Non-data-aided Research Articles

NDA SNR and CRLB Estimation Over MISO with STBC Channels

This paper discusses the problem of Non Data Aided (NDA) Signal to Noise Ratio (SNR) estimation of Binary Phase Shift keying (BPSK) modulated signals using the Expectation Maximization (EM) Algorithm. In addition, the Cramer-Rao Lower Bounds (CRLB) for the estimation of Data Aided (DA) and Non Data Aided (NDA) Signal to Noise Ratio (SNR) estimation is derived. Multiple Input Single Output (MISO) channels with Space Time Block Codes (STBC) is used. The EM algorithm is a method that finds the Maximum Likelihood (ML) solution iteratively when there are unobserved (hidden or missing) data. Extension of the proposed approach to other types of linearly modulated signals in estimating SNR is straight forward. The performance of the estimator is assessed using the NDA CRLBs. Alamouti coding technique is used in this paper with two transmit antennas and one receive antenna. The authors’ assumption is that the received signal is corrupted by additive white Gaussian noise (AWGN) with unknown variance, and scaled by fixed unknown complex channel gain. Monte Carlo simulations are used to show that the proposed estimator offers a substantial improvement over the conventional Single Input Single Output (SISO) NDA SNR estimator due to the use of the statistical dependences in space and time. Moreover, the proposed NDA SNR estimator works close to the NDA SNR estimator over Single Input Multiple Output (SIMO) channels.

Frequency-Domain Blind Equalization for Long-Haul Coherent Pol-Mux 16-QAM System With CD Prediction and Dual-Mode Adaptive Algorithm

The combination of polarization-multiplexing (pol-mux) high-order quadrature-amplitude-modulation (QAM) format and non-data-aided (NDA) channel equalization largely enhances the spectral efficiency of the coherent optical systems. In this paper, we present a two-stage frequency-domain equalization method for long-haul coherent pol-mux NDA system with 16-QAM modulation format. Chromatic dispersion (CD) is blindly estimated and compensated in the first stage of the equalizer, while multimodulus-algorithm-assisted decision-directed multimodulus algorithm (MMA-DDMA) is designed for the second stage to further enhance the equalization performance. The proposed algorithms are experimentally demonstrated in a 80-Gb/s coherent 16-QAM system over 800-km fiber transmission and 30-ps mean differential group delay to achieve wide-range precise CD estimation and better equalization performance compared with conventional adaptive algorithms.

Cramér–Rao lower bound for non-data-aided carrier phase estimation from general M-ary phase-shift keying modulation signals over flat Rayleigh fading channel

The authors derive the true Cramér–Rao lower bound (CRLB) for a non-data-aided (NDA) carrier phase estimation from general M-ary phase-shift keying (M-PSK) modulation signal over flat Rayleigh fading channels (FRFC). The numerical Monte Carlo method is used to compute the true CRLB from general M-PSK modulation signals over FRFC with complex additive white Gaussian noise. The efficiency of the proposed method is made obvious through the assessment of the true CRLBs from both symmetric and asymmetric 8-PSK modulation signals for various observation window sizes. The simulation results show that optimal NDA carrier phase recovery is harder to acquire from symmetric modulation signals for signal-to-noise ratio (SNR) range up to 5 dB, but depends on the constellation density, only for SNR range superior to 5 dB. For both constellations the CRLB decreases as long as the observation window size increases. The derived bound provides an efficient standard for evaluating the performance of any unbiased NDA carrier phase estimator from general M-PSK modulation signals over FRFC. The method presented here stands useful for general M-ary quadrature amplitude modulation signals as well.

Acquisition Probability Of Multi-User Uwb Systems In The Presence Of A Novel Synchronization Approach

In this paper, to synchronize Ultra Wideband (UWB) systems in ad-hoc multi-user environments, we propose a new timing acquisition approach for achieving a good performance despite the difficulties to get there. Synchronization constraints are caused by the ultra-short emitted waveforms nature of UWB signals. Used in [1, 2] for single-user environments, our timing acquisition approach is based on two successive stages or floors. Extended for multi-user environments, the used algorithm is a combination between coarse synchronization based on timing with dirty templates (TDT) acquisition scheme and a new fine synchronization scheme developed in [3-6] which conduct to an improved estimate of timing offset. In this work, we develop and test this method in both data-aided (DA) and non-data-aided (NDA) modes. Simulation results and comparisons are also given to confirm performance improvement of our approach (in terms of mean square error and acquisition probability) compared to the original TDT algorithm in multi-user environments, especially in the NDA mode.

