Opportunistic managed access to local in-network compute resources can improve the performance of distributed applications and reduce the dependence on shared network resources. Instead of backhauling application data to a centralized cloud data center for processing, networked services may be adaptively and continuously dispersed into shared compute resources that are closer to the source of need. While this approach has several benefits, support for mission-aware access to computation is often an afterthought, and is implemented as a brittle extension over traditional load-balancer solutions.In this work, we investigate the design of two priority-aware resource allocation strategies and two load-balancing dispatching strategies as first class citizens in an open-source dispersed computing middleware. We present a control theoretic analysis of these load-balancing primitives to identify weaknesses and strengths in our design, and recommend future directions. In parallel, we prototype two priority-aware allocation algorithms to validate our priority predictions. In initial experiments our prototype shows substantial gains in processing prioritized load. Finally, we make our source-code and experimental configurations open source.

We consider the problem of recovering the superposition of R distinct complex exponential functions from compressed non-uniform time-domain samples. Total Variation (TV) minimization or atomic norm minimization was proposed in the literature to recover the R frequencies or the missing data. However, in order for TV minimization and atomic norm minimization to recover the missing data or the frequencies, the underlying R frequencies are required to be well-separated, even when the measurements are noiseless. This paper shows that the Hankel matrix recovery approach can super-resolve the R complex exponentials and their frequencies from compressed nonuniform measurements, regardless of how close their frequencies are to each other. We propose a new concept of orthonormal atomic norm minimization (OANM), and demonstrate that the success of Hankel matrix recovery in separation-free super-resolution comes from the fact that the nuclear norm of a Hankel matrix is an orthonormal atomic norm. More specifically, we show that, in traditional atomic norm minimization, the underlying parameter values must be well separated to achieve successful signal recovery, if the atoms are changing continuously with respect to the continuously-valued parameter. In contrast, for the OANM, it is possible the OANM is successful even though the original atoms can be arbitrarily close.

We consider the problem of optimal precoder design for a multi-input single-output wideband wireless system to maximize two different figures of merit: the total communication capacity and the total received power, subject to individual power constraints on each transmit element. We show that the two optimal precoders satisfy a separation principle that reveals a simple structure for these precoders. We use this separation principle extensively to derive several interesting properties of these two optimal precoders. Some key analytical results are as follows. We show that the power-maximizing precoders must concentrate all their energy in a small number of active channels that cannot exceed the number of input terminals. The capacity-maximizing precoder turns out to be very different from the classical water filling solutions and also very different from the power-maximizing precoders except at asymptotically low SNRs where the power-maximizing precoders also maximize capacity. We also show that the capacity of the wideband system is lower bounded by the sum rate of a multiple-access channel with the same channel gains and power constraints. Finally, the separation principle also yields simple fixed-point algorithms that allow for the efficient numerical computation of the two optimal precoders.

We consider distributed nullforming using an array of wireless transmitters that coordinate their transmissions to achieve destructive interference at a designated receiver. We describe the first experimental demonstration of distributed nullforming to a target receiver from an array of three distributed transmitters using (mostly) off-the-shelf hardware and simple and standard signal processing techniques. We are motivated by the goal of using distributed arrays to achieve increased spectrum reuse through interference cancellation. Our results show interference suppression in excess of 25dB over uncoordinated transmission. We build on our recent experimental demonstration of beamforming from a distributed antenna array after estimating and compensate for the combined effects of unknown propagation channels, hardware mismatches and clock drifts between the array nodes. The transmitters do not share clocks or have any wired back channels. They coordinate achieve nullforming entirely using in-band wireless message exchanges. Thus these methods can be implemented on portable mobile devices rather than being limited to Base Stations.

We consider the problem of multicasting a common message signal from a distributed array of wireless transceivers by beamforming to a set of beam targets, while simultaneously protecting a set of null targets by nullforming to them. We describe a distributed algorithm in which each transmitter iteratively adapts its complex transmit weight using common aggregate feedback messages broadcast by the targets, and the local knowledge of only its own channel gains to the targets. This knowledge can be obtained using reciprocity without any explicit feedback. The algorithm minimizes the mean square error between the complex signal amplitudes at the targets and their desired values. We prove convergence of the algorithm, present geometric interpretations, characterize initializations that lead to minimum total transmit power, and prescribe designs for such initializations. We show that the convergence speed is nondecreasing in the number of transmitters N if a step size parameter is kept constant. For Rayleigh fading channels, as N goes to infinity: 1) convergence can be made arbitrarily fast and 2) beams and nulls can be achieved with vanishing total transmit power even with noise, both with probability one. These results add up to some remarkable scalability properties: the feedback overhead does not grow with the number of transmitters, and with high probability, the algorithm can be configured to converge arbitrarily fast and use vanishingly small total transmit power.

