Cross-Layer Optimization in OFDM Wireless Communication Network

The wide use of OFDM systems in multiuser environments to overcome problem of communication over the wireless channel has gained prominence in recent years. Cross-layer Optimization technique is aimed to further improve the efficiency of this network. This chapter demonstrates that significant improvements in data traffic parameters can be achieved by applying cross-layer optimization techniques to packet switched wireless networks. This work compares the system capacity, delay time and data throughput of QoS traffic in a multiuser OFDM system using two algorithms. The first algorithm, Maximum Weighted Capacity, uses a cross-layer design to share resources and schedule traffic to users on the network, while the other algorithm (Maximum Capacity) simply allocates resources based only on the users channel quality. The results of the research shows that the delay time and data throughput of the Maximum Weighted Capacity algorithm in cross layer OFDM system is much better than that of the Maximum Capacity in simply based users channel quality system. The cost incurred for this gain is the increased complexity of the Maximum Weighted Capacity scheme.

The Gelfond–Schnirelman Method in Prime Number Theory

The original Gelfond–Schnirelman method, proposed in 1936, uses polynomials with integer coefficients and small norms on [0, 1] to give a Chebyshev-type lower bound in prime number theory. We study a generalization of thismethod for polynomials inmany variables. Ourmain result is a lower bound for the integral of Chebyshev's ψ-function, expressed in terms of the weighted capacity. This extends previous work of Nair and Chudnovsky, and connects the subject to the potential theory with external fields generated by polynomial-type weights. We also solve the corresponding potential theoretic problem, by finding the extremal measure and its support.

Singular sets of anisotropic weighted capacity zero and degenerate quasilinear parabolic equations

The aim of this paper is to characterise sets of anisotropic weighted capacity zero. In this we generalise previous known results for the isotropic equivalent. A particular case of this zero capacity set is used to generalise removable singularity results for weak solutions of degenerate quasilinear parabolic equations and for their elliptic equivalent when its structure is still essentially isotropic, with the anisotropy confined to the mixed norms of the generalised Lebesgue spaces involved.