Modal couping effects in the free vibration of elastically interconnected beams

The problem of free vibration of a uniform beam elastically interconnected to a cantilevered beam, representing an idealized launch vehicle aeroelastic model in a wind tunnel, is studied. With elementary beam theory modelling, numerical results are obtained for the frequencies, mode shapes and the generalized modal mass of this elastically cou pled13; system, for a range of values of the spring constants and cantilevered beam stiffness and inertia values. The study shows that when the linear springs are supported at the nodal points corresponding to the first free-free beam mode, the modal interaction comes primarily from the rotational spring stiffness. The effect of the linear spring stiffness on the higher model modes is also found to be marginal. However, the rotational stiffness has a significant effect on all the predominantly model modes as it couples the model13; deformations and the support rod deformations. The study also shows that though the variations in the stiffness or the inertia values of the cantilever beam affect only the13; predominantly cantilever modes, these variations become important because of the fact that the cantilevered support rod frequencies may come close to, or even cross over, the13; predominantly model mode frequencies. The results also bring out the fact that shifting of the support points away from the first mode nodal points has a maximum effect only on the first model mode

Covariance Matrix Estimation for Massive MIMO

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.Comment: 6 pages, 4 figures. Accepted for publication in IEEE Signal Processing Letter

Downlink Performance of Superimposed Pilots in Massive MIMO systems

In this paper, we investigate the downlink throughput performance of a massive multiple-input multiple-output (MIMO) system that employs superimposed pilots for channel estimation. The component of downlink (DL) interference that results from transmitting data alongside pilots in the uplink (UL) is shown to decrease at a rate proportional to the square root of the number of antennas at the BS. The normalized mean-squared error (NMSE) of the channel estimate is compared with the Bayesian Cram\'{e}r-Rao lower bound that is derived for the system, and the former is also shown to diminish with increasing number of antennas at the base station (BS). Furthermore, we show that staggered pilots are a particular case of superimposed pilots and offer the downlink throughput of superimposed pilots while retaining the UL spectral and energy efficiency of regular pilots. We also extend the framework for designing a hybrid system, consisting of users that transmit either regular or superimposed pilots, to minimize both the UL and DL interference. The improved NMSE and DL rates of the channel estimator based on superimposed pilots are demonstrated by means of simulations.Comment: 28 single-column pages, 6 figures, 1 table, Submitted to IEEE Trans. Wireless Commun. in Aug 2017. Revised Submission in Feb. 201

Analysis of axisymmetric laminated composite shells subjected to asymmetric loading

A finite element formulation for the static analysis of a laminated composite shell of revolution with general meridional curvature, subjected to asymmetric loading, is presented. The analysis uses an axisymmetric laminated shell element where the shell geometry is satisfactorily represented; higher order polynomial approximations are used for the displacement fields. The asymmetric loading problem is handled through a Fourier series representation of the applied loads and the resultant displacements. Solutions are presented for typical aerospace shell structures like a composite cone and a tangent ogive shell subjected to wind loads

Transit Trade of Land-Locked States

With the emergence of many newly independent states after the Second World War, the number of land-locked states or states having no sea coast, has also grown significantly. More than one-fourth of the states in the world are land-locked. In Asia, land-locked states are Afghanistan, Bhutan, Laos, Outer Mongolia and Nepal. But the largest number of land-locked states is in Africa. There are 14 in number, comprising almost half the number of land-locked states in the world

Superimposed Pilots are Superior for Mitigating Pilot Contamination in Massive MIMO

In this paper, superimposed pilots are introduced as an alternative to time-multiplexed pilot and data symbols for mitigating pilot contamination in massive multiple-input multiple-output (MIMO) systems. We propose a non-iterative scheme for uplink channel estimation based on superimposed pilots and derive an expression for the uplink signal-to-interference-plus-noise ratio (SINR) at the output of a matched filter employing this channel estimate. Based on this expression, we observe that power control is essential when superimposed pilots are employed. Moreover, the quality of the channel estimate can be improved by reducing the interference that results from transmitting data alongside the pilots, and an intuitive iterative data-aided scheme that reduces this component of interference is also proposed. Approximate expressions for the uplink SINR are provided for the iterative data-aided method as well. In addition, we show that a hybrid system with users utilizing both time-multiplexed and superimposed pilots is superior to an optimally designed system that employs only time-multiplexed pilots, even when the non-iterative channel estimate is used to build the detector and precoder. We also describe a simple approach to implement this hybrid system by minimizing the overall inter and intra-cell interference. Numerical simulations demonstrating the performance of the proposed channel estimation schemes and the superiority of the hybrid system are also provided