Most prior research in distributed beamforming involves narrowband, frequency nonselective, channels, with the goal of sending a common message from cooperating nodes so that phases of the signals transmitted from the different nodes align at the receiver. The performance metric is the received SNR (directly related to the Shannon capacity for an AWGN channel). This "coherence metric" is maximized when each transmitter compensates its channel phase to the receiver, while transmitting at maximum allowable power. In this paper, we consider the problem of distributed transmit beam-forming over broadband, frequency selective channels, defining the coherence metric as the Shannon capacity, to be maximized subject to a power constraint at each transmitter. OFDM provides a natural decomposition of such channels into narrowband subchannels, hence the problem reduces to determining how each transmitter allocates its power across subchannels. A key technical result is that the optimal solution obeys a separation property that significantly simplifies computation. We show that it differs from classical water-filling due to the per-transmitter power constraints of the distributed beamforming setting. We compare it both structurally and numerically, to a centralized beamforming system with power constraint across transmitters. This is like waterfilling and upper bounds the performance of our setup.

We provide a two-step approach to recover a jointly k-sparse matrix X, (at most k rows of X are nonzero), with rank r <; <; k from its under sampled measurements. Unlike the classical recovery algorithms that use the same measurement matrix for every column of X, the proposed algorithm comprises two stages, in each of which the measurement is taken by a different measurement matrix. The first stage uses a standard algorithm, [4] to recover any r columns (e.g. the first r) of X. The second uses a new set of measurements and the subspace estimate provided by these columns to recover the rest. We derive conditions on the second measurement matrix to guarantee perfect subspace aware recovery for two cases: First a worst-case setting that applies to all matrices. The second a generic case that works for almost all matrices. We demonstrate both theoretically and through simulations that when r <; <; k our approach needs far fewer measurements. It compares favorably with recent results using dense linear combinations, that do not use column-wise measurements.

Despite intensive research in the area of network connectivity, there is an important category of problems that remain unsolved: how to characterize and measure the quality of connectivity of a wireless network which has a realistic number of nodes, not necessarily large enough to warrant the use of asymptotic analysis, and which has unreliable connections, reflecting the inherent unreliability of wireless communications? The quality of connectivity measures how easily and reliably a packet sent by a node can reach another node. It complements the use of capacity to measure the quality of a network in saturated traffic scenarios and provides an intuitive measure of the quality of (end-to-end) network connections. In this paper, we introduce a probabilistic connectivity matrix as a tool to measure the quality of network connectivity. Some interesting properties of the probabilistic connectivity matrix and their connections to the quality of connectivity are demonstrated. We demonstrate that the largest magnitude eigenvalue of the probabilistic connectivity matrix, which is positive, can serve as a good measure of the quality of network connectivity. We provide a flooding algorithm whereby the nodes repeatedly flood the network with packets, and by measuring just the number of packets a given node receives, the node is able to asymptotically estimate this largest eigenvalue.

We consider the problem of multicasting a common message signal to a set of designated receivers from a distributed antenna array, while simultaneously forming nulls to another set of null targets. We propose an algorithm under which each transmitter in the distributed array iteratively makes an incremental adjustment to its complex gain (which controls the amplitude and phase of its transmitted RF signal). The cumulative effect of these incremental adjustments is that the individual transmitted RF signals from the transmitters add up at the intended receivers to a desired SNR level, while simultaneously canceling each other perfectly at the null targets. A crucial feature of this algorithm is that it can be implemented in a purely distributed fashion at each transmitter using only an estimate of its own channel gain to each receiver, and an aggregate feedback signal from each of the receivers that is broadcast to all the transmitters. This is an important advantage of our approach and assures its scalability; in contrast any non-iterative approach to the beam/nullforming problem requires knowledge of all channel gains - from all transmitters to all receivers - to be available at every transmitter.

We design optimal 2 × N (2 <; N) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by using only three of N observations at a given time, this minimizes the worst-case achievable estimation error. It also captures the problem of optimum sensor placement for monitoring a source located in a plane, when only a minimum number of required sensors are active at any given time. For arbitrary N ≥ 3, we derive the optimal matrices which minimize the maximum condition number of all the submatrices of three columns. Surprisingly, a uniform distribution of the columns is not the optimal design for odd N ≥ 7.

