This paper investigates the positioning of the pilot symbols, as well as the power distribution between the pilot and the communication symbols for the orthogonal time frequency space (OTFS) modulation scheme. We analyze the pilot placements that minimize the mean squared error (MSE) in estimating the channel taps. This allows us to identify two new pilot allocations for OTFS that save approximately 50% of the pilot overhead compared to existing allocations. In addition, we optimize the average channel capacity by adjusting the power distribution. We show that this leads to a significant increase in average capacity. The results provide valuable guidance for designing the OTFS parameters to achieve maximum capacity. Numerical simulations are performed to validate the findings.

In this paper, we consider the problem of distributed nonlinear optimization of a separable convex cost function over a graph subject to cone constraints. We show how to generalize using convex analysis, monotone operator theory, and fixed-point theory, the primal-dual method of multipliers (PDMM), originally designed for equality constraint optimization and recently extended to include linear inequality constraints, so that it can also accommodate cone constraints. The resulting algorithm can be applied to a variety of optimization problems, including the important class of semidefinite programs with partially separable structure, in a fully distributed fashion without relying on interior-point methods. We derive update equations by applying the Peaceman--Rachford splitting algorithm to the monotonic inclusion related to the lifted dual problem. The cone constraints are implemented by a reflection method in the lifted dual domain where auxiliary variables are reflected with respect to the intersection of the polar cone and a subspace relating the dual and lifted dual domain. Convergence results are provided for both synchronous and stochastic update schemes, and the proposed algorithm is demonstrated through an application to fully distributed sensor localization based on semidefinite programming.

Direction-of-arrival (DOA) estimation can be used for many different applications. In this paper the classical DOA estimation is modified to estimate the attitude of an antenna array when the DOAs of sources are given. Usually DOA attitude estimation assumes knowledge on the structure of the used signals. In this paper signals with an unknown structure are used for attitude estimation. The theoretical best performance is determined by deriving the Cramér-Rao lower bounds for attitude estimation based on two different signal models: the deterministic and stochastic signal model. Next, the attitude estimation performance of both signal models are compared to each other. It is shown that for high signal-to-noise ratios (SNRs) both models perform equally well. If the SNR drops, both models perform equally if the number of sources is low with respect to the number of antenna elements. For a large number of sources, the stochastic model outperforms the deterministic model unless the SNR drops too low. For very low SNRs, the deterministic outperforms the stochastic model regardless of the number of sources.

Federated learning (FL) emerged as a paradigm designed to improve data privacy by enabling data to reside at its source, thus embedding privacy as a core consideration in FL architectures, whether centralized or decentralized. Contrasting with recent findings by Pasquini et al., which suggest that decentralized FL does not empirically offer any additional privacy or security benefits over centralized models, our study provides compelling evidence to the contrary. We demonstrate that decentralized FL, when deploying distributed optimization, provides enhanced privacy protection - both theoretically and empirically - compared to centralized approaches. The challenge of quantifying privacy loss through iterative processes has traditionally constrained the theoretical exploration of FL protocols. We overcome this by conducting a pioneering in-depth information-theoretical privacy analysis for both frameworks. Our analysis, considering both eavesdropping and passive adversary models, successfully establishes bounds on privacy leakage. In particular, we show information theoretically that the privacy loss in decentralized FL is upper bounded by the loss in centralized FL. Compared to the centralized case where local gradients of individual participants are directly revealed, a key distinction of optimization-based decentralized FL is that the relevant information includes differences of local gradients over successive iterations and the aggregated sum of different nodes' gradients over the network. This information complicates the adversary's attempt to infer private data. To bridge our theoretical insights with practical applications, we present detailed case studies involving logistic regression and deep neural networks. These examples demonstrate that while privacy leakage remains comparable in simpler models, complex models like deep neural networks exhibit lower privacy risks under decentralized FL. Extensive numerical tests further validate that decentralized FL is more resistant to privacy attacks, aligning with our theoretical findings.

Sparse array design is used to help reduce computational, hardware, and power requirements compared to uniform arrays while maintaining acceptable performance. Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown target directions. To handle the unknown target directions when optimizing the Cramér-Rao bound, we propose to use the worst-case Cramér-Rao bound of two uncorrelated equal power sources with arbitrary angles. This new worst-case two-target Cramér-Rao bound metric has some resemblance to the peak sidelobe level metric which is commonly used in unknown multi-target scenarios. We cast the sensor selection problem for 3-D arrays using the worst-case two-target Cramér-Rao bound as a convex semi-definite program and obtain the binary selection by randomized rounding. We illustrate the proposed method through numerical examples, comparing it to solutions obtained by minimizing the single-target Cramér-Rao bound, minimizing the Cramér-Rao bound for known target angles, the concentric rectangular array and the boundary array. We show that our method selects a combination of edge and center elements, which contrasts with solutions obtained by minimizing the single-target Cramér-Rao bound. The proposed selections also exhibit lower peak sidelobe levels without the need for sidelobe level constraints.

Privacy-preserving distributed average consensus has received significant attention recently due to its wide applicability. Based on the achieved performances, existing approaches can be broadly classified into perfect accuracy-prioritized approaches such as secure multiparty computation (SMPC), and worst-case privacy-prioritized approaches such as differential privacy (DP). Methods of the first class achieve perfect output accuracy but reveal some private information, while methods from the second class provide privacy against the strongest adversary at the cost of a loss of accuracy. In this paper, we propose a general approach named adaptive differentially quantized subspace perturbation (ADQSP) which combines quantization schemes with so-called subspace perturbation. Although not relying on cryptographic primitives, the proposed approach enjoys the benefits of both accuracy-prioritized and privacy-prioritized methods and is able to unify them. More specifically, we show that by varying a single quantization parameter the proposed method can vary between SMPC-type performances and DP-type performances. Our results show the potential of exploiting traditional distributed signal processing tools for providing cryptographic guarantees. In addition to a comprehensive theoretical analysis, numerical validations are conducted to substantiate our results.

