IRS-OTFS Systems: Design of Reflection Coefficients for Low-Complexity ZF Equalizer

The blend of both intelligent reflecting surface (IRS) and orthogonal time frequency space (OTFS) technologies can enhance the reliability of wireless systems for the high mobility scenarios by optimally designing the IRS coefficients. In this work, considering the fact that the conventional linear equalization technique experiences high computational complexity for IRS-OTFS based systems due to the presence of high dimensional delay-Doppler channel matrix and a large number of passive reflection elements in IRS, we initially develop a low-complexity zero-forcing (ZF) equalizer by exploiting the sparsity of the delay-Doppler cascaded channel for IRS-OTFS systems. We further derive the instantaneous bit-error-rate (BER) expression for the proposed ZF equalizer and develop an optimization framework to design the IRS coefficients with an objective to minimize the BER. We also propose Gradient-descent based solution to this optimization problem. Furthermore, we develop minimum mean squared error (MMSE) equalizer using the proposed ZF equalizer. Finally, through extensive numerical simulations, we compare the performances of the proposed techniques with that of the existing state-of-the-art techniques, in terms of computational calculations and BERs.