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A study of blind channel estimation method in the context of a multiuser orthogonal-frequency-domain-multiplexing (OFDM) system, where each user transmits utilizing all available subcarriers is illustrated. A linear nonredundant block precoding scheme is applied at the input of the OFDM system and a general description of precoding matrices is provided along with analytical expressions of symbol error probability and signal-to-interference ratio which could be used to obtain optimum precoding schemes.

We consider the problem of blind estimation of a communication channel based on the oversampled channel output. We propose a nonparametric approach that, based on the cyclic spectrum of the output, finds the channel phase response without neither the need of phase unwrapping nor channel length information. For band-limited channels, the cyclic spectrum has limited support. For this case, we propose an approximation for the discretized phase of the cyclic spectrum that, under certain conditions, results in a simpler channel estimation method. The proposed approach is applied to simulated data and real recordings and is compared to existing methods. Index Terms--Band-limited channel, blind channel estimation, cyclic spectrum, cyclostationary inputs.

Direction-dependent calibration of widefield radio interferometers estimates the systematic errors, along with multiple directions in the sky. This is necessary because with most systematic errors, which are caused by effects such as the ionosphere or the receiver beam shape, there is a significant spatial variation. Fortunately, there is some deterministic behaviour of these variations in most situations. We enforce this underlying smooth spatial behaviour of systematic errors as an additional constraint on to spectrally constrained direction-dependent calibration. Using both analysis and simulations, we show that this additional spatial constraint improves the performance of multifrequency direction-dependent calibration. [ABSTRACT FROM AUTHOR]

Modern radio telescopes produce unprecedented amounts of data, which are passed through many processing pipelines before the delivery of scientific results. Hyperparameters of these pipelines need to be tuned by hand to produce optimal results. Because many thousands of observations are taken during a lifetime of a telescope and because each observation will have its unique settings, the fine tuning of pipelines is a tedious task. In order to automate this process of hyperparameter selection in data calibration pipelines, we introduce the use of reinforcement learning. We test two reinforcement learning techniques, twin delayed deep deterministic policy gradient (TD3), and soft actor-critic, to train an autonomous agent to perform this fine tuning. For the sake of generalization, we consider the pipeline to be a black-box system where the summarized state of the performance of the pipeline is used by the autonomous agent. The autonomous agent trained in this manner is able to determine optimal settings for diverse observations and is therefore able to perform smart calibration, minimizing the need for human intervention. [ABSTRACT FROM AUTHOR]

A new cooperative scheme for a two-user orthogonal frequency division multiple access (OFDMA) uplink communication scenario is proposed. Each user is equipped with one transmit/receive antenna. Before transmission, inter-block linear precoding is introduced to pairs of blocks. The cooperative transmission is implemented in cycles of three time slots. During each slot, a user transmits either his data, or a weighted mixture of his data and the data that he received in previous slots of the same cycle. The weights are obtained in an optimum fashion, so that a user that faces deep fading on certain subcarriers can benefit from the other user's channel, without taxing significantly the resources of that user. It is shown that the proposed scheme achieves the maximum available diversity for both users (full cooperation), or for the weak user (half cooperation) without increasing the number of antennas needed as compared to an energy-equivalent noncooperative OFDMA system that also uses inter-block precoding. Further, the proposed use of inter-block precoding allows one to exploit the cooperation induced diversity in 1.5 slots on the average; 2 slots would be needed if intra-block precoding was used instead.

The emergence of MIMO communications systems as practical high-data-rate wireless communications systems has created several technical challenges to be met. On the one hand, there is potential for enhancing system performance in terms of capacity and diversity. On the other hand, the presence of multiple transceivers at both ends has created additional cost in terms of hardware and energy consumption. For coherent detection as well as to do optimization such as water filling and beamforming, it is essential that the MIMO channel is known. However, due to the presence of multiple transceivers at both the transmitter and receiver, the channel estimation problem is more complicated and costly compared to a SISO system. Several solutions have been proposed to minimize the computational cost, and hence the energy spent in channel estimation of MIMO systems. We present a novel method of minimizing the overall energy consumption. Unlike existing methods, we consider the energy spent during the channel estimation phase which includes transmission of training symbols, storage of those symbols at the receiver, and also channel estimation at the receiver. We develop a model that is independent of the hardware or software used for channel estimation, and use a divide-and-conquer strategy to minimize the overall energy consumption.

