Ramakrishna Janaswamy

Effect of element mutual coupling on the capacity of fixed length linear arrays

The effect of element mutual coupling on the capacity of multiple-input-multiple-output (MIMO) antenna systems is demonstrated by considering a fixed-length linear array of half-wave dipoles. Mutual coupling between elements, which influences both the spatial correlation and the received signal-to-noise ratio (SNR), is taken into account by means of the impedance matrix. Monte Carlo simulations are performed for both single-sided (i.e., transmitting end or receiving end) and double-sided fading correlations. It is shown that mutual coupling results in substantially lower capacity and, hence, in reduced degrees of freedom.

Analysis of the tapered slot antenna

A method for calculating the radiation pattern of end-fire tapered slot antennas with or without dielectric substrate is presented. The method involves a two-step procedure: 1) determine the field distribution of a traveling wave along the tapered slot, and 2) compute the radiation from this slot field by using the half-plane Greens function to account for termination effects. Acceptable estimates of the slot field usually can be obtained from a stepped approximation to the tapered geometry. The method has been verified by comparisons to measured patterns for various dielectric substrates and antenna dimensions. However, the effect of lateral truncation has not yet been successfully modeled. Experimental patterns showing this effect are presented.

Angle and time of arrival statistics for the Gaussian scatter density model

Starting from a Gaussian distribution of scatterers around a mobile station, expressions are provided for the probability density function (PDF) in the angle of arrival, the power azimuth spectrum, the PDF in the time of arrival, and the time delay spectrum, all as seen from a base station. Expressions are also provided for some of the quantities of practical interest such as the root-mean-square (RMS) angular spread, the RMS delay spread, and the spatial cross-correlation function. Results for the Gaussian scatter density model are compared with those for the circular scattering model and the elliptical scattering model as well as with experimental results available for outdoor and indoor environments. Comparison is shown for the PDFs as well as for the power spectra in angle and delay. It is shown that the present model, in contrast to the previous models, produces results that closely agree with experimental results. With an appropriate choice of the standard deviation of the scattering region, the Gaussian density model can be made suitable both for environments with very small angular spreads as well as those with very large angular spreads. Consequently, the results provided in the paper are applicable to both macrocellular as well as picocellular environments.

Path loss predictions in the presence of buildings on flat terrain: a 3-D vector parabolic equation approach

Starting from a parabolic approximation to the Helmholtz equation, a three-dimensional (3-D) vector parabolic equation technique for calculating path loss in an urban environment is presented. The buildings are assumed to be polygonal in cross section with vertical sides and flat rooftops and the terrain is assumed to be flat. Both buildings and ground are allowed to be lossy and present impedance-type boundary condition to the electromagnetic field. Vector fields are represented in terms of the two components of Hertzian potentials and depolarization of the fields is automatically included in the formulation. A split-step algorithm is presented for marching the aperture fields along the range. Boundary conditions on the building surfaces are treated by using a local Fourier representation of the aperture fields. Several test cases are considered to check the boundary treatment used in the technique as well as to validate the overall approach. Comparison is shown with uniform theory of diffraction (UTD), exact solutions, as well as with measurements.

Improved Fourier transform methods for solving the parabolic wave equation

[1]xa0A standard method for modeling electromagnetic propagation in the troposphere is the Fourier split-step algorithm for solving the parabolic wave equation. An important advance in this technique was the introduction of the mixed Fourier transform, which permitted the extension of the method from propagation over only smooth perfectly conducting surfaces to quite general surfaces with impedance boundary conditions. This paper describes improvements in the implementation of the mixed Fourier transform, which make the method more robust and efficient and avoid potential numerical instabilities, which occasionally caused problems in the previous implementation. Some examples are also presented.

