Design and Performance Analysis of AFDM with Multiple Antennas in Doubly Selective Channels

On the heels of orthogonal time frequency space (OTFS) modulation, the recently discovered affine frequency division multiplexing (AFDM) is a promising waveform for the sixth-generation wireless network. In this paper, we introduce the multiple-input multiple-output AFDM (MIMO-AFDM) system, which combines the superiorities of high multiplexing and diversity gain from MIMO and strong delay-Doppler spread resilience from AFDM. In the case of ideal channel state information (CSI), we first fomulate the vectorized input-output relationship, and then prove that the MIMO-AFDM system can achieve full diversity in doubly slective channels. Consequently, MIMO-AFDM has the bit error ratio (BER) performance identical to MIMO-OTFS while outperforming MIMO-OFDM significantly. Moreover, for the case of imperfect CSI, we propose a low-complexity embedded pilot-aided diagonal reconstruction (EPA-DR) channel estimation scheme. Simulation results show that MIMO-AFDM with estimated CSI establishes the BER performance similar to that with ideal CSI. Finally, we investigate the orthogonal resource allocation of affine frequency division multiple access (AFDMA) system, which shows great potential for multiple access in high mobility scenarios thanks to its high efficiency and flexibility.