A New Approach of Data Pre-processing for Data Compression in Smart Grids

The conventional approach to pre-process data for compression is to apply transforms such as the Fourier, the Karhunen-Lo\`{e}ve, or wavelet transforms. One drawback from adopting such an approach is that it is independent of the use of the compressed data, which may induce significant optimality losses when measured in terms of final utility (instead of being measured in terms of distortion). We therefore revisit this paradigm by tayloring the data pre-processing operation to the utility function of the decision-making entity using the compressed (and therefore noisy) data. More specifically, the utility function consists of an Lp-norm, which is very relevant in the area of smart grids. Both a linear and a non-linear use-oriented transforms are designed and compared with conventional data pre-processing techniques, showing that the impact of compression noise can be significantly reduced

Derivative-Free Optimization over Multi-User MIMO Networks

Accepted for presentation at the 10th International Conference on NETwork Games, COntrol and OPtimization (NETGCOOP), Cargèse.International audienceIn wireless communication, the full potential of multiple-input multiple-output (MIMO) arrays can only be realized through optimization of their transmission parameters. Distributed solutions dedicated to that end include iterative optimization algorithms involving the computation of the gradient of a given objective function, and its dissemination among the network users. In the context of large-scale MIMO, however, computing and conveying large arrays of function derivatives across a network has a prohibitive cost to communication standards. In this paper we show that multiuser MIMO networks can be optimized without using any derivative information. With focus on the throughput maximization problem in a MIMO multiple access channel, we propose a "derivative-free" optimization methodology relying on very little feedback information: a single function query at each iteration. Our approach integrates two complementary ingredients: exponential learning (a derivative-based expression of the mirror descent algorithm with entropic regularization), and a single-function-query gradient estimation technique derived from a classic approach to derivative-free optimization

A stochastic approximation algorithm for stochastic semidefinite programming

Motivated by applications to multi-antenna wireless networks, we propose a distributed and asynchronous algorithm for stochastic semidefinite programming. This algorithm is a stochastic approximation of a continous- time matrix exponential scheme regularized by the addition of an entropy-like term to the problem's objective function. We show that the resulting algorithm converges almost surely to an $\varepsilon$-approximation of the optimal solution requiring only an unbiased estimate of the gradient of the problem's stochastic objective. When applied to throughput maximization in wireless multiple-input and multiple-output (MIMO) systems, the proposed algorithm retains its convergence properties under a wide array of mobility impediments such as user update asynchronicities, random delays and/or ergodically changing channels. Our theoretical analysis is complemented by extensive numerical simulations which illustrate the robustness and scalability of the proposed method in realistic network conditions.Comment: 25 pages, 4 figure

Transmit without regrets: Online optimization in MIMO-OFDM cognitive radio systems

In this paper, we examine cognitive radio systems that evolve dynamically over time due to changing user and environmental conditions. To combine the advantages of orthogonal frequency division multiplexing (OFDM) and multiple-input, multiple-output (MIMO) technologies, we consider a MIMO-OFDM cognitive radio network where wireless users with multiple antennas communicate over several non-interfering frequency bands. As the network's primary users (PUs) come and go in the system, the communication environment changes constantly (and, in many cases, randomly). Accordingly, the network's unlicensed, secondary users (SUs) must adapt their transmit profiles "on the fly" in order to maximize their data rate in a rapidly evolving environment over which they have no control. In this dynamic setting, static solution concepts (such as Nash equilibrium) are no longer relevant, so we focus on dynamic transmit policies that lead to no regret: specifically, we consider policies that perform at least as well as (and typically outperform) even the best fixed transmit profile in hindsight. Drawing on the method of matrix exponential learning and online mirror descent techniques, we derive a no-regret transmit policy for the system's SUs which relies only on local channel state information (CSI). Using this method, the system's SUs are able to track their individually evolving optimum transmit profiles remarkably well, even under rapidly (and randomly) changing conditions. Importantly, the proposed augmented exponential learning (AXL) policy leads to no regret even if the SUs' channel measurements are subject to arbitrarily large observation errors (the imperfect CSI case), thus ensuring the method's robustness in the presence of uncertainties.Comment: 25 pages, 3 figures, to appear in the IEEE Journal on Selected Areas in Communication

Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part II: Algorithms

In this two-part paper, we address the problem of finding the optimal precoding/multiplexing scheme for a set of non-cooperative links sharing the same physical resources, e.g., time and bandwidth. We consider two alternative optimization problems: P.1) the maximization of mutual information on each link, given constraints on the transmit power and spectral mask; and P.2) the maximization of the transmission rate on each link, using finite order constellations, under the same constraints as in P.1, plus a constraint on the maximum average error probability on each link. Aiming at finding decentralized strategies, we adopted as optimality criterion the achievement of a Nash equilibrium and thus we formulated both problems P.1 and P.2 as strategic noncooperative (matrix-valued) games. In Part I of this two-part paper, after deriving the optimal structure of the linear transceivers for both games, we provided a unified set of sufficient conditions that guarantee the uniqueness of the Nash equilibrium. In this Part II, we focus on the achievement of the equilibrium and propose alternative distributed iterative algorithms that solve both games. Specifically, the new proposed algorithms are the following: 1) the sequential and simultaneous iterative waterfilling based algorithms, incorporating spectral mask constraints; 2) the sequential and simultaneous gradient projection based algorithms, establishing an interesting link with variational inequality problems. Our main contribution is to provide sufficient conditions for the global convergence of all the proposed algorithms which, although derived under stronger constraints, incorporating for example spectral mask constraints, have a broader validity than the convergence conditions known in the current literature for the sequential iterative waterfilling algorithm.Comment: Paper submitted to IEEE Transactions on Signal Processing, February 22, 2006. Revised March 26, 2007. Accepted June 5, 2007. To appear on IEEE Transactions on Signal Processing, 200

