Received Signal Statistics Research Articles

Noisy Fading Channel Distributions Parameter Estimation and Reconstruction based on Truncation

In this paper, Rayleigh and Nakagami-m fading channels are considered that are positively correlated. The received signal statistics specifically mean and variance of sum of fading and noise variables in cases where fading distributions are considered ranging from zero to infinity compared to cases where the fading and noise distributions are truncated due to applying the energy criterion to each distribution are considered. Average number of required bits are derived by calculating Shannon entropy for each case investigated. The number of measurements required for distribution reconstruction based on CS reduced complexity method for each case are also computed. Furthermore, the Bit-Error-Rate (BER) curves for all respective cases are derived and directly compared. The results impose the effect of truncation on the quantification of variances as well as average number of bits as measures of uncertainty and number of measurements for reconstruction. The BER curves produced account for the Gaussian statistical assumption adopted. Applications to 5G communications are provided and future directions are highlighted.

Channel Estimation of MIMO-OFDM through Wavelet Transform to Improve the Spectral Efficiency and Data Transmission Rate

We define a new wavelet transform that is based on a recently defined family of scaling functions: the fractional B-splines. The interest of this family is that they interpolate between the integer degrees of polynomial B- splines and that they allow a fractional order of approximation. The approximation can determine noise in communication signals and help in signal reconstruction and channel estimation in MIMO receiver system. In free space optical communication links, the turbulent atmospheric channel causes fluctuations in both intensity and phase of the transmitted optical signal which degrades their performance. In order to make free space optical communications commercially viable, there is a need for characterizing the atmospheric effects on the received signal statistics, and possibly correcting for the signal degradation using physical optics principles and advanced real-time signal processing techniques. As part of this work, we have constructed an experimental free space optical link over 100 meters so as to characterize the effects of inner-scale and outer-scale turbulence effects, and used it as the platform for carrying out the above objectives. Through these techniques, we have demonstrated bit error rate (BER) reduction and propose to estimate channel accurately.

Statistical Analysis of Interference for Nanoscale Electromechanical Wireless Communication at VHF-Band

Nanoscale electromechanical wireless communication with on-off keying in the very high frequency (VHF) band (30–300 MHz) is studied for a receiver using a carbon nanotube (CNT). Previous studies on this topic have only considered continuous wave (CW) on-off keying which suffers from spectral widening due to sharp changes in the signal. Effects of the inter-symbol interference (ISI), the co-channel interference, and the adjacent channel interference on the received signal statistics have not been analyzed. The rise- and fall-times associated with the filtering of the incoming signal by the mechanical frequency response of the receiver’s CNT have also been ignored. In this paper, Fourier-series based modeling and statistical analysis of decision variables are performed. The results and modeling in this study enable performance evaluation of CNT based receivers with an arbitrary number of interfering signals with arbitrary pulse shapes, and fully incorporates the transient signal components. Received signal statistics under interference are derived using the developed model. Numerical results are presented for Hanning pulse and trapezoidal pulse (which includes rectangular pulses corresponding to CW as a special case). The required guard intervals between pulses to mitigate ISI, required frequency separation between channels, and required spatial separation of co-channel networks (frequency reuse distance) are shown. These results show that large frequency reuse distance is required, limiting efficient spectrum utilization. However, the ISI and adjacent channel interference can be controlled more easily with a proper selection of parameters.

Evaluation of Relative Entropy for Distributed Passive Detection of Weak Acoustic Signals

Passive detection of weak signals in noise is formulated without assuming a parametric distribution of the received signal statistics. A binary likelihood-ratio test as to whether the probability densities of two candidate noise populations are the same, or significantly different, leads to the comparison of relative entropy with a Neyman-Pearson detection threshold. The method is demonstrated using the acoustical intensity of narrowband signals at the hydrophones of a bottom-mounted horizontal line array, which was deployed during the Transverse Acoustic Variability Experiment. Receiver operating characteristics of the relative entropy detector are compared with those for the mean signal-to-noise ratio on a set of hydrophones. It is found that at large false-alarm rates the relative entropy detector has comparatively inferior performance while remaining competitive in the region of small false-alarm probability. Relative entropy detection is insensitive to statistical dependence among the sensors, but is sensitive to data having nonstationary intensity statistics characteristic of the ocean environment in which it was tested.