We consider the robust localization of radioactive sources by using their gamma-ray count at the smallest number of sensors needed to theoretically localize. We formulate a class of non-convex cost functions and consider their gradient descent optimization. We show that in N-dimensions, if there are exactly N + 1 sensors and the source lies in their open convex hull, then this convex hull is devoid of false stationary points. Thus we augment gradient descent with random projections into the convex hull, when an estimate leaves it. We argue that convergence in probability to the correct source location, will occur. Simulations demonstrate the efficacy of this algorithm.

This work studies the problem of tracking signal-emitting mobile targets using navigated mobile sensors based on signal reception. Since the mobile target's maneuver is unknown, the mobile sensor controller utilizes the measurement collected by a wireless sensor network in terms of the mobile target signal's time of arrival (TOA). The mobile sensor controller acquires the TOA measurement information from both the mobile target and the mobile sensor for estimating their locations before directing the mobile sensor's movement to follow the target. We propose a min-max approximation approach to estimate the location for tracking which can be efficiently solved via semidefinite programming (SDP) relaxation, and apply a cubic function for mobile sensor navigation. We estimate the location of the mobile sensor and target jointly to improve the tracking accuracy. To further improve the system performance, we propose a weighted tracking algorithm by using the measurement information more efficiently. Our results demonstrate that the proposed algorithm provides good tracking performance and can quickly direct the mobile sensor to follow the mobile target.

Despite intensive research in the area of network connectivity, there is an important category of problems that remain unsolved: how to measure the quality of connectivity of a wireless multi-hop network which has a realistic number of nodes, not necessarily large enough to warrant the use of asymptotic analysis, and has unreliable connections, reflecting the inherent unreliable characteristics of wireless communications? The quality of connectivity measures how easily and reliably a packet sent by a node can reach another node. It complements the use of capacity to measure the quality of a network in saturated traffic scenarios and provides a native measure of the quality of (end-to-end) network connections. In this paper, we explore the use of probabilistic connectivity matrix as a tool to measure the quality of network connectivity. Some interesting properties of the probabilistic connectivity matrix and their connections to the quality of connectivity are demonstrated. We show that the largest eigenvalue of the probabilistic connectivity matrix can serve as a good measure of the quality of network connectivity.

Distributed beamforming requires phase and frequency synchronization. As oscillators drift, through Brownian motion induced phase noise, their instantaneous phases must be tracked and compensated. Several papers and IEEE 1588 have proposed Kalman Filter (KF) based tracking algorithms using the unwrapped phase measurements. This paper quantifies the effect of Brownian Motion induced drift at two levels. First we derive Cramer-Rao Lower Bounds (CRLB) manifest in one shot estimation of frequency and phase from unwrapped phase observations, and reveal fundamental and illuminating differences with the existing frequency and phase estimation CRLBs in the literature derived in the absence of Brownian motion. Second, we consider a KF that tracks the instantaneous phase in intervals where there is no beamforming, and is switched off during beamforming. Bounds are derived relating the error growth as a function of the underlying duty cycle.

We explore a class of techniques for distributed transmit beamforming where the beamforming target sends cumulative feedback that is broadcast to all of the beamforming nodes. The simplest technique in this class is a 1-bit RSS feedback algorithm that has been studied in detail in the literature. Under this 1-bit algorithm, transmitters make random phase perturbations and the receiver periodically sends 1 bit of feedback indicating whether the received signal strength has increased or not compared to what was observed in the past. While this simple algorithm has very attractive properties such as dynamic tracking of time-varying phases, robustness to noise and other disturbances and is also simple to implement, we show in this paper that it also has serious limitations such as slow convergence and poor tracking performance in the presence of frequency offsets between the transmitters. We then show that enhanced feedback algorithms where the receiver sends as feedback several bits of feedback indicating the amplitude and phase of the received signal over time, are able to achieve beamforming in the presence of frequency offsets and large feedback channel latencies, while retaining the scalability and robustness of the 1-bit algorithm.

In this work, we study the localization of mobile signal emitters using time of arrival (TOA) measurement and additional urban street information. Two algorithms are proposed to improve the localization performance by integrating street information with the TOA measurement. The first algorithm exhaustively searches of all possible road paths. For each possible path, the source location is estimated based a semidefinite programming (SDP) algorithm by minimizing the maximum error measurement between the observed propagation time and the modeled propagation time. Only location on a street that satisfies the minimum mean square error yields estimation output. To reduce complexity, our second joint optimization algorithm combines the two steps together and jointly optimizes the path selection and source location. Numerical results show that both algorithms can improve the localization performance. Our proposed joint optimization approach is more suitable for practical use because of lower complexity and good performance.

