MSGR-based Low Latency Complex Matrix Inversion Architecture

This paper presents a matrix inversion architecture based on the novel Modified Squared Givens Rotations (MSGR) algorithm, which extends the original SGR method to complex valued data, and also corrects erroneous results in the original SGR method when zeros occur on the diagonal of the matrix either initially or during processing. The MSGR algorithm also avoids complex dividers in the matrix inversion, thus minimising the complexity of potential real-time implementations. A systolic array architecture is implemented and FPGA synthesis results indicate a high-throughput low-latency complex matrix inversion solution. © 2008 IEEE.

QR decomposition-based matrix inversion for high performance embedded MIMO receivers

Real-time matrix inversion is a key enabling technology in multiple-input multiple-output (MIMO) communications systems, such as 802.11n. To date, however, no matrix inversion implementation has been devised which supports real-time operation for these standards. In this paper, we overcome this barrier by presenting a novel matrix inversion algorithm which is ideally suited to high performance floating-point implementation. We show how the resulting architecture offers fundamentally higher performance than currently published matrix inversion approaches and we use it to create the first reported architecture capable of supporting real-time 802.11n operation. Specifically, we present a matrix inversion approach based on modified squared Givens rotations (MSGR). This is a new QR decomposition algorithm which overcomes critical limitations in other QR algorithms that prohibits their application to MIMO systems. In addition, we present a novel modification that further reduces the complexity of MSGR by almost 20%. This enables real-time implementation with negligible reduction in the accuracy of the inversion operation, or the BER of a MIMO receiver based on this.

Determination of absolute configuration of conformationally flexible cis-dihydrodiol metabolites: Effect of diene substitution pattern on the circular dichroism spectra and optical rotations

Absolute configurations of a number of cis-dihydrodiols (cis-1,2-dihydroxy-3,5-cyclohexadienes), synthetically useful products of TDO-catalyzed dihydroxylations of 1,2- and 1,3-disubstituted benzene derivatives, have been determined by a comparison of calculated and experimental CD spectra and optical rotations and by methods involving X-ray crystallography, H-1 NMR spectra of diastereoisomeric derivatives, and by stereochemical correlations. The computations disclosed a significant effect of the substituents on conformational equilibria of cis-dihydrodiols and chiroptical properties of individual conformers. The assigned absolute configurations of cis-dihydrodiols have allowed the validity of a simple predictive model for TDO-catalyzed arene dihydroxylations to be extended.

Absolute configuration of conformationally flexible cis-dihydrodiol metabolites by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations

We have determined the absolute configurations of conformationally flexible cis-dihydrodiol metabolites (cis-1,2-dihydroxy-3,5-cyclohexadienes), bearing different substituents (e.g., Br, F, CF3, CN, Me) in 3- and 5-positions, by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations. Convergent results were obtained by both methods in eight out of ten cases. For the difficult cases, where either conformer population and/or chiroptical properties (calculated rotational strengths of the long-wavelength Cotton effect or optical rotations) of contributing conformers remain inconclusive, the absolute configuration could still be correctly assigned based on one of the biased properties (either ECD or optical rotation). This approach appears well-suited for a broad spectrum of conformationally flexible chiral molecules.

The efficacy of colour cues in facilitating adaptation to opposing visuomotor rotations

We investigated visuomotor adaptation using an isometric, target-acquisition task. Following trials with no rotation, two participant groups were exposed to a random sequence of 30 degrees clockwise (CW) and 60 degrees counter-clockwise (CCW) rotations, with (DUAL-CUE), or without (DUAL-NO CUE), colour cues that enabled each environment (non-rotated, 30 degrees CW and 60 degrees CCW) to be identified. A further three groups experienced only 30 degrees CW trials or only 60 degrees CCW trials (SINGLE rotation groups) in which each visuomotor mapping was again associated with a colour cue. During training, all SINGLE groups reduced angular deviations of the cursor path during the initial portion of the movements, indicating feedforward adaptation. Consistent with the view that the adaptation occurred automatically via recalibration of the visuomotor mapping (Krakauer et al. 1999), post-training aftereffects were observed, despite colour cues that indicated that no rotation was present. For the DUAL-CUE group, angular deviations decreased with training in the 60 degrees trials, but were unchanged in the 30 degrees trials, while for the DUAL-NO CUE group angular deviations decreased for the 60 degrees CW trials but increased for the 30 degrees CW trials. These results suggest that in a dual adaptation paradigm a colour cue can permit delineation of the two environments, with a subsequent change in behaviour resulting in improved performance in at least one of these environments. Increased reaction times within the training block, together with the absence of aftereffects in the post-training period for the DUAL-CUE group suggest an explicit cue-dependent strategy was used in an attempt to compensate for the rotations.

