This paper addresses the channel estimation problem for Orthogonal time frequency space (OTFS) systems in the presence of fractional Doppler. Channel estimation with fractional Doppler can be considered as an off-grid sparse signal recovery problem, where the virtual sampling grid is introduced in the delay-Doppler domain. First-order linear approximation as a conventional approach to estimate fractional Doppler and sparse signal in OTFS systems. However, linear approximation approach may incur considerable modeling errors, since the finite sampling grid may be insufficiently refined in the OTFS systems. Furthermore, this error will deteriorate recovery performance. To solve this problem, we propose an efficient sparse Bayesian learning (SBL) method to jointly estimate the fractional Doppler and sparse channel vectors. Specifically, we reformulate the input-output relationship for fractional Doppler, and further present an off-grid channel estimation model. Then, an in-exact block majorization-minimization (MM) algorithm is adopted to iteratively update the associated parameters under the SBL framework. Fractional Doppler can be iteratively refined to eliminate the off-grid gap using the gradient descent method. The proposed scheme presents an exact channel estimation model that avoids any approximation operation, so that it effectively alleviates the model error. Simulation results show that the proposed channel estimation method significantly outperforms state-of-the-art methods

Orthogonal time-frequency-space (OTFS) modulation has shown significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in time-varying channels. However, the symbols in OTFS frames still suffer from inter-Doppler interference (IDI) and inter-symbol interference (ISI). In this letter, we propose a two dimensional (2D) adaptive multichannel decision feedback equalizer (DFE) to combat the interference. The proposed receiver constructs the input signal and feedback signal of the DFE based on the characteristic of OTFS modulation. Meanwhile, by exploiting the sparsity feature of the channels in delay-Doppler domain, the iterative improved proportionate normalized least mean squares (IPNLMS) algorithm is employed to achieve fast convergence and fast tracking. The simulation results show that the proposed equalizer could achieve satisfied BER performance with lower complexity.

This letter proposes a learned denoising-based sparse adaptive channel estimation method in the delay-Doppler domain for time-varying underwater acoustic (UWA) channels in an orthogonal time-frequency space (OTFS) system. We first propose a symbol-wise adaptive channel estimation method for the OTFS system. By leveraging the sparsity characteristic of the channels, we employ the improved proportionate normalized least mean squares (IPNLMS) algorithm. Based on the characteristic that the channel in the delay-Doppler domain is invariant, the multiple estimates obtained from the adaptive filter could be regarded as multiple noisy images derived from the same clean image. A neural network called FastDVDNet, commonly used in video denoising, is utilized to exploit the correlation among the multiple images. The simulation results demonstrate that the proposed denoising strategies significantly enhance the estimation performance, thereby achieving superior channel estimation results.

With the development of the underwater acoustic (UWA) adaptive communication system, energy-efficient transmission has become a critical topic in underwater acoustic (UWA) communications. Due to the unique characteristics of the underwater environment, the transmitter node will almost always have outdated channel state information (CSI), which results in low energy efficiency. In this paper, we take full advantage of bidirectional links and propose an adaptive modulation and coding (AMC) scheme that aims to maximize the long-term energy efficiency of a single link by jointly scheduling the coding rate, modulation order, and transmission power. Considering the complexity characteristics of UWA channels, we proposed a bit error ratio (BER) estimation method based on deep neural networks (DNN). The proposed network could realize channel estimation, feature extraction, and BER estimation by using a fixed pilot of the feedback link. Then, we design a channel classification method based on the estimated BERs of the modulation and coding scheme (MCS) and further model the UWA channels as a finite-state Markov chain (FSMC) with an unknown transition probability. Thus, we formulate the AMC problem as a Markov Decision Process (MDP) and solve it through a reinforcement learning framework. Considering the large state-action pairs, a double deep Q-network (DDQN) based scheme is proposed. Simulation results demonstrate that the proposed AMC scheme outperforms the fixed MCS with a perfect channel information state, and achieves near-optimal energy efficiency.

Single-carrier frequency-domain equalization (SC-FDE) is a promising technique for coherent high-rate underwater acoustic communications. In this paper, a time-frequency domain turbo equalization (TFD-TE) scheme is proposed for single-carrier modulation. The TFD-TE scheme is to couple a multi-channel frequency domain equalizer with phase rotation compensation and a low-order single-channel time-domain turbo equalizer. To mitigate the error propagation and further enhance receiver performance, a bidirectional equalizer that combined the soft outputs of a conventional equalizer and a backward equalizer is introduced into the proposed TFD-TE scheme (Bi-TFD-TF). The sparse channel is estimated by the improved proportionate normalized least mean squares (IPNLMS) algorithm block by block. Both simulated and experimental results show the proposed TFD-TE can effectively improve system performance with acceptable complexity. The proposed TFD-TE scheme is evaluated using communication data collected from the DJK15 lake experiment. For the 1 ×4 single-input multiple-output (SIMO) communication system using quadrature phase shift keying (QPSK) and 8-phase shift keying (8PSK) modulations, the proposed scheme achieves error-free transmission after a few iterations. Our receiver achieves a maximum raw data rate of 12 kbit/s and a reliable net data rate of 4 kbit/s within 4 kHz bandwidth at a range of 10.8 km. Compared with conventional frequency domain turbo equalization (FD-TE), the proposed TFD-TE scheme can enhance 0.8-1.3 dB in terms of output signal-to-noise ratio (OSNR). The related Bi-TFD-TE provides additional 0.8-1.7 dB OSNR improvement.

This work proposes a novel interleave-division multiple access (IDMA) system based on cyclic shift keying (CSK) modulation, named CSK-IDMA, for multiuser underwater acoustic (UWA) communications. The CSK modulation uses a circular cyclic shift of the spreading sequence to represent the information, which can be viewed as a special M-ary spread spectrum modulation. Compared with conventional direct-sequence spread spectrum (DSSS) technique, CSK overcomes the spreading gain versus data rate limitations. The proposed scheme adopts the IDMA technique to reduce the cochannel interference. At the receiver, we employ passive time reversal (PTR) technique to compress the channels and improve the signal-to-interference-noise ratio (SINR) at first. In order to perfectly incorporate with the IDMA receive structure, we propose a soft CSK demodulation which can iteratively exchange extrinsic information with a soft channel decoder to form a turbo equalization. Simulation results show the proposed CSK-IDMA scheme can offer significantly improved performance. The data processing results from a lake experiment show that the proposed scheme can support 8 users and 10 users with zero error bits for 2.3 km transmission and 2.7 km transmission, respectively. The corresponding bit error rate (BER) for 16 users are $8.4 \times 10^4$ and $9.7 \times 10^4$ , respectively. The data rate is 62.5 bit/s per user within 4 kHz bandwidth and spreading sequences of 256 chips. To the best of our knowledge, this is the first work which can support more than 8 users for multiuser UWA communications with a high bandwidth efficiency.