In this paper, we describe our ongoing work on designing an underwater sensor network for monitoring the ecosystem of the Mississippi river using freshwater mussels as biological sensors.

We describe the key ideas behind our implementation of distributed beamforming on a GNU-radio based software-defined radio platform. Distributed beamforming is a cooperative transmission scheme whereby a number of nodes in a wireless network organize themselves into a virtual antenna array and focus their transmission in the direction of the intended receiver, potentially achieving orders of magnitude improvements in energy efficiency. This technique has been extensively studied over the past decade and its practical feasibility has been demonstrated in multiple experimental prototypes. Our contributions in the work reported in this paper are three-fold: (a) the first ever all-wireless implementation of distributed beamforming without any secondary wired channels for clock distribution or channel feedback, (b) a novel digital baseband approach to synchronization of high frequency RF signals that requires no hardware modifications, and (c) an implementation of distributed beamforming on a standard, open platform that allows easy reuse and extension. We describe the design of our system in detail, present some initial results and discuss future directions for this work.

We investigate the problem of source localization based on measuring time difference of signal arrivals (TDOA) from the source emitter. Taking into account the colored measurement noise, we adopt a min-max principle to develop two lower complexity semidefinite relaxation algorithms that can be reliably solved using semidefinite programming. The reduction of algorithm complexity is achieved through a simple, but effective method to select a reference node among participating measurement nodes such that only selective time differences of signal arrival are exploited. Our estimation methods are insensitive to the source locations and can be used either as the final location estimate or as the initial point for more traditional search algorithms.

Wireless source localization has found a number of applications in wireless sensor networks. In this work, we investigate source localization based on the practical time of arrival (TOA) measurement model. Unlike most existing works that transform TOA measurement into time differences before processing, we consider the original measurement model and investigate three methods for direct source localization. We also derive the Cramér-Rao lower bound (CRLB) under the TOA model and establish its connection with the CRLB under the more commonly used time-difference of arrival (TDOA) signal model. We present results that illustrate the performance advantage of source localization based on the original TOA model over the commonly used TDOA pre-processing.

Wireless source localization has found a number of applications in wireless sensor networks. In this work, we investigate robust and low complexity solutions to the problem of source localization based on the time-difference of arrivals (TDOA) measurement model. By adopting a min-max approximation to the maximum likelihood source location estimation, we develop two low complexity algorithms that can be reliably and rapidly solved through semi-definite relaxation. Our approach hinges on the use of a reference sensor node which can be optimized according to the Cramer-Rao lower bound or selected heuristically. Our low complexity estimate can be used either as the final location estimation output or as the initial point for other traditional search algorithms.

In source localization, one estimates the location of a source using a variety of relative position information. Many algorithms use certain powers of distances to effect localization. In practice, exact distance measurement is not directly available and must be estimated from information such as received signal strength (RSS), time of arrival, or time difference of arrival. This letter considers bias and variance issues in estimating powers of distances from RSS affected by practical log-normal shadowing. We show that the underlying estimation problem is inefficient and that the maximum likelihood estimate yields a bias and a mean-square error (MSE) that both increase exponentially with the noise power. We then characterize the class of unbiased estimates and show that there isonlyoneestimatorinthisclass, but that its MSE also grows exponentially with the noise power. Finally, we provide the linear minimum mean-square error (MMSE) estimate and show that its bias and MSE are both bounded in the noise power.

We propose a novel approach to the source localization and tracking problem in wireless sensor networks. By applying minimax approximation and semidefinite relaxation, we transform the traditionally nonlinear and nonconvex problem into convex optimization problems for two different source localization models involving measured distance and received signal strength. Based on the problem transformation, we develop a fast low-complexity semidefinite programming (SDP) algorithm for two different source localization models. Our algorithm can either be used to estimate the source location or be used to initialize the original nonconvex maximum likelihood algorithm.

We present an effective method for time domain channel estimation of wireless orthogonal frequency division multiplexing (OFDM) system. Relying on a bent-pipe mechanism, the mobile receiver sends a fraction of the received data back to the base station which can then estimate both the forward link and reserve link channel impulse responses. Given knowledge on the forward link channel response, the resource rich base station can employ effective adaptive modulation schemes to increase OFDM system capacity. In this paper, closed-form expressions for channel estimation Cramer Rao lower bound are derived for the feedback system. Impact of feedback parameters on channel estimation performance is discussed through Cramer Rao bound analysis and simulation. Identifiability issues associated with power loaded multicarrier systems are also addressed. Simulation results on the proposed feedback channel estimation scheme are shown.