Eigenspace dynamics of sample covariance matrices

Estimation of the sample covariance matrix is a challenge in array processing, particularly with large-aperture arrays operating in dynamic environments affected by fast maneuvering interferers and background noise. Minimizing the impact of time-dependent variations in the underlying signal statistics requires short observation intervals, thereby reducing the number of snapshots available for covariance estimation. Distinguishing between true variations in the received signal statistics and artifacts introduced by insufficient samples is still an open field of research. Recent developments in random matrix theory (RMT) have provided mathematical foundations to understand the behavior of sample eigenvalues and eigenvectors, and how they deviate from their population counterparts due to the lack of snapshot support. Similarly, expressions have been obtained to describe the “distance” between an initial eigenspace (spanned by p eigenvectors), relative to a subsequent eigenspace (spanned by q eigenvectors). In this paper, simulations corresponding to a horizontal array operating in a realistic environment are used to investigate RMT-based metrics that quantify time-dependent eigenspace stability. This research develops mathematically justifiable methods for proper data segmentation into intervals that exhibit local stationarity, providing data-driven higher bounds for the number of snapshots available for the computation of sample covariance matrices.

Definition of Antenna Diversity Gain in User-Distributed 3D-Random Line-of-Sight

The present paper defines diversity gain for stationary users. This deals in particular with gathering the received signal statistics over possible user positions and orientations in space rather than over time, and to define a meaningful diversity gain related to the cumulative improvement of the performances of the 1% users with the worst receiving conditions. The definition is used to evaluate diversity gain for some typical small antennas in an extreme environment with only line-of-sight (LOS). The LOS environment is regarded as user-distributed 3D-random LOS caused by the statistics of an ensemble of stationary users with arbitrary orientations in the horizontal plane (2D), and with arbitrary orientations of their wireless devices in the vertical plane. Thus, an overall 3D-random distribution of user orientation is assumed.

Characterization of atmospheric turbulence effects and their mitigation using wavelet-based signal processing

In free space optical communication links, the turbulent atmospheric channel causes fluctuations in both intensity and phase of the transmitted optical signal which degrades their performance. In order to make free space optical communications commercially viable, there is a need for characterizing the atmospheric effects on the received signal statistics, and possibly correcting for the signal degradation using physical optics principles and advanced real-time signal processing techniques. As part of this work, we have constructed an experimental free space optical link over 100 meters so as to characterize the effects of inner-scale and outer-scale turbulence effects, and used it as the platform for carrying out the above objectives. A key aspect of our work is the experimental determination of the individual contribution of scintillations and beam wandering to the received signal variance. We have proceeded to correlate such effects with atmospheric parameters with the aim of building a model through which the channel properties may be estimated based on a measurement of the atmospheric parameters. Such analysis has been carried out over a 24 hour period to include a full day-night cycle and also to consider the effect of temperature. In this paper, we have also investigated methods of reducing the atmospheric effects such as scintillations and beam wandering. Specifically, we have demonstrated reduced scintillation-related variance by aperture averaging technique, and reduced beam wandering-related variance using wavelet based signal processing. Through these techniques, we have demonstrated bit error rate (BER) reduction by a factor of 138 compared to the original signal for our experimental free space optical link.

Source depth classification of passive sonar signals using amplitude statistics.

A number of at-sea measurements have shown that fluctuations in the amplitude of passive sonar signals are affected by source depth, range, and the propagation path from the source to the receiver. However, to date, received signal statistics have not been incorporated into passive sonar classification algorithms because the field results have not been accompanied by development of a statistics-based classifier architecture whose performance can be assessed using accepted signal processing metrics, e.g., a receiver operating characteristic curve. The performance of a statistics-based classifier depends critically upon statistical knowledge of the received signal, which in turn depends upon statistical knowledge of relevant environment parameters (sound speed in the water column and sediment, for example). Thus the classifier architecture must make use of the environmental information which in reality is only approximately known and must be described in statistical terms. Given a statistical description of the environment, an ocean acoustic propagation model and Monte Carlo simulation can be used to predict received signal statistics. Once received signal statistics are available for the different classes, a classifier can be designed. Here we examine a likelihood ratio binary source depth classifier for passive sonar. [Work sponsored by ONR Undersea Signal Processing.]

