Quasi-convexity of the asymptotic channel MSE in regularized semi blind estimation

In this paper, the quasi-convexity of a sum of quadratic fractions in the form $\sum_{i=1}^n \frac{1+c_i x^2}{\left(1+d_ix\right)^2}$ is demonstrated where $c_i$ and $d_i$ are strictly positive scalars, when defined on the positive real axis $\mathbb{R}^{+}$. It will be shown that this quasi-convexity guarantees it has a unique local (and hence global) minimum. Indeed, this problem arises when considering the optimization of the weighting coefficient in regularized semi-blind channel identification problem, and more generally, is of interest in other contexts where we combine two different estimation criteria. Note that V. Buchoux {\it et.al} have noticed by simulations that the considered function has no local minima except its unique global minimum but this is the first time this result, as well as the quasi-convexity of the function is proved theoretically

Semi-blind Channel Identification for Individual Data Bursts in GSM Wireless Systems

In this paper, weinvestigate application of semi-blind equalization principles in practical wireless cellular systems. Speci#cally, we focus on the popular Global System for Mobile #GSM# communication system in our e#ort to improve the system e#ciency while maintaining the system performance at an acceptable level. We begin by brie#y introducing a linear Quadratic Amplitude Modulation #QAM# approximation for the Gaussian Minimum Shift Keying #GMSK# signal used in GSM systems, which can be modeled as a single input two output diversitymodelby a de-rotation scheme #7#. Based on the linear diversity model, two di#erent semi-blind algorithms are developed. These semi-blind algorithms can identify the channel bycombining both second order statistical #SOS# information and information from training, with which they can overcome some serious limitations of SOS blind algorithms. Semi-blind identi#ability conditions are also analyzed. Simulation results for GSM system based on bit error rates #..