This paper considers localization of a source or a sensor from distance measurements. We argue that linear algorithms proposed for this purpose are susceptible to poor noise performance. Instead given a set of sensors/anchors of known positions and measured distances of the source/sensor to be localized from them, we propose a potentially nonconvex weighted cost function whose global minimum estimates the location of the source/sensor one seeks. The contribution of this paper is to provide nontrivial ellipsoidal and polytopic regions surrounding these sensors/anchors of known positions, such that if the object to be localized is in this region localization occurs by globally convergent gradient descent. This has implication to the deployment of sensors/anchors to achieve a desired level of geographical coverage.

We consider the design of optimum ISI-free, discrete multitone transmission (DMT) systems designed to achieve a quality of service (QoS) requirement quantified by bit rate and symbol error rate specifications. The optimality is in the sense of minimizing the transmitted power given the QoS specifications subject to the knowledge of the channel and colored interference at the receiver input of the DMT system. Earlier papers, obtained their optimum DMT design based on approximations that included high bit rates and/or real (as opposed to integer) bit loading schemes, and showed that orthonormal transforms suffice for optimality. In this paper we relax both the high bit rate and the integer bitloading approximation, and provide sufficient conditions on the underlying modulation schemes for which orthonormal DMT remains optimum.

In this paper we present an efficient bitloading algorithm that applies to both subband coding and multicarrier communication. The goal is to effect an optimal distribution of positive integer bit values among various subchannels to achieve a minimum distortion error variance for subband coding and transmitted power for multicarrier communications. Existing algorithms in the literature grow with the total number of bits that must be distributed. The novelty of our algorithm lies in the fact that its complexity is independent of the total number of bits to be allocated

We consider the design of optimum discrete multitone (DMT) systems supporting multiple services with potentially differing quality of service (QoS) requirements. With the knowledge of channel and colored interference at the receiver input of the DMT system, our goal is to minimize the transmitted power while holding QoS specifications for different users. With redundancy in the form of a cyclic prefix, an optimum bit loading scheme, subchannel assigning scheme and transceiver design are found for DMT systems. As with our previous study involving zero padding redundancy, the key conclusions are: (i) the optimum transceiver is unaffected by changing service characteristics, and depends only on the channel and interference conditions; (ii) the QoS requirements, the number of users and the number of subchannels assigned to the different users only affect bitloading and subchannel assignment.

Broad-band wireless communication systems can effectively utilize transmitter precoding to compensate severe channel distortions based on forward link channel estimate. We demonstrate the integration of precoded transmission into a duplex channel estimation mechanism using bent-pipe signal feedback. We also present an effective fractionally spaced precoder design based on the base station transmitter estimation of the downlink channel. We focus on feedback of fractionally spaced samples and demonstrate the significant improvement when the channel estimator is given access to the precoder and filters used by the wireless transmitters.

In this paper, we present an efficient bit loading algorithm for subband coding. The goal is to effect an optimal distribution of positive integer bit values among various subchannels to achieve a minimum distortion error variance. Existing algorithms in the literature grow with the total number of bits that must be distributed. The novelty of our algorithm lies in the fact that its complexity is independent of the total number of bits to be allocated.

A recent development by Xu et al. presented an effective forward channel identification method in duplex wireless mobile communications. By letting the mobile receiver send a fraction of the received data back to the base station, both forward and reverse channel identification can be achieved at the base transmitter. In this work, we extend this bent-pine feedback approach to accommodate fractionally spaced sampling and to utilize known pulse shape for better performance. We demonstrate that the new method requires minor modification on the system structure. Furthermore, with the fractionally spaced channel output, we can use the known information such as the pulse shaping filter and anti-aliasing filter to improve the channel identification and significantly reduce the needed data sample size.

We present a novel dual-channel identification approach for mobile wireless communication systems. Unlike traditional channel-estimation methods that rely on training symbols, we propose a bent-pipe feedback mechanism which requires the mobile station (MS) to send portions of its received signal back to the base station (BS) for wireless channel identification. Using a filter-bank decomposition concept, we introduce an effective algorithm that can identify both the forward and the reverse channels based only on this feedback information. This new method permits transfer of computational burden from the MS to the resource-rich BS, and leads to significant savings in bandwidth-consuming training signals.

This paper considers the design of biorthogonal DMT multicarrier transceiver systems supporting multiple services. The supported user services may have differing quality of service (QoS) requirements, quantified in this paper by bit rate and symbol error rate specifications. To reflect their service priorities, different users on the system can be potentially assigned different number of subchannels. Our goal is to minimize the transmitted power given the QoS specifications for the different users, subject to the knowledge of colored interference at the receiver input of the DMT system. In particular we find an optimum bit loading scheme that distributes the bit rate transmitted across the various subchannels belonging to the different users, and subject to this bit allocation, determine an optimum transceiver. This work differs from our prior work where the same number of subchannels were assigned to each user.

