Rajesh Sundaresan

Spatial SINR Games Combining Base Station Placement and Mobile Association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

Guessing Revisited: A Large Deviations Approach

The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation property with a certain rate function, then the limiting guessing exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the rate function. Other sufficient conditions related to certain continuity properties of the information spectrum are briefly discussed. This approach highlights the importance of the information spectrum in determining the limiting guessing exponent. All known prior results are then re-derived as example applications of our unifying approach.

Robust decoding for timing channels

To transmit information by timing arrivals to a single-server queue, we consider using the exponential server channels maximum likelihood decoder. For any server with service times that are stationary and ergodic with mean 1//spl mu/ seconds, we show that the rate e/sup -1//spl mu/ nats per second (capacity of the exponential server timing channel) is achievable using this decoder. We show that a similar result holds for the timing channel with feedback. We also show that if the server jams communication by adding an arbitrary amount of time to the nominal service time, then the rate e/sup -1//spl mu//sub 1//spl mu//sub 2//(/spl mu//sub 1/+/spl mu//sub 2/) nats per second is achievable with random codes, where the nominal service times are stationary and ergodic with mean 1//spl mu//sub 1/ seconds, and the arithmetic mean of the delays added by the server does not exceed 1//spl mu//sub 2/ seconds. This is a model of an arbitrarily varying channel where the current delay and the current input can affect future outputs. We also show the counterpart of these results for single-server discrete-time queues.

Capacity of queues via point-process channels

A conceptually simple proof for the capacity formula of an exponential server timing channel is provided. The proof links the timing channel to the point-process channel with instantaneous noiseless feedback. This point-process approach enables a study of timing channels that arise in multiserver queues, queues in tandem, and other simple configurations. Although the capacities of such channels remain to be found, the paper provides some analytical bounds and highlights a method to find achievable rates via simulations.

Sequential decoding for the exponential server timing channel

We show the existence of a good tree code with a sequential decoder for the exponential server timing channel. The expected number of computations before moving one step ahead is upper-bounded by a finite number. The rate of information transfer for this code is /spl mu//(2e) nats per second i.e., one half of the capacity. The cutoff rate for the exponential server queue is therefore at least /spl mu//(2u) nats per second.

A measure of discrimination and its geometric properties

We study a measure of discrimination that arises in the context of redundancy in guessing the realization of a random variable. This discrimination measure satisfies a Pythagorean-type inequality. The analog of this inequality for Kullback-Leibler divergence is well-known.

Decentralized Sequential Change Detection Using Physical Layer Fusion

We study the problem of decentralized sequential change detection with conditionally independent observations. The sensors form a star topology with a central node called fusion center as the hub. The sensors transmit a simple function of their observations in an analog fashion over a wireless Gaussian multiple access channel and operate under either a power constraint or an energy constraint. Simulations demonstrate that the proposed techniques have lower detection delays when compared with existing schemes. Moreover we demonstrate that the energy-constrained formulation enables better use of the total available energy than a power-constrained formulation.

Power minimization for CDMA under colored noise

Rate-constrained power minimization (PMIN) over a code division multiple-access (CDMA) channel with correlated noise is studied. PMIN is shown to be an instance of a separable convex optimization problem subject to linear ascending constraints. PMIN is further reduced to a dual problem of sumrate maximization (RMAX). The results highlight the underlying unity between PMIN, RMAX, and a problem closely related to PMIN but with linear receiver constraints. Subsequently, conceptually simple sequence design algorithms are proposed to explicitly identify an assignment of sequences and powers that solve PMIN. The algorithms yield an upper bound of 2N - 1 on the number of distinct sequences where N is the processing gain. The sequences generated using the proposed algorithms are in general real-valued. If a rate-splitting and multi-dimensional CDMA approach is allowed, the upper bound reduces to N distinct sequences, in which case the sequences can form an orthogonal set and be binary plusmn1-valued.

Decentralized sequential change detection using physical layer fusion

The problem of decentralized sequential detection with conditionally independent observations is studied. The sensors form a star topology with a central node called fusion center as the hub. The sensors make noisy observations of a parameter that changes from an initial state to a final state at a random time where the random change time has a geometric distribution. The sensors amplify and forward the observations over a wireless Gaussian multiple access channel and operate under either a power constraint or an energy constraint. The optimal transmission strategy at each stage is shown to be the one that maximizes a certain Ali-Silvey distance between the distributions for the hypotheses before and after the change. Simulations demonstrate that the proposed analog technique has lower detection delays when compared with existing schemes. Simulations further demonstrate that the energy-constrained formulation enables better use of the total available energy than the power-constrained formulation in the change detection problem.

Spatial SINR games of base station placement and mobile association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.