	US 11,942,905 B2
	Method for determining filter coefficients and equalizer circuit
Bernhard Nitsch, Munich (DE)
Assigned to Rohde & Schwarz GmbH & Co. KG, Munich (DE)
Filed by Rohde & Schwarz GmbH & Co. KG, Munich (DE)
Filed on Mar. 17, 2022, as Appl. No. 17/697,608.
Claims priority of application No. 21171281 (EP), filed on Apr. 29, 2021.
Prior Publication US 2022/0368289 A1, Nov. 17, 2022
Int. Cl. H03F 1/32 (2006.01)

CPC H03F 1/3247 (2013.01) [H03F 1/3258 (2013.01); H03F 2201/3233 (2013.01)]

12 Claims

1. A method of determining filter coefficients of an equalizer circuit for equalizing a non-linear electronic system, wherein the equalizer circuit comprises a Volterra filter circuit, and wherein the method comprises the following steps:

providing an input signal;

processing the input signal by the non-linear electronic system, thereby obtaining an output signal;

providing a first mathematical model, wherein the first mathematical model describes the non-linear electronic system in terms of a first Volterra series;

providing a second mathematical model, wherein the second mathematical model describes the Volterra filter circuit in terms of a second Volterra series;

determining reference transfer functions of the Volterra filter circuit by a Pth order inverse technique based on the first Volterra series; and

determining filter coefficients of the Volterra filter circuit based on the determined reference transfer functions and based on the second Volterra series,

wherein the filter coefficients of the Volterra filter circuit are pruned such that frequency superpositions of contributions from different input signal frequencies contributing to the same output signal frequency are reduced;

wherein the filter coefficients of the Volterra filter circuit are determined based on the determined reference transfer functions via a least squares method,

wherein a cost function K=Ē²is provided, wherein the cost function describes a spectral error signal power Ē²in dependence of the reference transfer functions, wherein the cost function comprises a spectral weighting function W, and wherein the cost function is minimized in order to determine the filter coefficients of the Volterra filter circuit,

wherein the cost function is given by K=[X·h_eq−y_eq]^T·diag{W}·[X·h_eq−y_eq],

wherein X is a matrix comprising exponential functions of the respective Fourier transforms, wherein y_eqis a reference vector comprising the reference transfer functions, and wherein h_eqis a vector comprising the filter coefficients of the Volterra filter circuit.