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We report a beam-shaping technique whereby the output power from a high-power laser-diode stack is efficiently coupled, reconfigured, and transmitted to a thin-disk laser by means of a compact optical fiber bundle. By using this technique, the power density is increased by a factor of 2 when compared to direct coupling with a octagonal fused silica rod while the numerical aperture is kept constant. Transmission efficiency of 80% was measured for the beam shaper without antireflection coating. The top-hat distribution is numerically calculated at the thin-disk laser crystal. OCIS codes: 140.0140, 140.3300, 140.3460, 140.3480.

Ubiquitous radar systems look everywhere at all times and require both parallel radar processors and parallel beamformers. Current systems operate with subgigahertz bandwidths and produce a handful of angle-of-arrival (AOA) beams. We present an electro-optic radar processor that combines the multigigahertz wideband capabilities of a spectral hole burning correlator with wideband Doppler processing and the thousands of parallel channels available from an electro-optical beamformer. Preliminary experiments demonstrate 150 MHz bandwidth range correlations across 20 AOA beams. [c] 2010 Optical Society of America OCIS codes: 090.4220, 280.5110, 070.4340, 070.4550, 070.0070.

Normally, fly's eye condensers are used to homogenize light. However, in the case of fully coherent light, a fly's eye condenser, in connection with some simple optical elements, such as a diffractive axicon, a grating, and a telescope, can be used as a quite flexible beam shaping system, forming arrays of rings, parts of rings, or other structures with varying diameters. We present the principle, some simulation results, and some first experimental results. OCIS codes: 050.1970, 220.2560, 350.3950.

The applicability of layers of ion-implanted polymethyl methacrylate (PMMA) for beam splitting of laser light at the telecommunications wavelength of 1.55 [micro]m is examined. Bulk PMMA is studied, subjected to low-energy (50 keV) silicon ion implantation at various ion fluences in the range from [10.sup.14] to [10.sup.17] [cm.sup.-2]. The formed ultrathin near-surface ion-implanted layer of a thickness of about 100 nm, buried in a depth of ~100nm, can be used to split (or combine) laser beams at 1.55 [micro]m with a low absorption loss. OCIS codes: 130.1750, 230.1360, 240.1485.

We have achieved high-precision laser beam shaping by using a binary-amplitude spatial light modulator, a digital micromirror device (DMD), followed by an imaging telescope that contains a pinhole low-pass filter (LPF). An error diffusion algorithm was used to design the initial DMD pixel pattern based on the measured input beam profile. This pattern was iteratively refined by simulating the optically low-pass filtered DMD image and changing DMD pixels to lift valleys and suppress peaks. We noted the gap between the experimental result of 1.4% root-mean-square (RMS) error and the simulated result for the same DMD pattern of 0.3% RMS error. Therefore, we deemed it necessary to introduce iterative refinement based on actual measurements of the output image to further improve the uniformity of the beam. Using this method, we have demonstrated the ability to shape raw, non-spatially filtered laser beams (quasi-Gaussian beams) into beams with precisely controlled profiles that have an unprecedented level of RMS error with respect to the target profile. We have shown that our iterative refinement process is able to improve the light intensity uniformity to around 1% RMS error in a raw camera image for both 633 and 1064 nm laser beams. The use of a digital LPF on the camera image is justified in that it matches the performance of the pinhole filter in the experimental setup. The digital low-pass filtered results reveal that the actual optical beam profiles have RMS error down to 0.23%. Our approach has also demonstrated the ability to produce a range of target profiles as long as they have similar spatial-frequency content (i.e., a slowly varying beam profile). Circular and square cross-section flat-top beams and beams with a linear intensity variation within a circular and square cross section were produced with similarly low RMS errors. The measured errors were about twice the ultimate limit of 0.1% RMS error based on the number of binary DMD pixels that participate in the beam-formation process. OCIS codes: 070.6120, 140.3300, 230.6120.

A metal slit array arranged along a semicircular surface achieving subwavelength optical beam focusing along the lateral direction is proposed. Taking into consideration surface plasmon polaritons that pass through a metal slit array, we design the array with a curvature. By use of a genetic algorithm, the size of the metal slit and the corresponding curvature are to be determined. Based on our metal slit array configuration, the full width at half-maximum can be achieved on a subwavelength scale. OCIS codes: 240.6680, 230.3120.