The main focus of this paper is an active sensing application that involves selecting transmit and receive sensors to optimize the Cramér-Rao bound (CRB) on target parameters. Although the CRB is non-convex in the transmit and receive selection, we demonstrate that it is convex in the virtual array weight vector, which describes the multiplicity of the virtual array elements. Based on this finding, we propose a novel algorithm that optimizes the virtual array weight vector first and then finds a matching transceiver array. This greatly enhances the efficiency of the transmit and receive sensor selection problem.

Decentralized Federated Learning (FL) has attracted significant attention due to its enhanced robustness and scalability compared to its centralized counterpart. It pivots on peer-to-peer communication rather than depending on a central server for model aggregation. While prior research has delved into various factors of decentralized FL such as aggregation methods and privacy-preserving techniques, one crucial aspect affecting privacy is relatively unexplored: the underlying graph topology. In this paper, we fill the gap by deriving a stringent privacy bound for decentralized FL under the condition that the accuracy is not compromised, highlighting the pivotal role of graph topology. Specifically, we demonstrate that the minimum privacy loss at each model aggregation step is dependent on the size of what we term as 'honest components', the maximally connected subgraphs once all untrustworthy participants are excluded from the networks, which is closely tied to network robustness. Our analysis suggests that attack-resilient networks will provide a superior privacy guarantee. We further validate this by studying both Poisson and power law networks, showing that the latter, being less robust against attacks, indeed reveals more privacy. In addition to a theoretical analysis, we consolidate our findings by examining two distinct privacy attacks: membership inference and gradient inversion.

Hearing impairment is a prevalent problem with daily challenges like impaired speech intelligibility and sound localisation. One of the shortcomings of spatial filtering in hearing aids is that speech intelligibility is often not optimised directly, meaning that different auditory processes contributing to intelligibility are often not considered. One example is the perceptual phenomenon known as spatial release from masking (SRM). This paper develops a signal model that explicitly considers SRM in the beamforming design, achieved by transforming the binaural intelligibility prediction model (BSIM) into a signal processing framework. The resulting extended signal model is used to analyse the performance of reference beamformers and design a novel beamformer that more closely considers how the auditory system perceives binaural sound. It can be shown that the binaural minimum variance distortionless response (BMVDR) beamformer is also an optimal solution for the extended, perceived model, suggesting that SRM does not play a significant role in intelligibility enhancement after optimal beamforming. However, the optimal beamformer is no longer unique in the extended signal model. The additional secondary degrees of freedom can be used to preserve binaural cues of interfering sources while still achieving the same perceived performance of the BMVDR beamformer, though with a possible high sensitivity to intelligibility model mismatch errors.

Analyzing privacy leakage in distributed algorithms is challenging as it is difficult to track the information leakage across different iterations. In this paper, we take the first step to conduct a theoretical analysis of the information flow in distributed optimization ensuring that gradients at every iteration remain concealed from others. Specifically, we derive a privacy bound on the minimum information available to the adversary when the optimization accuracy is kept uncompromised. By analyzing the derived bound we show that the privacy leakage depends heavily on the optimization objectives, especially the linearity of the system. To understand how the bound affects privacy, we consider two canonical federated learning (FL) applications including linear regression and neural networks. We find that in the first case protecting the gradients alone is inadequate for protecting the private data, as the established bound potentially exposes all sensitive information. For more complex applications such as neural networks, protecting the gradients can provide certain privacy advantages as it will be more difficult for the adversary to infer the private inputs. Numerical validations are presented to consolidate our theoretical results.

Privacy-preserving distributed processing has received considerable attention recently. The main purpose of these algorithms is to solve certain signal processing tasks over a network in a decentralised fashion without revealing private/secret data to the outside world. Because of the iterative nature of these distributed algorithms, computationally complex approaches such as (homomorphic) encryption are undesired. Recently, an information theoretic method called subspace perturbation has been introduced for synchronous update schemes. The main idea is to exploit a certain structure in the update equations for noise insertion such that the private data is protected without compromising the algorithm's accuracy. This structure, however, is absent in asynchronous update schemes. In this paper we will investigate such asynchronous schemes and derive a lower bound on the noise variance after random initialisation of the algorithm. This bound shows that the privacy level of asynchronous schemes is always better than or at least equal to that of synchronous schemes. Computer simulations are conducted to consolidate our theoretical results.

In this article, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to modify the primal-dual method of multipliers (PDMM), originally designed for linear equality constraints, such that it can handle inequality constraints as well. The proposed algorithm does not need any slack variables, which is similar to the recent work (He et al., 2023) which extends the alternating direction method of multipliers (ADMM) for addressing decomposable optimisation with linear equality and inequality constraints. Using convex analysis, monotone operator theory and fixed-point theory, we show how to derive the update equations of the modified PDMM algorithm by applying Peaceman-Rachford splitting to the monotonic inclusion related to the lifted dual problem. To incorporate the inequality constraints, we impose a non-negativity constraint on the associated dual variables. This additional constraint results in the introduction of a reflection operator to model the data exchange in the network, instead of a permutation operator as derived for equality constraint PDMM. Convergence for both synchronous and stochastic update schemes of PDMM are provided. The latter includes asynchronous update schemes and update schemes with transmission losses. Experiments show that PDMM converges notably faster than extended ADMM of (He et al., 2023).