Embedded Delay-Doppler Channel Estimation for Orthogonal Time Frequency Space Modulation

Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) over delay-Doppler channels. The channel impulse response is needed at the receiver to perform OTFS detection. In this work, we analyze OTFS-based channel estimation using a pilot symbol embedded in the data frame: the pilot symbol with a number of guard zero-symbols is suitably located on the delay-Doppler grid containing the information symbols. Different symbol arrangements are proposed depending on whether the channel has integer or fractional Doppler paths relative to an integer grid. The channel information is first estimated from a group of received symbols using a simple threshold method. The estimated information is then used for data detection within the same frame, via a message passing (MP) algorithm. Numerical results compare the error performance of the proposed schemes and the OTFS scheme with ideal channel estimation under similar spectral and energy efficiency. Moreover, our results show that OTFS with non-ideal channel estimation can still outperform OFDM with ideal channel estimation.

I. Introduction

While the orthogonal frequency division multiplexing (OFDM) modulation scheme currently deployed in fourth-generation (4G) mobile systems achieves high spectral efficiency for time-invariant frequency selective channels, it is not so robust to time-varying channels, especially for channels with high Doppler spreads (e.g., high-speed railway mobile communications). Hence, new modulation schemes/waveforms that are robust to channel time-variations are being extensively explored. Recently, orthogonal time frequency space (OTFS) modulation was proposed in [1], showing significant advantages over OFDM, in delay–Doppler channels with a number of paths, with different delay and Doppler values. The delay-Doppler domain is an alternative representation of a time-varying channel geometry due to moving objects (e.g. transmitters, receivers, reflectors) in the scene. Leveraging on this representation, the OTFS modulator spreads each of the information (e.g., QAM) symbols over a set of two dimensional (2D) orthogonal basis functions, which span across the frequency–time resources required to transmit a burst. The basis function set is specifically designed to combat the dynamics of the time-varying multi-path channel. At the receiver, the channel impulse response needs to be known to perform OTFS detection with any detection algorithm such as [2] [6]. Therefore, an accurate pilot-driven channel estimation is required, and depending on the dynamics of the channel relative to the OTFS burst length, the estimation can be rapidly outdated. For example, in [6], since an entire OTFS frame is used for pilot transmission, the resulting estimated channel information can be outdated for data detection in the following OTFS frame. In [5], [8], channel estimation techniques for delay–Doppler channels in time–frequency domain have been discussed, which have high implementation complexity.