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Deep learning is envisioned to facilitate the operation of wireless receivers, with emerging architectures integrating deep neural networks (DNNs) with traditional modular receiver processing. While deep receivers were shown to operate reliably in complex settings for which they were trained, the dynamic nature of wireless communications gives rise to the need to repeatedly adapt deep receivers to channel variations. However, frequent re-training is costly and ineffective, while in practice, not every channel variation necessitates adaptation of the entire DNN. In this paper, we study concept drift detection for identifying when does a deep receiver no longer match the channel, enabling asynchronous adaptation, i.e., re-training only when necessary. We identify existing drift detection schemes from the machine learning literature that can be adapted for deep receivers in dynamic channels, and propose a novel soft-output detection mechanism tailored to the communication domain. Moreover, for deep receivers that preserve conventional modular receiver processing, we design modular drift detection mechanisms, that simultaneously identify when and which sub-module to re-train. The provided numerical studies show that even in a rapidly time-varying scenarios, asynchronous adaptation via modular drift detection dramatically reduces the number of trained parameters and re-training times, with little compromise on performance.

The least mean-square (LMS) filter is one of the most common adaptive linear estimation algorithms. In many practical scenarios, and particularly in digital communications systems, the signal of interest (SOI) and the input signal are jointly wide-sense cyclostationary. Previous works analyzing the performance of LMS filters for this important case assume specific probability distributions of the considered signals or specific models that relate the input signal and the SOI. In this work, we provide a general transient and steady-state performance analysis that is free of specific distributional or model assumptions. We obtain conditions for convergence and derive analytical expressions for the non-asymptotic and steady-state mean-squared error. The accuracy of our analysis is demonstrated in simulation studies that correspond to practical communications scenarios.

In this paper, we develop a generalization of the Gaussian quasi score test (GQST) for composite binary hypothesis testing. The proposed test, called measure transformed GQST (MT-GQST), is based on the score-function of the measure transformed Gaussian quasi maximum likelihood estimator (MT-GQMLE) that operates by empirically fitting a Gaussian model to a transformed probability measure of the data. By judicious choice of the transform we show that, unlike the GQST, the proposed MT-GQST involves higher-order statistical moments and can gain resilience to outliers, leading to significant mitigation of the model mismatch effect on the decision performance. A data-driven procedure for optimal selection of the measure transformation parameters is developed that minimizes the spectral norm of the empirical asymptotic error-covariance of the MT-GQMLE. This amounts to maximization of an empirical worst-case asymptotic local power at a fixed asymptotic size. The MT-GQST is applied to location mismatch detection of a near-field point source in a simulation example that illustrates its robustness to outliers., Comment: arXiv admin note: text overlap with arXiv:1609.07958, arXiv:1511.00237

In this paper, the Gaussian quasi likelihood ratio test (GQLRT) for non-Bayesian binary hypothesis testing is generalized by applying a transform to the probability distribution of the data. The proposed generalization, called measure-transformed GQLRT (MT-GQLRT), selects a Gaussian probability model that best empirically fits a transformed probability measure of the data. By judicious choice of the transform we show that, unlike the GQLRT, the proposed test is resilient to outliers and involves higher-order statistical moments leading to significant mitigation of the model mismatch effect on the decision performance. Under some mild regularity conditions we show that the MT-GQLRT is consistent and its corresponding test statistic is asymptotically normal. A data driven procedure for optimal selection of the measure transformation parameters is developed that maximizes an empirical estimate of the asymptotic power given a fixed empirical asymptotic size. A Bayesian extension of the proposed MT-GQLRT is also developed that is based on selection of a Gaussian probability model that best empirically fits a transformed conditional probability distribution of the data. In the Bayesian MT-GQLRT the threshold and the measure transformation parameters are selected via joint minimization of the empirical asymptotic Bayes risk. The non-Bayesian and Bayesian MT-GQLRTs are applied to signal detection and classification, in simulation examples that illustrate their advantages over the standard GQLRT and other robust alternatives., Comment: Important notice - The paper: N. Halay and K. Todros, "Plug-in measure-transformed quasi likelihood ratio test for random signal detection," IEEE Signal Processing Letters, vol. 24, no. 6, pp. 838-842, Jun. 2017, refers to the first arxiv version of this article https://arxiv.org/pdf/1609.07958v1.pdf

