Chirp parameter selection for affine frequency division multiplexing with MMSE equalization

Affine Frequency Division Multiplexing (AFDM) is a chirp-transform modulation technique that has shown reliable performance in high-mobility scenarios, making it an attractive option for next generation communication systems. Recent literature suggests that under chirp parameter adjustment, AFDM can achieve optimal diversity performance in delay-doppler channels with maximum likelihood (ML) detection. However, the performance of AFDM with minimum mean square error equalization (MMSE-Eq) has not been extensively investigated in the existing literature. In this paper, we analyze the performance of AFDM with MMSE-Eq, derive a lower bound for the theoretical bit error rate (BER) of the AFDM system, and discuss the relationship between chirp parameters and performance degradation. To optimize BER performance, we propose two distinct chirp parameter selection strategies for frequency selective and doubly selective channels, respectively. These strategies offer the advantage of avoiding extensive computations. Additionally, we propose a low-complexity and high-performance iterative MMSE-Eq algorithm based on time-domain channel matrix operations. The algorithm resolves the issue encountered in existing low-complexity methods, where different chirp parameter selections significantly impact the complexity. Simulation results demonstrate the efficacy of our proposed parameter selection strategies and the outstanding BER performance achieved by the iterative MMSE-Eq algorithm.