Limits to multi-antenna capacity of spatially selective channels

Abstract

-In this paper we present a new upper bound on the mutual information of MIMO systems. By characterizing the fundamental communication modes between two physical regions, we develop an intrinsic capacity which is independent of antenna array geometries and array signal processing, and depends only on the size of the regions and the statistics of the scattering environment.Multiple-Input Multiple-Output (MIMO) communications systems using multi-antenna arrays simultaneously during transmission and reception have generated significant interest in recent years. Theoretical work of [1] showed the potential for significant capacity increases in wireless channels via spatial multiplexing with sparse antenna arrays. However, in reality the capacity is significantly reduced when the antennas are constrained to within spatial apertures of finite size so the signals received by different antennas become correlated [2].The excited plane waves of a single isotropic radiating antenna may be mathematically described by a modal series expansion, where each mode corresponds to a different solution of the governing electromagnetic equations (Maxwell's equations) for the given boundary conditions. The complex channel gain between a transmit antenna and receive antenna can then be considered as spatial-to-mode coupling at the transmitter, mode-to-spatial coupling at the receiver, and a modeto-mode gain due to the scattering environment connecting the two [3]. Theorem 1 (Aperture Mode Cardinality) Antennas constrained within a 2D circular aperture of radius r can only excite (couple with) a finite set of communication modes with maximum cardinalityregardless of the number of antennas within the aperture. Corollary 1 (Upper Bound on Capacity) The instantaneous mutual information between a transmit region of radius rT and receive region of radius rR has supremumwhere H S is a Nr R × Nr T scattering environment matrix, which defines the random complex gains between the Nr T transmit region modes and the Nr R receive region modes.The mode-to-mode capacity (2) represents the intrinsic capacity for communication between two spatial apertures, giving 1 National ICT Australia is funded through the Australian Government's Backing Australia's Ability initiative, in part through the Australian Research Council. the maximum mutual information for all possible array configurations and array signal processing. From Theorem 1, the intrinsic capacity is determined by the size of the regions containing the antenna arrays (number of available modes), along with the statistics of the scattering channel matrix (modal correlation). Fig. 1 shows the impact of modal correlation on the ergodic mode-to-mode capacity for increasing angular spread at the transmitter and isotropic scattering at the reciever 2 for 10dB SNR. We consider transmit and receive apertures of radius 0.8λ, corresponding to 2 πe0.8 + 1 = 15 modes at each aperture. For comparison, also shown is the capacity for an 15 antenna uniform linear (ULA), uniform circular (UCA), and uni...

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