Generalisation between opposing visuomotor rotations when each is associated with visual targets and movements of different amplitude

Previous studies have attempted to identify sources of contextual information which can facilitate dual adaptation to two variants of a novel environment, which are normally prone to interference. The type of contextual information previously used can be grouped into two broad categories: that which is arbitrary to the motor system, such as a colour cue, and that which is based on an internal property of the motor system, such as a change in movement effector. The experiments reported here examined whether associating visuomotor rotations to visual targets and movements of different amplitude would serve as an appropriate source of contextual information to enable dual adaptation. The results indicated that visual target and movement amplitude is not a suitable source of contextual information to enable dual adaptation in our task. Interference was observed in groups who were exposed to opposing visuomotor rotations, or a visuomotor rotation and no rotation, both when the onset of the visuomotor rotations was sudden, or occurred gradually over the course of training. Furthermore, the pattern of interference indicated that the inability to dual adapt was a result of the generalisation of learning between the two visuomotor mappings associated with each of the visual target and movement amplitudes. (C) 2008 Elsevier B.V. All rights reserved.

Dual adaptation to two opposing visuomotor rotations when each is associated with different regions of workspace

Studies examining dual adaptation to opposing novel environments have yielded contradictory results, with previous evidence supporting both successful dual adaptation and interference leading to poorer adaptive performance. Whether or not interference is observed during dual adaptation appears to be dependent on the method used to allow the performer of the task to distinguish between two novel environments. This experiment tested if colour cues, a separation in workspace, and presentation schedule, could be used to distinguish between two opposing visuomotor rotations and enable dual adaptation. Through the use of a purpose designed manipulandum, each visuomotor rotation was either presented in the same region of workspace and associated with colour cues (Group 1), different regions of workspace in addition to colour cues (Groups 2 and 3) or different regions of workspace only (Groups 4 and 5). We also assessed the effectiveness of the workspace separation with both randomised and alternating presentation schedules (Groups 4 and 5). The results indicated that colour cues were not effective at enabling dual adaptation when each of the visuomotor rotations was associated with the same region of workspace. When associated with different regions of workspace, however, dual adaptation to the opposing rotations was successful regardless of whether colour cues were present or the type of presentation schedule.

Visual target separation determines the extent of generalisation between opposing visuomotor rotations

Here we investigated the influence of angular separation between visual and motor targets on concurrent adaptation to two opposing visuomotor rotations. We inferred the extent of generalisation between opposing visuomotor rotations at individual target locations based on whether interference (negative transfer) was present. Our main finding was that dual adaptation occurred to opposing visuomotor rotations when each was associated with different visual targets but shared a common motor target. Dual adaptation could have been achieved either within a single sensorimotor map (i.e. with different mappings associated with different ranges of visual input), or by forming two different internal models (the selection of which would be based on contextual information provided by target location). In the present case, the pattern of generalisation was dependent on the relative position of the visual targets associated with each rotation. Visual targets nearest the workspace of the opposing visuomotor rotation exhibited the most interference (i.e. generalisation). When the minimum angular separation between visual targets was increased, the extent of interference was reduced. These results suggest that the separation in the range of sensory inputs is the critical requirement to support dual adaptation within a single sensorimotor mapping.

QRD and SVD processor design based on an approximate rotations algorithm

A silicon implementation of the Approximate Rotations algorithm capable of carrying the computational load of algorithms such as QRD and SVD, within the real-time realisation of applications such as Adaptive Beamforming, is described. A modification to the original Approximate Rotations algorithm to simplify the method of optimal angle selection is proposed. Analysis shows that fewer iterations of the Approximate Rotations algorithm are required compared with the conventional CORDIC algorithm to achieve similar degrees of accuracy. The silicon design studies undertaken provide direct practical evidence of superior performance with the Approximate Rotations algorithm, requiring approximately 40% of the total computation time of the conventional CORDIC algorithm, for a similar silicon area cost. © 2004 IEEE.