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Title: Asymptotic Analysis of Large Antenna Arrays for Communications and Radar Applications
Authors: Kamath, Ajith Mulki
Advisors: Brian L.Hughes, Committee Chair
Hamid Krim, Committee Member
Jack W. Silverstein, Committee Member
Alexandra Duel-Hallen, Committee Member
Keywords: diversity multiplexing tradeoff
outage capacity
vector antenna
mutual information
Cramer Rao bound
antenna array
tripole array
Issue Date: 28-Mar-2006
Degree: PhD
Discipline: Electrical Engineering
Abstract: In recent years there has been a growing interest in using antenna arrays at both ends of a wireless communication link. Such multiple input multiple output (MIMO) systems are beneficial both in terms of providing greatly improved data rates, as well as in terms of robustness in combating errors compared to systems which use only one antenna. These benefits are obtained without requiring extra transmit power or spectral bandwidth, but come at the cost of additional processing power. In radar, multiple antenna arrays have been in use for several decades. Even so, the idea of measuring the full received electro-magnetic (EM) wave for parameter estimation has been a recent one. In this dissertation, we address two issues through asymptotics: in MIMO systems, we develop insights into finite MIMO array performance by deriving precise results for asymptotically large MIMO arrays, and in radar we derive the gain from measuring the complete field over a spherical surface versus measuring only one polarization component using an equal number of sensors. First, we consider the distribution of the mutual information of a MIMO system with an uncorrelated Rayleigh fading channel. We show that, as the transmit and receive array sizes tend to infinity while maintaining their ratio constant, the mutual information distribution tends to Gaussian distribution at all signal to noise ratios (SNRs), and give a closed-form expression for its mean and variance. Through simulations, we observe that the mutual information distribution of a finite MIMO system with as few as 4 array elements at either end has a variance which depends only on the ratio of the two arrays and is also closely approximated by the asymptotic distribution variance. We show that the mean of the distribution can also be approximated much closer than previously shown, and hence combined with the asymptotic variance, this yields close approximations for outage capacities. We next consider the problem of determining the best possible tradeoff between diversity and multiplexing gains in an uncorrelated Rayleigh fading channel. Zheng and Tse have characterized this tradeoff in the large signal to noise ratio(SNR) limit. We apply our asymptotic results on mutual information to compute the finite SNR diversity-multiplexing tradeoffs at high outage probabilities in the range of practical interest. We show that the asymptotic results match the tradeoffs derived by Zheng and Tse only in the equal antenna MIMO array case. We then propose a linear dispersion coding scheme which modulates a block of data by picking a random unitary matrix, which was previously shown to produce full-rank full-diversity code-books with probability one. Through simulations using rectangular code-books, we show that these may also achieve the full Zheng-Tse diversity multiplexing tradeoff after using a maximum likelihood (ML) decoder. Having developed fundamental insights into MIMO arrays through the use of asymptotic analysis, we consider the impact of using vector antennas in large radar arrays. Specifically, we compare the performance of range and direction-of-arrival (DOA) estimation of a single source using an array of vector electro-magnetic (EM) sensors packed densely on the surface of a sphere, with a similarly shaped array with identically oriented dipole elements. We compute the Cramer-Rao lower bound on maximum-likelihood range and DOA estimation using either array. By taking the ratio of the confidence volumes as the gain, we compare the vector array estimate with the uni-polarized array as a function of target location.
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