Data-aided Maximum Likelihood Estimator 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.

Data-Aided and Non-Data-Aided SNR Estimators for CPM Signals in Ka-Band Satellite Communications

Adaptive coded and modulation (ACM) is an effective measure to resist rain attenuation in Ka-band satellite communications. The accuracy of the estimator for signal-to-noise ratio (SNR) is one of the main factors that affect ACM performance. This paper establishes the channel model of satellite communication in Ka-band and derives and analyzes data-aided (DA) maximum likelihood (ML) and method-of-moments estimators for SNR of continuous phase modulation (CPM) in Ka-band fading channel. Simulations and analysis indicate that the normalized mean square error (NMSE) of the DA ML estimator is closer to the Cramer-Rao bounds (CRB) at low SNR, but the performance worsens with the SNR increases from medium to high values. The M2M4 estimator performs poorly at low SNR and best at medium SNR. When the SNR is low, the performance of the DA ML estimator is better than the M2M4 estimator; however, the two estimators have similar performance when SNR is high. The performances of the two estimators will become increasingly better the greater the lengths of the observation signals become. However, the influence of the signal length will become increasingly smaller as the SNR becomes larger.

Blind SNR estimation for M-ARY Frequency Shift Keying signal using covariance technique

This paper presents a blind SNR (signal-to-noise-ratio) estimation algorithm for an M-ARY Frequency Shift Keying (MFSK) signal in Rayleigh and Rician fading channels with additive white Gaussian noise (AWGN). The SNR is estimated by comparing the test statistic of the received signal with a calibrated signal. The estimated SNR corresponds to the SNR that minimizes the difference between the computed and calibrated test statistics. The test statistic of both the received and calibrated signal is calculated using the sample covariance matrix (SCM). The proposed algorithm performance is compared with the Partially Data Aided Maximum Likelihood Estimator (PDA MLE). The numerical results show that the Normalized Mean Square Error (NMSE) of the proposed algorithm is better than the PDA MLE. The NMSE is consistently less than 10-2 over the SNR range −20dB to +20dB using 512 samples. Further, the algorithm can detect the signal with a probability of detection 0.9 upto −8dB SNR without any extra computation. However, the detection performance can be improved by increasing the number of samples. The proposed algorithm can be used for signal detection and SNR estimation for a broad range of SNR.

Data-Aided and Non-Data-Aided Maximum Likelihood SNR Estimators for CPM

Data-aided (DA) and non-data-aided (NDA) maximum likelihood (ML) estimators for the SNR of CPM in the presence of phase and frequency offset are derived and analyzed. Cramer-Rao bounds for both are obtained and compared to the simulated performance of these estimators for a full response example, CPSFK and a partial response example, GMSK. Analysis and simulations show that the performance of the DA ML estimator suffers from an unremovable bias caused by uncompensated frequency offset due to frequency offset estimation errors. As a consequence, the estimator error variance of the DA ML estimator is not able to achieve its lower bound. In contrast, the estimator error variance of the NDA ML estimator is capable of achieving its lower bound (although the lower bound for NDA ML estimator is higher than the lower bound for the DA ML estimator). This is because the NDA ML estimator is not burdened with the requirement of relying on estimates of nuisance parameters. The NDA estimator only achieves its lower bound when the observation length or true SNR are sufficiently large.

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.

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.

Timing Synchronization for Cooperative Communications with Detect and Forward Relaying

A non-data-aided near maximum likelihood (NDA-NML) symbol timing estimator is presented, which is applied to a cooperative communication system with a source, relay and destination. A Cramer rao bound (CRB) for the estimator for asymptotically low signal-to-noise (SNR) ratio case is derived. The timing complexity of the NDA-NML estimator is derived and compared with the correlation based data-aided maximum likelihood (DA-ML) estimator. It is demonstrated that the complexity of the NDA-NML estimator is much less than that of correlation based DA-ML estimator. The bit-error-rate (BER) performance of this system operating in a detect-and-forward (DAF) mode is studied where the channel state information (CSI) is available at the receiver and the symbol timings are estimated independently for each channel. SNR combining (SNRC) and equal ratio combining (ERC) methods are considered. It is found that timing estimation error has a significant effect on BER performance. It is also found that for large timing error the benefit of cooperative diversity could vanish. It is demonstrated that significant gains can be made with both combining methods with cooperation and timing estimation, where the gains are the same for both estimators.

Symbol timing estimation in MIMO correlated flat‐fading channels

AbstractIn this paper, the data aided (DA) and non‐data aided (NDA) maximum likelihood (ML) symbol timing estimators and their corresponding conditional Cramer–Rao bound (CCRB) and modified Cramer–Rao bound (MCRB) in multiple‐input‐multiple‐output (MIMO) correlated flat‐fading channels are derived. It is shown that the approximated ML algorithm in References [4,13] is just a special case of the DA ML estimator; while the extended squaring algorithm in Reference [14] is just a special case of the NDA ML estimator. For the DA case, the optimal orthogonal training sequences are also derived. It is found that the optimal orthogonal sequences resemble the Walsh sequences, but present different envelopes. Simulation results under different operating conditions (e.g. number of antennas and correlation between antennas) are given to assess and compare the performances of the DA and NDA ML estimators with respect to their corresponding CCRBs and MCRBs. It is found that (i) the mean square error (MSE) of the DA ML estimator is close to the CCRB and MCRB, (ii) the MSE of the NDA ML estimator is close to the CCRB but not to the MCRB, (iii) the MSEs of both DA and NDA ML estimators are approximately independent of the number of transmit antennas and are inversely proportional to the number of receive antennas, (iv) correlation between antennas has little effect on the MSEs of DA and NDA ML estimators and (v) DA ML estimator performs better than NDA ML estimator at the cost of lower transmission efficiency and higher implementation complexity. Copyright © 2004 John Wiley &amp; Sons, Ltd.

SNR Threshold Indicator in Data-Aided Frequency Synchronization

The signal-to-noise ratio (SNR) threshold behavior is studied in the frame of data-aided carrier synchronization in additive white Gaussian noise. The closed form expression of the Chapman-Robbins bound, relative to the carrier frequency offset estimation is first established then used to derive an indicator of the SNR threshold. For a given sequence of pilot symbols, the threshold region is localized at the departure of the Chapman-Robbins bound from the Cramer-Rao bound. The data-aided maximum likelihood estimator is considered to examine the derived indicator usefulness.