SNR and Noise Variance Estimation for MIMO Systems

Accurate signal-to-noise ratio (SNR) and noise variance estimation are extremely important aspects of receiver design in multiple-input multiple-output (MIMO) systems. Typically, these parameters are estimated using known pilot/training symbols. However, significant improvements may be made by using both the known pilot symbols as well as the unknown data symbols. In this paper, we address SNR and noise variance estimation of MIMO systems for both a data aided (DA) model, a non-data aided (NDA) model, as well as a mixed model that uses known and unknown data symbols. The Cramér-Rao lower bound (CRLB) and modified Cramér-Rao lower bound (MCRLB) for MIMO SNR and MIMO noise variance estimation are determined for digital constellations such as BPSK, QPSK, 8PSK, and 16QAM. Maximum-likelihood estimators are derived in closed form for the DA model. For the NDA model, closed form approximations are derived in addition to iterative expectation-maximization (EM) algorithm based estimators, all of which are demonstrated to perform very close to the CRLB.

A Non-Data-Aided Rapid Synchronization Method for UWB Impulse Radio

Timing synchronization is a critical as well a challenging issue in ultra-wideband impulse radio (UWB-IR) due to their particular transmission characteristics. This letter proposes a rapid synchronization algorithm which can achieve frame-level synchronization in non-data-aided (NDA) mode. Relying on a unique transmit signal pattern based on orthogonal pulses and asymmetric modulation, synchronization is achieved without the need to search among thousands of bins, thereby significantly reducing the mean synchronization time. Simulation results prove that the proposed synchronization algorithm is efficient in single as well as in multi-user scenarios.

Non Data Aided SNR Estimation for OFDM Signals in Frequency Selective Fading Channels

This paper deals with the problem of non data aided (NDA) signal to noise ratio (SNR) estimation of OFDM signals transmitted through unknown multipath fading channel. Most of present day's SNR estimators are based on the knowledge of pilot sequences which is not applicable in some contexts such as cognitive radio for example. Moreover in Multipath fading channels SNR also depends on frequency offset which is caused by mismatch between the oscillator in the transmitter and that in the receiver. Previous NDA SNR estimation schemes assumed a perfect synchronization at reception (i.e. ? = 0 and $${\varepsilon = 0}$$ ) which results estimation of SNR with less accuracy. The frequency offset attenuates the desired signal and causes intercarrier interference, thus reducing the SNR. In this paper we propose a new NDA SNR estimator which uses periodic redundancy induced by the cyclic prefix, considering SNR degradation due to frequency offset ( $${\varepsilon}$$ ).

Blind Carrier Phase Recovery for General 2 Π/M-Rotationally Symmetric Constellations

This paper introduces a novel blind carrier phase recovery estimator for general 2{\Pi}/M-rotationally symmetric constellations. This estimation method is a generalization of the non-data-aided (NDA) nonlinear Phase Metric Method (PMM) estimator already designed for general quadrature amplitude constellations. This unbiased estimator is seen here as a fourth order PMM then generalized to Mth order (Mth PMM) in such manner that it covers general 2{\Pi}/M-rotationally symmetric constellations such as PAM, QAM, PSK. Simulation results demonstrate the good performance of this Mth PMM estimation algorithm against competitive blind phase estimators already published for various modulation systems of practical interest.

Performance Analysis and Optimization of Non-Data-Aided Carrier Frequency Estimator for APSK Signals

This paper investigates the non-data-aided (NDA) carrier frequency estimation of amplitude and phase shift keying (APSK) signals. The true Cramer-Rao bound (CRB) for NDA frequency estimation of APSK signals are derived and evaluated numerically. Characteristic and jitter variance of NDA Luise and Reggiannini (L&R) frequency estimator are analyzed. Verified by Monte Carlo simulations, the analytical results are shown to be accurate for medium-to-high signal-to-noise ratio (SNR) values. Using the proposed closed-form expression, parameters of the algorithm are optimized efficiently to minimize the jitter variance.

Non-data-aided SNR estimation method for APSK exploiting rank discrimination test

Presented is a non-data-aided (NDA) signal-to-noise ratio (SNR) estimation method for amplitude-phase shift-keying (APSK) in the presence of additive white Gaussian noise over a quasi-static channel. The proposed estimator is based on a rank discrimination test and uses a look-up table for SNR estimation. The performance of the proposed estimator is evaluated for 8APSK and 16APSK. It is shown through Monte-Carlo simulations that the proposed estimator outperforms existing NDA moment-based SNR estimators in terms of normalised mean-square error.

Cramer–Rao lower bounds and maximum likelihood timing synchronization for dirty template UWB communications

Timing acquisition constitutes a major challenge in realizing ultra-wideband communications. In this paper, we propose the timing with dirty template (TDT) approach as a promising candidate for achieving rapid, accurate and low-complexity acquisition. We describe the dirty template (DT) technique, in order to develop and test timing algorithms in both modes: data-aided (DA) and non-data- aided (NDA) modes. First, we derive the Cramer–Rao lower bound, which is used as a fundamental performance limit for any timing estimator. Next, the TDT acquisition estimator is achieved by using the Maximum Likelihood concept. Then we propose a new method, based on Time-Hoping codes, to improve the performance estimation of the original dirty template algorithms. Simulation shows the estimation error results of the modified method in the DA and NDA modes. It confirms the high performance and fast timing acquisition of DA mode, compared with NDA mode, but with less bandwidth efficiency.

