A performance lower bound for quadratic timing recovery accounting for the symbol transition density

The symbol transition density in a digitally modulated signal affects the performance of practical synchronization schemes designed for timing recovery. This paper focuses on the derivation of simple performance limits for the estimation of the time delay of a noisy linearly modulated signal in the presence of various degrees of symbol correlation produced by the various transition densities in the symbol streams. The paper develops high- and low-signal-to-noise ratio (SNR) approximations of the so-called (Gaussian) unconditional Cramér–Rao bound (UCRB), as well as general expressions that are applicable in all ranges of SNR. The derived bounds are valid only for the class of quadratic, non-data-aided (NDA) timing recovery schemes. To illustrate the validity of the derived bounds, they are compared with the actual performance achieved by some well-known quadratic NDA timing recovery schemes. The impact of the symbol transition density on the classical threshold effect present in NDA timing recovery schemes is also analyzed. Previous work on performance bounds for timing recovery from various authors is generalized and unified in this contribution.Peer Reviewe

Conditional maximum likelihood timing recovery

The conditional maximum likelihood (CML) principle, well known in the context of sensor array processing, is applied to the problem of timing recovery. A new self-noise free CML-based timing error detector is derived. Additionally, a new (conditional) Cramer-Rao bound (CRB) for timing estimation is obtained, which is more accurate than the extensively used modified CRB (MCRB).Peer ReviewedPostprint (published version

Non-data-aided frequency offset and symbol timing estimation for binary CPM: performance bounds

The use of (spectrally efficient) CPM modulations may lead to a serious performance degradation of the classical non-data-aided (NDA) frequency and timing estimators due to the presence of self noise. The actual performance of these estimators is usually much worse than that predicted by the classical modified Cramer-Rao bound. We apply some well known results in the field of signal processing to these two important problems of synchronization. In particular we propose and explain the meaning of the unconditional CRB in the synchronization task. Simulation results for MSK and GMSK, along with the performance of some classical and previously proposed synchronizers, show that the proposed bound (along with the MCRB) is useful for a better prediction of the ultimate performance of the NDA estimators.Peer ReviewedPostprint (published version

Robust beamforming for interference rejection in mobile communications

The problem of robust beamformer design in the presence of moving sources is considered. A new technique based on a generalization of the constrained minimum variance beamformer is proposed. The method explicitly takes into account changes in the scenario due to the movement of the desired and interfering sources, requiring only estimation of the desired DOA. Computer simulations show that the resulting performance constitutes a compromise between interference and noise rejection, computational complexity, and sensitivity to source movement.Peer ReviewedPostprint (published version

Near-far resistant CML propagation delay estimation and multi-user detection for asynchronous DS-CDMA systems

Multi-user receivers in asynchronous direct sequence code division multiple access (DS-CDMA) systems require the knowledge of several parameters such as timing delay between users. The goal of this work is to present a near-far resistant joint multi-user synchronization and detection algorithm for DS-CDMA systems. The solution is based on the conditional maximum likelihood (CML) estimation method (classically used in the context of sensor array processing) that leads to a fast convergence algorithm to estimate the time delays among users. At the same time the estimator implements the decorrelating detector, identifying the transmitted symbols for the different users.Peer ReviewedPostprint (published version

On infinite past predictability of cyclostationary signals

This paper explores the asymptotic spectral decomposition of periodically Toeplitz matrices with finite summable elements. As an alternative to polyphase decomposition and other approaches based on Gladyshev representation, the proposed route exploits the Toeplitz structure of cyclic autocorrelation matrices, thus leveraging on known asymptotic results and providing a more direct link to the cyclic spectrum and spectral coherence. As a concrete application, the problem of cyclic linear prediction is revisited, concluding with a generalized Kolmogorov-Szeg theorem on the predictability of cyclostationary signals. These results are finally tested experimentally in a prediction setting for an asynchronous mixture of two cyclostationary pulse-amplitude modulation signals.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB-C22 / MCIN / AEI / 10.13039/501100011033). Authors are within Signal Processing and Communications group (SPCOM) (Signal Theory and Communications Department) at Technical University of Catalonia (UPC).Peer ReviewedPostprint (author's final draft

Squared-loss mutual information via high-dimension coherence matrix estimation

Squared-loss mutual information (SMI) is a surro- gate of Shannon mutual information that is more advantageous for estimation. On the other hand, the coherence matrix of a pair of random vectors, a power-normalized version of the sample cross-covariance matrix, is a well-known second-order statistic found in the core of fundamental signal processing problems, such as canonical correlation analysis (CCA). This paper shows that SMI can be estimated from a pair of independent and identically distributed (i.i.d.) samples as a squared Frobenius norm of a coherence matrix estimated after mapping the data onto some fixed feature space. Moreover, low computation complexity is achieved through the fast Fourier transform (FFT) by exploiting the Toeplitz structure of the involved autocorrelation matrices in that space. The performance of the method is analyzed via computer simulations using Gaussian mixture models.This work is supported by projects TEC2016-76409-C2-1-R (WINTER), Ministerio de Economia y Competividad, Spanish National Research Plan, and 2017 SGR 578 - AGAUR, Catalan Government.Peer ReviewedPostprint (published version

Sparse-aware approach for covariance conversion in FDD systems

This paper proposes a practical way to solve the Uplink-Downlink Covariance Conversion (UDCC) problem in a Frequency Division Duplex (FDD) communication system. The UDCC problem consists in the estimation of the Downlink (DL) spatial covariance matrix from the prior knowledge of the Uplink (UL) spatial covariance matrix without the need of a feedback transmission from the User Equipment (UE) to the Base Station (BS). Estimating the DL sample spatial covariance matrix is unfeasible in current massive Multiple-Input Multiple-Output (MIMO) deployments in frequency selective or fast fading channels due to the required large training overhead. Our method is based on the application of sparse filtering ideas to the estimation of a quantized version of the so-called Angular Power Spectrum (APS), being the common factor between the UL and DL spatial channel covariance matrices.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB-C22 / AEI / 10.13039/501100011033) and by the Catalan Government (AGAUR) under grant 2017 SGR 578.Peer ReviewedPostprint (author's final draft

A novel formulation of independence detection based on the sample characteristic function

A novel independence test for continuous random sequences is proposed in this paper. The test is based on seeking for coherence in a particular fixed-dimension feature space based on a uniform sampling of the sample characteristic function of the data, providing significant computational advantages over kernel methods. This feature space relates uncorrelation and independence, allowing to analyze the second order statistics as it is encountered in traditional signal processing. As a result, the possibility of utilizing well known correlation tools arises, motivating the usage of Canonical Correlation Analysis as the main tool for detecting independence. Comparative simulation results are provided using a model based on fading AWGN channels.Peer ReviewedPostprint (published version

Data driven joint sensor fusion and regression based on geometric mean squared error

This paper explores the problem of estimating a temporal series measured from multiple independent sensors with unequal and stationary measurement errors with unknown variances. By formulating the data fusion problem as a joint Maximum Likelihood estimation of sensor covariances and a fusion rule, a batch data driven method is derived involving a residual covariance determinant minimization of a diagonal matrix. It is shown that yielding useful learning from data with good generalization properties in the joint regression and fusion approach requires the assumption of some structure on the sensor noises and/or on the temporal series to be estimated. An efficient data driven algorithm is proposed to obtain the best linear sensor combiner, whose performance is numerically analyzed and compared with the Cramer-Rao Lower Bound of the estimated parameters.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB-C22 / AEI / 10.13039/501100011033) and by the Catalan Government (AGAUR) under grant 2017 SGR 578.Peer ReviewedPostprint (author's final draft