Matched Filtering-Based Channel Estimation for AFDM Systems in Doubly Selective Channels

TL;DR

The paper tackles channel estimation for AFDM in doubly selective channels using matched filtering in the DAFT domain. It derives the I/O relation in time and DAFT domains, analyzes ICCI and SINR across IDID, IDFD, and FDFD channels, and proposes two low-complexity channel-matrix construction methods (FFT-based and segment-wise) to enable efficient CE. Two MF-based CE schemes are introduced for FDFD channels (MF-JE and MF-DE) along with a MF-GFS-DE variant that uses generalized Fibonacci search to reduce redundant computations, and the methods are extended to IDFD channels. Extensive simulations show significant complexity reductions and performance gains over existing CE schemes, validating the practical viability for wide-band AFDM systems. The work provides a pathway to practical, low-complexity CE in high-mobility scenarios using AFDM with fractionally-shifted delays and Dopplers.

Abstract

Affine frequency division multiplexing (AFDM) has recently emerged as an excellent backward-compatible 6G waveform. In this paper, we study matched filtering (MF) assisted channel estimation (CE) for AFDM systems in complex doubly selective channels. By deriving the complete input-output relationship of the continuous-time signal, the inter-chirp-carrier interference, signal-to-interference-plus-noise ratio (SINR), and the effective SINR loss of AFDM, are investigated in discrete affine Fourier transform (DAFT) domain. Further, we propose two low-complexity methods for constructing the channel matrix by taking advantage of its inherent discrete Fourier transform structure and the staircase structure of the piecewise functions in the channel matrix, respectively. It is shown that complexity reduction by at least two orders of magnitude can be achieved for a large number of chirp subcarriers. For the CE problem in doubly selective channels, we introduce an MF assisted CE scheme. This allows us to sequentially estimate the parameters of each path by exploiting the separability and approximate orthogonality of different paths in the DAFT domain, thus leading to significantly reduced complexity. Furthermore, based on generalized Fibonacci search (GFS), an MF-GFS scheme is proposed to avoid significantly redundant computation, which can be extended to typical wide-band systems. Extensive simulation results indicate that the proposed schemes offer superior advantages in terms of their improved communication performance and lower complexity.

Figures (14)

• Figure 1: AFDM system block diagram.
• Figure 2: Planform of SINR loss.
• Figure 3: Single pilot pattern for AFDM systems.
• Figure 4: The diagram of the GFS algorithm.
• Figure 5: Complexity comparison of different CE schemes.