Ananthanarayanan Chockalingam

In this paper, we present a novel low-complexity receiver that performs detection and channel estimation tasks in Zak-OTFS modulation using over-sampling in the delay-Doppler (DD) domain. Towards this, we partition the over-sampled signal into multiple two-dimensional (2D) blocks, which is equivalent to parallel branch conventional sampling of delay- and Doppler-shifted signals. This partitioning along with processing only a subset of the partitioned 2D blocks aids in reducing complexity. Specifically, in terms of detection, we propose a symbol-wise selection-based detection (SSD) algorithm which makes symbol-wise decisions based on selection among parallel branch outputs. While the partition based processing reduces complexity, the selection-based symbol decisions offer good performance. We also exploit the proposed partitioning for low-complexity path-wise estimation of the DD channel taps based on maximum energy across blocks. Simulation results with fractional DDs show that the proposed detection and channel estimation algorithms for Zak-OTFS achieve good performance at low complexity.

New delay and Doppler (DD)-domain channel state information (CSI) estimation schemes are conceived for multi-user (MU)-orthogonal time frequency space (OTFS) multiple-input multiple-output (MIMO) systems, for both uplink (UL) and downlink (DL)-scenarios. An important feature of the proposed schemes is that the pilots are modulated and transmitted directly in the time-domain, leading to a low pilot-overhead, flexible training duration, and reduced complexity. These techniques, therefore, achieve a high bandwidth efficiency, since they eliminate the need for DD-domain guard bands corresponding to all the transmit antennas. Moreover, the DD-domain CSI of the MU-UL system is shown to be row-sparse in nature, while that of the MU-DL scenario exhibits block-sparsity. The multiple measurement vector (MMV)-based Bayesian learning (BL) technique for UL MIMO OTFS (MB-ULMO) is then proposed for exploiting the row-sparsity and for enhancing the UL channel estimation performance. Similarly, for the downlink, the block BL (BB) for DL MIMO OTFS (BB-DLMO) algorithm is proposed in order to exploit the block-sparsity for CSI recovery. Furthermore, the BCRLBs are derived for characterizing the MSEs of the proposed DD-domain channel estimation schemes. A low-complexity linear MMSE detector (LCLMD) is derived for data detection that is ideally suited for practical implementation since it does not require any prior information about the number of active multipath components at the receiver. Our simulation results demonstrate the improved performance of the proposed BL-based schemes both in comparison to extensions of other sparse schemes and to conventional estimation techniques.

Linear time-varying (LTV) systems model radar scenes where each reflector/target applies a delay, Doppler shift and complex amplitude scaling to a transmitted waveform. The receiver processes the received signal using the transmitted signal as a reference. The self-ambiguity function of the transmitted signal captures the cross-correlation of delay and Doppler shifts of the transmitted waveform. It acts as a blur that limits resolution, at the receiver, of the delay and Doppler shifts of targets in close proximity. This paper considers resolution of multiple targets and compares performance of traditional chirp waveforms with the Zak-OTFS waveform. The self-ambiguity function of a chirp is a line in the delay-Doppler domain, whereas the self-ambiguity function of the Zak-OTFS waveform is a lattice. The advantage of lattices over lines is better localization, and we show lattices provide superior noise-free estimation of the range and velocity of multiple targets. When the delay spread of the radar scene is less than the delay period of the Zak-OTFS modulation, and the Doppler spread is less than the Doppler period, we describe how to localize targets by calculating cross-ambiguities in the delay-Doppler domain. We show that the signal processing complexity of our approach is superior to the traditional approach of computing cross-ambiguities in the continuous time / frequency domain.