We report the focusing of a normally incident plane wave of 405 nm through a Ag/dielectric annular ring structure, using finite-difference time domain analysis. We first study the dependency of the focusing efficiency on slit width when the incident wave is transmitted through a single ring whose slit is filled with a dielectric. Then, light focusing by the multiple-ring structure is investigated as a function of the dielectric thickness. It is observed that the focusing is tunable between near-field and quasi-far-field regimes in the Ag/dielectric layered annular ring structure. Also, the focal intensities are remarkably enhanced by the addition of the dielectric layer, showing a Fabry--Perot-like resonance with respect to the thickness of the dielectric layer. The controllable near-field and far-field focusing offers more flexibility for applications of future nano-optic devices. [c] 2010 Optical Society of America OCIS codes: 240.6680, 240.0240.

A new approach to the deconvolution of acoustic sources has been developed and is presented in this work. The goal of this postprocessing is to simplify the beamforming output by suppressing the side lobes and reducing the sources' main lobes to single (or a small number of) points that accurately identify the noise sources' positions and their actual levels. In this work, a new modeling technique for the beamforming output is proposed. The idea is to use an image-processing-like approach to identify the noise sources from the beamforming maps: that is, recognizing lobe patterns in the beamformed output and relating them to the noise sources that would produce that map. For incoherent sources, the beamforming output is modeled as a superposition of point-spread functions and a linear system is posted. For coherent sources, the beamforming output is modeled as a superposition of complex point-spread functions and a nonlinear system of equations in terms of the sources' amplitudes is posted. As a first approach to solving this difficult problem, the system is solved using a new two-step procedure. In the first step, an approximated linear problem is solved. In the second step, an optimization is performed over the nonzero values obtained in the previous step. The solution to this system of equations renders the sources' positions and amplitudes. In the case of coherent sources, their relative phase can also be recovered. The technique is referred as noise source localization and optimization of phased-array results. A detailed analytical formulation, numerical simulations, and sample experimental results are shown for the proposed postprocessing. DOI: 10.2514/1.38073

An adaptive wideband beamforming structure is proposed with combined spatial/temporal subband decomposition. The received signals are first processed by a transformation matrix, and then split into a series of subbands, where independent beamformers can be operated. A special property is that some of the lower subbands can be discarded without affecting its performance, which leads to a system with a lower computational complexity and higher convergence speed. Index Terms--Adaptive arrays, array signal processing, linear arrays.

We propose a framework based on the use of a set of beampattern shaping constraints. The proposed beamformer possesses not only adaptive interference-rejection ability and robustness against large steering direction errors, but also direct sidelobe control. It contains a new weighing ratio that can automatically control the relative proportions of interference-rejection and sidelobe suppression in different scenarios, without ambiguity. Unlike other beamformers, the proposed beamformer is robust against strong moving interferences, requiring only a coarse estimation of their directions-of-arrival. The generic framework encompasses different optimization strategies for specific application problems. Index Terms--Adaptive arrays, array signal processing, robustness.

A calibration technique is proposed in this paper for an arbitrary array. This technique estimates the array sensor gain/ phase and geometry with a set of simultaneous equations formed by using the MUSIC null spectrum property. Note that the technique does not use iterative calculation in estimating the array parameters and hence it has no convergent problem; however, it requires that n directions of arrival (DOAs) of signal sources to be known to calibrate the array which is perturbed n-dimensionally. The efficacy of the method is demonstrated by means of simulations and on experimental data collected with an antenna array operating in high-frequency radio band. Index Terms--Array calibration, beamforming, direction-of-arrival (DOA) estimation.

