DSP Laboratory - DIEI

In this paper, coordinated beamforming based on relaxed zero forcing (RZF) for $K$ transmitter-receiver pair multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) interference channels is considered. In the RZF coordinated beamforming, conventional zero-forcing interference leakage constraints are relaxed so that some predetermined interference leakage to undesired receivers is allowed in order to increase the beam design space for larger rates than those of the zero-forcing (ZF) scheme or to make beam design feasible when ZF is impossible. In the MISO case, it is shown that the rate-maximizing beam vector under the RZF framework for a given set of interference leakage levels can be obtained by sequential orthogonal projection combining (SOPC). Based on this, exact and approximate closed-form solutions are provided in two-user and three-user cases, respectively, and an efficient beam design algorithm for RZF coordinated beamforming is provided in general cases. Furthermore, the rate control problem under the RZF framework is considered. A centralized approach and a distributed heuristic approach are proposed to control the position of the designed rate-tuple in the achievable rate region. Finally, the RZF framework is extended to MIMO interference channels by deriving a new lower bound on the rate of each user.

Superoscillating signals are band-limited signals that oscillate in some region faster their largest Fourier component. While such signals have many scientific and technological applications, their actual use is hampered by the fact that an overwhelming proportion of the energy goes into that part of the signal, which is not superoscillating. In the present paper, we consider the problem of optimization of such signals. The optimization that we describe here is that of the superoscillation yield, the ratio of the energy in the superoscillations to the total energy of the signal, given the range and frequency of the superoscillations. The constrained optimization leads to a generalized eigenvalue problem, which is solved numerically. It is noteworthy that it is possible to increase further the superoscillation yield at the cost of slightly deforming the oscillatory part of the signal, while keeping the average frequency. We show, how this can be done gradually, which enables a tradeoff between the distortion and the yield. We show how to apply this approach to nontrivial domains, and explain how to generalize this to higher dimensions.

This paper addresses the problem of parameter estimation in a quantized and online setting. A sensing unit collects random vector-valued samples from the environment. These samples are quantized and transmitted to a central processor which generates an online estimate of the unknown parameter. This paper provides a closed-form expression of the excess mean square error (MSE) caused by quantization in the high-rate regime i.e., when the number of quantization levels is supposed to be large. Next, we determine the quantizers which mitigate the excess MSE. The optimal quantization rule unfortunately depends on the unknown parameter. To circumvent this issue, we introduce a novel adaptive learning vector quantization scheme which allows to simultaneously estimate the parameter of interest and select an efficient quantizer.

We study how to invest optimally in a financial market having a finite number of assets from a signal processing perspective. Specifically, we investigate how an investor should distribute capital over these assets and when he/she should reallocate the distribution of the funds over these assets to maximize the expected cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using “threshold rebalanced portfolios”, where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are provided in the paper. As predicted from our derivations, we significantly improve the achieved wealth with respect to the portfolio selection algorithms from the literature on historical data sets under both mild and heavy transaction costs.

In multi-relay cooperative systems, the signal at the destination is affected by impairments such as multiple channel gains, multiple timing offsets (MTOs), and multiple carrier frequency offsets (MCFOs). In this paper we account for all these impairments and propose a new transceiver structure at the relays and a novel receiver design at the destination in distributed space-time block code (DSTBC) based amplify-and-forward (AF) cooperative networks. The Cramér-Rao lower bounds and a least squares (LS) estimator for the multi-parameter estimation problem are derived. In order to significantly reduce the receiver complexity at the destination, a differential evolution (DE) based estimation algorithm is applied and the initialization and constraints for the convergence of the proposed DE algorithm are investigated. In order to detect the signal from multiple relays in the presence of unknown channels, MTOs, and MCFOs, novel optimal and sub-optimal minimum mean-square error receiver designs at the destination node are proposed. Simulation results show that the proposed estimation and compensation methods achieve full diversity gain in the presence of channel and synchronization impairments in multi-relay AF cooperative networks.

Recently, optimal linearly constrained minimum variance (LCMV) filtering methods have been applied to fundamental frequency estimation. Such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid. In this paper, we therefore consider fast implementations of LCMV-based fundamental frequency estimators, exploiting the estimators' inherently low displacement rank of the used Toeplitz-like data covariance matrices, using as such either the classic time domain averaging covariance matrix estimator, or, if aiming for an increased spectral resolution, the covariance matrix resulting from the application of the recent iterative adaptive approach (IAA). The proposed exact implementations reduce the required computational complexity with several orders of magnitude, but, as we show, further computational savings can be obtained by the adoption of an approximative IAA-based data covariance matrix estimator, reminiscent of the recently proposed Quasi-Newton IAA technique. Furthermore, it is shown how the considered pitch estimators can be efficiently updated when new observations become available. The resulting time-recursive updating can reduce the computational complexity even further. The experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution. Finally, it is shown that the time-recursive implementations are able to track pitch fluctuations of synthetic as well as real-life signals.

