Performance limits and design issues in wireless networks

The increasing utilization of networks, especially wireless networks, for different applications and in different aspects of modern life, has directed a great deal of attention towards the analysis and optimal design of networks. Distinguishing features of the wireless environment and the distributed nature of the network setup have raised many important challenges in finding the performance limits of different tasks such as communication, control, and computation over networks. There are also many design issues concerning the complexity and the robustness of wireless systems that should be addressed for a thorough understanding and an efficient operation of wireless networked systems. This thesis deals with a few of the challenges associated with the fundamental performance limits and optimal design of wireless networks. In the first part, we analyze performance limits of two applications for a special class of wireless networks called wireless erasure networks. These networks incorporate some of the essential features of the wireless environment. We look at the performance limits of two applications over these networks. The first application is data transmission with two different traffic patterns, namely multicast and broadcast. The capacity region and the optimal coding scheme for the multicast scenario are found, and outer and inner bounds on the capacity region for the broadcast scenario are provided. The second application considered in this thesis is estimation and control of a dynamical process at a remote location connected through a wireless erasure network to a sensor observing the process. In this case, we characterize the minimum steady-state error and its dependency on the parameters of the network. The final problem considered in the first part of the thesis concerns power consumption (as a performance measure) in wireless networks. We propose and analyze a simple scheme based on the idea of distributed beamforming that saves us in terms of power consumption for dense sensor and ad-hoc networks. We quantify this gain compared to the case when nodes have isolated communications without participating in the network. The second part of the thesis deals with two design issues in the downlink of cellular wireless networks. The first issue is related to quality of service provisioning in the downlink scenario. We investigate the problem of differentiated rate scheduling in which different users demand different sets of rates. We obtain explicit and practical scheduling schemes to achieve the rate constraints and at the same time maximize the throughput. These schemes are based on the idea of opportunistic beamforming, are simple, and require little amount of feedback to the transmitter. We further show that the throughput loss due to imposing the rate constraints is negligible for large systems. The next issue considered in this thesis is the robustness of the capacity region of multiple antenna Gaussian broadcast channels to the channel estimation error at the transmitter and the users. These channels are mathematical models for the downlink of cellular systems. We provide an inner bound on the capacity region of these channels and show that this inner bound is equivalent to the capacity region of a dual multiple access channel with a noise covariance that depends on the transmit powers. This duality is explored to show the effect of the estimation error on the sum-rate for a large number of users and in the large power regime. Finally, a training-based scheme for the block fading multiple antenna broadcast channels is proposed.