# Converting the equalizer coefficients from VSA at 2 sample/Symbol to 1.5 sample/Symbol

I was looking for some feedback on conversion of equalizer/filter coefficients at different sampler rate.

Problem Statement: We have built a transmitter system whose output is at 1.5 sample/symbol (i.e. ratio of Output sample rate/Input sample rate). The signal going through this transmitter is modulated carrier of bandwidth 1 GHz.I have run this signal through a Digital-to-Analog Converter (DAC) and equalized the signal by generating and storing the coefficients from Rohde & Schwarz VSA. The goal is to use minimum equalizer taps to meet some specific EVM requirement. The VSA gives option to generate equalizer coefficients at 2, 4 or 8 sample/symbol thereby giving some oversampling gain.The goal is to translate the equalizer coefficients in 1.5 sample/symbol to be used as hard coded values in hardware design/implementation.

Approach: The approach I am taking is to take 8 sample/Symbol coefficients and converting it into 1.5 sample/Symbol. I have done this by Interpolation of 3, Low pass Filtering, Decimation of 16. I have also done this decimation using variable decimator (9th order Lagrange based). Now my equalizer coefficients are at 1.5 sample/symbol,I convert them to frequency domain (by same FFT size and 10 times the size of coefficients for better resolution). I then take inverse 1/Eq (f) to model the RF slope/impairments. Then I have taken IFFT of equalizer and RF slope coefficients and their spectrum plots are exact mirror images. I have then applied those coefficients (Distortion and equalizer) to the modulated carrier in MATLAB and measured the EVM. However, my EVM is bad i.e. -27 dB whereas my original carrier EVM is around -55 dB. I am not sure if I am doing something wrong in this process. Any opinion, feedback or ideas would be highly appreciated. Thanks

Also,Information about a similar VSA is given below

https://www.rohde-schwarz.com/ca/product/fsw-productstartpage_63493-11793.html