Recently, directed information graphs have been proposed as concise graphical representations of the statistical dynamics among multiple random processes. A directed edge from one node to another indicates that the past of one random process statistically affects the future of another, given the past of all other processes. When the number of processes is large, computing those conditional dependence tests becomes difficult. Also, when the number of interactions becomes too large, the graph no longer facilitates visual extraction of relevant information for decision-making. This work considers approximating the true joint distribution on multiple random processes by another, whose directed information graph has at most one parent for any node. Under a Kullback–Leibler (KL) divergence minimization criterion, we show that the optimal approximate joint distribution can be obtained by maximizing a sum of directed informations. In particular, each directed information calculation only involves statistics among a pair of processes and can be efficiently estimated and given all pairwise directed informations, an efficient minimum weight spanning directed tree algorithm can be solved to find the best tree. We demonstrate the efficacy of this approach using simulated and experimental data. In both, the approximations preserve the relevant information for decision-making.

The goal of this paper is to study the learning abilities of adaptive networks in the context of cognitive radio networks and to investigate how well they assist in allocating power and communications resources in the frequency domain. The allocation mechanism is based on a social foraging swarm model that lets every node allocate its resources (power/bits) in the frequency regions where the interference is at a minimum while avoiding collisions with other nodes. We employ adaptive diffusion techniques to estimate the interference profile in a cooperative manner and to guide the motion of the swarm individuals in the resource domain. A mean square performance analysis of the proposed strategy is provided and confirmed by simulation results. The proposed approach endows the cognitive network with powerful learning and adaptation capabilities, allowing fast reaction to dynamic changes in the spectrum. Numerical examples show how cooperative spectrum sensing remarkably improves the performance of the resource allocation technique based on swarming.

In this paper, we propose a family of low-complexity adaptive filtering algorithms based on dichotomous coordinate descent (DCD) iterations for identification of sparse systems. The proposed algorithms are appealing for practical designs as they operate at the bit level, resulting in stable hardware implementations. We introduce a general approach for developing adaptive filters with different penalties and specify it for exponential and sliding window RLS. We then propose low-complexity DCD-based RLS adaptive filters with the lasso, ridge-regression, elastic net, and $ell_0$ penalties that attract sparsity. We also propose a simple recursive reweighting of the penalties and incorporate the reweighting into the proposed adaptive algorithms to further improve the performance. For general regressors, the proposed algorithms have a complexity of ${cal O}(N^2)$ operations per sample, where $N$ is the filter length. For transversal adaptive filters, the algorithms require only ${cal O}(N)$ operations per sample. A unique feature of the proposed algorithms is that they are well suited for implementation in finite precision, e.g., on FPGAs. We demonstrate by simulation that the proposed algorithms have performance close to the oracle RLS performance.

An important sensing operation is to detect the presence of specific signals with unknown transmission parameters. This task, referred to as “link acquisition,” is typically a sequential search over the transmitted signal space. Recently, the use of sparsity in similar estimation or detection problems has received considerable attention. These works typically focus on the benefits of compressed sensing, but not generally on the cost brought by sparse recovery. Our goal is to examine the tradeoff in complexity and performance when using sparse recovery with compressed or uncompressed samples. To do so, we propose a compressive sparsity aware (CSA) acquisition scheme, where a compressive multichannel sampling (CMS) front-end is followed by a sparsity regularized likelihood ratio test (SR-LRT) module. The CSA scheme borrows insights from the models studied in sub-Nyquist sampling and finite rate of innovation (FRI) signals. We further optimize the CMS front-end by maximizing the average Kullback–Leibler distance of all the hypotheses in the SR-LRT. We compare the CSA scheme vis-à-vis other popular alternatives in terms of performance and complexity. Simulations suggest that one can use the CSA scheme to scale down the implementation cost with greater flexibility than other alternatives. However, we find that they both have overall complexities that scale linearly with the search space. Furthermore, it is shown that compressive measurements used in the SR-LRT lead to a performance loss when noise prevails, while providing better performance in spite of the compression when noise is mild.

In this paper, we address the problem of minimizing the energy cost of positioning nodes in a wireless sensor network, using time of arrival measurements. A sensor needs to receive at least three distance measurements to known anchors in order to position itself. The accuracy of its position estimation depends on the signal to noise ratio of the beacons from the anchor nodes, whose power levels are to be selected according to a two-fold criterion: minimum power level and desired positioning quality for users, determined by the error covariance metric. We derive a solution based on modeling the positioning problem as a non-cooperative game. We show that the resulting game is supermodular and that it possesses a unique Nash equilibrium, which can be quickly reached with best response dynamics. Finally, in the numerical results we find the price of anarchy of our game.