Cramer-Rao Lower Bounds of DOA Estimates from Square QAM-Modulated Signals

In this paper, we derive for the first time analytical expressions for the inphase/quadrature (I/Q) non-data-aided (NDA) Cramér-Rao lower bounds (I/Q NDA CRLBs) of the direction of arrival (DOA) estimates from square quadrature amplitude (QAM)-modulated signals corrupted by additive white circular complex Gaussian noise (AWCCGN) with any antenna configuration. Yet the main contribution embodied by this paper consists in deriving for the first time analytical expressions for the NDA Fisher information matrix (FIM) and then for the stochastic CRLB of the NDA DOA estimates in the case of square QAM-modulated signals. It will be shown that in the presence of any unknown phase offset (i.e., non-coherent estimation), the ultimate achievable performance on the NDA DOA estimates holds almost the same irrespectively of the modulation order. However, the NDA CRLBs obtained in the absence of the phase offset (i.e., coherent estimation) vary, in the high SNR region, from one modulation order to another.

Robust Weighted Non-Coherent Receiver for Impulse Radio UWB PPM Signals

This letter proposes an energy detection based robust weight estimation scheme for pulse-position modulated (PPM) impulse radio ultra-wideband (IR-UWB) signals using weighted non-coherent receiver (WNCR). Conventional data-aided WNCR (DA-WNCR) scheme estimates the weighting coefficients, or channel state information (CSI), using a large number of training symbols over time-varying channels. In contrast, the proposed Robust WNCR (R-WNCR) scheme is non-data-aided (NDA), adaptive and robust to channel variations. The proposed R-WNCR estimates the weighting coefficients adaptively based on the received stochastic data, and the weight estimation process is refined using a decision directed approach.

Fine Synchronization Through UWB TH-PPM Impulse Radios

In this paper, a novel fine timing algorithm has been tested and developed to synchronize UltraWideband (UWB) signals with pulse position modulation (PPM). By applying this algorithm, we evaluate timing algorithms in both data-aided (DA) and non-data-aided (NDA) modes. Based on correlation operations, our algorithm remains operational in practical UWB settings. The proposed timing scheme consists of two complementary floors or steps. The first floor consists on a coarse synchronization which is founded on the recently proposed acquisition scheme based on dirty templates (TDT). In the second floor, we investigate a new fine synchronization algorithm which gives an improved estimate of timing offset. Simulations confirm performance improvement of our timing synchronization compared to the original TDT algorithm in terms of mean square error.

Bayesian and Hybrid Cramér–Rao Bounds for the Carrier Recovery Under Dynamic Phase Uncertain Channels

In this paper, we study Bayesian and hybrid Cramér-Rao bounds (BCRB and HCRB) for the code-aided (CA), the data-aided (DA), and the non-data-aided (NDA) dynamical phase estimation of QAM modulated signals. We address the bounds derivation for both the offline scenario, for which the whole observation frame is used, and the online which only takes into account the current and the previous observations. For the CA scenario we show that the computation of the Bayesian information matrix (BIM) and of the hybrid information matrix (HIM) is NP hard. We then resort to the belief-propagation (BP) algorithm or to the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to obtain some approximate values. Moreover, in order to avoid the calculus of the inverse of the BIM and of the HIM, we present some closed form expressions for the various CRBs, which greatly reduces the computation complexity. Finally, some simulations allow us to compare the possible improvements enabled by the offline and the CA scenarios.

Design and performance analysis of non-data-aided carrier phase estimators for amplitude and phase shift keying signals

This study studies the feedforward (FF) non-data-aided (NDA) carrier phase estimation of the amplitude and phase shift keying (APSK) signals. The true Cramer–Rao bounds (CRBs) for NDA phase estimation of APSK signals are derived and evaluated numerically using Gauss–Hermite quadrature. The jitter variance of the FF Viterbi–Viterbi (V&V) algorithm is analysed assuming the absence of data pattern noise. It is proved that, when the design parameter μ=2, the jitter variance is able to converge asymptotically to the modified CRB (MCRB) at high signal-to-noise ratios (SNRs). For practical application, the parameter μ is also optimised for 16/32/64-APSK signals at different SNRs. The analytical results of the jitter variance are verified by Monte-Carlo evaluations. It is shown that, for 32/64-APSK signals, the plain V&V algorithm cannot approach the CRBs due to the data pattern noise. A modified V&V algorithm based on the constellation partition and a linear combination of the sub-estimators is proposed to eliminate the divergence. Simulation results show that the jitter variance of the proposed estimator is very close to the CRB at the SNRs of interest and converges to the MCRB at high SNRs.

