Peer to peer networks are becoming increasingly popular among Internet users as the downloading peers share the storage and upload bandwidth load of the system. This makes it possible for a large number of users to share a data file available at a server without the server upload bandwidth becoming a bottleneck. The P2P technology is being widely used not only for file sharing but also for video on demand, live streaming and IPTV. The delay deadlines are more stringent in live streaming and IPTV than those in file sharing as the traffic is real time. The performance perceived by a user depends upon whether the video stream is being downloaded at the streaming rate. Coolstreaming is the first large scale P2P IPTV system. We model the multi-channel Coolstreaming system via an open queueing network. The peer dynamics at a channel is modelled by a closed queueing network working at a faster rate. We compute the expected number of substreams in the overlay of New Coolstreaming which are not being received at the proper rate. The computation of the Markov chain with a very large state space is handled using the two time scale decomposition. Further we characterize the end to end delay encountered by a video stream originating from the server and received at a user of New Coolstreaming. Three factors contribute towards the delay. The first factor is the mean path length in terms of overlay hops of the partnership graph. The second factor is the mean number of routers between any two overlay peers in the network layer and the third factor is the queueing delay at a router in the Internet. The mean shortest path length in terms of overlay peers in the New Coolstreaming graph is shown to be O(logn)where nis the number of peers in the overlay. This is done by modelling the overlay by a random graph. The mean shortest path in terms of routers in the Internet’s router level topology is seen to be at most O(logNI)where NIis the number of routers in the Internet. We also discuss a method by which we can get the mean delay at a router in the Internet. Thus, the mean end to end delay in New Coolstreaming is shown to be upper bounded by O(lognlogNIE[W])where E[W]is the mean delay at a router in the Internet.

Network utility maximization has emerged as a powerful tool in studying flow control, resource allocation and other cross-layer optimization problems. In this work, we study a flow control problem in the optimization framework. The objective is to maximize the sum utility of the users subject to the flow constraints of the network. The utility maximization is solved in a distributed setting; the network operator does not know the user utility functions and the users know neither the rate choices of other users nor the flow constraints of the network. We build upon a popular decomposition technique proposed by Kelly [Eur. Trans. Telecommun., 8(1), 1997] to solve the utility maximization problem in the aforementioned distributed setting. The technique decomposes the utility maximization problem into a user problem, solved by each user and a network problem solved by the network. We propose an iterative algorithm based on this decomposition technique. In each iteration, the users communicate to the network their willingness to pay for the network resources. The network allocates rates in a proportionally fair manner based on the prices communicated by the users. The new feature of the proposed algorithm is that the rates allocated by the network remains feasible at all times. We show that the iterates put out by the algorithm asymptotically tracks a differential inclusion. We also show that the solution to the differential inclusion converges to the system optimal point via Lyapunov theory. We use a popular benchmark algorithm due to Kelly et al. [J. of the Oper. Res. Soc., 49(3), 1998] that involves fast user updates coupled with slow network updates in the form of additive increase and multiplicative decrease of the user flows. The proposed algorithm may be viewed as one with fast user update and fast network update that keeps the iterates feasible at all times. Simulations suggest that our proposed algorithm converges faster than the aforementioned benchmark algorithm. When the flows originate or terminate at a single node, the network problem is the maximization of a so-called d-separable objective function over the bases of a polymatroid. The solution is the lexicographically optimal base of the polymatroid. We map the problem of finding the lexicographically optimal base of a polymatroid to the geometrical problem of finding the concave cover of a set of points on a two-dimensional plane. We also describe an algorithm that finds the concave cover in linear time. Next, we consider the minimization of a more general objective function, i.e., a separable convex function, over the bases of a polymatroid with a special structure. We propose a novel decomposition algorithm and show the proof of correctness and optimality of the algorithm via the theory of polymatroids. Further, motivated by the need to handle piece-wise linear concave utility functions, we extend the decomposition algorithm to handle the case when the separable convex functions are not continuously differentiable or not strictly convex. We then provide a proof of its correctness and optimality.

Sound Source Separation refers to separating sound signals according to their sources from a given observed sound. It is efficient to code and very easy to analyze and manipulate sounds from individual sources separately than in a mixture. This thesis deals with the problem of source separation in monaural recordings of harmonic musical instruments. A good amount of literature is surveyed and presented since sound source separation has been tried by many researchers over many decades through various approaches. A prediction driven approach is first presented which is inspired by old-plus-new heuristic used by humans for Auditory Scene Analysis. In this approach, the signals from different sources are predicted using a general model and then these predictions are reconciled with observed sound to get the separated signal. This approach failed for real world sound recordings in which the spectrum of the source signals change very dynamically. Considering the dynamic nature of the spectrums, an approach which uses covariance matrix of amplitudes of harmonics is proposed. The overlapping and non-overlapping harmonics of the notes are first identified with the knowledge of pitch of the notes. The notes are matched on the basis of their covariance profiles. The second order properties of overlapping harmonics of a note are estimated with the use of co-variance matrix of a matching note. The full harmonic is then reconstructed using these second order characteristics. The technique has performed well over sound samples taken from RWC musical Instrument database.

