Preconditioned Conjugate Gradient for MIMO-AFDM System

Affine frequency division multiplexing (AFDM) is a promising chirp-assisted multicarrier waveform for future high mobility communications. A significant challenge in MIMO-AFDM systems is the multi-user interference (MUI), which can be effectively addressed by employing precoding techniques. However, the complexity introduced by AFDM makes the precoding process computationally expensive and challenging. To overcome this issue, We combine AFDM channel sparse property and using Preconditioned Conjugate Gradient (PCG) method to iteratively process the precoding, thereby reducing the complexity of the precoding design. Simulation results demonstrate that the proposed sparsification approach, coupled with the PCG method, achieving quite precoding performance while significantly reducing computational complexity. This makes the application of AFDM more feasible and efficient for high-mobility communication scenarios, paving the way for its broader implementation in next-generation communication systems.