coefficients) penalty in the PNLMS cost function which favors sparsity. This results in certain “zero attractor” terms in the PNLMS weight update equation which help in the shrinkage of the coefficients, especially the inactive taps, thereby arresting the slowing down of convergence and also producing lesser steady state excess mean square error (EMSE). We also demonstrate both analytically and also intuitively, that the EMSE can not, however, be reduced significantly by the zero attractors due to some fundamental shortcoming of the PNLMS algorithm, and propose methods to counter it by deploying a variable step size and also a variable proportionality constant for the zero attractors. Simulation results confirm excellent performance of the proposed algorithm vis-a-vis existing methods.

The generalized Orthogonal Matching Pursuit (gOMP) is a recently proposed compressive sensing greedy recovery algorithm which generalizes the OMP algorithm by selecting N( ≥ 1) atoms in each iteration. In this letter, we demonstrate that the gOMP can successfully reconstruct a K-sparse signal from a compressed measurement y=Φx by a maximum of K iterations if the sensing matrix Φ satisfies the Restricted Isometry Property (RIP) of order NK, with the RIP constant δNKsatisfying δNKNK. We also show that by increasing the RIP order just by one (i.e., NK+1 from NK), it is possible to refine the bound further to δNK+1K+1in OMP.

In this paper, we provide an overview of the major developments in the area of sparse adaptive filters, starting from the celebrated works on PNLMS algorithm and its several variants to more recent approaches that use compressed sensing framework, more specifically, LASSO and basis pursuit or matching pursuit, to develop sparse adaptive algorithms with improved mean square error and tracking properties. Subsequently, we also present a new approach to identify sparse systems with time varying sparseness, for which a novel scheme of cooperative learning involving a PNLMS and a NLMS based adaptive filters is developed.

The complex behavior of load resonant converters is investigated by using a newly developed stability analysis tool. In this paper we specifically consider the series-parallel load resonant converter with L-C output filter, controlled by the frequency modulation technique. The close loop variable frequency control consists of a feedback loop and a PI controller with voltage controlled oscillator (VCO). The VCO is used to convert the error in output voltage into a change of frequency to control the voltage in close loop system. Two converter designs are considered with different combinations of L-C output filter. With the variation of the proportional gain, Neimark-Sacker and symmetry-breaking bifurcations are observed.

In the context of system identification, it is shown that sometimes the level of sparseness in the system impulse response can vary greatly depending on the time-varying nature of the system. When the response is strongly sparse, convergence of the conventional approach such as least mean square (LMS) is poor. The recently proposed, compressive sensing based sparsity- aware ZA-LMS algorithm performs satisfactorily in strongly sparse environments, but is shown to perform worse than the conventional LMS when sparseness of the impulse response reduces. We propose an algorithm which works well both in sparse and non-sparse circumstances and adapts dynamically to the level of sparseness, using a convex combination based approach. The proposed algorithm is supported by simulation results that show its robustness against variable sparsity.

This paper presents a bit serial realization of the sign-LMS based adaptive filter which enjoys multiplier free weight update loop. To reduce the complexity of the multipliers that arise in the filtering process, the filter weights are represented in the so-called canonic SPT form which guarantees presence of at least one zero between every two non-zero power-of-two terms. As the filter weights are not fixed but updated in time, it is essential to ensure that the canonic SPT format is retained in the updated filter coefficients. For this, a bit serial adder is proposed that takes as input two numbers in canonic SPT and produces an output also in canonic SPT. It is further shown how the canonic SPT property of the input can be used to reduce the complexity of the adder. For the filtering part, a bit serial multiplier is developed that takes one input (i.e., data bits) in 2's complement form and the other input (i.e., weight bits) in canonic SPT, producing the result in 2's complement. The multiplication can not, however, be realized using a few fixed shift and add operations, since the position of the non-zero SPT terms in the canonic SPT expression of each coefficient changes with time. The proposed multiplier instead multiplies the 2's complement number with pairs of consecutive SPT bits of the other number. The resulting partial products can be realized using simple AND-OR logic.

Recently, a block based adaptive decision feedback equalizer (ADFE) is presented which first uses an iterative scheme to evaluate a block of unknown decisions. FFT based block processing is then used on the received input block and the decision block to carry out the block ADFE operation. A direct floating point (FP) based realization of this scheme, however, pushes up the cost and complexity of processing hugely, as each FP operation involves several additional steps not present in its fixed point (FxP) counterpart. To overcome this problem, a block floating point (BFP) based treatment is presented in this paper for realization of the block ADFE. The proposed scheme, while maintaining FP like high dynamic range, deploys mostly FxP operations and thus reduces the processing cost and complexity substantially.