Selection of the signal synchronization method in software GPS receivers

Introduction This paper presents a critical analysis of the signal processing flow carried out in a software GPS receiver and a critical comparison of different architectures for signal processing within the GPS receiver. A model of software receivers is shown. Based on the displayed model, a receiver has been realized in the MATLAB software package, in which the simulations of signal processing were carried out. The aim of this paper is to demonstrate the advantages and disadvantages of different methods of the synchronization of signals in the receiver, and to propose a solution acceptable for possible implementation. The signal processing flow was observed from the input circuit to the extraction of the bits of the navigation message. The entire signal processing was performed on the L1 signal and the data collected by the input circuit SE4110. A radio signal from the satellite was accepted with the input circuit, filtered and translated into a digital form. The input circuit ends with the hardware of the receiver. A digital signal from the input circuit is brought into the PC Pentium 4 (AMD 3000 +) where the receiver is realized in Matlab. Model of software GPS receiver The first level of processing is signal acquisition. Signal acquisition was realized using the cyclic convolution. The acquisition process was carried out by measuring signals from satellites, and these parameters are passed to the next level of processing. The next level was done by monitoring the synchronization signal and extracting the navigation message bits. On the basis of the detection of the navigation message the receiver calculates the position of a satellite and then, based on the position of the satellite, its own position. Tracking of GPS signal synchronization In order to select the most acceptable method of signal synchronization in the receiver, different methods of signal synchronization are compared. The early-late-DLL (Delay Lock Loop), TDL (Tau Dither Loop) and Costas's PLL (Phase Lock Loop) models of loop tracking of signal synchronization are presented. The analysis is performed by processing the signals from the same satellite and under the same conditions of the initial signal synchronization. The multiple signal processing showed the advantages and disadvantages of the particular methods and the most acceptable solution proved to be the implementation of the DLL tracking loop phase synchronization and the code tracking loop PLL carrier frequency synchronization. The influence of the parameters of the loop itself is shown as well. After the extraction of navigation bits, all bit extracts do not come with an equal phase. This may lead to a wrong decision in rejecting the Decider and bits. Therefore, the paper proposes an additional synchronization of the extracted bits selected by the navigation messages NDA (Non-Data-Aided) algorithm in order to perform their correct detection and to position the receiver much faster. Comparison of methods of signal synchronization Based on the analysis of the methods, the simulation results are compared. The results showed that the TDL loop is not resistant to dynamic disturbances of signals, since the synchronization tracking breaks up. In addition, this loop shows susceptibility to the noise from free space. These are sufficient reasons to propose the implementation of the DLL signal tracking loop as an acceptable solution. In addition to the proposal of the tracking loop, tracking loop coefficient values are determined. Conclusion The performed analysis showed that the TDL loop is not resistant to noise and dynamic disorders of the input signal. Therefore, an appropriate solution for the implementation is the DLL loop with six correlates. The DLL tracking loop coefficients are determined as a compromise solution and they are B = 2Hz and γ = 0.7. Also, the coefficients of the PLL tracking loop of frequency synchronization are B = 20Hz and γ = 0.7. The application of the NDA algorithm results in an additional synchronization of the navigation bit message, thus making the receiver operate faster and more precisely.

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.

Cramer-Rao Lower Bounds for NDA SNR Estimates of Square QAM Modulated Transmissions

In this paper, we derive for the first time analytical expressions for the exact Cramér-Rao lower bounds on the variance of unbiased non-data-aided (NDA) signal-to-noise ratio (SNR) estimators of square QAM-modulated signals. The channel is assumed to be constant over the observation interval and the received signal is supposed to be corrupted by additive white Gaussian noise (AWGN). The derived expressions corroborate previous attempts to numerically compute the considered CRLBs. It will be shown that the NDA CRLBs differ widely from one modulation order to another especially at moderate SNR levels.

A Nondata-Aided SNR Estimation Technique for Multilevel Modulations Exploiting Signal Cyclostationarity

Signal-to-noise ratio (SNR) estimators of linear modulation schemes usually operate at one sample per symbol at the matched filter output. In this paper we propose a new method for estimating the SNR in the complex additive white Gaussian noise (AWGN) channel that operates directly on the oversampled cyclostationary signal at the matched filter input. Exploiting cyclostationarity proves to be advantageous due to the fact that a signal-free Euclidean noise subspace can be identified such that only second order moments of the received waveform need to be computed. The proposed method is nondata-aided (NDA), as well as constellation and phase independent, and only requires prior timing synchronization to fully exploit the cyclostationarity property. The estimator can also be applied to nonconstant modulus constellations without requiring any tuning, which is a feature not found in existing approaches. Implementation aspects and simpler suboptimal solutions are also provided.