In this paper, we consider the problem of locating multiple active spectrum subbands in a wide range of frequency bands. A major challenge associated with such wideband spectrum sensing is that it is either infeasible or too expensive to perform Nyquist sampling on the wideband signal. In this paper, we propose a sensing scheme based on a sub-Nyquist sampling method called multicoset sampling, which is similar to the polyphase implementation of the Nyquist sampling, but requires less A/D converters. In contrast to the traditional sub-Nquist approaches where the wideband signal is first reconstructed from the sub-Nyquist samples, we develop a method that directly estimates the power spectrum of the wideband signal of interest using the sub-Nyquist samples, by exploiting its statistical properties. We also characterize the statistical distribution of the proposed power spectrum estimator, based on which we obtain a constant-false-alarm energy detector for the frequency bins. Simulation results are provided to demonstrate the effectiveness of the proposed multiband spectrum sensing method based on sub-Nyquist sampling.

Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean-square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer, and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.

The full potential of multi-input multi-output (MIMO) communication systems relies on exploiting channel state information at the transmitter (CSIT), which is, however, often subject to some uncertainty. In this paper, following the worst-case robust philosophy, we consider a robust MIMO precoding design with deterministic imperfect CSIT, formulated as a maximin problem, to maximize the worst-case received signal-to-noise ratio or minimize the worst-case error probability. Given different types of imperfect CSIT in practice, a unified framework is lacking in the literature to tackle various channel uncertainty. In this paper, we address this open problem by considering several classes of uncertainty sets that include most deterministic imperfect CSIT as special cases. We show that, for general convex uncertainty sets, the robust precoder, as the solution to the maximin problem, can be efficiently computed by solving a single convex optimization problem. Furthermore, when it comes to unitarily-invariant convex uncertainty sets, we prove the optimality of a channel-diagonalizing structure and simplify the complex-matrix problem to a real-vector power allocation problem, which is then analytically solved in a waterfilling manner. Finally, for uncertainty sets defined by a generic matrix norm, called the Schatten norm, we provide a fully closed-form solution to the robust precoding design, based on which the robustness of beamforming and uniform-power transmission is investigated.

Using multicast probes to infer network topologies and internal link/node characteristics is an attractive approach due to its bandwidth efficiency and suitability for large-scale measurements. In this paper, we propose a new approach to tree topologies inference by exploiting dependence among end-point receivers. We first show that under the assumption of independent failure of intermediate nodes or links, inferring tree topology is a special instance of the more general problem of binary independent component analysis (bICA), and thus is amiable to existing analytical results and algorithms for bICA. Then, we propose the seqBICA algorithm that is tailored for tree topology inference. Evaluation study shows that the proposed algorithm outperforms existing approaches in convergence speed and accuracy even when the number of measurements is small.

A mathematical characterization of serially pruned permutations (SPPs) employed in variable-length permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct to coding for error correction. Typically, only a small set of discrete permuter lengths are supported. Serial pruning is a simple technique to alter the length of a permutation to support a wider range of lengths, but results in a serial processing bottleneck. In this paper, parallelizing SPPs is formulated in terms of recursively computing sums involving integer floor functions using integer operations, in a fashion analogous to evaluating Dedekind sums. A mathematical treatment for bit-reversal permutations (BRPs) is presented, and closed-form expressions for BRP statistics including descents/ascents, major index, excedances/descedances, inversions, and serial correlations are derived. It is shown that BRP sequences have weak correlation properties. Moreover, a new statistic called permutation inliers that characterizes the pruning gap of pruned interleavers is proposed. Using this statistic, a recursive algorithm that computes the minimum inliers count of a pruned BR interleaver (PBRI) in logarithmic time is presented. This algorithm enables parallelizing a serial PBRI algorithm by any desired parallelism factor by computing the pruning gap in lookahead rather than a serial fashion, resulting in significant reduction in interleaving latency and memory overhead. Extensions to 2-D block and stream interleavers, as well as applications to pruned fast Fourier transforms and LTE turbo interleavers, are also presented. Moreover, hardware-efficient architectures for the proposed algorithms are developed. Simulation results of interleavers employed in modern communication standards demonstrate three to four orders of magnitude improvement in interleaving time compared to ex- sting approaches.

Even though parallel multiple-input multiple-output (MIMO) broadcast channels are known to be separable from an information theoretic point of view, performing separate encoding and decoding on each of the parallel channels has been shown to be potentially suboptimal in broadcast channels with linear transceivers. In this paper, we show that suboptimality of such a carrier-noncooperative transmission also occurs in broadcast channels with zero-forcing and quality of service constraints if time-sharing is not allowed. The proof is given by constructing a minimal example and identifying a rate tuple that is achievable using carrier-cooperative zero-forcing with a certain sum power but requires a higher sum power with carrier-noncooperative zero-forcing. This observation is of practical relevance since zero-forcing without time-sharing is a popular assumption in the design of low-complexity optimization algorithms.

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