Abstract-In this paper, we derive the explicit series expansion of the eigenvalue distribution of various models, namely the case of non-central Wishart distributions, as well as correlated zero mean Wishart distributions. The tools used extend those of the free probability framework, which have been quite successful for high dimensional statistical inference (when the size of the matrices tends to infinity), also known as free deconvolution. This contribution focuses on the finite Gaussian case and proposes algorithmic methods to compute the moments. Cases where asymptotic results fail to apply are also discussed.

One of the main objectives of data mining is to help companies determine to which potential customers to market and how many resources to allocate to these potential customers. Most previous works on competitive influence in social networks focus on the first issue. In this work, our focus is on the second issue, i.e., we are interested on the competitive influence of marketing campaigns who need to simultaneously decide how many resources to allocate to their potential customers to advertise their products. Using results from game theory, we are able to completely characterize the optimal strategic resource allocation for the voter model of social networks and prove that the price of competition of this game is unbounded. This work is a step towards providing a solid foundation for marketing advertising in more general scenarios.

In this paper, we analyze the optimal (blockwise) subcarrier allocation schemes in single-carrier frequency division multiple access (SC-FDMA) uplink systems without channel state information at the transmitter side. The presence of the discrete Fourier transform (DFT) in SC-FDMA/orthogonal frequency division multiple access OFDMA systems induces correlation between subcarriers which degrades the transmission performance, and thus, only some of the possible subcarrier allocation schemes achieve better performance. We propose as a performance metric a novel sum-correlation metric which is shown to exhibit interesting properties and a close link with the outage probability. We provide the set of optimal block-sizes achieving the maximum diversity and minimizing the inter-carrier sum-correlation function. We derive the analytical closed-form expression of the largest optimal block-size as a function of the system's parameters: number of subcarriers, number of users, and the cyclic prefix length. The minimum value of sum-correlation depends only on the number of subcarriers, number of users and on the variance of the channel impulse response. Moreover, we observe numerically a close strong connection between the proposed metric and diversity: the optimal block-size is also optimal in terms of outage probability. Also, when the considered system undergoes carrier frequency offset (CFO), we observe the robustness of the proposed blockwise allocation policy to the CFO effects. Numerical Monte Carlo simulations which validate our analysis are illustrated.