Maximum Likelihood Signal-to-noise Ratio Research Articles

FPGA-SDR Integration and Experimental Validation of a Joint DA ML SNR and Doppler Spread Estimator for 5G Cognitive Transceivers

In a multi-connected, multi-technology, and pervasive mobile infrastructure, such as what is being planned for 5G, artificial intelligence and cognition will play a major role. An important goal of future mobile infrastructures is to self-adapt their characteristics to their operating conditions, at the physical link, as well as at the network and application layers, which gives rise to a new paradigm known as context-aware cognitive radio (CR). CR transceivers (CTRs) mostly incorporate a cognitive engine that relies on various sensorial entities, which attempt to provide sufficient information about the quality of the link through the estimation of various key channel parameters. Two important parameters are required in a wide range of CTR architectures: the signal-to-noise ratio (SNR) and the Doppler spread. Within this context, we tackle the hardware design and integration of a joint data-aided (DA) maximum likelihood (ML) SNR and Doppler spread estimator recently shown to outperform main state-of-the-art solutions both in terms of accuracy and complexity. We propose a deep-pipelined and resource-efficient architecture for the outlined joint DA ML estimator, and we integrate our design on an FPGA-based software-defined radio (SDR) platform. We finally validate and test this prototype in real time under realistic over-the-air propagation conditions reproduced by a highly-scalabile channel emulator. Compared to its MATLAB floating-point version, our hardware prototype suggests negligible losses in performance despite the existence of several hardware impairments, thereby confirming its very strong potential and attractiveness for possible integration in future 5G CTRs.

Maximum Likelihood SNR Estimation of Hyper Cubic Signals Over Gaussian Channel

In this letter, we address the problem of closed-form data aided (DA) and non-data aided (NDA) maximum likelihood (ML) signal-to-noise ratio (SNR) estimation for hyper-cubic modulated signals over Gaussian channel. The requirement of high SNR is exploited to derive closed-form expression of unbiased NDA ML SNR estimator. Exact expressions for the DA and NDA Cramer-Rao lower bound (CRLB) on the variance of these estimators are also determined analytically. The Monte Carlo simulation method is used to compute the normalized mean squared error (NMSE) of the estimators, and the results show that the NMSEs approach the respective normalized CRLBs.

Maximum Likelihood SNR Estimation of Linearly-Modulated Signals Over Time-Varying Flat-Fading SIMO Channels

In this paper, we tackle for the first time the problem of maximum likelihood (ML) estimation of the signal-to-noise ratio (SNR) parameter over time-varying single-input multiple-output (SIMO) channels. Both the data-aided (DA) and the non-data-aided (NDA) schemes are investigated. Unlike classical techniques where the channel is assumed to be slowly time-varying and, therefore, considered as constant over the entire observation period, we address the more challenging problem of instantaneous (i.e., short-term or local) SNR estimation over fast time-varying channels. The channel variations are tracked locally using a polynomial-in-time expansion. First, we derive in closed-form expressions the DA ML estimator and its bias. The latter is subsequently subtracted in order to obtain a new unbiased DA estimator whose variance and the corresponding Cram\'er-Rao lower bound (CRLB) are also derived in closed form. Due to the extreme nonlinearity of the log-likelihood function (LLF) in the NDA case, we resort to the expectation-maximization (EM) technique to iteratively obtain the exact NDA ML SNR estimates within very few iterations. Most remarkably, the new EM-based NDA estimator is applicable to any linearly-modulated signal and provides sufficiently accurate soft estimates (i.e., soft detection) for each of the unknown transmitted symbols. Therefore, hard detection can be easily embedded in the iteration loop in order to improve its performance at low to moderate SNR levels. We show by extensive computer simulations that the new estimators are able to accurately estimate the instantaneous per-antenna SNRs as they coincide with the DA CRLB over a wide range of practical SNRs.

Non-data-aided ML SNR estimation for AWGN channels with deterministic interference

Abstract Communication channels not only suffer from ambient noise but also from deterministic interference. In this paper, we consider signal-to-noise ratio (SNR) estimation in the presence of constant deterministic interference. A maximum likelihood (ML) non-data-aided algorithm is proposed for SNR estimation. We first consider a real-valued model and then extend this to a complex-valued model. The proposed algorithm applies an iterative approach initialized with approximate closed form estimates so as to guarantee stability and convergence. Furthermore, the Cramer-Rao bound (CRB) is also derived as the theoretical limit of the jitter variance. Computer simulations based on pulse-amplitude modulation (PAM) and quadrature amplitude modulation (QAM) sources show that the performance of the proposed algorithm is close to the CRB.

SNR and Noise Variance Estimation in Polarimetric SAR Data

Thermal noise affects polarimetric measurements; but a first order noise correction can be applied if the noise variance (or power) is known. This letter deals with the estimation of the noise variance and the signal-to-noise ratio (SNR) of the cross-polarized channels in polarimetric synthetic aperture radar (SAR) data. Cramér-Rao lower bounds (CRLB) and maximum likelihood (ML) estimators are derived. The ML noise variance estimator is unbiased and efficient, while the ML SNR estimator is biased, but an unbiased SNR estimator can be derived from the biased one. It is also shown that commonly used noise variance and SNR estimators are biased. The results are finally validated using TerraSAR-X fully polarimetric data.

SNR Estimation Over SIMO Channels From Linearly Modulated Signals

In this paper, we address the problem of data-aided (DA) and nondata-aided (NDA) per-antenna signal-to-noise ratio (SNR) estimation over wireless single-input multiple-output (SIMO) channels from linearly modulated signals. Under constant channels and additive white Gaussian noise (AWGN), we first derive the DA maximum-likelihood (ML) SNR estimator in closed-form expression. The performance of the DA ML estimator is analytically carried out by deriving the closed-form expression of its bias and variance. Besides, in order to compare its performance with the fundamental limit, we derive the DA Cramér-Rao lower bound (CRLB) in closed-form expression. In the NDA case, the expectation-maximization (EM) algorithm is derived to iteratively maximize the log-likelihood function. The performance of the NDA ML estimator is empirically assessed using Monte Carlo simulations. Moreover, we introduce an efficient algorithm, which applies to any one/two-dimensional <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary constellation, to numerically compute the NDA CRLBs. In this paper, the noise components are assumed to be spatially uncorrelated over all the antenna elements and temporally white. In both cases, we show that our new inphase and quadrature I/Q-based estimators offer substantial performance improvements over the single-input single-output (SISO) ML SNR estimator due to the optimal usage of the statistical dependence between the antenna branches, and that it reaches the corresponding CRLB over a wide SNR range. We also show that the use of the I/Q-based ML estimators can lead to remarkable performance improvements over the moment-based estimators for the same antenna-array size. Moreover, it is shown that SIMO configurations can contribute to decreasing the required number of iterations of the EM algorithm.