With ever-increasing data rates produced by modern radio telescopes like LOFAR and future telescopes like the SKA, many data-processing steps are overwhelmed by the amount of data that needs to be handled using limited compute resources. Calibration is one such operation that dominates the overall data processing computational cost; none the less, it is an essential operation to reach many science goals. Calibration algorithms do exist that scale well with the number of stations of an array and the number of directions being calibrated. However, the remaining bottleneck is the raw data volume, which scales with the number of baselines, and which is proportional to the square of the number of stations. We propose a 'stochastic' calibration strategy where we read only in a mini-batch of data for obtaining calibration solutions, as opposed to reading the full batch of data being calibrated. None the less, we obtain solutions that are valid for the full batch of data. Normally, data need to be averaged before calibration is performed to accommodate the data in size-limited compute memory. Stochastic calibration overcomes the need for data averaging before any calibration can be performed, and offers many advantages, including: enabling the mitigation of faint radio frequency interference; better removal of strong celestial sources from the data; and better detection and spatial localization of fast radio transients. [ABSTRACT FROM AUTHOR]

New and upcoming radio interferometers will produce unprecedented amount of data that demand extremely powerful computers for processing. This is a limiting factor due to the large computational power and energy costs involved. Such limitations restrict several key data processing steps in radio interferometry. One such step is calibration where systematic errors in the data are determined and corrected. Accurate calibration is an essential component in reaching many scientific goals in radio astronomy and the use of consensus optimization that exploits the continuity of systematic errors across frequency significantly improves calibration accuracy. In order to reach full consensus, data at all frequencies need to be calibrated simultaneously. In the SKA regime, this can become intractable if the available compute agents do not have the resources to process data from all frequency channels simultaneously. In this paper, we propose a multiplexing scheme that is based on the alternating direction method of multipliers with cyclic updates. With this scheme, it is possible to simultaneously calibrate the full data set using far fewer compute agents than the number of frequencies at which data are available. We give simulation results to show the feasibility of the proposed multiplexing scheme in simultaneously calibrating a full data set when a limited number of compute agents are available. [ABSTRACT FROM AUTHOR]

Increasing data volumes delivered by a new generation of radio interferometers require computationally efficient and robust calibration algorithms. In this paper, we propose distributed calibration as a way of improving both computational cost as well as robustness in calibration. We exploit the data parallelism across frequency that is inherent in radio astronomical observations that are recorded as multiple channels at different frequencies. Moreover, we also exploit the smoothness of the variation of calibration parameters across frequency. Data parallelism enables us to distribute the computing load across a network of compute agents. Smoothness in frequency enables us to reformulate calibration as a consensus optimization problem. With this formulation, we enable flow of information between compute agents calibrating data at different frequencies, without actually passing the data, and thereby improving robustness. We present simulation results to show the feasibility as well as the advantages of distributed calibration as opposed to conventional calibration. [ABSTRACT FROM AUTHOR]

Full polarimetric radio interferometric calibration is performed by estimating 2 × 2 Jones matrices representing instrumental and propagation effects. The solutions obtained in this way differ from the true solutions by a 2 × 2 unitary matrix ambiguity. This ambiguity is common to all stations for which a solution is obtained, but it is different for solutions obtained at different time and frequency intervals. Therefore, straightforward interpolation of solutions obtained at different time and frequency intervals is not possible. In this paper, we propose to use the theory of quotient manifolds for obtaining correct interpolants that are immune to unitary matrix ambiguities. [ABSTRACT FROM AUTHOR]

One of the aims of the Low Frequency Array (LOFAR) Epoch of Reionization (EoR) project is to measure the power spectrum of variations in the intensity of redshifted 21-cm radiation from the EoR. The sensitivity with which this power spectrum can be estimated depends on the level of thermal noise and sample variance, and also on the systematic errors arising from the extraction process, in particular from the subtraction of foreground contamination. We model the extraction process using realistic simulations of the cosmological signal, the foregrounds and noise, and so estimate the sensitivity of the LOFAR EoR experiment to the redshifted 21-cm power spectrum. Detection of emission from the EoR should be possible within 360 h of observation with a single station beam. Integrating for longer, and synthesizing multiple station beams within the primary (tile) beam, then enables us to extract progressively more accurate estimates of the power at a greater range of scales and redshifts. We discuss different observational strategies which compromise between depth of observation, sky coverage and frequency coverage. A plan in which lower frequencies receive a larger fraction of the time appears to be promising. We also study the nature of the bias which foreground fitting errors induce on the inferred power spectrum and discuss how to reduce and correct for this bias. The angular and line-of-sight power spectra have different merits in this respect, and we suggest considering them separately in the analysis of LOFAR data. [ABSTRACT FROM AUTHOR]