Fast Optimization with Zeroth-Order Feedback in Distributed, Multi-User MIMO Systems

In this paper, we develop a gradient-free optimization methodology for efficient resource allocation in Gaussian MIMO multiple access channels. Our approach combines two main ingredients: (i) an entropic semidefinite optimization based on matrix exponential learning (MXL); and (ii) a one-shot gradient estimator which achieves low variance through the reuse of past information. This novel algorithm, which we call gradient-free MXL algorithm with callbacks (MXL0$^{+}$), retains the convergence speed of gradient-based methods while requiring minimal feedback per iteration$-$a single scalar. In more detail, in a MIMO multiple access channel with $K$ users and $M$ transmit antennas per user, the MXL0$^{+}$ algorithm achieves $\epsilon$-optimality within $\text{poly}(K,M)/\epsilon^2$ iterations (on average and with high probability), even when implemented in a fully distributed, asynchronous manner. For cross-validation, we also perform a series of numerical experiments in medium- to large-scale MIMO networks under realistic channel conditions. Throughout our experiments, the performance of MXL0$^{+}$ matches$-$and sometimes exceeds$-$that of gradient-based MXL methods, all the while operating with a vastly reduced communication overhead. In view of these findings, the MXL0$^{+}$ algorithm appears to be uniquely suited for distributed massive MIMO systems where gradient calculations can become prohibitively expensive.Comment: Final version; to appear in IEEE Transactions on Signal Processing; 16 pages, 4 figure

Simultaneous iterative water-filling for Gaussian frequency-selective interference channels

The sequential Iterative Water-Filling Algorithm (IWFA) proposed by Yu et al. is by now a popular lowcomplexity algorithm to compute the Nash equilibrium point of the power allocation game in a Gaussian frequency-selective multiuser interference channel. The algorithm is based on a distributed sequential updating where, at each iteration, the users choose their power allocation, one after the other. However, this sequential updating strategy may slow down its convergence time excessively when the number of users is high. In this paper, we propose an alternative distributed algorithm, called Simultaneous Iterative Water-Filling Algorithm (SIWFA), where at each iteration, all the users update their power allocations simultaneously, rather than sequentially. This reduces the convergence time considerably, specially when the number of users is large. Our main contribution is to provide a unified set of sufficient conditions for the convergence of both IWFA and SIWFA, that are less stringent than those known in the literature for IWFA. These conditions guarantee the convergence of both algorithms also in the presence of spectral mask constraints imposed on the power allocations of the users. © 2006 IEEE

Signaling in Frequency Selective Gaussian Interference Channels

Sharing communication resources in wireless communication networks, due to the ever increasing growth in the number of users and the growing demand for higher data rates, appears to be inevitable. Consequently, present wireless communication networks should provide service for a large number of users through a frequency selective and interference limited medium rather than a single band, noise limited channel. In this thesis, we study a Gaussian interference network with orthogonal frequency sub-bands with slow faded and frequency-selective channel coefficients. The network is decentralized in the sense that there is no central node to assign the frequency sub-bands to the users. Moreover, due to lack of a feedback link between the two ends of any transmitter-receiver pair, all transmitters are unaware of the channel coefficients. Since the channel is assumed to be static during the communication period of interest, the concept of outage probability is employed in order to assess the performance of the network. In a scenario where all transmitters distribute their available power uniformly across the sub-bands, we investigate the problem of how establishing a nonzero correlation ρ among the Gaussian signals transmitted by each user along different frequency sub-bands can improve the outage probability at each of the receivers. Specifically, we show in a general k-user interference channel over N orthogonal frequency sub-bands that , when receivers treat interference as noise, ρ=0 is a point of local extremum for the achievable rate at each receiver, for any realization of channel coefficients. Moreover, in the case of K=2 with arbitrary number of sub-bands, it is verified that there exists a finite level of Signal-to-Noise Ratio (SNR) such that the achievable rate has a local minimum at ρ=0, which is not necessarily the case when K>2. We then concentrate on a 2-user interference channel over 2 orthogonal frequency sub-bands and characterize the behavior of the outage probability in the high SNR regime. We consider two simple decoding strategies at the receiver. In the first scenario, receivers simply treat interference as noise. In the second scenario, the receivers have the choice either to decode the desired signal treating interference as noise or to decode interference treating the desired signal as noise before decoding the interference free signal. Indeed, in both cases, we first show that the achievable rate is an increasing function of ρ in the high SNR regime, which suggests to repeat the same signal over the sub-bands. This observation, in a sense, reflects to the behavior of the outage probability, the scaling behavior of which in the high SNR regime is characterized for the Rayleigh fading scenario.1 yea

Distributed field estimation in wireless sensor networks

This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks