On Zak transform based OTFS modulation for high mobility channels

Abstract

As we rapidly progress towards next generation wireless technologies, e.g., 6G and beyond, the air interface and modulation waveform must cater to diverse scenarios including high-mobility wireless environments. The performance of legacy multicarrier waveforms such as orthogonal frequency division multiplexing (OFDM) suffer in such environments due to severe inter-carrier interference resulting due to large Doppler spreads. Orthogonal time frequency space (OTFS) modulation waveform provides reliable and robust performance in such environments owing to its information multiplexing and signal processing in the delay-Doppler (DD) domain. In this thesis, we focus on Zak transform based OTFS.

In first part of the thesis, we consider discrete Zak transform based OTFS (DZT-OTFS). In this, we first develop a generalized DD domain matrix-vector input-output (I/O) relation that decouples the contributions of path delays and Dopplers. Leveraging this relation, we carry out an early investigation of the bit error rate (BER) performance of DZT-OTFS. Next, we study the peak-to-average power ratio (PAPR) of DZT-OTFS, for which we derive an upper bound on the PAPR for general transmit pulse shapes using Cauchy-Schwartz inequality. Finally, we consider the problem of channel estimation in DZT-OTFS. We develop a channel estimation algorithm for DZT-OTFS with embedded pilot frame and superimposed pilot frame. For the embedded pilot frame, we develop a low-complexity path-wise iterative channel estimation algorithm by decoupling the estimation of path delays and Dopplers. For the superimposed pilot frame, we propose a channel estimation algorithm that exploits the DD channel invariance across multiple frames and incorporate turbo iterations between channel estimation and data detection to mitigate the mutual interference between pilot and data symbols.

In second part of the thesis, we consider continuous Zak transform based OTFS (Zak-OTFS). In this, we first consider the problem of signal detection in Zak-OTFS assuming perfect channel knowledge, focusing on achieving near-optimal performance using mixed Gibbs sampling, where sampling is done on a mixed distribution. Next, we consider the problem of channel estimation and data detection in Zak-OTFS under an over-sampled receiver framework. We present an analysis that compares the performance of conventional sampling and over-sampling in Zak-OTFS. To reduce the computational complexity due to over-sampling, instead of directly over-sampling the received signal, we propose to perform conventional sampling on multiple parallel branches whose inputs are the delay- and Doppler-shifted versions of the received signal. For channel estimation, we consider exclusive pilot frame, embedded pilot frame, and superimposed spread pilot frame. For the exclusive and embedded pilot frames, we propose a low-complexity path-wise estimation of the DD channel taps based on maximum energy across blocks. For detection, we propose a symbol-wise selection-based detection (SSD) algorithm which makes symbol-wise decisions based on selection among parallel branch outputs. For the superimposed spread pilot frame, we derive the maximum-likelihood (ML) channel estimate on each branch, which is the cross-ambiguity between the received signal on the branch and the transmitted spread pilot. To alleviate the pilot-data interference issue, turbo iterations between channel estimation and detection are performed.