SNR Estimation

This repository contains the Matlab function for estimating the Signal-to-noise ratio (SNR) in linear systems with Gaussian matrices. This function is the official implementation of the paper SNR Estimation in Linear Systems With Gaussian Matrices, IEEE Signal Processing Letters, v. 24, issue 12, December 2017.

Summary

Given a linear system in the form:

$y = Wx + n$

where:

• $W$ = $\Psi^{1/2} \bar{W}$.
• $\bar{W}$ : is a Gaussian matrix with i.i.d. entries of zero mean and unit variance.
• The entries of $x$, and those of the noise $n$, are drawn from any two distributions and they are i.i.d. with zero mean and unknown variances.

the function snr_estimate estimates the snr of the system.

Inputs:

• $y$: The bservations vector of length $M$.
• $\bar{W}$: Channel/Data matrix of dimension $M \times N$.
• $\Psi$ : Hermitian non negative left correlation matrix of dimension $M \times M$ (can be set to the identity matrix).

Outputs:

• SNR : The SNR of the linear system.
• signal_var: The varince of $x$ (i.e., $\sigma_{x}^{2})$.
• noise_var : The noise varince (i.e., $\sigma_{n}^{2})$.

Citation

Please cite this work if you found it useful:

SNR Estimation in Linear Systems With Gaussian Matrices

@article{suliman2017snr,
  title={SNR estimation in linear systems with Gaussian matrices},
  author={Suliman, Mohamed A and Alrashdi, Ayed M and Ballal, Tarig and Al-Naffouri, Tareq Y},
  journal={IEEE Signal Processing Letters},
  volume={24},
  number={12},
  pages={1867--1871},
  year={2017},
  publisher={IEEE}
}