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In decentralized optimization, multiple nodes in a network collaborate to minimize the sum of their local loss functions. The information exchange between nodes required for this task, is often limited by network connectivity. We consider a setting in which communication between nodes is hindered by both (i) a finite rate-constraint on the signal transmitted by any node, and (ii) additive noise corrupting the signal received by any node. We propose a novel algorithm for this scenario: Decentralized Lazy Mirror Descent with Differential Exchanges (DLMD-DiffEx), which guarantees convergence of the local estimates to the optimal solution under the given communication constraints. A salient feature of DLMD-DiffEx is the introduction of additional proxy variables that are maintained by the nodes to account for the disagreement in their estimates due to channel noise and rate-constraints. Convergence to the optimal solution is attained by having nodes iteratively exchange these disagreement terms until consensus is achieved. In order to prevent noise accumulation during this exchange, DLMD-DiffEx relies on two sequences: one controlling the power of the transmitted signal, and the other determining the consensus rate. We provide insights on the design of these two sequences which highlights the interplay between consensus rate and noise amplification. We investigate the performance of DLMD-DiffEx both from a theoretical perspective as well as through numerical evaluations on synthetic data and MNIST. MATLAB and Python implementations can be found at https://github.com/rajarshisaha95/DLMD-DiffEx. [ABSTRACT FROM AUTHOR]

The relationship of different optimal waveform design criteria in signal-dependent interference, as well as additive channel noise for stochastic extended target, is investigated here. Within constraints on waveform energy and bandwidth, the optimal waveform design based on the signal-to-interference plus noise ratio criterion, probability of detection criterion, and mutual information criterion are modelled. Afterwards, the relationship of these criteria is presented. Simulations are conducted to illustrate that under the same bandwidth and energy constraints, the three criteria lead to the similar optimal waveform. The energy of optimal waveform can be distributed in some narrow bands where target power is large and interference power is small.

The relationship of different optimal waveform design criteria in signal-dependent interference, as well as additive channel noise for stochastic extended target, is investigated here. Within constraints on waveform energy and bandwidth, the optimal waveform design based on the signal-to-interference plus noise ratio criterion, probability of detection criterion, and mutual information criterion are modelled. Afterwards, the relationship of these criteria is presented. Simulations are conducted to illustrate that under the same bandwidth and energy constraints, the three criteria lead to the similar optimal waveform. The energy of optimal waveform can be distributed in some narrow bands where target power is large and interference power is small. [ABSTRACT FROM AUTHOR]

This work investigates the effect of channel noise on the performances of the constant modulus algorithm (CMA), the multimodulus algorithm (MMA), and a phase tracker (PT), following the CMA for carrier phase recovery, when various symmetrical two-dimensional complex-valued source constellations are used. The contributions of this work are two-fold. First, a generalized formulation of the relocation of stationary points toward the origin owing to channel noise is derived for both the CMA and the MMA, allowing their sensitivity to channel noise to be explicitly compared when various constellations are used. Second, the curvatures of the error surface at the stationary points in both the radial and the angular directions are reduced in a way that is linearly proportional to the square of the distances between the stationary points and the origin as the stationary points of the CMA and the MMA relocate toward the origin in the presence of additive channel noise. The reduction of the error surface curvature in the radial direction reduces the rate of blind equalization convergence, whereas the reduction in the angular direction degrades the capacity for carrier phase recovery. [ABSTRACT FROM AUTHOR]

Recently proposed decentralized, distributed estimation and power scheduling methods for wireless sensor networks (WSNs) do not consider errors occurring during the transmission of binary observations from the sensors to fusion center. In this letter, we extend the decentralized estimation model to the case in which imperfect transmission channels are considered. The proposed estimators, which operate on additive channel noise corrupted versions of quantized noisy sensor observations, are approached from a maximum likelihood (ML) perspective. Complicating this approach is the fact that the noise distribution is rarely fully known to the fusion center. Here we assume the distribution is known but not the defining parameters, e.g., variance. The resulting incomplete data estimation problem is approached from a expectation-maximization (EM) perspective. The critical initialization and convergence aspects of the EM algorithm are investigated. Furthermore, the estimation of the source parameter is extended to the blind case where both the channel and sensor noise parameters are unknown. Finally, numerical experiments are provided to show the effectiveness of the proposed estimators. [ABSTRACT FROM PUBLISHER]

We consider a RAKE receiver for coherent binary orthogonal signaling employing predetection maximal-ratio combining (MRC), in which the tap weights are estimated by adding two matched filtered outputs using the two reference signals. The weight estimation errors here are not independent of the additive channel noise, and therefore do not fit into the Gaussian error model for MRC. Instead of analyzing the distribution of the weight estimation errors, we find the characteristic function of the decision variable, and from it we obtain a formula for the symbol error probability [ABSTRACT FROM PUBLISHER]