One of the problems facing experiments designed to detect redshifted 21-cm emission from the epoch of reionization (EoR) is the presence of foregrounds which exceed the cosmological signal in intensity by orders of magnitude. While fitting them so that they can be removed, we must be careful to minimize ‘overfitting’, in which we fit away some of the cosmological signal, and ‘underfitting’, in which real features of the foregrounds cannot be captured by the fit, polluting the signal reconstruction. We argue that in principle it would be better to fit the foregrounds non-parametrically – allowing the data to determine their shape – rather than selecting some functional form in advance and then fitting its parameters. Non-parametric fits often suffer from other problems, however. We discuss these before suggesting a non-parametric method, Wp smoothing, which seems to avoid some of them. After outlining the principles of Wp smoothing, we describe an algorithm used to implement it. Some useful results for implementing an alternative algorithm are given in an appendix. We apply Wp smoothing to a synthetic data cube for the Low Frequency Array (LOFAR) EoR experiment. This cube includes realistic models for the signal, foregrounds, instrumental response and noise. The performance of Wp smoothing, measured by the extent to which it is able to recover the variance of the cosmological signal and to which it avoids the fitting residuals being polluted by leakage of power from the foregrounds, is compared to that of a parametric fit, and to another non-parametric method (smoothing splines). We find that Wp smoothing is superior to smoothing splines for our application, and is competitive with parametric methods even though in the latter case we may choose the functional form of the fit with advance knowledge of the simulated foregrounds. Finally, we discuss how the quality of the fit is affected by the frequency resolution and range, by the characteristics of the cosmological signal and by edge effects. [ABSTRACT FROM AUTHOR]

Detecting redshifted 21-cm emission from neutral hydrogen in the early Universe promises to give direct constraints on the epoch of reionization (EoR). It will, though, be very challenging to extract the cosmological signal (CS) from foregrounds and noise which are orders of magnitude larger. Fortunately, the signal has some characteristics which differentiate it from the foregrounds and noise, and we suggest that using the correct statistics may tease out signatures of reionization. We generate mock data cubes simulating the output of the Low Frequency Array (LOFAR) EoR experiment. These cubes combine realistic models for Galactic and extragalactic foregrounds and the noise with three different simulations of the CS. We fit out the foregrounds, which are smooth in the frequency direction, to produce residual images in each frequency band. We denoise these images and study the skewness of the one-point distribution in the images as a function of frequency. We find that, under sufficiently optimistic assumptions, we can recover the main features of the redshift evolution of the skewness in the 21-cm signal. We argue that some of these features – such as a dip at the onset of reionization, followed by a rise towards its later stages – may be generic, and give us a promising route to a statistical detection of reionization. [ABSTRACT FROM AUTHOR]

We present an efficient method to generate large simulations of the epoch of reionization without the need for a full three-dimensional radiative transfer code. Large dark-matter-only simulations are post-processed to produce maps of the redshifted 21-cm emission from neutral hydrogen. Dark matter haloes are embedded with sources of radiation whose properties are either based on semi-analytical prescriptions or derived from hydrodynamical simulations. These sources could either be stars or power-law sources with varying spectral indices. Assuming spherical symmetry, ionized bubbles are created around these sources, whose radial ionized fraction and temperature profiles are derived from a catalogue of one-dimensional radiative transfer experiments. In case of overlap of these spheres, photons are conserved by redistributing them around the connected ionized regions corresponding to the spheres. The efficiency with which these maps are created allows us to span the large parameter space typically encountered in reionization simulations. We compare our results with other, more accurate, three-dimensional radiative transfer simulations and find excellent agreement for the redshifts and the spatial scales of interest to upcoming 21-cm experiments. We generate a contiguous observational cube spanning redshift 6 to 12 and use these simulations to study the differences in the reionization histories between stars and quasars. Finally, the signal is convolved with the Low Frequency Array (LOFAR) beam response and its effects are analysed and quantified. Statistics performed on this mock data set shed light on possible observational strategies for LOFAR. [ABSTRACT FROM AUTHOR]