Abstract: Wall coverings for anechoic chambers are disclosed having an array of lossy pyramid cone material mounted on multiple backing layers of absorbing material. The number of backing layers to be used, their physical dimension (thickness) and their material properties (conductivity and permittivity) are selected so as not to modify the high frequency (UHF) behavior of the pyramid structure, while at the same time providing a greatly reduced low frequency (VHF) reflection coefficient for the composite absorbing wall. The physical dimension and the material properties of each of the multiple backing layers are selected by a constrained nonlinear optimization data processing procedure or method. The optimization method utilizes known S parameters of the pyramid array, and either known properties of the backing layers, or constrained backing layer properties that are defined by the wall designer.