The effects of surface variability on received signal statistics.

Acoustic propagation through the ocean can result in significant variability in the received signal. The degree of variability depends on the signal frequency and source-receiver range as well as medium variability along the propagation path. Our overall research goal is to develop the capability to classify passive sonar signals using the statistics of the received signal, and to support this goal, we require the capability to simulate statistically-valid signals. When the propagation path interacts with a rough ocean surface, the received signal will vary with time. We have employed the rough surface RAM parabolic wave equation code (Rosenberg, J. Acoust. Soc. Am. 105, 1999) to predict the statistics of low-frequency received signals that interact with the surface (such as in a shallow ocean channel) in order to calculate the effects of the time-varying rough surface scattering on frequency and amplitude statistics. Using a temporally-evolving rough surface, frequency and amplitude statistics are calculated for several ranges and depths. Received signal parameter statistics are compared with published analytical and empirical models. [Work sponsored by ONR Undersea Signal Processing.]

The Estimated Signal Parameter Detector: Incorporating Signal Parameter Statistics Into the Signal Processor

Acoustic propagation through a time-varying and spatially varying environment can produce variations in the received signal over multiple observations, possibly degrading receiver performance. This paper presents a signal processing structure that utilizes knowledge of received signal statistics to recoup lost performance. Recent research has shown that received signal parameter statistics can be calculated using Monte Carlo simulation and knowledge of ocean environment properties and processes. The processor possesses an estimator-correlator structure, and is referred to in this paper as the estimated signal parameter detector (ESPD). To demonstrate ESPD performance, the derivation is implemented to distinguish between monotone sinusoids with Gaussian-distributed amplitudes with identical means but different variances, embedded in zero-mean white Gaussian noise. In general, the amplitude distributions can possess any form and the noise distribution must belong to a general class of probability density functions (pdfs). The present assumptions allow for analytical results, and performance of the ESPD is seen to depend upon the signal-to-noise ratio (SNR) as well as the difference between the amplitude variances. Larger SNR and greater difference in amplitude variance result in better receiver performance, eventually leading to an asymptotic performance bound prediction.

Model based target depth estimation using received signal statistics.

The overall goal of our research is to develop model based sonar signal processing techniques that utilize predictions of the acoustic field while being robust to environmental variability and uncertainty. Specifically, we are estimating the depth of a target broadcasting a tonal signal in shallow water using a single passive hydrophone. Three different techniques, naive Bayes, histogram filter, and estimator correlator, are examined. Each is applied to event S5 of the SWellEX‐96 measurement that took place in shallow water off the coast of California. The data consist of sinusoidal signals transmitted simultaneously from moving sources at two different depths and received at a bottomed horizontal array. Received signal amplitudes are modeled using random access memory for the two sources at different depths, and these modeling results are used in the design of the target depth estimation algorithms. Thus, the ability of each of the techniques to estimate target depth depends on an accurate representation...

Efficient statistical parallel interference cancellation for DS-CDMA in Rayleigh fading channels

We present a reduced-complexity parallel interference cancellation (PIC) technique, in which PIC is performed only on "unreliable" bits (blocks). We term our technique statistical PIC (STPIC), since the decision to employ PIC for any user signal is based upon received signal statistics. Here we propose two different methods: one is bitwise (instantaneous) STPIC (ISTPIC), in which IC is performed only on the bits whose absolute log likelihood ratio (LLR) is below a pre-selected threshold; the other method is block STPIC (BSTPIC), in which IC is performed only on the blocks whose average signal-to-noise-plus-interference ratio (SNIR) is below a pre-selected threshold. Both LLR and SNIR statistics reduce to quantities simple to obtain. We show that STPIC can achieve performance equivalent to conventional full PIC (FPIC) and other partial PIC techniques in flat Rayleigh fading channels, but with reduced computational complexity. We also show our proposed ISTPIC can achieve performance better than FPIC in good channel conditions (e.g., AWGN), still with reduced computational complexity. The ISTPIC performance gain over conventional FPIC is larger in conditions of larger loading factor where efficient IC techniques are more likely to be needed