We have previously presented a novel dual channel identification approach for mobile wireless communication systems (Xu, H. et al., Proc. ICC, vol.8, p.2443-8, 2001). Unlike traditional channel estimation methods that rely on training symbols, this approach used a bent-pipe feedback mechanism requiring the mobile station (MS) to send portions of its received signal back to the base station (BS) for wireless channel identification. Using a filter-bank decomposition concept, we introduced an effective algorithm for identifying both the forward and the reverse channels based only on this feedback information. This new method permits transfer of the computational burden from the MS to the resource rich BS and leads to significant savings in bandwidth consuming training signals. This paper proposes a more informative feedback method leading to significant performance improvement over our earlier scheme.

This paper considers the design of multicarrier transceiver systems like OFDM/DMT supporting multiple users. The supported users may have differing quality of service (QoS) requirements, quantified by their respective bit rate and symbol error rate specifications. Different users on the system can be potentially assigned different number of subchannels, to reflect their service priorities. Our goal is to minimize the transmitted power given the QoS specifications for the different users, subject to the knowledge of colored interference at the receiver input of the OFDM system. In particular we find an optimum bit loading scheme that distributed the bit rate transmitted across the various subchannels belonging to the different users, and subject to this bit allocation, determine an optimum transceiver.

We provide a complete characterization of discrete multitone transmission (DMT) systems that employ a cyclic prefix redundancy and that can be equalized by a bank of one-tap equalizers in each subchannel, for almost all values of channel parameters. We show that among all possible finite-impulse response transmitting and receiving filters of arbitrary order, such channel-resistant transmission requires 1) that the receive filters be matched to the transmit filters and 2) that to within a scaling and delay, the transmit and receive filters have inverse discrete Fourier transform and discrete Fourier transform (DFT) coefficients. Thus, we prove that, should cyclic prefix be applied, only trivial variants of traditional DFT-based DMT systems are channel resistant.

The paper considers discrete multitone (DMT) modulation for multiuser communications when multiple users are supported by the same system, a zero-padding redundancy is employed at the transmitter output, and linear redundancy removal is used at the channel output. These users may have differing quality of service (QoS) requirements, as quantified by bit rate and symbol-error rate specifications, and are each assigned an equal number of subchannels. Our goal is to minimize the transmitted power, given the QoS specifications and subject to the knowledge of the channel and the second-order statistics of the colored interference at the receiver input. In particular, we find an optimum bit-loading scheme that distributes the bit rate transmitted across the various subchannels belonging to each user, and, subject to this bit allocation, we determine the precise subchannels assigned to each user, the optimum transceiver characterized by the input/output block transforms, and the redundancy removal operation. A major conclusion is that even though the optimum bit-rate allocation differs from the single-user case, the optimum transceiver does not. Further, it is determined entirely by the channel and interference conditions, and is unaffected by the QoS requirements.

Integral quadratic constraints (IQC) arise in many optimal and/or robust control problems. The IQC approach can be viewed as a generalization of the classical multiplier approach in the absolute stability theory. In this paper, we study the relationship between the two approaches for robust stability analysis. The key result shows that for many applications, the existence of an IQC is equivalent to the existence of a multiplier. Because the multiplier approach is typically simpler and more intuitive, this result suggests that the multiplier approach may be more useful than the IQC approach in many applications.

This paper considers the energy compaction problem for wide-sense cyclostationary (WSCS) signals. Periodic Nyquist-N filters and optimum compaction filters are defined and their properties examined. A procedure for designing compaction filters is given, and application to subband coding of WSCS signals is explored.

This paper considers the blind equalization problem for nonlinear Volterra type channels excited by real IID (independent and identically distributed) symbols. Previous work has shown that under the right conditions the equalizers can be found from the second order statistics of the channel output as long as the number of subchannels exceeds the number of kernels. In order to alleviate this requirement, we consider the use of a simple precoding device previous to transmission which provides a tradeoff between effective data rate and number of subchannels required. Necessary and sufficient conditions for blind equalizability under this scheme are given, and an algorithm for the computation of the equalizers is presented.

