# Seperation of multi-carrier signal using Square Root Nyquist filter

My goal is to separate multi-carrier to single carrier outputs. I intend to do it using Polyphase FBMC.

Each of my carrier is 10 MHz in bandwidth. I have 256 such carrier in the channel. Thus I have to use a sampling frequency of at least 2.56 GHz.

It would be difficult to design a one stage FBMC system to separate 256 carrier as the prototype filter design would be next to impossible because of transition band constraint. Thus, I intend to do it in 2 stages ie 16x16.

First stage i'll decimate by 16. Second stage, each of the 16 outputs (having 16 carriers) will be further decimated by 16 to give 1 carrier.

I referred to Filter Bank Multicarrier Modulation: A Waveform Candidate for 5G and Beyond and A UNIVERSAL SQUARE-ROOT NYQUIST (M) FILTER DESIGN FOR DIGITAL COMMUNICATION SYSTEMS(pdf) by Behrouz Farhang-Boroujeny for designing my prototype filter.

h=srNyquistM(512,16,0.10,0.1,0,0,50);


I am using 512 tap filter, for decimation factor of 16 & roll off factor of 0.1. The other parameters are default according to the author. But even using such a filter, my transition band is spanning 12 MHz

This would mean I will lose 1 carrier on each side (each carrier is 10 MHz). So 2 carriers per polyphase path (16) ie 32 carriers in 1st stage. And 32 carriers in 2nd stage.

How can I avoid this. How can I build a prototype filter that will allow me to separate 256 carries, each of 10 MHz into individual carriers at the output. Is FBMC not the best method to do this?