Dual-Domain Sparse Adaptive Filtering: Exploiting Error Memory for Improved Performance

Many signal processing applications such as acoustic echo cancellation and wireless channel estimation require identifying systems where only a small fraction of coefficients are actually active, i.e. sparse systems. Zero-attracting adaptive filters tackle this by adding a penalty that pulls inactive coefficients toward zero, speeding up convergence. However, these algorithms determine which coefficients to penalize based solely on their current size. This creates a problem during early adaptation since active coefficients that should eventually grow large start out small, making them look identical to truly inactive coefficients. The algorithm ends up applying strong penalties to the very coefficients it needs to develop, slowing down the initial convergence. This paper provides a solution to this problem by introducing a dual-domain approach that looks at coefficients from two perspectives simultaneously. Beyond just tracking coefficient magnitude, we introduce an error-memory vector that monitors how persistently each coefficient contributes to the adaptation error over time. If a coefficient keeps showing up in the error signal, it is probably active even if it is still small. By combining both views, the proposed dual-domain sparse adaptive filter (DD-SAF) can identify active coefficients early and eliminate penalties accordingly. Moreover, complete theoretical analysis is derived. The analysis shows that DD-SAF maintains the same stability properties as standard least-mean-square (LMS) while achieves provably better steady-state performance than existing methods. Simulations demonstrate that the DD-SAF converges to the steady-state faster and/or convergences to a lower mean-square-deviation (MSD) than the standard LMS and the reweighted zero-attracting LMS (RZA-LMS) algorithms for sparse system identification settings.

Closed-form Single UAV-aided Emitter Localization and Trajectory Design Using Doppler and TOA Measurements

In this paper, a single Unmanned-Aerial-Vehicle (UAV)-aided localization algorithm which uses both Doppler and Time of Arrival (ToA) measurements is presented. In contrast to Doppler-based localization algorithms which are based on non-convex functions, exploiting ToA measurements in a Least-Square (LS) Doppler-based cost function, leads to a quadratic convex function whose minimizer lies on a line. Utilizing the ToA measurements in addition to the linear equation of minimizer, a closed form solution is obtained for the emitter location using a constrained LS optimization. In addition, a trajectory design of the UAV is provided which has also closed-form solution. Simulation experiments demonstrate the effectiveness of the proposed algorithm in comparison to some others in the literature.

Secure Blind Graph Signal Recovery and Adversary Detection Using Smoothness Maximization

In this letter, we propose a secure blind Graph Signal Recovery (GSR) algorithm that can detect adversary nodes. Some unknown adversaries are assumed to be injecting false data at their respective nodes in the graph. The number and location of adversaries are not known in advance and the goal is to recover the graph signal in the presence of measurement noise and False Data Injection (FDI) caused by the adversaries. Consequently, the proposed algorithm would be a perfect candidate to solve this challenging problem. Moreover, due to the presence of malicious nodes, the proposed method serves as a secure GSR algorithm. For adversary detection, a statistical measure based on differential smoothness is used. Specifically, the difference between the current observed smoothness and the average smoothness excluding the corresponding node. This genuine statistical approach leads to an effective and low-complexity adversary detector. In addition, following malicious node detection, the GSR is performed using a variant of smoothness maximization, which is solved efficiently as a fractional optimization problem using a Dinkelbach's algorithm. Analysis of the detector, which determines the optimum threshold of the detector is also presented. Simulation results show a significant improvement of the proposed method in signal recovery compared to the median GSR algorithm and other competing methods.