Issues with ZF and LMMSE Equalization in Multicarrier-FTN Receiver Implementation (BPSK, AWGN)

I am working on implementing the attached paper in MATLAB. I have successfully implemented the transmitter, but I am facing challenges with the receiver.

The main issue is that the Zero-Forcing (ZF) equalizer (i.e., the inverse of the HH matrix) does not provide an acceptable BER when τ<1. However, when τ=1, the performance is acceptable.

To improve performance, I also tried implementing the standard LMMSE equalizer, since my system does not include channel coding. However, the performance gap between τ=1 and τ=0.9 is still very large.

I am using BPSK modulation and only AWGN noise in my simulation. What could be causing this significant degradation in performance for τ<1? Are there any recommended techniques to improve BER in this scenario?

Any insights or suggestions would be greatly appreciated!