The opportunistic beamforming system (OBS) is currently receiving much attention in the field of downlink beamforming due to its simple random beamforming, low feedback complexity, and same throughput scaling obtained with perfect channel-state information using dirty paper coding at the transmitter. In this paper, we focus on its closed-form throughput evaluation over Rayleigh fading channels, based on the asymptotic theory of extreme order statistics. First, the throughput of a single-beam OBS is investigated, and an analytical solution tighter than the previously reported one is derived. Then, the asymptotic throughput bounds on a multibeam OBS are presented, and also, our analytical expression is shown to be very tight with the simulation results even with fewer users. After that, we argue that the reported conclusion that the single-beam OBS is much preferable to the multibeam OBS in the high-signal-to-noise-ratio (SNR) regime is inaccurate, but that, instead, it is satisfied only when the number of users is very small, due to its limited multiuser diversity gain. Finally, we show that four transmit beams is the most preferable in the multibeam OBS with a large number of users and moderate SNR, which arrives at the tradeoff between increasing spatial multiplexing gain and disappearing multiuser diversity gain. Index Terms--Multiple-input single-output (MISO), multiuser diversity, opportunistic beamforming system (OBS), spatial multiplexing, throughput.

In this paper, we consider an adaptive modulation system with multiple-input-multiple-output (MIMO) antennas in conjunction with orthogonal frequency-division multiplexing (OFDM) operating over frequency-selective Rayleigh fading environments. In particular, we consider a type of beamforming with a maximum ratio transmission/maximum ratio combining (MRT-MRC) transceiver structure. For this system, we derive a central limit theorem for various block-based performance metrics. This motivates an accurate Gaussian approximation to the system data rate and the number of outages per OFDM block. In addition to the data rate and outage distributions, we also consider the subcarrier signal-to-noise ratio (SNR) as a process in the frequency domain and compute level crossing rates (LCRs) and average fade bandwidths (AFBs). Hence, we provide fundamental but novel results for the MIMO OFDM channel. The accuracy of these results is verified by Monte Carlo simulations, and applications to performance analysis and system design are discussed. Index Terms--Adaptive modulation, average fade bandwidth (AFB), beamforming, eigenvalues, level crossing rate (LCR), multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO OFDM), Rayleigh fading channels.

A 24-beams slot array antenna, which achieves 360-degrees coverage over azimuth direction, based on substrate integrated waveguide (SIW) technology is designed, fabricated and measured for supporting the concept of triangle cell, beam diversity and multiple input multiple output (MIMO) wireless communications. Constructed by six 4-beams single layer SIW antennas which integrate the 4 x 8 modified Butler matrix with a low side lobe level (SLL) amplitude distribution, measured SLLs are reduced as low as -14.5 dB for all beams in E-plane. The size of the SIW single layer multibeam antenna is 385 mm x 110 mm including feeding network. The usable bandwidth of the proposed antenna is 3.75% at 16 GHz. Index Terms--Beam-forming, Butler matrix, substrate integrated waveguide (SIW).

A Nolen matrix design method is proposed as an asymptotic singular case of a recent Blass matrix design algorithm. The procedure is illustrated by a 4 x 4 Nolen matrix, which design is centred at 2.2 GHz, with the amplitude and phase output excitation laws of a Butler matrix using 90[degrees] hybrids. Simulation and measurement results are presented in this paper. Such a matrix may find applications on multiport amplifiers as well as multiple beam antennas required on satellite digital multimedia broadcasting systems. This is illustrated by the use of such a matrix to feed a four-element multiple beam linear array antenna. Beam squint effects are investigated. Index Terms--Beam forming network, multiple beam antenna, Nolen matrix.

We report on the design and measurement of an eight-by-eight modular phased array that uses analog quadrature baseband phase shifters. The array is designed for 2.4 GHz and has a few MHz of bandwidth. Though for such frequency, bandwidth and number of elements, digital beam forming is still feasible with contemporary analog-to-digital converters (ADC), the design is a proof of concept for analog baseband beam forming and shows that this technique will work at frequencies and bandwidths beyond ADCs capabilities. Besides covering the architecture, implementation and the measurement of the array, the calibration is discussed extensively, as this is an inevitable step in activating the antenna. Index Terms--Active arrays, array signal processing, phase shifters, printed circuits.

Two approaches towards beamforming based on constrained particle swarm optimization (PSO) are presented. One approach relies on the penalty function method, for which a new mathematical expression to select the penalty factors is derived. The other method uses a new PSO strategy for solving constrained optimization problems. To maximize performance of the beamforming procedure, the optimal system parameters for the PSO algorithm are derived. Mutual coupling and platform effects are fully accounted for by using the measured active element radiation patterns. The new PSO strategy is compared with a standard genetic algorithm. Using the measured radiation patterns of a seven-element antenna array, a real-life example is presented that demonstrates the possibilities of the new approach. Index Terms--Beamforming, constrained optimization, mutual coupling, particle swarm optimization (PSO), smart antenna system.

