arXiv subjects

H. Vincent Poor

Publications and source records attributed to H. Vincent Poor.

At least 991 records · Page 55Linked to original sources

arXiv2005

Distributed Learning in Wireless Sensor Networks

The problem of distributed or decentralized detection and estimation in applications such as wireless sensor networks has often been considered in the framework of parametric models, in which strong assumptions are made about a statistical description of nature. In certain applications, such assumptions are warranted and systems designed from these models show promise. However, in other scenarios, prior knowledge is at best vague and translating such knowledge into a statistical model is undesirable. Applications such as these pave the way for a nonparametric study of distributed detection and estimation. In this paper, we review recent work of the authors in which some elementary models for distributed learning are considered. These models are in the spirit of classical work in nonparametric statistics and are applicable to wireless sensor networks.

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arXiv2005

Uplink User Capacity in a CDMA System with Hotspot Microcells: Effects of Finite Transmit Power and Dispersion

This paper examines the uplink user capacity in a two-tier code division multiple access (CDMA) system with hotspot microcells when user terminal power is limited and the wireless channel is finitely-dispersive. A finitely-dispersive channel causes variable fading of the signal power at the output of the RAKE receiver. First, a two-cell system composed of one macrocell and one embedded microcell is studied and analytical methods are developed to estimate the user capacity as a function of a dimensionless parameter that depends on the transmit power constraint and cell radius. Next, novel analytical methods are developed to study the effect of variable fading, both with and without transmit power constraints. Finally, the analytical methods are extended to estimate uplink user capacity for multicell CDMA systems, composed of multiple macrocells and multiple embedded microcells. In all cases, the analysis-based estimates are compared with and confirmed by simulation results.

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arXiv2005

Soft Handoff and Uplink Capacity in a Two-Tier CDMA System

This paper examines the effect of soft handoff on the uplink user capacity of a CDMA system consisting of a single macrocell in which a single hotspot microcell is embedded. The users of these two base stations operate over the same frequency band. In the soft handoff scenario studied here, both macrocell and microcell base stations serve each system user and the two received copies of a desired user's signal are summed using maximal ratio combining. Exact and approximate analytical methods are developed to compute uplink user capacity. Simulation results demonstrate a 20% increase in user capacity compared to hard handoff. In addition, simple, approximate methods are presented for estimating soft handoff capacity and are shown to be quite accurate.

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arXiv2005

Uplink Throughput in a Single-Macrocell/Single-Microcell CDMA System, with Application to Data Access Points

This paper studies a two-tier CDMA system in which the microcell base is converted into a data access point (DAP), i.e., a limited-range base station that provides high-speed access to one user at a time. The microcell (or DAP) user operates on the same frequency as the macrocell users and has the same chip rate. However, it adapts its spreading factor, and thus its data rate, in accordance with interference conditions. By contrast, the macrocell serves multiple simultaneous data users, each with the same fixed rate. The achieveable throughput for individual microcell users is examined and a simple, accurate approximation for its probability distribution is presented. Computations for average throughputs, both per-user and total, are also presented. The numerical results highlight the impact of a desensitivity parameter used in the base-selection process.

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arXiv2005

Impulse Radio Systems with Multiple Types of Ultra-Wideband Pulses

Spectral properties and performance of multi-pulse impulse radio ultra-wideband systems with pulse-based polarity randomization are analyzed. Instead of a single type of pulse transmitted in each frame, multiple types of pulses are considered, which is shown to reduce the effects of multiple-access interference. First, the spectral properties of a multi-pulse impulse radio system is investigated. It is shown that the power spectral density is the average of spectral contents of different pulse shapes. Then, approximate closed-form expressions for bit error probability of a multi-pulse impulse radio system are derived for RAKE receivers in asynchronous multiuser environments. The theoretical and simulation results indicate that impulse radio systems that are more robust against multiple-access interference than a "classical" impulse radio system can be designed with multiple types of ultra-wideband pulses.

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arXiv2005

On the Typicality of the Linear Code Among the LDPC Coset Code Ensemble

Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binary-input/symmetric-output channels. The case of non-symmetric channels is tackled either by the LDPC coset code ensemble (a channel symmetrizing argument) or by the generalized DE for linear codes on non-symmetric channels. Existing simulations show that the bit error rate performances of these two different approaches are nearly identical. This paper explains this phenomenon by proving that as the minimum check node degree $d_c$ becomes sufficiently large, the performance discrepancy of the linear and the coset LDPC codes is theoretically indistinguishable. This typicality of linear codes among the LDPC coset code ensemble provides insight into the concentration theorem of LDPC coset codes.