Non-line-of-sight identification in ultra-wideband systems based on received signal statistics

Non-line-of-sight (NLOS) propagation can severely degrade the reliability of communication and localisation accuracy in indoor ultra-wideband (UWB) ‘location-aware’ networks. Link adaptation and NLOS bias mitigation techniques have respectively been proposed to alleviate these effects, but implicitly rely on the ability to accurately distinguish between LOS and NLOS propagation scenarios. A statistical NLOS identification technique based on the hypothesis-testing of received signal parameters in UWB propagation channels is discussed. In contrast to narrowband and wideband signals, UWB signals possess higher temporal resolution and robustness to multipath fading. We show that these characteristics result in differences in the statistics of (a) the time-of-arrival (TOA), (b) the received signal strength (RSS) and (c) the root-mean-squared delay spread (RDS) of the received signals, between LOS and NLOS propagation scenarios, which can be exploited for accurate channel identification. We statistically characterise the ability of TOA, RSS and RDS estimates to distinguish between LOS and NLOS propagation based on an extensive indoor measurement campaign. Our measurement results suggest that the RDS of UWB signals can, even in isolation and without complete statistical information, serve as a robust and computationally efficient indicator of the LOS/NLOS nature of propagation. Finally, we demonstrate the efficacy of the discussed NLOS identification method in a location-tracking application based on indoor UWB measurements.

Incorporating environmental variability into received signal statistics

We have developed a Monte Carlo-based method for estimating the variability of acoustic signal parameters caused by uncertain ocean environments. The method begins with a physics-based model for the environmental properties and uses the maximum entropy (MaxEnt) method to construct probability density functions (pdf’s) describing the measured deviations from the model mean. Random realizations of environmental variability, with proper depth correlation, are constructed from the pdf’s and added to the mean model parameters. A parabolic equation code (ram) is used to propagate acoustic energy through each realization of the environment. Fourier synthesis is used to recreate the arrival structure. The method is demonstrated using measurements from the Strait of Gibraltar, which is a particularly complicated region dominated by strong tidal fluctuations and internal waves. During 1996, an international group carried out the Strait of Gibraltar Acoustic Monitoring Experiment (SGAME), in which detailed environmental and 250-Hz acoustic data were collected. Here, pdf’s of the received signal level are compared with results of the Monte Carlo method to demonstrate performance. [Gibraltar data and SVP model provided by Chris Tiemann (ARL:UT) and Peter Worcester (SIO). Work supported by ONR Undersea Signal Processing.]

Joint Parameter Estimation for UWB Energy Detectors Using OOK

In this paper, joint estimation of the optimal threshold, synchronization point, and integration interval is developed for ultrawideband (UWB) energy detectors employing on-off keying (OOK) modulation. Gaussian approximation of the received signal statistics is shown to enable low complexity solutions at the expense of some performance degradation. The performances of the optimal and suboptimal solutions are evaluated and compared. It is shown that explicit BER minimization is required for parameter optimization. Using simulations, number of training symbols required to converge to ideal parameter estimates is demonstrated to be increasing with increasing SNR.

Optical spectral amplitude coding CDMA systems using perfect difference codes and interference estimation

The spectral amplitude coding (SAC) technique is applied to a synchronous optical code-division multiple-access (OCDMA) system, using perfect difference code (PDC). The use of the SAC technique removes the codeword synchronisation requirement of time-spreading OCDMA systems using PDCs. In the proposed system, the unity cross-correlation property of PDCs is exploited by the interference estimator of the proposed system to estimate the number of active users simultaneously transmitting bit 1. This estimate is then employed to modify the threshold used to differentiate between transmitted bits 1 and 0. In contrast to the variance expansion of the decision statistics used in synchronous OCDMA systems with interference cancellation, the proposed system preserves the characteristics of the received signal statistics, thereby avoiding data decision errors. As the estimation rules and the decision thresholds are important factors influencing the estimates and the bit-error rates, the effects of these two factors are thoroughly investigated. A second SAC-PDC OCDMA system is developed, which mitigates multiple-access interference (MAI) by means of an interference cancellation technique and makes data decisions based on the estimated MAI. The numerical results reveal that the two systems provide a better performance and a larger capacity than the synchronous OCDMA system.