The purpose of this paper is to present a robust and fast beamforming algorithm for the low-cost mobile phased array antennas. The proposed beamforming algorithm uses a sequentially perturbation gradient estimation method to update the control voltages of the phase shifters, with the objective of maximizing the received power by the array. This algorithm does not require either the knowledge of phase shifter characteristics or signal Direction-of-Arrival. Moreover, in this paper, the algorithm parameters are derived for the stationary and mobile platform configurations. For the stationary array, it is shown how the proper selection of the beamforming parameters limits the noise effects and increases the array output power. For the mobile array, a condition for the fast convergence is derived and the advantage of using nonuniform step size to update the control voltages is illustrated. When phase shifters suffer from the imbalanced insertion loss the proposed beamforming technique perturbs the phase-conjugate condition to increase the total received power. This algorithm has been implemented with the low-cost microwave components and applied to a Ku-band phased array antenna with 34 sub-arrays. The experimental results verify the broadband performance, and the fast convergence of the algorithm for different platform maneuvers. Index Terms--Adaptive array, beamforming, mobile phased array antenna, satellite communications, smart antenna.

This paper proposes an efficient beamforming scheme which attains optimality as singular value decomposition (SVD) based systems with low complexity utilizing transmit maximum-ratio combining (TMRC) techniques. The TMRC scheme is the optimum structure for single beamforming systems in terms of received signal-to-noise ratio (SNR) in multiple-input single-output (MISO) channels. In this paper, we generalize the TMRC scheme to multiple beamforming multiple-input multiple-output (MIMO) systems which support more than one data stream in coded systems. We express each beamforming vector as a linear combination of TMRC vectors whose coefficients are optimized in a successive manner. Optimization of the beamforming vector is followed by the decorrelation process. All TMRC vectors used as a basis of the remaining beamforming vectors are made orthogonal to previously computed beamforming vectors. Exploiting the concept of the gradient ascent algorithm, we propose a simple non-iterative method of computing the precoder which obtains the near optimal performance. Also we derive a closed form expression of the output SNR distribution for the proposed scheme. Simulation results demonstrate that the proposed scheme achieves the almost identical link performance as the SVD-based system for arbitrary configurations with reduced complexity. Index Terms--Closed-loop multiple-input multiple-output (MIMO) systems, transmit beamforming.

In multiuser multiple-input-multiple-output (MIMO) downlink channels, zero-forcing beamforming (ZFBF), though it is simpler than dirty-paper coding (DPC), has been shown to achieve an optimal sum-capacity growth as the number of users goes to infinity. However, the result is based on the assumption that perfect channel information at the transmitter from all the users is known, which is prohibitive especially for a large number of users due to feedback congestion. In this case, wisely preventing the users with poor channel quality from sending the feedback might relieve the burdensome feedback load, which is often called quality-based channel state reporting (QBR). In this letter, we prove ZFBF with QBR also can achieve the asymptotic optimal growth. With numerical investigations, the optimality is confirmed. In addition, we numerically show how much feedback burden can be reduced by QBR at a negligible cost of the sum-capacity. Index Terms--Multiuser multiple-input-multiple-output (MIMO), zero-forcing beamforming (ZFBF), quality-based channel state reporting (QBR), asymptotic optimal sum-rate growth.

We present the design and fabrication of a novel dual-function subwavelength fused-silica grating that can be used as a polarization-selective beam splitter. For TM polarization, the grating can be used as a two-port beam splitter at a wavelength of 1550 nm with a total diffraction efficiency of 98%. For TE polarization, the grating can function as a high-efficiency grating, and the diffraction efficiency of the-1st order is 95% under Littrow mounting. This dual-function grating design is based on a simplified modal method. By using the rigorous coupled-wave analysis, the optimum grating parameters can be determined. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results are in agreement with the theoretical values. OCIS codes: 050.1950, 230.1360, 230.5440, 050.6624, 060.4510..