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arXiv2005

Sensor Configuration and Activation for Field Detection in Large Sensor Arrays

The problems of sensor configuration and activation for the detection of correlated random fields using large sensor arrays are considered. Using results that characterize the large-array performance of sensor networks in this application, the detection capabilities of different sensor configurations are analyzed and compared. The dependence of the optimal choice of configuration on parameters such as sensor signal-to-noise ratio (SNR), field correlation, etc., is examined, yielding insights into the most effective choices for sensor selection and activation in various operating regimes.

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arXiv2005

Analysis of Second-order Statistics Based Semi-blind Channel Estimation in CDMA Channels

The performance of second order statistics (SOS) based semi-blind channel estimation in long-code DS-CDMA systems is analyzed. The covariance matrix of SOS estimates is obtained in the large system limit, and is used to analyze the large-sample performance of two SOS based semi-blind channel estimation algorithms. A notion of blind estimation efficiency is also defined and is examined via simulation results.

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arXiv2005

A low-cost time-hopping impulse radio system for high data rate transmission

We present an efficient, low-cost implementation of time-hopping impulse radio that fulfills the spectral mask mandated by the FCC and is suitable for high-data-rate, short-range communications. Key features are: (i) all-baseband implementation that obviates the need for passband components, (ii) symbol-rate (not chip rate) sampling, A/D conversion, and digital signal processing, (iii) fast acquisition due to novel search algorithms, (iv) spectral shaping that can be adapted to accommodate different spectrum regulations and interference environments. Computer simulations show that this system can provide 110Mbit/s at 7-10m distance, as well as higher data rates at shorter distances under FCC emissions limits. Due to the spreading concept of time-hopping impulse radio, the system can sustain multiple simultaneous users, and can suppress narrowband interference effectively.

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arXiv2005

The Noncoherent Rician Fading Channel -- Part I : Structure of the Capacity-Achieving Input

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients. First the structure of the capacity-achieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacity-achieving input amplitude distribution is discrete with a finite number of mass points in the low-power regime. A similar discrete structure for the optimal amplitude is proven over the entire SNR range when there is only a peak power constraint. The Rician fading with phase-noise channel model, where there is phase uncertainty in the specular component, is analyzed. For this model it is shown that, with only an average power constraint, the capacity-achieving input amplitude is discrete with a finite number of levels. For the classical average power limited Rician fading channel, it is proven that the optimal input amplitude distribution has bounded support.

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arXiv2005

The Noncoherent Rician Fading Channel -- Part II : Spectral Efficiency in the Low-Power Regime

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients. The spectral-efficiency/bit-energy tradeoff in the low-power regime is examined when the input has limited peakedness. It is shown that if a fourth moment input constraint is imposed or the input peak-to-average power ratio is limited, then in contrast to the behavior observed in average power limited channels, the minimum bit energy is not always achieved at zero spectral efficiency. The low-power performance is also characterized when there is a fixed peak limit that does not vary with the average power. A new signaling scheme that overlays phase-shift keying on on-off keying is proposed and shown to be optimally efficient in the low-power regime.

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arXiv2005

Consistency Problems for Jump-Diffusion Models

In this paper consistency problems for multi-factor jump-diffusion models, where the jump parts follow multivariate point processes are examined. First the gap between jump-diffusion models and generalized Heath-Jarrow-Morton (HJM) models is bridged. By applying the drift condition for a generalized arbitrage-free HJM model, the consistency condition for jump-diffusion models is derived. Then we consider a case in which the forward rate curve has a separable structure, and obtain a specific version of the general consistency condition. In particular, a necessary and sufficient condition for a jump-diffusion model to be affine is provided. Finally the Nelson-Siegel type of forward curve structures is discussed. It is demonstrated that under regularity condition, there exists no jump-diffusion model consistent with the Nelson-Siegel curves.

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arXiv2005

Stochastic Differential Games in a Non-Markovian Setting

Stochastic differential games are considered in a non-Markovian setting. Typically, in stochastic differential games the modulating process of the diffusion equation describing the state flow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method is not applicable. To examine the non-Markovian case, this paper considers the situation in which the modulating process is a fractional Brownian motion. Fractional noise calculus is used for such models to find the Nash equilibria explicitly. Although fractional Brownian motion is taken as the modulating process because of its versatility in modeling in the fields of finance and networks, the approach in this paper has the merit of being applicable to more general Gaussian stochastic differential games with only slight conceptual modifications. This work has applications in finance to stock price modeling which incorporates the effect of institutional investors, and to stochastic differential portfolio games in markets in which the stock prices follow diffusions modulated with fractional Brownian motion.

