Signal Processing

A symmetric alternating minimization algorithm for total variation minimization.

MATLAB code for the paper " Coherence-penalty minimization method for incoherent unit-norm tight frame design" with DOI: 10.1016/j.sigpro.2022.108864

This capsule reproduces the main results given in the manuscript titled Maximum Likelihood Estimator for Noisy Autoregressive Model Parameter Estimation Problem with Multiple Snapshots by Omer Cayir and Cagatay Candan to be submitted to Elsevier Signal Processing (September 2020). In this manuscript, an expectation-maximization method is suggested, and, by judiciously utilizing the structure of the problem, an approximate, yet computationally efficient, version of the solution is also developed.

This capsule implements a method for frequency estimation of real-valued sinusoidal signals. $r[n] = A \cos(\omega n + \phi) + w[n], n = \{0,1, \ldots , N-1\}$ is the signal model with the unknown parameters of $A$, $\omega$, and $\phi$. The main goal is to estimate $\omega$ given the noisy observations $r[n], n = \{0,1, \ldots , N-1\}$ where noise $w[n]$ is assumed to be white and Gaussian distributed.

In this work, we address the problem of optimally detecting signals in correlated noise using a predictive Viterbi algorithm (PVA). We derive expressions for the probabilityof error for both coded and uncoded systems employing the PVA, which are corrupted by coloured noise. As an application, the PVA is used in conjunction with a fractionally spaced linear equalizer (LE-PVA), thereby improving the bit-error-rate performance by as much as 11dB, over the conventional decision feedback equalizer with estimated decisions, when the channel has spectral nulls. The LE-PVA is also about 1dB better than the DFE that uses per-survivor processing. Simulation results also show that the performance difference between the LE-PVA and the decision feedback equalizer with correct decisions fed back (ideal DFE), is just 1dB, even when the channel has spectral nulls. Simulation results are also presented for multipath fading channels, where we again demonstrate that the LE-PVA is just 1dB inferior to the ideal DFE and about 1dB better than the DFE using per-survivor processing. Thus, we clearly demonstrate the superiority of the LE-PVA over apractical DFE. Part 1 contains the conventional Viterbi algorithm in coloured/white noise. The VA is implemented using linked list, which is memory efficient compared to array-based implementation.

In this work, we address the problem of optimally detecting signals in correlated noise using a predictive Viterbi algorithm (PVA). We derive expressions for the probabilityof error for both coded and uncoded systems employing the PVA, which are corrupted by coloured noise. As an application, the PVA is used in conjunction with a fractionally spaced linear equalizer (LE-PVA), thereby improving the bit-error-rate performance by as much as 11dB, over the conventional decision feedback equalizer with estimated decisions, when the channel has spectral nulls. The LE-PVA is also about 1dB better than the DFE that uses per-survivor processing. Simulation results also show that the performance difference between the LE-PVA and the decision feedback equalizer with correct decisions fed back (ideal DFE), is just 1dB, even when the channel has spectral nulls. Simulation results are also presented for multipath fading channels, where we again demonstrate that the LE-PVA is just 1dB inferior to the ideal DFE and about 1dB better than the DFE using per-survivor processing. Thus, we clearly demonstrate the superiority of the LE-PVA over apractical DFE. Part 2 contains the predictive Viterbi algorithm in coloured/white noise. The VA is implemented using linked list, which is memory efficient compared to array-based implementation.