A scheme for efficient finite precision realization of the adaptive decision feedback equalizer using block floating point (BFP) arithmetic is presented. The scheme adopts separate BFP formats for the feed forward and the feedback filter weights and works out separate update relations for their respective mantissas and exponents. Care is taken to prevent overflow in all computations by using a dynamic scaling of the data and a carefully chosen upper bound for the step sizeμ. Since no block processing of the feedback input is possible, an efficient scheme is presented for block formatting the data stored in the feedback filter memory, at each time index. The proposed scheme mostly employs simple fixed point operations and achieves considerable speed up over its floating point counterpart.

In this letter, we address the problem of adaptively estimating the time delay of a noisy sinusoid received at two spatially separated sensors. By choosing the sampling frequency equal to four times the signal frequency, a simple adaptive algorithm for direct delay estimation is derived. Algorithm convergence in mean and mean square error is proved. Computer simulations are also included to demonstrate the effectiveness of the proposed method.

We present a novel scheme to implement the gradient adaptive lattice (GAL) algorithm using block floating point (BFP) arithmetic that permits processing of data over a wide dynamic range at a cost significantly less than that of a floating point (FP) processor. Appropriate formats for the input data, the prediction errors, and the reflection coefficients are adopted, taking care so that for the prediction errors and the reflection coefficients, they remain invariant to the respective order and time update processes. Care is also taken to prevent overflow during prediction error computation and reflection coefficient updating by using an appropriate exponent assignment algorithm and an upper bound on the step-size mantissa.

Often one encounters the presence of tonal noise in many active noise control applications. Such noise, usually generated by periodic noise sources like rotating machines, is cancelled by synthesizing the so-called antinoise by a set of adaptive filters which are trained to model the noise generation mechanism. Performance of such noise cancellation schemes depends on, among other things, the convergence characteristics of the adaptive algorithm deployed. In this paper, we consider a multireference complex least mean square (LMS) algorithm that can be used to train a set of adaptive filters to counter an arbitrary number of periodic noise sources. A deterministic convergence analysis of the multireference algorithm is carried out and necessary as well as sufficient conditions for convergence are derived by exploiting the properties of the input correlation matrix and a related product matrix. It is also shown that under convergence condition, the energy of each error sequence is independent of the tonal frequencies. An optimal step size for fastest convergence is then worked out by minimizing the error energy.

We present a novel scheme to implement the gradient adaptive lattice (GAL) algorithm using block floating point (BFP) arithmetic that permits processing of data over a wide dynamic range, at a cost significantly less than that of a floating point processor. Appropriate formats for the input data, the prediction errors and the reflection coefficients are adopted, taking care so that for the latter, they remain invariant to the coefficient updating process. Care is also taken to prevent overflow during prediction error computation and reflection coefficient updating by using an appropriate exponent assignment algorithm and an upper bound on the step size mantissa.

An efficient scheme is presented for implementing the LMS-based transversal adaptive filter in block floating point (BFP) format which permits processing of data over a wide dynamic range at a processor cost marginally higher than that of a fixed point processor. Appropriate BFP formats for both the data and the filter coefficients have been adopted and adjustments made in filtering as well as weight updating operations in order to sustain the adopted format and also to prevent overflow in both these operations jointly. For the presented method to work properly, the algorithm step size is to be chosen below an upper limit, which is, however, not very restrictive when compared with the upper bound for convergence, thereby having marginal effect on convergence speed.

This paper presents a class of pipelined CORDIC architectures for the LMS-based transversal adaptive filter. For this, an alternate formulation of the LMS algorithm is considered, obtained by expressing the mean square error as a convex function of a set of angle variables that are monotonically related to the filter tap weights. The proposed architectures employ microlevel pipelining and are adjustable to strike tradeoffs between throughput efficiency vis-a-vis hardware complexity.

An attempt is made to develop algorithms for the adaptive autoregressive moving average (ARMA) modeling of a linear, slowly time-varying, multichannel system using scalar computations only. The multivariate ARMA process is mapped to an equivalent scalar, periodic ARMA process. By properly defining the input and output vectors corresponding to the scalar process, the problem is formulated as the order-recursive computation of the orthogonal projection of the input vector on an appropriate data subspace. This is carried out by first orthogonalizing the data vectors through the Gram-Schmidt procedure resulting in the least squares circular lattice (LSCL) algorithm. The LSCL algorithm evaluated all possible lower-order ARMA lattice filters. It consists of several identical sections, one for each channel, pipelined in a circular manner, and is therefore well suited for implementation in modular architecture.>