Conditional Sampling via Wasserstein Autoencoders and Triangular Transport

We present Conditional Wasserstein Autoencoders (CWAEs), a framework for conditional simulation that exploits low-dimensional structure in both the conditioned and the conditioning variables. The key idea is to modify a Wasserstein autoencoder to use a (block-) triangular decoder and impose an appropriate independence assumption on the latent variables. We show that the resulting model gives an autoencoder that can exploit low-dimensional structure while simultaneously the decoder can be used for conditional simulation. We explore various theoretical properties of CWAEs, including their connections to conditional optimal transport (OT) problems. We also present alternative formulations that lead to three architectural variants forming the foundation of our algorithms. We present a series of numerical experiments that demonstrate that our different CWAE variants achieve substantial reductions in approximation error relative to the low-rank ensemble Kalman filter (LREnKF), particularly in problems where the support of the conditional measures is truly low-dimensional.

Error Analysis of Triangular Optimal Transport Maps for Filtering

We present a systematic analysis of estimation errors for a class of optimal transport based algorithms for filtering and data assimilation. Along the way, we extend previous error analyses of Brenier maps to the case of conditional Brenier maps that arise in the context of simulation based inference. We then apply these results in a filtering scenario to analyze the optimal transport filtering algorithm of Al-Jarrah et al. (2024, ICML). An extension of that algorithm along with numerical benchmarks on various non-Gaussian and high-dimensional examples are provided to demonstrate its effectiveness and practical potential.

Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps

In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF.

RIS-enabled Multi-user M-QAM Uplink NOMA Systems: Design, Analysis, and Optimization

Non-orthogonal multiple access (NOMA) is widely recognized for enhancing the energy and spectral efficiency through effective radio resource sharing. However, uplink NOMA systems face greater challenges than their downlink counterparts, as their bit error rate (BER) performance is hindered by an inherent error floor due to error propagation caused by imperfect successive interference cancellation (SIC). This paper investigates BER performance improvements enabled by reconfigurable intelligent surfaces (RISs) in multi-user uplink NOMA transmission. Specifically, we propose a novel RIS-assisted uplink NOMA design, where the RIS phase shifts are optimized to enhance the received signal amplitudes while mitigating the phase rotations induced by the channel. To achieve this, we first develop an accurate channel model for the effective user channels, which facilitates our BER analysis. We then introduce a channel alignment scheme for a two-user scenario, enabling efficient SIC-based detection and deriving closed-form BER expressions. We further extend the analysis to a generalized setup with an arbitrary number of users and modulation orders for quadrature amplitude modulation signaling. Using the derived BER expressions, we develop an optimized uplink NOMA power allocation (PA) scheme that minimizes the average BER while satisfying the user transmit power constraints. It will be shown that the proposed NOMA detection scheme, in conjunction with the optimized PA strategy, eliminate SIC error floors at the base station. The theoretical BER expressions are validated using simulations, which confirms the effectiveness of the proposed design in eliminating BER floors.

Waveform Design of Multi-User-Multi-Target ISAC System based on Kullback-Leibler Divergence

This paper presents a novel framework that leverages the Kullback-Leibler divergence (KLD) to analyze and optimize performance trade-offs in integrated sensing and communication (ISAC) systems. We consider a multiple-input-multiple-output (MIMO) base station that simultaneously serves communication user equipments (UEs) and detects multiple targets using shared antenna deployment. The proposed KLD-based approach provides a unified performance measure encompassing both UE error rate and target detection capability. We apply this approach on two well-known communication beamforming techniques, maximum ratio transmission (MRT) and zero-forcing (ZF), and evaluate the effect on the radar subsystem. Furthermore, two optimization problems are formulated and solved. The first one optimizes the KLD of the radar subsystem for given constraints on the communication KLD, whereas the second one focuses on communication waveform KLD-based optimization and constrained radar KLD. These optimization problems are solved using a projected gradient method with an adaptive penalty for the radar waveform and a gradient-assisted interior point method for the communication waveform. Through theoretical derivations and extensive simulations, it is demonstrated that our approach can be a powerful tool for characterizing and optimizing the performance trade-offs of ISAC under various configurations. The results also show significant improvements in both sensing and communication performance by the KLD-optimized system compared to well-known benchmarks, such as conventional MRT and ZF for the communication subsystem, and the conventional identity covariance design for the radar subsystem. These findings support the holistic design and optimization of ISAC in next-generation wireless networks.

