# Multi-path equalization in SERDES system analysis

In transmitter I send the data 1 sample per bit, then received in Rx passing by ADC then FFE adaptive filter and then a slicer to return the samples in bits and calculate the BER and it works well

When I try to make multi-path each path contains ADC and FFE adaptive filter it fails, as I make a functions named as FFE and another function called ADC

for example if data is abcdefghijklmnop if there are 2 paths so the 2 paths are :

1. acegikmo
2. bdfhjlnp

Which means that the bit rate are different now for the delays of the FFE filter as the delay should be 2*old_delay

but really the implementation is vector based, as I took the first sample multiplied by a coefficient and the second with another coefficient and LMS algorithm to get the optimum coefficients

When I plot the magnitude response of FFE using fvtool: 1) if 1 path >> the response if HPF (opposite to LPF of channel) 2) if 2 paths >> it HPF but much worse 3) if 4 paths >> not HPF

Is there any change in Rx can be done to solve the problem ?

ِAlso How to determine sampling frequency in fvtool or how to convert x-axis from normalized axis to Hertz

Each path in the multipath as received by the ADC's and FFE would not have the data itself segregated as the OP indicated. The data received by antenna/ADC for receiver $$r_1$$ would be the sum of data stream 1 convolved with the channel from transmitter $$t_1$$ to receiver $$r_1$$ ($$c_{11}$$) with data stream 2 convolved with the channel from transmitter $$t_2$$ to receiver $$r_1$$ ($$c_{12}$$).
$$r_1[n] = t_1[n] \circledast c_{11}[n] + t_2[n] \circledast c_{12}[n]$$
Similarly $$r_2$$ would be given by:
$$r_2[n] = t_1[n] \circledast c_{21}[n] + t_2[n] \circledast c_{22}[n]$$
Where $$c_{nm}$$ is the channel from $$t_m$$ to $$r_n$$.