In building highly efficient transmitters of today, one is forced to sacrifice linearity for efficiency. Some of the highest power amplifier efficiency figures are reported by envelope tracking (ET) amplifiers. These amplifiers can generate strong higher-order harmonics, which can lead to interference with receivers operating at the harmonic frequencies. Using non-linear interference cancellation, we can help to remove the interference being caused in those receivers. This paper looks at the problem of modeling the third and second-order harmonic emission from an ET amplifier. It derives the non-linear kernel for estimating such interference. This kernel has been rigorously expanded to show its correlation with the various harmonics and its effectiveness in predicting the harmonic content. We then set up an envelope amplifier test-bench to capture harmonic signal content and cancel it using the derived kernel model. The experiment yields excellent agreement with theory and provides a validation of the system and concept.

This paper presents a new model of asymmetric bifurcating autoregressive process withrandom coefficients. We couple this model with a Galton−Watson tree to take into account possiblymissing observations. We propose least-squares estimators for the various parameters ofthe model and prove their consistency, with a convergence rate, and asymptotic normality.We use both the bifurcating Markov chain and martingale approaches and derive new resultsin both these frameworks.

Let observations (X1, X2, …, Xn) be obtained from a time series {Xt} such that where the ɛt are independently and identically distributed random variables each having mean zero and finite variance, and the gu(θ) are specified functions of a vector-valued parameter θ. This paper presents a rigorous derivation of the asymptotic distributions of the estimators of A, B, ω and θ obtained by an approximate least-squares method due to Whittle (1952). It is a sequel to a previous paper (Walker (1971)) in which a similar derivation was given for the special case of independent residuals where gu(θ) = 0 for u > 0, the parameter θ thus being absent.