We report on an experimental realization of polarization-holographic optical elements (PHOEs) for laser beam shaping. The PHOEs were written into an azobenzene polymer layer by illumination with linearly polarized, focused light with spatially varying orientation. We propose a noniterative design method for the calculation of PHOEs that transform laser beams into arbitrary rotationally symmetric or separable intensity distributions such as flattop or ring profiles. The experimentally observed intensity distributions are compared with those predicted by numerical simulations based on the Fresnel diffraction approximation. Diffraction efficiencies up to 79% were determined experimentally. OCIS codes: 050.1970, 090.1760, 220.4000.

A detector of targets behind walls and in enclosed structures is presented. The detector is applied to through-the-wall radar images obtained by wideband delay and sum beamforming. We consider the detection problem using single- and multiple-view imaging. The statistics of noise, clutter, and target images are examined and formulated using sample scenes. The effects of wall parameter errors on the image statistics are shown. An iterative detection scheme, which adapts itself to the image statistics, is presented. The proposed detection schemes are evaluated using real data. Index Terms--Detection theory, radar imaging, through the wall (TTW).

Laser beam shaping is an important subject for industrial and medical applications since different applications may require different laser intensity distributions. We present an all-fiber beam-shaping device that could transform a Gaussian-shaped laser beam into an intensity uniform beam in the 1.0 [micro]m wavelength region using a long-period grating (LPG). The device can be used to shape the beam of a Yb-doped high-power fiber laser. The mode structure of the LPGs made of HI1060 fiber is analyzed. The design parameters that affect the beam shaping are discussed, and the results of the beam shaping using two cladding modes, [LP.sub.03] and [LP.sub.04], are presented. OCIS codes: 060.2340, 060.2310, 140.3300, 230.2285.

Synthetic Aperture Radar (SAR) is a well-proven imaging technique for remote sensing of the Earth. However, conventional SAR systems are not capable of fulfilling the increasing demands for improved spatial resolution and wider swath coverage. To overcome these inherent limitations, several innovative techniques have been suggested which employ multiple receive-apertures to gather additional information along the synthetic aperture. These digital beamforming (DBF) on receive techniques are reviewed with particular emphasis on the multi-aperture signal processing in azimuth and a multi-aperture reconstruction algorithm is presented that allows for the unambiguous recovery of the Doppler spectrum. The impact of Doppler aliasing is investigated and an analytic expression for the residual azimuth ambiguities is derived. Further, the influence of the processing on the signal-to-noise ratio (SNR) is analyzed, resulting in a pulse repetition frequency (PRF) dependent factor describing the SNR scaling of the multi-aperture beamforming network. The focus is then turned to a complete high-resolution wide-swath SAR system design example which demonstrates the intricate connection between multi-aperture azimuth processing and the system architecture. In this regard, alternative processing approaches are compared with the multi-aperture reconstruction algorithm. In a next step, optimization strategies are discussed as pattern tapering, prebeamshaping-on-receive, and modified processing algorithms. In this context, the analytic expressions for both the residual ambiguities and the SNR scaling factor are generalized to cascaded beamforming networks. The suggested techniques can moreover be extended in many ways. Examples discussed are a combination with ScanSAR burst mode operation and the transfer to multistatic sparse array configurations.

Spatial filtering (SF) constitutes an integral part of building EEG-based brain-computer interfaces (BCIs). Algorithms frequently used for SF, such as common spatial patterns (CSPs) and independent component analysis, require labeled training data for identifying filters that provide information on a subject's intention, which renders these algorithms susceptible to over-fitting on artifactual EEG components. In this study, beamforming is employed to construct spatial filters that extract EEG sources originating within predefined regions of interest within the brain. In this way, neurophysiological knowledge on which brain regions are relevant for a certain experimental paradigm can be utilized to construct unsupervised spatial filters that are robust against artifactual EEG components. Beamforming is experimentally compared with CSP and Laplacian spatial filtering (LP) in a two-class motor-imagery paradigm. It is demonstrated that beamforming outperforms CSP and LP on noisy datasets, while CSP and beamforming perform almost equally well on datasets with few artifactual trials. It is concluded that beamforming constitutes an alternative method for SF that might be particularly useful for BCIs used in clinical settings, i.e., in an environment where artifact-free datasets are difficult to obtain. Index Terms--Beamforming, brain-computer interfaces, common spatial patterns, electroencephalography, motor imagery, spatial filtering.