Hardware Modelling of a PLC Multipath Channel Transfer Function

Abstract

PLC channel transfer functions are critical in developing channel emulators. Emulators are used to test PLC transceivers that would have been otherwise tested on a live network which is not only hazardous but also is not repetitive since the PLC network's characteristics vary with time and frequency. The PLC channel transfer function that is considered here is the multipath channel model of Zimmermann and Dostert. Zimmermann's multipath channel transfer function includes not only the attenuation experienced by the signal, but also the phase change due to the multipath. The inclusion of the phase in the transfer function requires the processing of imaginary numbers in the FPGA. Euler's theorem is used to convert from the polar form to the rectangular form of the transfer function. This paper focuses on the hardware modelling of the rectangular form using Hardware Description Language. The real and imaginary components of the rectangular form are modelled as two circuit models. The designed channel transfer function module uses fixed point (FP) format. The HDL model was successfully synthesized to a hardware equivalence using the XILINX ISE tool. XILINX core generator was used for the CORDIC module that computes the sine, cosine, hyperbolic sine and hyperbolic cosine functions. Simulation result of the hardware model revealed an accuracy of up to at least 3 decimal places when compared to the theoretical results using Excel or Matlab.