An ADI-PE Approach for Modeling Radio Transmission Loss in Tunnels

Alternate direction implicit (ADI) method is used to study radio wave propagation in tunnels using the parabolic equation (PE). We formulate the ADI technique for use in tunnels with rectangular, circular and arched cross sections and with lossy walls. The electrical parameters of the lossy walls are characterized by an equivalent surface impedance. A vector PE is also formulated for use in tunnels with lossy walls. It is shown that the ADI is more computationally efficient than the Crank Nicolson method. However, boundary conditions become more difficult to model. The boundary conditions of the ADI intermediate planes are given the same boundary conditions as the physical plane and the overall accuracy is reduced. Also, when implementing the ADI in tunnels with circular cross sections the order at which the line by line decomposition occurs becomes important. To validate the ADI-PE, we show simulation results for tunnel test cases with known analytical solutions. Furthermore, the ADI-PE is used to simulate real tunnels in order to compare with experimental data. It is shown that the PE models the electric fields most accurately in real tunnels at large distances, where the lower order modes dominate.

On the asymptotic capacity of MIMO systems with antenna arrays of fixed length

Previous authors have shown that the asymptotic capacity of a multiple-element-antenna (MEA) system with N transmit and N receive antennas [termed an (N,N) MEA] grows linearly with N if, for all l, the correlation of the fading for two antenna elements whose indices differ by l remains fixed as antennas are added to the array. However, in practice, the total size of the array is often fixed, and thus the correlation of the fading for two elements separated in index by some value l will change as the number of antenna elements is increased. In this paper, under the condition that the size of an array of antennas is fixed, and assuming that the transmitter does not have access to the channel state information (CSI) while the receiver has perfect CSI, the asymptotic properties of the instantaneous mutual information I/sub N,N/ of an (N,N) MEA wireless system employing uniform linear arrays in a quasi-static fading channel are derived analytically and tested for accuracy for finite N through simulations. For many channel correlation structures, it is demonstrated that the asymptotic performance converges almost surely, implying that such MEA systems have a certain strong robustness to the instantiation of the channel fading values.

The effect of mutual coupling on the capacity of the MIMO cube

The effect of mutual coupling on the capacity of the multiple-input-multiple output (MIMO) cube antenna is demonstrated using numerical simulations. The twelve edges of the cube constitute center-fed electrical dipole antennas. A simple double bouncing scattering model is used to form the MIMO channel matrix. Mutual coupling between the elements that has impact on both the spatial correlation and the received signal-to-noise ratio (SNR) is taken into account using the mutual impedance matrix of the cube. Results of Monte Carlo simulations show that the theoretical capacity due to mutual coupling is lower than without mutual coupling for cube side lengths less than about 0.3/spl lambda/ but the results roughly match those for higher side lengths.

Electromagnetic Degrees of Freedom in 2-D Scattering Environments

The electromagnetic (EM) degrees of freedom (DOF) of a noise limited system in two dimensions with random multiple scattering is evaluated numerically following a rigorous DOF theory first developed by Miller and Piestun for optical systems. The received EM fields are efficiently calculated by fast multipole method (FMM), and the ensemble average of the DOF number is obtained through Monte Carlo simulation technique. The results show that the average EM DOF number is strongly dependent on the sizes of the transmit volume, the receive volume, and the scattering region. In particular, the average number of DOF generally increases with both the transmit and receive volumes. However this increase is a non-linear process and will not continue indefinitely. As the transmit volume or the receive volume expands, an upper-bound of the average DOF number is expected due to noise effects. Due to the lack of criteria for choosing a critical parameter involved in Miller and Piestuns original DOF definition, a modified definition is also considered. Even though the modified definition is SNR dependent, it provides a clearer physical meaning of the DOF. In addition, the simulations also suggest that it might not be appropriate to ignore the influence of the SNR on the DOF number when the system concerned is of general form and relative small, where no critical point of the channel quality can be identified. A logarithmic dependence of the DOF number on the total source power is demonstrated for such systems

Modeling Radio Transmission Loss in Curved, Branched and Rough-Walled Tunnels With the ADI-PE Method

We discuss the use of the parabolic equation (PE) along with the alternate direction implicit (ADI) method in predicting the loss for three specialized tunnel cases: curved tunnels, branched tunnels, and rough-walled tunnels. This paper builds on previous work which discusses the use of the ADI-PE in modeling transmission loss in smooth, straight tunnels. For each specialized tunnel case, the ADI-PE formulation is presented along with necessary boundary conditions and tunnel geometry limitations. To complete the study, examples are presented where the ADI-PE numerical results for the curved and rough-walled tunnel are compared to known analytical models and experimental data, and the branched tunnel data is compared to the numerical solutions produced by HFSS.