Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

OFDM joint data detection and phase noise cancellation based on minimum mean square prediction error

This paper proposes a new iterative algorithm for orthogonal frequency division multiplexing (OFDM) joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the relatively less studied problem of "overfitting" such that the iterative approach may converge to a trivial solution. Specifically, we apply a hard-decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the PHN, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical Simulations are also given to verify the proposed algorithm. (C) 2008 Elsevier B.V. All rights reserved.

A general model of error-prone PCR

In this paper, we generalise a previously-described model of the error-prone polymerase chain reaction (PCR) reaction to conditions of arbitrarily variable amplification efficiency and initial population size. Generalisation of the model to these conditions improves the correspondence to observed and expected behaviours of PCR, and restricts the extent to which the model may explore sequence space for a prescribed set of parameters. Error-prone PCR in realistic reaction conditions is predicted to be less effective at generating grossly divergent sequences than the original model. The estimate of mutation rate per cycle by sampling sequences from an in vitro PCR experiment is correspondingly affected by the choice of model and parameters. (c) 2005 Elsevier Ltd. All rights reserved.

A block coprocessor for user data rate improvements to GPRS coding scheme 4

The general packet radio service (GPRS) has been developed to allow packet data to be transported efficiently over an existing circuit-switched radio network, such as GSM. The main application of GPRS are in transporting Internet protocol (IP) datagrams from web servers (for telemetry or for mobile Internet browsers). Four GPRS baseband coding schemes are defined to offer a trade-off in requested data rates versus propagation channel conditions. However, data rates in the order of > 100 kbits/s are only achievable if the simplest coding scheme is used (CS-4) which offers little error detection and correction (EDC) (requiring excellent SNR) and the receiver hardware is capable of full duplex which is not currently available in the consumer market. A simple EDC scheme to improve the GPRS block error rate (BLER) performance is presented, particularly for CS-4, however gains in other coding schemes are seen. For every GPRS radio block that is corrected by the EDC scheme, the block does not need to be retransmitted releasing bandwidth in the channel and improving the user's application data rate. As GPRS requires intensive processing in the baseband, a viable field programmable gate array (FPGA) solution is presented in this paper.

Improving CS-4 user data rate in GPRS enabled devices by using a BLER co-processor

The General Packet Radio Service (GPRS) was developed to allow packet data to be transported efficiently over an existing circuit switched radio network. The main applications for GPRS are in transporting IP datagram’s from the user’s mobile Internet browser to and from the Internet, or in telemetry equipment. A simple Error Detection and Correction (EDC) scheme to improve the GPRS Block Error Rate (BLER) performance is presented, particularly for coding scheme 4 (CS-4), however gains in other coding schemes are seen. For every GPRS radio block that is corrected by the EDC scheme, the block does not need to be retransmitted releasing bandwidth in the channel, improving throughput and the user’s application data rate. As GPRS requires intensive processing in the baseband, a viable hardware solution for a GPRS BLER co-processor is discussed that has been currently implemented in a Field Programmable Gate Array (FPGA) and presented in this paper.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

A bagging-based correction for the mixture model estimator of population size

Estimation of a population size by means of capture-recapture techniques is an important problem occurring in many areas of life and social sciences. We consider the frequencies of frequencies situation, where a count variable is used to summarize how often a unit has been identified in the target population of interest. The distribution of this count variable is zero-truncated since zero identifications do not occur in the sample. As an application we consider the surveillance of scrapie in Great Britain. In this case study holdings with scrapie that are not identified (zero counts) do not enter the surveillance database. The count variable of interest is the number of scrapie cases per holding. For count distributions a common model is the Poisson distribution and, to adjust for potential heterogeneity, a discrete mixture of Poisson distributions is used. Mixtures of Poissons usually provide an excellent fit as will be demonstrated in the application of interest. However, as it has been recently demonstrated, mixtures also suffer under the so-called boundary problem, resulting in overestimation of population size. It is suggested here to select the mixture model on the basis of the Bayesian Information Criterion. This strategy is further refined by employing a bagging procedure leading to a series of estimates of population size. Using the median of this series, highly influential size estimates are avoided. In limited simulation studies it is shown that the procedure leads to estimates with remarkable small bias.