Generalized BER Performance Analysis for SIC-based Uplink NOMA Systems

Non-orthogonal multiple access (NOMA) is widely recognized for its spectral and energy efficiency, which allows more users to share the network resources more effectively. This paper provides a generalized bit error rate (BER) performance analysis of successive interference cancellation (SIC)-based uplink NOMA systems under Rayleigh fading channels, taking into account error propagation resulting from SIC imperfections. Exact closed-form BER expressions are initially derived for scenarios with 2 and 3 users using quadrature phase shift keying (QPSK) modulation. These expressions are then generalized to encompass any arbitrary rectangular/square M-ary quadrature amplitude modulation (M-QAM) order, number of NOMA users, and number of BS antennas. Additionally, by utilizing the derived closed-form BER expressions, a simple and practically feasible power allocation (PA) technique is devised to minimize the sum bit error rate of the users and optimize the SIC-based NOMA detection at the base-station (BS). The derived closed-form expressions are corroborated through Monte Carlo simulations. It is demonstrated that these expressions can be effective for optimal uplink PA to ensure optimized SIC detection that mitigates error floors. It is also shown that significant performance improvements are achieved regardless of the users' decoding order, making uplink SIC-based NOMA a viable approach.

Novel KLD-based Resource Allocation for Integrated Sensing and Communication

In this paper, we introduce a novel resource allocation approach for integrated sensing-communication (ISAC) using the Kullback-Leibler divergence (KLD) metric. Specifically, we consider a base-station with limited power and antenna resources serving a number of communication users and detecting multiple targets simultaneously. First, we analyze the KLD for two possible antenna deployments, which are the separated and shared deployments, then use the results to optimize the resources of the base-station through minimising the average KLD for the network while satisfying a minimum predefined KLD requirement for each user equipment (UE) and target. To this end, the optimisation is formulated and presented as a mixed integer nonlinear programming (MINLP) problem and then solved using two approaches. In the first approach, we employ a genetic algorithm, which offers remarkable performance but demands substantial computational resources; and in the second approach, we propose a rounding-based interior-point method (RIPM) that provides a more computationally-efficient alternative solution at a negligible performance loss. The results demonstrate that the KLD metric can be an effective means for optimising ISAC networks, and that both optimisation solutions presented offer superior performance compared to uniform power and antenna allocation.

Optimal Transport-based Nonlinear Filtering in High-dimensional Settings

This paper addresses the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. The primary focus is on scenarios involving degenerate likelihoods or high-dimensional states, where traditional sequential importance resampling (SIR) particle filters face the weight degeneracy issue. Our proposed method builds on an optimal transport interpretation of nonlinear filtering, leading to a simulation-based and likelihood-free algorithm that estimates the Brenier optimal transport map from the current distribution of the state to the distribution at the next time step. Our formulation allows us to harness the approximation power of neural networks to model complex and multi-modal distributions and employ stochastic optimization algorithms to enhance scalability. Extensive numerical experiments are presented that compare our method to the SIR particle filter and the ensemble Kalman filter, demonstrating the superior performance of our method in terms of sample efficiency, high-dimensional scalability, and the ability to capture complex and multi-modal distributions.

Optimization of Energy-Constrained IRS-NOMA Using a Complex Circle Manifold Approach

This work investigates the performance of intelligent reflective surfaces (IRSs) assisted uplink non-orthogonal multiple access (NOMA) in energy-constrained networks. Specifically, we formulate and solve two optimization problems, one for minimizing the users' sum transmit power and another for maximizing the energy efficiency (EE) of the system. The two problems are solved by jointly optimizing the users' transmit powers and the passive beamforming coefficients at the IRS reflectors subject to the users' individual uplink rate constraints. A novel algorithm is developed to optimize the IRS passive beamforming coefficients by optimizing the objective function over the \textit{complex circle manifold} (CCM), exploiting the manifold optimization technique. The proposed manifold optimization-based solution is bench-marked against the rather \textit{standard} semi-definite relaxation method (SDR). The results show that the manifold optimization-based algorithm achieves significantly better performance for both transmit power minimization and EE maximization problems at a computational complexity lower than the SDR approach. The results also reveal that IRS-NOMA is superior to the orthogonal multiple access (OMA) counterpart only when the users' target achievable rate requirements are relatively high.