Effects of amplitude and phase errors on linear predictive array processors

Low sidelobe levels may be a crucial factor in the success of achieving high gain using linear receiving arrays, since the level of the sidelobes determines the degree to which noisy nearby sources can be prohibited from interfering with the detection of a weak source on a different azimuth. In real world experiments at sea, one frequently operates with an array which has not only errors in amplitude and phase between channels but also dead elements. The effect of random errors in both amplitude and phase is to yield a sidelobe level of the average beam pattern which is the sum of the error-free pattern and an additional level due to the random errors. The sidelobe level due to the random errors depends upon the details of the amplitude shading function, the distribution function from which the random errors are drawn, and increases with the mean square value of the errors. Thus, given rms values of amplitude and phase errors, there is a practical limit to which the sidelobes can be reduced by amplitude shading the array. The effect of element failure on the sidelobe level can be drastic and depends on the sum of the amplitude weights of the dead elements. Thus, a failure of a highly-weighted element will have a greater effect on the sidelobe level than the failure of two or three whose combined weights are less. [Work supported by NAVMAT.]

The authors present a system performance analysis of an optical single sideband system (OSSB) when phase errors occur in the modulating signal driving the dual-arm Mach–Zehnder modulator (MZM). The performance is evaluated in terms of the optical sideband suppression, received subcarrier power, frequency response, and power-penalty measurements. Experiments were carried out and a mathematical model of the OSSB system, incorporating the phase error, was developed. Both the theoretical and experimental results show that, although optical sideband suppression reduces with phase errors, the received subcarrier power can increase as high as 3 dB for positive phase errors. However, for transmission over longer fiber, the frequency response of the OSSB system is not only dependent on the phase error, but also on the phase shift due to chromatic dispersion (CD). The power penalty was found to be dependent on the frequency response of the OSSB system. At any frequency-response null point, the power-penalty slope is reversed as the received subcarrier power is reduced. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1574–1578, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21724

Efficient implementation of global computations on a linear array of processors is complicated due to the small communication bandwidth and the large communication diameter of the array. This paper presents efficient parallel techniques for partitioning, movement, and reduction of data on linear arrays. Also, efficient data structures are used to enable fast sequential access of query points within each processor. This combination of serial and parallel techniques is used to derive an optimal parallel algorithm for computing the convex hull of each connected region in an n×n image. The algorithm takes O(n 2/p) time on a linear array with p processors, where 1≤p≤n/log n. This result is processor-time optimal since an optimal sequential algorithm takes O(n 2) to solve the problem. Thus, a linear array with n/log n processors can solve the above problem in O(n log n) time. In comparison, a two dimensional mesh-connected array of processors can solve this problem in O(n) time using n 2 processors. The processor-time product for the mesh is O(n 3), which is not optimal.KeywordsConvex HullExtreme PointLinear ArrayLocal MemoryQuery PointThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The amplitude and phase errors deteriorate the low-sidelobe level characteristic of phased array antenna, which degrades radar performance seriously. Therefore an improved calibration method of amplitude and phase errors based on diagonal loading is proposed to address the problem of amplitude and phase errors in this paper. Initially, the mathematical models of amplitude and phase errors are developed and the impact of amplitude and phase errors is analyzed. It is found that although the interference can be suppressed when there is amplitude and phase errors in the array, the low-sidelobe level characteristic of adaptive antenna is badly deteriorated. An improved calibration method of amplitude and phase errors based on diagonal loading is proposed. Compared with traditional calibration method, proposed method can reduce the sidelobe level efficiently. At last simulations were carried out to verify the effectiveness of proposed method.

