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Estimation of third-order statistics relies on the availability of a huge amount of data records, which can pose severe challenges on the data collecting hardware in terms of considerable storage costs, overwhelming energy consumption, and unaffordably high sampling rate especially when dealing with high-dimensional data such as wideband signals. To overcome these challenges, this paper focuses on the reconstruction of the third-order cumulants under the compressive sensing framework. Specifically, this paper derives a transformed linear system that directly connects the cross-cumulants of compressive measurements to the desired third-order statistics. We provide sufficient conditions for lossless third-order statistics reconstruction via solving simple least-squares, along with the strongest achievable compression ratio. To reduce the computational burden, we also propose an approach to recover diagonal cumulant slices directly from compressive measurements, which is useful when the cumulant slices are sufficient for the inference task at hand. All the proposed techniques are tested via extensive simulations. The developed joint sampling and reconstruction approach to third-order statistics estimation is able to reduce the required sampling rates significantly by exploiting the cumulant structure resulting from signal stationarity, even in the absence of any sparsity constraints on the signal or cumulants.

In this paper, we propose a weighted alternating direction method of multipliers (ADMM) to solve the consensus optimization problem over a decentralized network. In the proposed algorithm, every node holds its local objective function, exchanges its current iterate with a subset of neighbors, carries on local computation, and eventually reaches an optimal and consensual solution that minimizes the summation of the local objective functions. Compared with the conventional ADMM that is popular in decentralized network optimization, the weighted ADMM is able to reduce the communication cost spent in the optimization process through tuning the weight matrices, which assign beliefs on the neighboring iterates. We first prove convergence and establish linear convergence rate of the weighted ADMM. Second, we maximize the derived convergence speed and obtain the best weight matrices on a given topology. Third, observing that exchanging information with all the neighbors is expensive, we maximize the convergence speed while limit the number of communication arcs. This strategy finds a subset of arcs within the underlying topology to fulfill the optimization task while leads to a favorable tradeoff between the number of iterations and the communication cost per iteration. Numerical experiments demonstrate advantages of the weighted ADMM over its conventional counterpart in expediting the convergence speed and reducing the communication cost.

This paper develops an optimal decentralized algorithm for sparse signal recovery and demonstrates its application in monitoring localized phenomena using energy-constrained large-scale wireless sensor networks. Capitalizing on the spatial sparsity of localized phenomena, compressive data collection is enforced by turning off a fraction of sensors using a simple random node sleeping strategy, which conserves sensing energy and prolongs network lifetime. In the absence of a fusion center, sparse signal recovery via decentralized in-network processing is developed, based on a consensus optimization formulation and the alternating direction method of multipliers. In the proposed algorithm, each active sensor monitors and recovers its local region only, collaborates with its neighboring active sensors through low-power one-hop communication, and iteratively improves the local estimates until reaching the global optimum. Because each sensor monitors the local region rather than the entire large field, the iterative algorithm converges fast, in addition to being scalable in terms of transmission and computation costs. Further, through collaboration, the sensing performance is globally optimal and attains a high spatial resolution commensurate with the node density of the original network containing both active and inactive sensors. Simulations demonstrate the performance of the proposed approach.

With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultra-wideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless services. Meanwhile, orthogonal pulse sets are often desired in order to apply high-rate multidimensional modulation and (carrier-free) orthogonal frequency-division multiple access. Motivated by these considerations, we suggest a digital finite impulse response (FIR) filter approach to synthesizing UWB pulses and propose filter design techniques by which optimal waveforms that satisfy the spectral mask can be efficiently obtained. For single pulse design, we develop a convex formulation for the design of the FIR filter coefficients that maximize the spectrum utilization efficiency in terms of both the bandwidth and power allowed by the spectral mask. For orthogonal pulse design, a sequential strategy is derived to formulate the overall pulse design problem as a set of convex subproblems, which are then solved in a sequential manner to yield a set of mutually orthogonal pulses. Our design techniques not only provide waveforms with high spectrum utilization and guaranteed spectral mask compliance but also permit simple modifications that can accommodate several other system objectives.

