Compensation for HPA nonlinearity and I/Q imbalance in MIMO beamforming systems

In this paper, we investigate the effects of high-power amplifier (HPA) nonlinearity and in-phase and quadrature-phase (I/Q) imbalance on the performance of multiple-input multiple-output (MIMO) transmit beamforming (TB) systems. Specifically, we propose a compensation method for HPA nonlinearity and I/Q imbalance together in MIMO TB systems. The performance of the MIMO TB system under study is evaluated in terms of the average symbol error probability (SEP) and system capacity, considering transmission over uncorrelated frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, such as the HPA parameters, image-leakage ratio, numbers of transmit and receive antennas, length of pilot symbols, and modulation order of phase-shift keying (PSK), on performance.

Optimal beamforming in MIMO systems with HPA nonlinearity

In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance.

Impact of HPA nonlinearity on MIMO systems with quantized equal gain transmission

In this paper, we investigate the performance of multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of nonlinear high-power amplifiers (HPAs). Due to the suboptimality of maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, quantized equal gain transmission (QEGT) is suggested as a feasible TB scheme. The effect of HPA nonlinearity on the performance of MIMO QEGT/MRC is evaluated in terms of the average symbol error probability (SEP) and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, such as the parameters of nonlinear HPA, cardinality of the beamforming weight vector codebook, and modulation order of quadrature amplitude modulation (QAM), on performance.

On the effect of I/Q imbalance on MIMO transmit-receive diversity systems

In practice, all I/Q signal processing receivers face the problem of I/Q imbalance. In this paper, we investigate the effect of I/Q imbalance on the performance of MIMO maximal ratio combining (MRC) systems that perform the combining at the radio frequency (RF) level, thereby requiring only one RF chain. Based on a system modeling that takes the I/Q imbalance into account, we evaluate the performance in terms of average symbol error probability (SEP), outage probability and system capacity, which are derived considering transmission over uncorrelated Rayleigh fading channels. Numerical results are provided to illustrate the effects of system parameters, such as the image- leakage ratio, numbers of transmit and receive antennas, and modulation order of quadrature amplitude modulation (QAM), on the system performance.

On the effect of power amplifier nonlinearity on MIMO transmit diversity systems

Nonlinearity of high-power amplifier (HPA) plays a crucial role in the performance of multiple-input multiple-output (MIMO) systems. In this paper, we investigate the performance of MIMO orthogonal space-time block coding (STBC) systems in the presence of nonlinear HPA. Specifically, we assess the impact of HPA nonlinearity on the average symbol error probability (SEP), total degradation (TD), and system capacity of orthogonal STBC in uncorrelated Nakagami-m fading channels. Numerical results are provided and show the effects of several system parameters, such as the output back-off (OBO) of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of quadrature amplitude modulation (QAM), on performance.

Performance analysis of MIMO MRC in 3D mobile-to-mobile double-correlated channels

In this paper, we consider multiple-input multiple- output (MIMO) maximal ratio combining (MRC) systems and assess the system performance in terms of average symbol error probability (SEP), outage probability and ergodic capacity in double-correlated Rayleigh-and-Lognormal fading channels. In order to derive the receive and transmit correlation functions needed for the performance analysis, a three-dimensional (3D) MIMO mobile-to-mobile (M-to-M) channel model, which takes into account the effects of fast fading and shadowing is used. Numerical results are provided to show the effects of system parameters, such as maximum elevation angle of scatterers, orientation angle of antenna array in the x-y plane, angle between x-y plane and the antenna array orientation, and degree of scattering in the x-y plane, on the system performance.

Optimal frame length for keeping normalized goodput with lowest requirement on BER

This paper presents an adaptive frame length mechanism based on a cross-layer analysis of intrinsic relations between the MAC frame length, bit error rate (BER) of the wireless link and normalized goodput. The proposed mechanism selects the optimal frame length that keeps the service normalized goodput at required levels while satisfying the lowest requirement on the BER, thus increasing the transmission reliability. Numerical results are provided and show that an optimal frame length satisfying the lowest BER requirement does indeed exist. The performance of BER requirement as a function of the MAC frame length is evaluated and compared for transmission scenarios with and without automatic repeat request (ARQ). Furthermore, issues related to the MAC overhead length are also discussed to illuminate the functionality and performance of the proposed mechanism.

A new error measure for forecasts of household-level, high resolution electrical energy consumption

As low carbon technologies become more pervasive, distribution network operators are looking to support the expected changes in the demands on the low voltage networks through the smarter control of storage devices. Accurate forecasts of demand at the single household-level, or of small aggregations of households, can improve the peak demand reduction brought about through such devices by helping to plan the appropriate charging and discharging cycles. However, before such methods can be developed, validation measures are required which can assess the accuracy and usefulness of forecasts of volatile and noisy household-level demand. In this paper we introduce a new forecast verification error measure that reduces the so called “double penalty” effect, incurred by forecasts whose features are displaced in space or time, compared to traditional point-wise metrics, such as Mean Absolute Error and p-norms in general. The measure that we propose is based on finding a restricted permutation of the original forecast that minimises the point wise error, according to a given metric. We illustrate the advantages of our error measure using half-hourly domestic household electrical energy usage data recorded by smart meters and discuss the effect of the permutation restriction.