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A Broadcast Channel is a communication path between a single source and two or more receivers or users. The source intends to communicate independent information to the users. A particular case of interest is the Gaussian Broadcast Channel (GBC) where the noise at each user is additive white Gaussian noise (AWGN). The capacity region of GBC is well known and the input to the channel is distributed as Gaussian. The capacity region of another special case of GBC namely Fading Broadcast Channel (FBC)was given in [Li and Goldsmith, 2001]and was shown that superposition of Gaussian codes is optimal for the FBC (treated as a vector degraded Broadcast Channel). The capacity region obtained when the input to the channel is distributed uniformly over a finite alphabet(Constellation)is termed as Constellation Constrained(CC) capacity region [Biglieri 2005]. In this thesis the CC capacity region for two-user GBC and the FBC are obtained. In case of GBC the idea of superposition coding with input from finite alphabet and CC capacity was explored in [Hupert and Bossert, 2007]but with some limitations. When the participating individual signal sets are nearly equal i.e., given total average power constraint P the rate reward α (also the power sharing parameter) is approximately equal to 0.5, we show via simulation that with rotation of one of the signal sets by an appropriate angle the CC capacity region is maximally enlarged. We analytically derive the expression for optimal angle of rotation. In case of FBC a heuristic power allocation procedure called finite-constellation power allocation procedure is provided through which it is shown (via simulation)that the ergodic CC capacity region thus obtained completely subsumes the ergodic CC capacity region obtained by allocating power using the procedure given in[Li and Goldsmith, 2001].It is shown through simulations that rotating one of the signal sets by an optimal angle (obtained by trial and error method)for a given α maximally enlarges the ergodic CC capacity region when finite-constellation power allocation is used. An expression for determining the optimal angle of rotation for the given fading state, is obtained. And the effect of rotation is maximum around the region corresponding to α =0.5. For both GBC and FBC superposition coding is done at the transmitter and successive decoding is carried out at the receivers.

A Wireless Sensor Network (WSN) is a dense network of autonomous devices (or motes) with sensors that cooperatively monitor some physical or environmental conditions. These devices are resource constrained -limited memory, power and computational resources. Thus, any algorithm developed for WSN should be deigned such that the algorithm consumes the resources as minimal as possible. The problem addressed in this thesis is developing a low-complexity algorithm for intrusion detection in the presence of clutter arising from moving vegetation, using Passive Infra-Red (PIR) sensors. The algorithm is based on a combination of Haar Transform (HT) and Support-Vector-Machine (SVM) based training. The spectral signature of the waveforms is used to separate between the intruder and clutter waveforms. The spectral signature is computed using HT and this is fed to SVM which returns an optimal hyperplane that separates the intruder and clutter signatures. This hyperplane obtained by offline training is used online in the mote for surveillance. The algorithm is field-tested in the Indian Institute of Science campus. Based on experimental observations about the PIR sensor and the lens system, an analytical model for the waveform generated by an intruder moving along a straight line with uniform velocity in the vicinity of the sensor is developed. Analysis on how this model can be exploited to track the intruder path by optimally positioning multiple sensor nodes is provided. Algorithm for tracking the intruder path using features of the waveform from three sensors mounted on a single mote is also developed.

This thesis investigates the problem of detecting an intruder in the presence of clutter in a Passive Infra-Red (PIR) based Wireless Sensor Network (WSN). As one of the major objectives in a WSN is to maximize battery life, data transmission and local computations must be kept to a minimum as they are expensive in terms of energy. But, as intrusion being a rare event and cannot be missed, local computations expend more energy than data transmission. Hence, the need for a low-complexity algorithm for intrusion detection is inevitable. A low-complexity algorithm for intrusion detection in the presence of clutter arising from wind-blown vegetation, using PIR sensors is presented. The algorithm is based on a combination of Haar Transform (HT) and Support Vector Machine (SVM) based training. The amplitude and frequency of the intruder signature is used to differentiate it from the clutter signal. The HT was preferred to Discrete Fourier Transform (DFT) in computing the spectral signature because of its computational simplicity -just additions and subtractions suffice (scaling coefficients taken care appropriately). Intruder data collected in a laboratory and clutter data collected from various types of vegetation were fed into SVM for training. The optimal decision rule returned by SVM was then used to separate intruder from clutter. Simulation results along with some representative samples in which intrusions were detected and the clutter being rejected by the algorithm is presented. The implementation of the proposed intruder-detection algorithm in a network setting comprising of 20 sensing nodes is discussed. The field testing performance of the algorithm is then discussed. The limitations of the algorithm is also discussed. A closed-form analytical expression for the signature generated by a human moving along a straight line in the vicinity of the PIR sensor at constant velocity is provided. It is shown to be a good approximation by showing a close match with the real intruder waveforms. It is then shown how this expression can be exploited to track the intruder from the signatures of three well-positioned sensing nodes.