To meet the ever-increasing demand for higher data rates in mobile networks across generations, many novel schemes have been proposed in the standards. One such scheme is carrier aggregation (CA). Simply put, CA is a technique that allows mobile networks to combine multiple carriers to increase data rate and improve network efficiency. On the uplink, for power constrained users, this translates to the need for an efficient resource allocation scheme, where each user distributes its available power among its assigned uplink carriers. Choosing a good set of carriers and allocating appropriate power on the carriers is of paramount importance for good performance. Another factor that is critical to obtaining good performance is how well the degradation caused by the harmonic/intermodulation terms generated by the user’s transmitter non-linearities is handled. Specifically, for example, if the carrier allocation is such that a harmonic of a user’s uplink carrier falls on the downlink frequency of that user, it leads to a self coupling-induced sensitivity degradation of that user’s downlink receiver. Considering these factors, in this paper, we model the uplink carrier aggregation problem as an optimal resource allocation problem with the associated constraints of non-linearities induced self interference (SI). This involves optimization over a discrete variable (which carriers need to be turned on) and a continuous variable (what power needs to be allocated on the selected carriers) in dynamic environments, a problem which is hard to solve using traditional methods owing to the mixed nature of the optimization variables and the additional need to consider the SI constraint in the problem. Therefore, in this paper, we adopt a reinforcement learning (RL) framework involving a compound-action actor-critic (CA2C) algorithm for the uplink carrier aggregation problem. We propose a novel reward function that is critical for enabling the proposed CA2C algorithm to efficiently handle SI. The CA2C algorithm along with the proposed reward function learns to assign and activate suitable carriers in an online fashion. Numerical results demonstrate that the proposed RL based scheme is able to achieve higher sum throughputs compared to naive schemes. The results also demonstrate that the proposed reward function allows the CA2C algorithm to adapt the optimization both in the presence and absence of SI.

In this paper, we consider the problem of estimating the delay-Doppler (DD) domain inputoutput (I/O) relation in Zak-OTFS modulation, which is needed for signal detection. Two approaches, namely, model-dependent and model-free approaches, can be employed for this purpose. The modeldependent approach requires explicit estimation of the physical channel parameters (path delays, Dopplers, and gains) to obtain the I/O relation. Such an explicit estimation is not required in the model-free approach, where the I/O relation can be estimated by reading off the samples in the fundamental DD period of the received pilot frame. Model-free approach has the advantage of acquiring fractional DD channels with simplicity. However, the read-off in the model-free approach provides an estimate of the effective channel only over a limited region in the DD plane but it does not provide an estimate for the region outside, and this can affect the estimation performance depending on the pulse shaping characteristics of the DD pulse shaping filter used. A poorly localized DD pulse shape leads to an increased degradation in performance. Motivated by this, in this paper, we propose a novel, yet simple, I/O relation estimation scheme that alleviates the above issue in the model-free approach. We achieve this by obtaining a coarse estimate of the effective channel outside the model-free estimation region using a novel model-dependent scheme and using this estimate along with the model-free estimate to obtain an improved estimate of the overall I/O relation. We devise the proposed estimation scheme for both exclusive and embedded pilot frames. Our simulation results using Vehicular-A, TDL-A and TDL-C channel models with fractional DDs show that the proposed hybrid estimation approach achieves superior performance compared to the pure model-free approach. For example, at a bit error rate (BER) of 1.5 W 10-3, the proposed scheme achieves an SNR gain of about 3.5 dB compared to the model-free approach for sinc filter in Veh-A channel, and this performance gain is achieved with a moderate increase in complexity (e.g., about 2.95W108 and 8.1W108 real operations for model-free approach and the proposed scheme, respectively). Also, the proposed scheme performs close to that of the sparse Bayesian learning (SBL) based estimation but at a significantly lesser complexity (e.g., about 8.3W1012 and 8.1W108 real operations for the SBL based method and the proposed scheme, respectively).

The choice of delay-Doppler domain (DD) pulse shaping filter plays an important role in determining the performance of Zak-OTFS. Sinc filter has good main lobe characteristics (with nulls at information grid points) which is good for equalization/detection, but has high side lobes which are detrimental for input-output (I/O) relation estimation. Whereas, Gaussian filter is highly localized with very low side lobes which is good for I/O relation estimation, but has poor main lobe characteristics which is not good for equalization/detection In this paper, we propose a new filter, termed as Gaussian-sinc (GS) filter, which inherits the complementary strengths of both Gaussian and sinc filters. The proposed filter does not incur time or bandwidth expansion. We derive closed-form expressions for the I/O relation and noise covariance of Zak-OTFS with the proposed GS filter. We evaluate the Zak-OTFS performance for different pulse shaping filters with I/O relation estimated using exclusive and embedded pilots. Our results show that the proposed GS filter achieves better bit error rate (BER) performance compared to other filters reported in the literature. For example, with model-free I/O relation estimation using embedded pilot and 8-QAM, the proposed GS filter achieves an SNR gain of about 4 dB at 10⁻² uncoded BER compared to Gaussian and sinc filters, and the SNR gain becomes more than 6 dB at a coded BER of 10⁻⁴ with rate-1/2 coding.