Comprehensive evaluation of chip interleaving effect on turbo‐coded DS‐SS in a Rayleigh fading channel with antenna diversity reception

AbstractIn this paper, we present a comprehensive performance evaluation of chip interleaving effect on turbo coded direct sequence spread spectrum (DS‐SS) system in a frequency non‐selective Rayleigh fading channel with antenna diversity reception. At the transmitter, chip interleaver scrambles the SF (spreading factor) chips associated with a data symbol and transforms the transmission channel into a highly time‐selective or highly memoryless channel at the chip level. The use of chip interleaving is equivalent to using SF‐antenna diversity reception with correlated fading among the branches and with reduced average received signal power per antenna by a factor of SF. We theoretically analyze how chip interleaving alters the received signal statistics. Then, the effect of the various parameters, viz. interleaver size, interleaving depth, information sequence length, spreading factor and the fading maximum Doppler frequency, are also evaluated. It is found that the bit error rate (BER) performance improves with increasing spreading factor and increasing frame length. Chip interleaving is found to be effective in the presence of receive antenna diversity as well. Copyright © 2005 John Wiley & Sons, Ltd.

A survey of ionospheric effects on space-based radar

In this survey, we fully review almost all potential ionospheric effects on the performance of space-based radar systems (SBRs), which operate in the ambient ionosphere environment; in particular, we review the use of space-based synthetic aperture radar systems (SARs) for imaging. There are two families of effects involved. One is the effects of the background ionosphere (non-turbulent ionosphere), such as dispersion, group delay, refraction, Faraday rotation, and phase shift. The other is the effects due to ionospheric irregularities, such as refractive index fluctuation, phase perturbation, angle-of-arrival fluctuation, pulse broadening, clutter, and amplitude scintillation. These effects adversely affect SAR imaging in several respects, such as by causing image shift in the range, and degradations of the range resolution, azimuthal resolution, and/or the resolution in height (elevation). We also review ionospheric irregularity characteristics and descriptions, propagation channel statistics, received signal statistics, and detection performance of SBRs in ionospheric scintillation situations. First, a brief outline of SBR systems and principles, and theories of wave propagation in random media, especially some effects caused by two-way propagation, is given. Finally, several of the most probable directions of future research are pointed out.

Received signal statistics in ds-cdma channels with flat rayleigh fading and fast closed-loop power control

The statistics of received signal power at the receiver in a cellular direct-sequence code-division multiple-access (DS-CDMA) system with flat Rayleigh fading and fast closed-loop power control mechanism are studied. A simple model for the fast closed-loop power control mechanism is proposed to ease the analysis. The probability density function (pdf) of the received signal power is derived by taking into consideration the updating frequency of power control mechanism, maximum allowable transmitted power, and Doppler frequency of the fading channel. The pdf derived can be used to study the performance of a reverse-link DS-CDMA system with noncoherent M-ary orthogonal modulation. The result shows that when optimum maximum allowable transmitted power is used, system capacity can be substantially increased for typical normalized Doppler frequency in cellular communication.

Review on radio propagation into and within buildings

The paper reviews the published information on radio propagation into and within buildings particular to microcellular portable mobile radio channel at frequencies from 150 MHz upwards. However, no particular attention has been paid to the work carried out at millimetre wavelengths. The review has been carried out because such propagation information is required for the design of future portable mobile communication systems.The need for propagation information and the types of information required is described. The buildings, where a portable handset is likely to be used, have been categorised to put bounds on the received signal statistics and provide channel models for any particular type of building. The results published by different authors are then summarised by considering all the proposed categories. The results have been divided into narrowband and wideband measurements. This information is tentative as it is based on only a few measurements. As more measured results become available the design information and channel models can be modified. Suggestions for new measurements required are made in the light of existing information.