In this paper the Gaussian quasi maximum likelihood estimator (GQMLE) is generalized by applying a transform to the probability distribution of the data. The proposed estimator, called measure-transformed GQMLE (MT-GQMLE), minimizes the empirical Kullback-Leibler divergence between a transformed probability distribution of the data and a hypothesized Gaussian probability measure. By judicious choice of the transform we show that, unlike the GQMLE, the proposed estimator can gain sensitivity to higher-order statistical moments and resilience to outliers leading to significant mitigation of the model mismatch effect on the estimates. Under some mild regularity conditions we show that the MT-GQMLE is consistent, asymptotically normal and unbiased. Furthermore, we derive a necessary and sufficient condition for asymptotic efficiency. A data driven procedure for optimal selection of the measure transformation parameters is developed that minimizes the trace of an empirical estimate of the asymptotic mean-squared-error matrix. The MT-GQMLE is applied to linear regression and source localization and numerical comparisons illustrate its robustness and resilience to outliers.

In this paper, we introduce a new framework for robust multiple signal classification (MUSIC). The proposed framework, called robust measure-transformed (MT) MUSIC, is based on applying a transform to the probability distribution of the received signals, i.e., transformation of the probability measure defined on the observation space. In robust MT-MUSIC, the sample covariance is replaced by the empirical MT-covariance. By judicious choice of the transform we show that: 1) the resulting empirical MT-covariance is B-robust, with bounded influence function that takes negligible values for large norm outliers, and 2) under the assumption of spherically contoured noise distribution, the noise subspace can be determined from the eigendecomposition of the MT-covariance. Furthermore, we derive a new robust measure-transformed minimum description length (MDL) criterion for estimating the number of signals, and extend the MT-MUSIC framework to the case of coherent signals. The proposed approach is illustrated in simulation examples that show its advantages as compared to other robust MUSIC and MDL generalizations.

In this paper we derive a new framework for independent component analysis (ICA), called measure-transformed ICA (MTICA), that is based on applying a structured transform to the probability distribution of the observation vector, i.e., transformation of the probability measure defined on its observation space. By judicious choice of the transform we show that the separation matrix can be uniquely determined via diagonalization of several measure-transformed covariance matrices. In MTICA the separation matrix is estimated via approximate joint diagonalization of several empirical measure-transformed covariance matrices. Unlike kernel based ICA techniques where the transformation is applied repetitively to some affine mappings of the observation vector, in MTICA the transformation is applied only once to the probability distribution of the observations. This results in performance advantages and reduced implementation complexity. Simulations demonstrate the advantages of the proposed approach as compared to other existing state-of-the-art methods for ICA.

In this paper linear canonical correlation analysis (LCCA) is generalized by applying a structured transform to the joint probability distribution of the considered pair of random vectors, i.e., a transformation of the joint probability measure defined on their joint observation space. This framework, called measure transformed canonical correlation analysis (MTCCA), applies LCCA to the data after transformation of the joint probability measure. We show that judicious choice of the transform leads to a modified canonical correlation analysis, which, in contrast to LCCA, is capable of detecting non-linear relationships between the considered pair of random vectors. Unlike kernel canonical correlation analysis, where the transformation is applied to the random vectors, in MTCCA the transformation is applied to their joint probability distribution. This results in performance advantages and reduced implementation complexity. The proposed approach is illustrated for graphical model selection in simulated data having non-linear dependencies, and for measuring long-term associations between companies traded in the NASDAQ and NYSE stock markets.