A note on the analysis error associated with 3D-FGAT

The analysis-error variance of a 3D-FGAT assimilation is examined analytically using a simple scalar equation. It is shown that the analysis-error variance may be greater than the error variances of the inputs. The results are illustrated numerically with a scalar example and a shallow-water model.

The 11-yr solar cycle in ERA-40 data: an update to 2008

Multiple linear regression is used to diagnose the signal of the 11-yr solar cycle in zonal-mean zonal wind and temperature in the 40-yr ECMWF Re-Analysis (ERA-40) dataset. The results of previous studies are extended to 2008 using data from ECMWF operational analyses. This analysis confirms that the solar signal found in previous studies is distinct from that of volcanic aerosol forcing resulting from the eruptions of El Chichón and Mount Pinatubo, but it highlights the potential for confusion of the solar signal and lower-stratospheric temperature trends. A correction to an error that is present in previous results of Crooks and Gray, stemming from the use of a single daily analysis field rather than monthly averaged data, is also presented.

Synchronisation error resistant CDMA detection

A bit-level linear CDMA detector is presented which is based on the minimum variance distortionless response (MVDR) principle. Owing to the interference suppression capability made possible by basing the detector on the MVDR principle and the fact that no inversion of the user correlation matrix is involved, the influence of synchronisation errors is greatly suppressed.

Synchronisation error resistant multiuser detection for asynchronous CDMA

Linear CDMA detectors have emerged as a promising solution to multiple access interference (MAI) suppression. Unfortunately, most existing linear detectors suffer from high sensitivity to synchronisation errors (also termed parameter estimation error), and synchronisation error resistant detectors have so far not been as widely investigated as they should have. This paper extends the minimum variance distortionless response (MVDR) detector, proposed previously by this author (Zheng 2000) for synchronous systems, to asynchronous systems. It has been shown that the MVDR structure is equally effective for asynchronous systems, especially for the weaker users.

Correcting for local oscillator phase offset in a DVB-T compliant receiver under multipath conditions

In 1997, the UK implemented the worlds first commercial digital terrestrial television system. Under the ETS 300 744 standard, the chosen modulation method, COFDM, is assumed to be multipath resilient. Previous work has shown that this is not necessarily the case. It has been shown that the local oscillator required for demodulation from intermediate-frequency to baseband must be very accurate. This paper shows that under multipath conditions, standard methods for obtaining local oscillator phase lock may not be adequate. This paper demonstrates a set of algorithms designed for use with a simple local oscillator circuit which will allow correction for local oscillator phase offset to maintain a low bit error rate with multipath present.

Forecast impact of targeted observations: sensitivity to observation error and proximity to steep orography

For a targeted observations case, the dependence of the size of the forecast impact on the targeted dropsonde observation error in the data assimilation is assessed. The targeted observations were made in the lee of Greenland; the dependence of the impact on the proximity of the observations to the Greenland coast is also investigated. Experiments were conducted using the Met Office Unified Model (MetUM), over a limited-area domain at 24-km grid spacing, with a four-dimensional variational data assimilation (4D-Var) scheme. Reducing the operational dropsonde observation errors by one-half increases the maximum forecast improvement from 5% to 7%–10%, measured in terms of total energy. However, the largest impact is seen by replacing two dropsondes on the Greenland coast with two farther from the steep orography; this increases the maximum forecast improvement from 5% to 18% for an 18-h forecast (using operational observation errors). Forecast degradation caused by two dropsonde observations on the Greenland coast is shown to arise from spreading of data by the background errors up the steep slope of Greenland. Removing boundary layer data from these dropsondes reduces the forecast degradation, but it is only a partial solution to this problem. Although only from one case study, these results suggest that observations positioned within a correlation length scale of steep orography may degrade the forecast through the anomalous upslope spreading of analysis increments along terrain-following model levels.