Statistical description of non‐coherent automatic gain control

Abstract

Automatic gain control (AGC) is an important function in many different systems. It is the objective of this paper to introduce an analysis method for the statistical tracking performance of non-coherent AGC. The method presented can easily be adapted to a wide variety of different applications and systems, e.g. the power control in communications networks such as CDMA systems, or the design of gain control circuits along receiver down-conversion chains possibly including analogue-to-digital conversions.We describe the fluctuation of the controlled gain by stochastic differential equations. For some typical operational cases the physical probability density function of the AGC gain variation is compared with different approximation techniques, i.e. the Fokker-Planck (F-P) approach and the assumption of Gaussian distributions. The limitations of the approximation methods are emphasized because in telecommunications literature the F-P method is often applied without sufficient verification of the actual conditions for the method's applicability.