In order to improve the transmission performance of multi-user communication system, the deployment of symmetrical nonuniform linear array (SNLA) on the base station (BS) and its associated channel estimation algorithm are concerned in this paper. Based on antenna array theory, the profiles of every scattering path are decomposed into channel angle information and channel gain information. In this spirit, the architecture of SNLA is designed to facilitate the direction-of-arrival (DOA) estimation of every scattering path, where the Vandermonde decomposition lemma is employed. Then, the channel gain information is estimated through least-square method only at the cost of a small amount of training resources. According to matrix reconstruction (MR) method, the proposed SNLA performances are equivalent to a virtual linear array that has much more antenna elements, which results in a higher degree of freedom. Our numerical results are in accordance with this advantage that significantly lower mean-square-error of channel estimation, biterror of data transmission, as well as complexity over traditional schemes are observed.

The mathematical problem consists of determining the spread of the Fourier transform of function when the function is modified by a multiplicative factor exp j?(t), where ? is a stationary random process. Let F(?) be the Fourier transform of f(t) and Fm(?) be the transform of f(t) exp j?(t). For example, f may be the illumination function of a linear antenna and ? accounts for imperfect phasing of the antenna. The major results consist of simple formulas for the rms tilting (or shifting) of the pattern |Fm|2 and the rms radius of gyration (or beamwidth) of the pattern. These positional errors and resolution degradations are formulated in terms of the pattern in the absence of phase errors and the power density spectrum of ??. The problem of calculating the best obtainable resolution, i.e., minimizing the mean-square resolution over all possible illumination functions, requires numerical solution; however, it is shown that it is always possible to obtain a rms resolution better than the smaller of rms ?? and ?rms ??. The actual numerical solution is compared to this simple approximation for the case of sinusoidal phase errors. The general results have a broad scope of applications, and here the spreading of the ambiguity function in time and frequency in the presence of time phase errors and dispersion (frequency phase errors) is described with particular attention to linear FM pulses. Finally, some observations are made about quadratic phase errors, signal-to-noise performance, and mean-square point-target response.

On the quadrature accuracy of in-phase coupled quadrature LC oscillator

This paper studies the influence of random phase and amplitude fabrication errors on the performance of optical filters based on fiber Bragg gratings (FBG's). In particular, we analyze two effects of particular importance for optical communications: the excess crosstalk induced in apodized gratings commonly used in wavelength-division-multiplexing (WDM) systems, and the time-delay fluctuations that appear in chirped gratings employed to compensate the fiber dispersion. A statistical model is presented to explain these effects in terms of the coherence length of the grating fabrication procedure.

Optically pumped magnetometer (OPM) has gained popularity as a viable alternative to the superconducting quantum interference device (SQUID) for biomagnetic measurements. However, the presence of amplitude and phase errors in the OPM can degrade the signal quality of, e.g., magnetoencephalography (MEG) signals. This study presents a dual-PI closed-loop control (DPCC) method aimed at suppressing amplitude and phase errors of the OPM when operated in the spin-exchange relaxation-free (SERF) regime, thereby enhancing MEG localization accuracy. The main sources of the amplitude and phase errors in the OPM are identified through a theoretical analysis of the inertial element characteristics and static residual magnetic fields. The experimental results demonstrate that the utilization of DPCC for the OPM reduces the amplitude and phase errors in static MEG measurements by 94.2% and 95.6%, respectively. At a residual magnetic field of 6.5 nT, the amplitude and phase errors are further suppressed by 97.8% and 87.2%, respectively. Furthermore, the fluctuation of the residual magnetic field is reduced by a factor of 25, significantly enhancing the robustness of the OPM. This straightforward and effective arrangement of the OPM holds promise in the field of biomagnetism and is expected to enhance the localization and calibration accuracy of OPM-based MEG (OPM-MEG) systems.

A PE (Processing Element) LSI for a DTW (Dynamic Time Warping) linear array processor has been designed. In designing this LSI, major effort has been focused on achieving regular data-flow among adjacent PEs maintaining pipelined operation in the array. A three data channel structure, a triple buffer structure and sophisticated control schemes make it possible for the designed LSI to carry out MIMD (Multiple Instruction and Multiple Data streams) and continuous pipelined DTW processing in sync with regular pattern input. Due to the high speed real time operation, and the versatile function of this PE-LSI, a high performance linear array processor can be constructed using a small number of PEs. The high speed operation of LSI is pursuited to achieve real time processing. Continuous speech recognition with an approximate vocabulary of 1000 words can be achieved using only 20 to 30 of these PE-LSIs.

