Radio propagation modeling and prediction is fundamental for modern cellular network planning and optimization. Conventional radio propagation models fall into two categories. Empirical models, based on coarse statistics, are simple and computationally efficient, but are inaccurate due to oversimplification. Deterministic models, such as ray tracing based on physical laws of wave propagation, are more accurate and site specific. But they have higher computational complexity and are inflexible to utilize site information other than traditional global information system (GIS) maps.

In this paper, we consider the problem of quickly detecting an abrupt change of linear coefficients in linear regression models. In particular, the observer sequentially observes a sequence of observations {(xn, yn)}∞n=1, which is assumed to obey a linear regression model at each time slot n. Some of the coefficients in the linear model change at a fixed but unknown time t. The post-change linear coefficients are unknown to the observer. The observer aims to design an online algorithm to detect the model change based on his sequential observations. Two performance metrics, namely the worst case detection delay (WADD) and the average run length to false alarm (ARL2FA), are adopted to evaluate the performance of detection algorithms. We design a low complexity algorithm, termed as parallel sum algorithm, for the detection purpose. An asymptotic upper bound on WADD is provided under any given ARL2FA constraint.

Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as ℓ1minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization. Our proof builds on Donoho, Johnstone and Montanari's conjectured phase transition curve for the TV approximate message passing algorithm (AMP), together with the linkage between the minmax Mean Square Error (MSE) of a denoising problem and the high-dimensional convex geometry for TV minimization.