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arXiv2005

Arbitrage in Fractal Modulated Markets When the Volatility is Stochastic

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brownian motion. Work has been done previously on this problem for the case with constant `volatility' and without a time change; here these results are extended to the case of stochastic volatility models when the modulator is fractional Brownian motion or a time change of it. (Volatility in fractional Black-Scholes models does not carry the same meaning as in the classic Black-Scholes framework, which is made clear in the text.) Since fractional Brownian motion is not a semi-martingale, the Black-Scholes differential equation is not well-defined sense for arbitrary predictable volatility processes. However, it is shown here that any almost surely continuous and adapted process having zero quadratic variation can act as an integrator over functions of the integrator and over the family of continuous adapted semi-martingales. Moreover it is shown that the integral also has zero quadratic variation, and therefore that the integral itself can be an integrator. This property of the integral is crucial in developing the arbitrage strategy. Since fractional Brownian motion and a time change of fractional Brownian motion have zero quadratic variation, these results are applicable to these cases in particular. The appropriateness of fractional Brownian motion as a means of modeling stock price returns is discussed as well.

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arXiv2005

On The Tradeoff Between Two Types of Processing Gain

One of the features characterizing almost every multiple access (MA) communication system is the processing gain. Through the use of spreading sequences, the processing gain of Random CDMA systems (RCDMA), is devoted to both bandwidth expansion and orthogonalization of the signals transmitted by different users. Another type of multiple access system is Impulse Radio (IR). In many aspects, IR systems are similar to time division multiple access (TDMA) systems, and the processing gain of IR systems represents the ratio between the actual transmission time and the total time between two consecutive ransmissions (on-plus-off to on ratio). While CDMA systems, which constantly excite the channel, rely on spreading sequences to orthogonalize the signals transmitted by different users, IR systems transmit a series of short pulses and the orthogonalization between the signals transmitted by different users is achieved by the fact that most of the pulses do not collide with each other at the receiver. In this paper, a general class of MA communication systems that use both types of processing gain is presented, and both IR and RCDMA systems are demonstrated to be two special cases of this more general class of systems. The bit error rate (BER) of several receivers as a function of the ratio between the two types of processing gain is analyzed and compared under the constraint that the total processing gain of the system is large and fixed. It is demonstrated that in non inter-symbol interference (ISI) channels there is no tradeoff between the two types of processing gain. However, in ISI channels a tradeoff between the two types of processing gain exists. In addition, the sub-optimality of RCDMA systems in frequency selective channels is established.

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arXiv2005

Bandit Problems with Side Observations

An extension of the traditional two-armed bandit problem is considered, in which the decision maker has access to some side information before deciding which arm to pull. At each time t, before making a selection, the decision maker is able to observe a random variable X_t that provides some information on the rewards to be obtained. The focus is on finding uniformly good rules (that minimize the growth rate of the inferior sampling time) and on quantifying how much the additional information helps. Various settings are considered and for each setting, lower bounds on the achievable inferior sampling time are developed and asymptotically optimal adaptive schemes achieving these lower bounds are constructed.

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arXiv2005

Estimation of the Number of Sources in Unbalanced Arrays via Information Theoretic Criteria

Estimating the number of sources impinging on an array of sensors is a well known and well investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is known to be a consistent estimator, robust against deviations from the Gaussian assumption, and non-robust against deviations from the point source and/or temporally or spatially white additive noise assumptions. Over the years several alternative estimation algorithms have been proposed and tested. Usually, these algorithms are shown, using computer simulations, to have improved performance over the MDL estimator, and to be robust against deviations from the assumed spatial model. Nevertheless, these robust algorithms have high computational complexity, requiring several multi-dimensional searches. In this paper, motivated by real life problems, a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken. An MDL type estimator that is robust against deviation from assumption of equal noise level across the array is studied. The consistency of this estimator, even when deviations from the equal noise level assumption occur, is proven. A novel low-complexity implementation method avoiding the need for multi-dimensional searches is presented as well, making this estimator a favorable choice for practical applications.

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arXiv2005

A Non-Cooperative Power Control Game for Multi-Carrier CDMA Systems

In this work, a non-cooperative power control game for multi-carrier CDMA systems is proposed. In the proposed game, each user needs to decide how much power to transmit over each carrier to maximize its overall utility. The utility function considered here measures the number of reliable bits transmitted per joule of energy consumed. It is shown that the user's utility is maximized when the user transmits only on the carrier with the best "effective channel". The existence and uniqueness of Nash equilibrium for the proposed game are investigated and the properties of equilibrium are studied. Also, an iterative and distributed algorithm for reaching the equilibrium (if it exists) is presented. It is shown that the proposed approach results in a significant improvement in the total utility achieved at equilibrium compared to the case in which each user maximizes its utility over each carrier independently.

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