We present a detailed study of parameter sweeps of silicon photonic arrayed waveguide gratings (AWG), looking into the effects of phase errors in the delay lines, which are induced by fabrication variation. We fabricated AWGs with 8 wavelength channels spaced 200 GHz and 400 GHz apart. We swept the waveguide width of the delay lines, and also performed a sweep where we introduced increments of length to the waveguides to emulate different AWG layouts and look into the effect of the phase errors. With this more detailed study we could quantitatively confirm the results of earlier studies, showing the wider waveguides reduce the effect of phase errors and dramatically improve the performance of the AWGs in terms of insertion loss and crosstalk. We also looked into the effect of rotating the layout of the circuit on the mask, and here we could show that, contrary to results with older technologies, this no longer has an effect on the current generation of devices.

The phase error is inevitable in the whole-angle control system and has a great impact on the gyroscope’s performance. In this article, the identification and correction of phase errors are carried out to eliminate the effects of phase errors under the whole-angle mode. The sources of phase errors are analyzed at first from the phase delay of the whole-angle control system. Furthermore, the effects of phase errors are also investigated from the theoretical and experimental analyses. It demonstrates that the phase error would produce coupling effects between the pattern angle and quadrature control loops and produce additional angle drift (AAD) affecting the performance of the whole-angle gyroscope. Therefore, the identification method of phase errors is presented on the basis of the observation of the AAD and the correction of phase errors can also be carried out by the phase shift module. After the correction of phase errors, the performance of bias instability and scale-factor nonlinearity improves by five and nine times, respectively.

Mixed source localization and gain-phase perturbation calibration in partly calibrated symmetric uniform linear arrays

Interleaved echo-planar imaging (EPI) is a fast clinical magnetic resonance imaging (MRI) scheme that obtains multiple echoes with a proper phase encoding (PE) strategy to generate multiple k-space PE lines. Since these PE data lines are from different echoes that may carry different phase and amplitude errors originating from the static magnetic field inhomogeneity and nuclear spin relaxation, to form an image free of artifacts, both phase and amplitude errors need to be compensated properly. To address this issue, we have developed a general image reconstruction technique which is capable of accomplishing two-dimensional (2D) phase correction for image reconstruction of interleaved EPI data. In this technique we formulated the reconstruction as a problem of finding an optimal solution to a set of linear algebraic equations corresponding to an imaging measurement. The phase errors, as well as other constraints, can be incorporated into these equations. The final solution can be obtained by inverting the coefficient matrix of the equation via a complex singular value decomposition (SVD) procedure, free of k-space data gridding. 2D phase corrected images have been successfully reconstructed using a set of imaging data acquired on a clinical MRI scanner. The significance of the work is that it has demonstrated that the 2D spatial phase correction can be accomplished for a set of interleaved EPI acquisition. Also, this is a flexible image reconstruction method for further improving the resulting image quality.

An 8-elements Ku-band phased-array transmitter with built-in-self-test (BIST) capability is presented. A fully symmetrical coupler feed line is used to improve the accuracy of the BIST and calibration procedure. 5-bit phase shifters and 4-bit attenuators with less phase and amplitude errors are designed to control the beam direction and side lobes. The RMS phase and amplitude errors of the phase shifters are less than 3.6° and 0.8 dB, respectively. The RMS amplitude and phase errors of the attenuators are less than 0.94 dB and 3.2°. The measured single path power gain including the power divider is 11.9 dB. The output referred PldB is 13 dBm for each channel. ESD protection and temperature sensors are integrated. The chip is fabricated in 180 nm bulk CMOS technology. Compact design is adopted to minimize the size of each channel, which is suitable for the larze-scale phased-array system. The size of the whole chip is $\mathbf{8.5x3 mm}^{\mathbf{2}}$ , and that of each channel is $\mathbf{3.8x0.5 mm}^{\mathbf{2}}$ .