  An orthogonal affine-precoded superimposed pilot-based architecture is
developed for the cyclic prefix (CP)-aided SISO and MIMO orthogonal time
frequency space systems relying on arbitrary transmitter-receiver pulse
shaping. The data and pilot symbol matrices are affine-precoded and
superimposed in the delay Doppler-domain followed by the development of an
end-to-end DD-domain relationship for the input-output symbols. At the
receiver, the decoupled pilot and data symbol are extracted by employing
orthogonal precoder matrices, which eliminates the mutual interference.
Furthermore, a novel pilot-aided Bayesian learning (PA-BL) technique is
conceived for the channel state information (CSI) estimation of SISO OTFS
systems based on the expectation-maximization (EM) technique. Subsequently, a
data-aided Bayesian learning (DA-BL)-based joint CSI estimation and data
detection technique is proposed, which beneficially harnesses the estimated
data symbols for improved CSI estimation. In this scenario our sophisticated
data detection rule also integrates the CSI uncertainty of channel estimation
into our the linear minimum mean square error (LMMSE) detectors. The AP-SIP
framework is also extended to MIMO OTFS systems, wherein the DD-domain input
matrix is affine-precoded for each transmit antenna (TA). Then an EM
algorithm-based PA-BL scheme is derived for simultaneous row-group sparse CSI
estimation for this system, followed also by our data-aided DA-BL scheme that
performs joint CSI estimation and data detection. Moreover, the Bayesian
Cramer-Rao bounds (BCRBs) are also derived for both SISO as well as MIMO OTFS
systems. Finally, simulation results are presented for characterizing the
performance of the proposed CSI estimation techniques in a range of typical
settings along with their bit error rate (BER) performance in comparison to an
ideal system having perfect CSI.
