Single-Carrier Delay-Doppler Domain Equalization

TL;DR

This work addresses the high PAPR of OTFS in doubly-selective channels by proposing single-carrier delay-Doppler domain equalization (SC-DDE), which performs equalization in the delay-Doppler domain after converting the time-domain SC signal via the discrete Zak transform (DZT). It introduces an embedded pilot-aided channel estimation scheme that preserves peak power while enabling DD-domain CSI, and provides a MMSE 2D DD-domain equalizer together with post-processing to recover symbols. Through simulations, SC-DDE shows significantly lower PAPR than OTFS while delivering comparable coded BER performance, and it outperforms SC-FDE in BER at the cost of higher receiver complexity. The approach is particularly attractive for uplink scenarios where PA efficiency is critical, offering a practical alternative to OTFS with favorable PAPR characteristics and robust performance under channel estimation.

Abstract

For doubly-selective channels, delay-Doppler (DD) modulation, mostly known as orthogonal time frequency space (OTFS) modulation, enables simultaneous compensation of delay and Doppler shifts. However, OTFS modulated signal has high peak-to-average power ratio (PAPR) because of its precoding operation performed over the DD domain. In order to deal with this problem, we propose a single-carrier transmission with delay-Doppler domain equalization (SC-DDE). In this system, the discretized time-domain SC signal is converted to the DD domain by discrete Zak transform (DZT) at the receiver side, followed by delay-Doppler domain equalization (DDE). Since equalization is performed in the DD domain, the SC-DDE receiver should acquire the channel delay-Doppler response. To this end, we introduce an embedded pilot-aided channel estimation scheme designed for SC-DDE, which does not affect the peak power property of transmitted signals. Through computer simulation, distribution of PAPR and bit error rate (BER) performance of the proposed system are compared with those of the conventional OTFS and SC with frequency-domain equalization (SC-FDE). As a result, our proposed SC-DDE significantly outperforms SC-FDE in terms of BER at the expense of additional computational complexity at the receiver. Furthermore, SC-DDE shows much lower PAPR than OTFS even though they achieve comparable coded BER performance.

Figures (10)

• Figure 1: A block diagram of the SC transmitter with $J$-times oversampling for the block length $N$.
• Figure 2: Symbol representation in the time, DD, and vectorized DD domain, where we set $N = 64$ and $(L, K) = (8, 8)$.
• Figure 3: A block diagram of the SC-DDE receiver.
• Figure 4: System block diagram comparison of (a) OFDM, (b) SC-FDE, (c) OTFS, and (d) SC-DDE, where the vectorization process is omitted.
• Figure 5: Pilot symbol configuration in the DD domain for SC-DDE, where $(L,K) = (16,16)$, $L_\text{guard} = 2$, and $(l_\text{max}, k_\text{max}) = (2, 7)$.