Diurnal warm-layer events in the western Mediterranean and European shelf seas

We characterize near-surface ocean diurnal warm-layer events, using satellite observations and fields from numerical weather forecasting. The study covers April to September, 2006, over the area 11°W to 17°E and 35°N to 57°N, with 0.1° cells. We use hourly satellite SSTs from which peak amplitudes of diurnal cycles in SST (dSSTs) can be estimated with error ∼0.3 K. The diurnal excursions of SST observed are spatially and temporally coherent. The largest dSSTs exceed 6 K, affect 0.01% of the surface, and are seen in the Mediterranean, North and Irish Seas. There is an anti-correlation between the magnitude and the horizontal length scale of dSST events. Events wherein dSST exceeds 4 K have length scales of ≤40 km. From the frequency distribution of different measures of wind-speed minima, we infer that extreme dSST maxima arise where conditions of low wind speed are sustained from early morning to mid afternoon.

Sea surface temperature estimation from the Geostationary Operational Environmental Satellite 12 (GOES-12)

This paper describes the techniques used to obtain sea surface temperature (SST) retrievals from the Geostationary Operational Environmental Satellite 12 (GOES-12) at the National Oceanic and Atmospheric Administration’s Office of Satellite Data Processing and Distribution. Previous SST retrieval techniques relying on channels at 11 and 12 μm are not applicable because GOES-12 lacks the latter channel. Cloud detection is performed using a Bayesian method exploiting fast-forward modeling of prior clear-sky radiances using numerical weather predictions. The basic retrieval algorithm used at nighttime is based on a linear combination of brightness temperatures at 3.9 and 11 μm. In comparison with traditional split window SSTs (using 11- and 12-μm channels), simulations show that this combination has maximum scatter when observing drier colder scenes, with a comparable overall performance. For daytime retrieval, the same algorithm is applied after estimating and removing the contribution to brightness temperature in the 3.9-μm channel from solar irradiance. The correction is based on radiative transfer simulations and comprises a parameterization for atmospheric scattering and a calculation of ocean surface reflected radiance. Potential use of the 13-μm channel for SST is shown in a simulation study: in conjunction with the 3.9-μm channel, it can reduce the retrieval error by 30%. Some validation results are shown while a companion paper by Maturi et al. shows a detailed analysis of the validation results for the operational algorithms described in this present article.

Optimal estimation of sea surface temperature from split-window observations

Optimal estimation (OE) improves sea surface temperature (SST) estimated from satellite infrared imagery in the “split-window”, in comparison to SST retrieved using the usual multi-channel (MCSST) or non-linear (NLSST) estimators. This is demonstrated using three months of observations of the Advanced Very High Resolution Radiometer (AVHRR) on the first Meteorological Operational satellite (Metop-A), matched in time and space to drifter SSTs collected on the global telecommunications system. There are 32,175 matches. The prior for the OE is forecast atmospheric fields from the Météo-France global numerical weather prediction system (ARPEGE), the forward model is RTTOV8.7, and a reduced state vector comprising SST and total column water vapour (TCWV) is used. Operational NLSST coefficients give mean and standard deviation (SD) of the difference between satellite and drifter SSTs of 0.00 and 0.72 K. The “best possible” NLSST and MCSST coefficients, empirically regressed on the data themselves, give zero mean difference and SDs of 0.66 K and 0.73 K respectively. Significant contributions to the global SD arise from regional systematic errors (biases) of several tenths of kelvin in the NLSST. With no bias corrections to either prior fields or forward model, the SSTs retrieved by OE minus drifter SSTs have mean and SD of − 0.16 and 0.49 K respectively. The reduction in SD below the “best possible” regression results shows that OE deals with structural limitations of the NLSST and MCSST algorithms. Using simple empirical bias corrections to improve the OE, retrieved minus drifter SSTs are obtained with mean and SD of − 0.06 and 0.44 K respectively. Regional biases are greatly reduced, such that the absolute bias is less than 0.1 K in 61% of 10°-latitude by 30°-longitude cells. OE also allows a statistic of the agreement between modelled and measured brightness temperatures to be calculated. We show that this measure is more efficient than the current system of confidence levels at identifying reliable retrievals, and that the best 75% of satellite SSTs by this measure have negligible bias and retrieval error of order 0.25 K.

Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman–Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

Error, reproducibility and sensitivity: a pipeline for data processing of Agilent oligonucleotide expression arrays

Background: Expression microarrays are increasingly used to obtain large scale transcriptomic information on a wide range of biological samples. Nevertheless, there is still much debate on the best ways to process data, to design experiments and analyse the output. Furthermore, many of the more sophisticated mathematical approaches to data analysis in the literature remain inaccessible to much of the biological research community. In this study we examine ways of extracting and analysing a large data set obtained using the Agilent long oligonucleotide transcriptomics platform, applied to a set of human macrophage and dendritic cell samples. Results: We describe and validate a series of data extraction, transformation and normalisation steps which are implemented via a new R function. Analysis of replicate normalised reference data demonstrate that intrarray variability is small (only around 2 of the mean log signal), while interarray variability from replicate array measurements has a standard deviation (SD) of around 0.5 log(2) units (6 of mean). The common practise of working with ratios of Cy5/Cy3 signal offers little further improvement in terms of reducing error. Comparison to expression data obtained using Arabidopsis samples demonstrates that the large number of genes in each sample showing a low level of transcription reflect the real complexity of the cellular transcriptome. Multidimensional scaling is used to show that the processed data identifies an underlying structure which reflect some of the key biological variables which define the data set. This structure is robust, allowing reliable comparison of samples collected over a number of years and collected by a variety of operators. Conclusions: This study outlines a robust and easily implemented pipeline for extracting, transforming normalising and visualising transcriptomic array data from Agilent expression platform. The analysis is used to obtain quantitative estimates of the SD arising from experimental (non biological) intra- and interarray variability, and for a lower threshold for determining whether an individual gene is expressed. The study provides a reliable basis for further more extensive studies of the systems biology of eukaryotic cells.