  Delay alignment modulation (DAM) is a novel transmission technique for
wireless systems with high spatial resolution by leveraging delay compensation
and path-based beamforming, to mitigate the inter-symbol interference (ISI)
without resorting to complex channel equalization or multi-carrier
transmission. However, most existing studies on DAM consider a simplified
scenario by assuming that the channel multi-path delays are integer multiples
of the signal sampling interval. This paper investigates DAM for the more
general and practical scenarios with fractional multi-path delays. We first
analyze the impact of fractional multi-path delays on the existing DAM design,
termed integer DAM (iDAM), which can only achieve delay compensations that are
integer multiples of the sampling interval. It is revealed that the existence
of fractional multi-path delays renders iDAM no longer possible to achieve
perfect delay alignment. To address this issue, we propose a more generic DAM
design called fractional DAM (fDAM), which achieves fractional delay
pre-compensation via upsampling and fractional delay filtering. By leveraging
the Farrow filter structure, the proposed approach can eliminate ISI without
real-time computation of filter coefficients, as typically required in
traditional channel equalization techniques. Simulation results demonstrate
that the proposed fDAM outperforms the existing iDAM and orthogonal frequency
division multiplexing (OFDM) in terms of symbol error rate (SER) and spectral
efficiency, while maintaining a comparable peak-to-average power ratio (PAPR)
as iDAM, which is considerably lower than OFDM.