This paper considers discrete multitone (DMT) modulation for multiuser communications where different users are supported by the same system. These users may have differing quality of service (QoS) requirements, as quantified by their respective bit rate and symbol error rate specifications. Our goal is to minimize the transmitted power given the QoS specifications for the different users, subject to the knowledge of colored interference at the receiver input. In particular we find an optimum bit loading scheme that distributes the bit rate transmitted across the various subchannels belonging to the different users, and subject to this bit allocation, determine an optimum transceiver.

We present a novel dual channel identification approach for fast time-varying wireless communication systems. Unlike traditional channel methods that rely on training symbols, we propose a bent-pipe feedback mechanism which requires the mobile unit to send portions of its received signal back to the transmitter for wireless channel identification. Using a filter-bank decomposition concept, we introduce an effective algorithm that can identify both the forward and the reverse channels based only on this feedback information without reverse-link training. This new method has great potential in the design of future high data rate wireless communication systems.

Potential applications of blind channel identification and equalizationinwireless communication systems have been recently explored. For multi-user systems that areirreducible and column-reduced,second order statistical methods normally can identify channel dynamics up to a unitary mixing matrix. In this paper, we investigate the equalizability of desired users and the cancellation of unwanted interfering signals basedonsecond order output statistics. We show that a desired user channel can beequalizedifithas the longest memory. Furthermore, interfering user signals can becancelled under a morerelaxed multi-user channel condition.

We explore the utility of second-order statistics for blind identification/equalization of nonlinear channels. Under standard assumptions it is shown that the channel cannot be identified to within a scaling factor from the output second order statistics, but that the ambiguity is at a level that permits equalization. We show that these results cover cases that the prior literature does not address.

We consider the optimal orthonormal subband coding of zero mean cyclostationary signals, with N-periodic second order statistics. A 2-channel uniform filter bank, with N-periodic analysis and synthesis filters, is used as the subband coder. A dynamic scheme involving N-periodic bit allocation is employed. An average variance condition is used to measure the output distortion. The conditions for maximizing the coding gain parallel those for the case when the signals are wide sense stationary (WSS) and the analysis and synthesis filters and the bit allocation time invariant, in that the blocked subband signals must be decorrelated and the subband power spectral densities must obey an ordering. Some additional conditions on this ordering, over and above those required for the WSS case, are needed.

This work provides conditions on the input sequence that ensure the exponential asymptotic stability of the inverse of the forward prediction error filter obtained by means of the recursive weighted least squares algorithm. Note that this filter is in general time-varying. Thus this result is a natural extension to the well-known minimum phase property of forward prediction error filters obtained by the autocorrelation method.

This paper proposes a new lattice filter structure that has the following properties. When the filter is linear time invariant (LTI), it is equivalent to the celebrated Gray-Markel lattice. When the lattice parameters vary with time it sustains arbitrary rate of time variations without sacrificing a prescribed degree of stability, provided that the lattice coefficients are magnitude bounded in a region where all LTI lattices have the same degree of stability. We also show that the resulting linear time varying (LTV) lattice obeys an energy contraction condition. This structure thus generalizes the normalized Gray-Markel lattice which has similar properties but only with respect to stability as opposed to relative stability.

Some previous works have shown that under an autoregressive constraint on the input signal, least-squares equation-error methods provide stable models of the estimated transfer function. We present an alternative proof of this fact which allows one to increase the order of the autoregressive input by one, for both the monic and unit-norm approaches.

We consider the optimal orthonormal subband coding of zero mean wide sense cyclostationary signals (WSCS), with N-periodic second order statistics. An M-channel uniform filterbank, with N-periodic analysis and synthesis filters, is used as the subband coder. A static bit allocation scheme is used. An average variance condition is used to measure the output distortion. The conditions for maximizing the coding gain parallel those for the case when the signals are wide sense stationary (WSS) and the analysis and synthesis filters and the bit allocation time invariant.

This paper contains results on the design of optimum equalizers to eliminate intersymbol interference in linear non-minimum phase channels conveying binary signals. The optimization is with respect to an open eye condition with a given delay. For causal stable channels with non-minimum phase zeros, we argue that this problem requires only the consideration of the FIR modified channel that has all the non-minimum phase zeros of the original channel. We show that if this modified channel can be equalized to yield an equalized system that is open eye with a specified delay, then the optimizing equalizer is, in fact FIR with all zeros outside the unit circle, and the impulse response of the equalised channel does not extend beyond the delay. We also give a simple necessary and sufficient condition to determine if for a particular delay, a given channel can be equalized to achieve an equalized response that is open eye.

