Faster chirp choice and a lower‑complexity receiver for AFDM wireless in high‑mobility channels
This paper studies how to make a new kind of wireless waveform called affine frequency division multiplexing (AFDM) work better and faster in fast‑moving settings. AFDM can resist the rapid changes in radio channels that happen when transmitters, receivers or reflectors move quickly. But to get good error rates you must pick the right “chirp” setting (a parameter called c1) and use a receiver that does not need heavy computation. The authors propose algorithms to pick the chirp and to build a simpler minimum mean square error (MMSE) receiver that still keeps performance high.
The team first used a mathematical property of the AFDM transform, the discrete affine Fourier transform (DAFT), which gives the channel matrix special diagonal and circulant structure. From that they derived a simplified bit error rate (BER) metric that is much cheaper to compute than a full BER evaluation. Using this metric they built a fast circulant‑diagonal aggregation (FCDA) algorithm to find a good c1. In simulations the FCDA reduced the search time for the best c1 by about an order of magnitude compared with a direct BER‑based search.
To reduce receiver complexity they exploit sparsity in the AFDM effective channel matrix (ECM). The researchers build a cyclic, banded version of the ECM by pruning less important channel paths in a structured way. This lets them design a low‑complexity banded MMSE (LC‑BMMSE) receiver. Instead of inverting a large matrix, the receiver uses banded Cholesky factorization, a standard linear‑algebra trick that is much cheaper when the matrix is banded.
The paper brings the ideas together in a hierarchical search called HS‑JCPS (hierarchical‑search joint chirp parameter and structured sparsification). This routine jointly chooses the chirp parameter and the sparsification (pruning) pattern under a target complexity limit. The authors also derive a lower bound on MMSE performance for the sparsified ECM to guide the search. In simulations the HS‑JCPS with the LC‑BMMSE receiver finds a near‑optimal c1 and pruning width and achieves about a 1 dB gain in BER at 10^-3, giving a better tradeoff between performance and computation.