Time series forecasting relies on predicting future values from historical data, yet most state-of-the-art approaches—including transformer and multilayer perceptron-based models—optimize using Mean Squared Error (MSE), which has two fundamental weaknesses: its point-wise error computation fails to capture temporal relationships, and it does not account for inherent noise in the data. To overcome these limitations, we introduce the Residual-Informed Loss (RI-Loss), a novel objective function based on the Hilbert-Schmidt Independence Criterion (HSIC). RI-Loss explicitly models noise structure by enforcing dependence between the residual sequence and a random time series, enabling more robust, noise-aware representations. Theoretically, we derive the first non-asymptotic HSIC bound with explicit double-sample complexity terms, achieving optimal convergence rates through Bernstein-type concentration inequalities and Rademacher complexity analysis. This provides rigorous guarantees for RI-Loss optimization while precisely quantifying kernel space interactions. Empirically, experiments across eight real-world benchmarks and five leading forecasting models demonstrate improvements in predictive performance, validating the effectiveness of our approach.

Time series forecasting is an important task that involves analyzing temporal dependencies and underlying patterns (such as trends, cyclicality, and seasonality) in historical data to predict future values or trends. Current deep learning-based forecasting models primarily employ Mean Squared Error (MSE) loss functions for regression modeling. Despite enabling direct value prediction, this method offers no uncertainty estimation and exhibits poor outlier robustness. To address these limitations, we propose OCE-TS, a novel ordinal classification approach for time series forecasting that replaces MSE with Ordinal Cross-Entropy (OCE) loss, preserving prediction order while quantifying uncertainty through probability output. Specifically, OCE-TS begins by discretizing observed values into ordered intervals and deriving their probabilities via a parametric distribution as supervision signals. Using a simple linear model, we then predict probability distributions for each timestep. The OCE loss is computed between the cumulative distributions of predicted and ground-truth probabilities, explicitly preserving ordinal relationships among forecasted values. Through theoretical analysis using influence functions, we establish that cross-entropy (CE) loss exhibits superior stability and outlier robustness compared to MSE loss. Empirically, we compared OCE-TS with five baseline models—Autoformer, DLinear, iTransformer, TimeXer, and TimeBridge—on seven public time series datasets. Using MSE and Mean Absolute Error (MAE) as evaluation metrics, the results demonstrate that OCE-TS consistently outperforms benchmark models.

We consider a mixed analog-to-digital converter (ADC) based architecture for direction of arrival (DOA) estimation using a uniform linear array (ULA). We derive the Cramér-Rao bound (CRB) of the DOA under the optimal time-varying threshold, and find that the asymptotic CRB is related to the arrangement of high-precision and one-bit ADCs for a fixed number of ADCs. Then, a new concept called "mixed-precision arrangement" is proposed. It is proven that better performance for DOA estimation is achieved when high-precision ADCs are distributed evenly around the edges of the ULA. This result can be extended to a more general case where the ULA is equipped with various precision ADCs. Simulation results show the validity of the asymptotic CRB and better performance under the optimal mixed-precision arrangement.

We consider the problem of angle estimation and ghost target identification for automotive multiple-input multiple-output (MIMO) radar in multipath scenarios. Firstly, we establish the multipath propagation model for the case of horizental MIMO arrays, and divide the multipath into two categories, i.e., Type 1: multipath with direction-of-arrival (DOA) $\neq$ direction-of-departure (DOD); Type 2: multipath with DOA$=$DOD. In the presence of multipath, the different DOA and DOD angles corrupt the notion of virtual array for MIMO radar, making angle estimation a major challenge. To jointly estimate the DOA and DOD of the target reflections, including both the direct path and multipath scenarios, we introduce a multipath iterative adaptive approach (MP-IAA), which possesses the super resolution, low sidelobe level, and robust properties for DOA and DOD estimation. Then, the Type 1 multipath with DOA$\neq$DOD can be directly identified based on the MP-IAA’s DOA and DOD estimates. Regarding to the Type 2 multipath with DOA$=$DOD, we solve the triangle relationships to identify the corresponding ghost targets. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithm for angle estimation and ghost target identification using automotive MIMO radar.

We consider code optimization and angle-Doppler imaging for slow-time code division multiplexing (ST-CDM) linear frequency-modulated continuous-wave (LFMCW) multiple-input multiple-output (MIMO) radar systems. We optimize the slow-time code via the minimization of a Cramér-Rao Bound (CRB)-based metric to enhance the parameter estimation performance. Then, a computationally efficient RELAX-based algorithm is presented to obtain the maximum likelihood (ML) estimates of the target angle-Doppler parameters. Numerical examples show that the proposed approaches can be used to improve the performance of parameter estimation and angle-Doppler imaging of ST-CDM LFMCW MIMO radar systems.

We consider efficient channel estimation for massive multiple-input multiple-output (MIMO) systems using one-bit analog-to-digital converters (ADCs) with antenna-varying thresholds at the receivers. We introduce a computationally efficient majorization-minimization (MM) based maximum likelihood (ML) channel matrix estimator (referred to as 1bMM-ML), which maximizes the one-bit likelihood function iteratively by solving simple linear least squares problems. Moreover, to take into account the low-rank property of the millimeter-wave (mmWave) massive MIMO channels, we add a nuclear-norm based penalty term to the negative log-likelihood function and solve the resulting problem efficiently using the MM approach (referred to as 1bMM-LR). To further enhance the channel estimation performance, we consider an angular-domain channel model and introduce a hybrid approach (referred to as 1bLR-RELAX), which combines 1bMM-LR with an existing parametric algorithm called 1bRELAX, to recover the angular-domain channel parameters. Numerical examples are provided to demonstrate the effectiveness and efficiency of the proposed channel estimation algorithms.

We consider the problem of phase modulated continuous wave (PMCW) radar signal processing when the receiver utilizes one-bit sampling with known time-varying thresholds. We formulate the target parameter estimation problem as a sparse signal recovery problem and use the alternating direction method of multipliers (ADMM) to solve it efficiently. Specifically, the log-norm approximation is used to replace the `0-norm to make the optimization problem more tractable. We then judiciously design the detailed updating steps of ADMM for the log-norm approximation, so that all updating steps involve computationally efficient closed-form solutions. Numerical examples are provided to demonstrate the effectiveness of our algorithm.