It is well known that the standard equation-error (EE) method for the identification of linear systems yields biased estimates if the data are noise corrupted. Due to this bias, the resulting estimate can be unstable in some cases, depending on the spectral characteristics of the input and the noise, the signal-to-noise ratio (SNR), and the unknown system. The set of all-pole linear systems whose equation-error estimate is stable for all wide sense stationary inputs and white measurement noise is investigated. Some results concerning the structure of this set are given.

We consider a multi-input, multi-output lattice realization for linear time-varying analysis banks which are all pass. Such a realization was given by Vaidyanathan and Mitra (1985) for linear time invariance (LTI) systems; and under certain conditions generalizes to the linear time varying (LTV) case. Moreover, our implementation is simpler than the one presented by Vaidyanathan et al. Finally, we describe the anticausal inverse of a lattice realization which is used in the synthesis bank.

We consider adaptive periodic IIR filtering and present an extension of the hyperstable adaptive recursive filter (HARF). We give conditions for convergence of the parameter estimate error, involving passivity of certain operators in the identification loop, identifiability of the system parameters, and persistent excitation (PE). A necessary and sufficient condition for identifiability is given and subject to its satisfaction, input-only conditions guaranteeing PE are given.

This paper gives a sufficient condition on the average rate of quantizer step size adaptation rate that preserves adaptive differential pulse code modulated (ADPCM) stability under the assumption that the predictor is nonadaptive. The result appeals to some new developments in the passivity analysis of linear time varying systems.

A procedure for the adaptation of multistage multirate filters is developed in the context of a system identification perspective. The system to be identified is the cascade of a multistage decimator followed by a multistage interpolator. For this structure, an identifiability condition is established which is sufficient to guarantee that the stagewise systems may be uniquely determined from input-output data in the ideal, exact model order case. An algorithm is then described that achieves exponential convergence of the system parameter estimates to their desired values given satisfaction of these identifiability conditions.

An adaptive approach for estimating all (or some) of the orthogonal eigenvectors of the data covariance matrix (of a time series consisting of real narrowband signals in additive white noise) is presented. The inflation approach is used to estimate each of these vectors as minimum eigenvectors (eigenvectors corresponding to the minimum eigenvalue) of appropriately constructed symmetric positive definite matrices. This reformulation of the problem is made possible by the fact that the problem of estimating the minimum eigenvector of a symmetric positive definite matrix can be restated as the unconstrained minimization of an appropriately constructed nonlinear nonconvex cost function. The modular nature of the algorithm that results from this reformation makes the proposed approach highly parallel, resulting in a high-speed adaptive approach for subspace estimation.>

A class of symmetric Hopfield networks with nonpositive synapses and zero threshold is analyzed in detail. It is shown that all stationary points have a one-to-one correspondence with the minimal vertex covers of certain undirected graphs, that the sequential Hopfield algorithm as applied to this class of networks converges in at most 2n steps (n being the number of neurons), and that the parallel Hopfield algorithm either converges in one step or enters a two-cycle in one step. The necessary and sufficient condition on the initial iterate for the parallel algorithm to converge in one step are given. A modified parallel algorithm which is guaranteed to converge in [3n/2] steps ([x] being the integer part of x) for an n-neuron network of this particular class is also given. By way of application, it is shown that this class naturally solves the vertex cover problem. Simulations confirm that the solution provided by this method is better than those provided by other known methods.

The sign-sign adaptive least-mean-square (LMS) identifier filter is a computationally efficient variant of the LMS identifier filter. It involves the introduction of signum functions in the traditional LMS update term. Consideration is given to global convergence of parameter estimates offered by this algorithm, to a ball with radius proportional to the algorithm step size for white input sequences, specially from Gaussian and uniform distributions.>

One of the simplest optimization problems solved by Ising spin models of neural memory is associative memory retrieval. The authors study deterministic convergence properties of the Hopfield synchronous retrieval algorithm for such models. In this case a memory, stored in the network by an appropriate choice of connections, is retrieved by setting the neural outputs to the binary pattern of the recall key (probe) and allowing the network to converge to a stable state. Precise conditions are developed that ensure that all stored memories are fixed points of the retrieval algorithm. An orthogonality-nearness criterion is then obtained for a memory probe itself to be a stationary point and thus outside the error-correcting capability of the memory. A local stability result quantifies the spatial relationship required for fast convergence.>

Continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances. An algorithm which eliminates these difficulties is investigated. Based on a set theoretic assumption, the algorithm yields modified least-squares estimates with a forgetting factor. It updates the estimates selectively depending on whether the observed data contain sufficient information. The information evaluation required at each step involves very simple computations. In addition, the parameter estimates are shown to converge asymptotically, at an exponential rate, to a region around the true parameter.