Modulation Symbol Pulse Shaping Transceiver for Affine Frequency Division Multiplexing

Abstract

The recently proposed affine frequency division multiplexing (AFDM) waveform can adjust the time-frequency diversity gain by tuning chirp-rate parameter. Therefore, it is a candidate waveform in doubly-selective channels. This letter reveals that the modulation-symbol-domain shaping pulse of AFDM is generated by a convolution-like operation between the time-domain and frequency-domain shaping pulses, indicating that the modulation-symbol-domain pulse shaping of AFDM can be achieved by separately shaping in the time domain and frequency domain. Based on this, this letter presents an AFDM modulation-symbol-domain pulse shaping transceiver which has an ability to achieve the Nyquist pulse shaping, and provides the corresponding input-output relationship. Numerical results demonstrate the effectiveness of the proposed transceiver in improving the channel sparsity and pilot-to-data interference.

Figures (6)

• Figure 1: Illustration of the pulse shaping in AFDM, from time-domain pulse $g_{t}$ and frequency-domain pulse $g_{f}$ to modulation-symbol-domain pulse $g_{x}$.
• Figure 2: Proposed modulation symbol pulse shaping method for AFDM at (a) transmitter side, (b) receiver side.
• Figure 3: Illustration of the embedded pilot for simulations (P2D-I: pilot-to-data interference, D2P-I: data-to-pilot interference).
• Figure 4: Cumulative distribution functions of the highlight tap numbers $P_{\text{HL}}$ (the lower is better) for (a) using different shaping pulses with $\eta=-30$dB and $\zeta=1$, (b) using rectangular window shaping with different $\zeta$.
• Figure 5: Magnitude profiles of one realization of $y\left[m\right]$ using different shaping pulses wih the subcarrier number of (a) $M=4096$, (b) $M=512$.