We investigate timing tolerances of ultra-wideband (UWB) impulse radios. We quantify the bit-error rate (BER) sensitivity to epoch timing offset under different operating conditions, including frequency-flat fading channels, dense multipath fading channels, multiple access with time hopping, and various receiver types including sliding correlators and RAKE combiners. For a general correlation-based detector, we derived in Part I unifying expressions for the decision statistics as well as BER formulas under mistiming, given fixed channel realizations. In Part II, we provide a systematic approach to BER analysis under mistiming for fading channels. The BER is expressed in terms of the receiver's energy capture capability, which we quantify under various radio operating conditions. We also develop the optimal demodulator in the presence of timing offset and show a proper design of the correlation-template that is robust to mistiming. Through analyses and simulations, we illustrate that the reception quality of a UWB impulse radio is highly sensitive to both timing acquisition and tracking errors.

We investigate timing tolerances of ultra wideband (UWB) impulse radios. We quantify the bit-error-rate (BER) sensitivity to epoch timing offset under different operating conditions, including frequency flat fading channels, dense multipath fading channels, multiple access with time hopping, and various receiver types including sliding correlators and RAKE combiners. Our systematic approach to BER derivations under mistiming can be extended to a wide range of channel fading types. Through analyses and simulations, we illustrate that the reception quality of a UWB impulse radio is highly sensitive to both timing acquisition and tracking errors. In particular, time-hopping-based multiple-access systems exhibit little tolerance to acquisition errors, and the energy capture capability of a RAKE combiner can be severely compromised by mistiming.

In this paper, we develop soft decision equalization (SDE) techniques for frequency selective multiple-input multiple-output (MIMO) channels in the quest for low-complexity equalizers with error performance competitive to that of maximum likelihood (ML) sequence detection. We demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered and linear in the signal constellation size. Building on the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. The first SDE algorithm adopts a zero-padded transmission structure to convert the challenging sequence detection problem into a block-by-block least-square formulation. It introduces key enhancement to the original PDA to enable applications in rank-deficient channels and for higher level modulations. The second SDE algorithm takes advantage of the Toeplitz channel matrix structure embodied in an equalization problem. It processes the data samples through a series of overlapping sliding windows to reduce complexity and, at the same time, performs implicit noise tracking to maintain near-optimum performance. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Simulation comparisons of our SDE methods with minimum-mean-square error (MMSE)-based MIMO DFE and sphere decoded quasi-ML detection are presented.

For code-division multiple access (CDMA) communication systems, many constrained linear receivers have been developed to suppress multiple access interference. The linearly constrained formulations are generally sensitive to multipath fading and other types of signal mismatch. We develop robust linear receivers by exploring appropriate constraints. Multiple linear constraints are exploited to preserve the output energy that is scattered in multipath channels. In addition, a quadratic inequality constraint on the weight vector norm is used to improve robustness with respect to imprecise signal modeling. These constraints can be applied to the minimum output energy (MOE) detector to mitigate the signal mismatch problem and to the decision directed minimum mean square error (MMSE) detector to prevent error propagation and eliminate the need for training sequences at startup. Adaptive implementations for the proposed detectors are presented using recursive least square (RLS) updating in both the direct form and the partitioned linear interface canceller (PLIC) structure. Simulations are performed in a multipath propagation environment to illustrate the performance of the proposed detectors.

Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power (LCMP) beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters. We propose a technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating. A variable diagonal loading term is added at each step, where the amount of loading has a closed-form solution. Simulations under different scenarios demonstrate that this algorithm has better interference suppression than both the RLS beamformer with no quadratic constraint and the RLS beamformer using the scaled projection technique, as well as faster convergence than LMS beamformers.