The Space Frontier: Physical Limits of Multiple Antenna Information Transfer

Abstract

In this paper, we study the capacity limits of dense multiantenna systems. We derive asymptotic capacity expressions for point-to-point and broadcast channels by applying recent tools from random matrix theory. In the case of broadcast channels, we focus on linear precoding techniques. We found that the asymptotic capacity depends only on the ratio between the size of the antenna array and the wavelength. This provides useful guidelines on the achievable limits of information transfer. In particular, it is shown that the total capacity grows unbounded if the transmitter has perfect knowledge on the channel, while the capacity saturates in the absence of channel knowledge at the transmitter. We provide numerical results supporting the theoretical derivations.

Base Station Cooperation on the Downlink: Large System Analysis

“…, 0,2 = 1+ √ 8a− 7 4 , one can show that (235) will be positive if (a ≥ 1, and 0 ≤ ≤ 0,2 ), or ( 7 8 ≤ a ≤ 1, and 0,1 ≤ ≤ 0,2 ). One can further establish that if this is the case, all of the other coefficients of the polynomial (234) will be positive 16 , and consequently h(γ * ) will be a decreasing function, and hence h(γ * ) < 0 ∀γ * > 0. In this case, r(γ * ) is a decreasing function and the optimum will occur at γ * = 0, which corresponds to β * = ∞.…”

“…Surprisingly, there has been limited work on the DL until quite recently, despite a well established UL-DL duality theory. Recently, however, a large systems analysis of regularized ZF (RZF) beamforming was carried out to characterize its limiting performance in a single cell context, allowing the optimization of the regularization parameter [15], and [16] considers ZF and RZF for correlated channel models. The present paper generalizes [15] to the multicell context, and to a wider class of beamformers, exploiting an UL-DL duality theory.…”

Min-max fair coordinated beamforming via large systems analysis

“…In the large systems analysis, the optimal rates are deterministic, but if the corresponding beamforming structures are used in the finite case, the rates obtained are random variables, just as the optimal solution to P α provides rates that vary with the channel state. Figure 4 illustrates the cumulative distribution function (cdf) of the rate supported by the proposed beamforming strategy 13 at the first user in cell 2, for α 1 = α 2 = .5, for increasing number of antennas (and users in each cell). As the number of antennas tends to infinity, 13 log 2 (1 + SINR u,k ), where SINR u,k is obtained from beamforming vectors constructed using the asymptotically optimal dual parameters and power levels both instantaneous and average rates converge to the value predicted by the large systems analysis, but the convergence rate is quite slow.…”

“…Figure 4 illustrates the cumulative distribution function (cdf) of the rate supported by the proposed beamforming strategy 13 at the first user in cell 2, for α 1 = α 2 = .5, for increasing number of antennas (and users in each cell). As the number of antennas tends to infinity, 13 log 2 (1 + SINR u,k ), where SINR u,k is obtained from beamforming vectors constructed using the asymptotically optimal dual parameters and power levels both instantaneous and average rates converge to the value predicted by the large systems analysis, but the convergence rate is quite slow. It turns out that if we want a reasonably close approximation to the finite system average rate region but using beamformer structures obtained from the large systems analysis, we need to include some adaptive power control into the solution.…”

“…RMT large system analysis (LSA) has also allowed analysis of the uplink (UL) of cellular systems [6], [7], [8], [9], [10]. Recently, LSA has also been applied to the DL: in [11], duality between the multiple access channel (MAC) and the broadcast channel (BC) is used to characterize and optimize asymptotic ergodic capacity for correlated channels; Focusing on beamforming strategies, a LSA of regularized ZF (RZF) beamforming was undertaken to find its limiting performance for a single cell, allowing the optimization of the regularization parameter [12]; [13] considers ZF and RZF for correlated channel models.…”