Because of its superior multipath channel performance and spectrum efficiency, orthogonal frequency-division multiplexing (OFDM) is one of the most suitable candidates for the 6G physical layer in contemporary applications like smart cities and crowded environments in a social Internet of Things (S-IoT) ecosystem. The terahertz (THz) band, 1Tb/s data rate, low latency, spectrum efficacy, and mobility of 1000 km/h are just a few of the requirements that 6G must meet. Using single-tap equalization, OFDM may reduce the multipath channel impact optimally. However, when the channel has doubly dispersive fading, inter-carrier interference starts to create errors. The worst doubly dispersive fading channel will be produced when THz and high-speed mobility are combined with OFDM as the physical layer for 6G. OFDM requires a complicated equalizer when using channels with doubly dispersive fading. On the basis of band factorization, time domain least squares QR (LSQR) iterative computing, and banded minimum mean squared error (BMMSE), a number of low-complexity equalizers for OFDM have been proposed. Conjugate gradient least squares (CGLS), a revolutionary iterative computation algorithm, is proposed in this study; the proposed equalization technique obtains the trade-off between computations and performance. Simulation results show that the proposed equalizer outperforms the existing BMMSE and LSQR algorithms over doubly dispersive fading channels.