On the Capacity of Block Multiantenna Channels

Abstract

Abstract-In this paper we consider point-to-point multiantenna channels with certain block distributional symmetries which do not require the entries of the channel matrix to be either Gaussian, or independent, or identically distributed. A main contribution is a capacity theorem for these channels, which might be regarded as a generalization of Telatar's theorem (1999), which reduces the numerical optimization domain in the capacity computation. With this information theoretic result and some free probability arguments, we prove an asymptotic capacity theorem that, in addition to reducing the optimization domain, does not depend on the dimension of the channel matrix. This theorem allows us to apply free probability techniques to numerically compute the asymptotic capacity of the channels under consideration. These theorems provide a very efficient method for numerically approximating both the capacity and a capacity achieving input covariance matrix of certain channels.

Low Complexity Optimization of the Asymptotic Spectral Efficiency in Massive MIMO NOMA

“…In this section we compare: (i) the bisection algorithm described in [20], which relies on the traditional method of capacity computation given in (4) and (5) and finds the optimal power allocation, (ii) the suboptimal algorithm also derived in [20] which omits the need for repeated bisections but still relies on computing the expectation over multiple realizations of the determinant of a matrix, and (iii) the bisection method Figure 2: Sum-capacity vs total transmission power using our asymptotic capacity equations (9) and (10) in placec of the traditional method. For the sake of simplicity, we have considered the cases where N S = N i = N in our results.…”

“…In comparison the asymptotic approach also loops over the capacity computation M times but computes the capacity using the closed form in (9), for which the complexity is invariant with respect to N S , N i , K and M , thus the overall complexity order of this method is O(M ).…”

On the symmetries and the capacity achieving input covariance matrices of multiantenna channels

“…In the context of [4], a block symmetry is a matrix of the form I d ⊗V with V ∈ U N such that H(I d ⊗V ) L = H where H is the dN × dN matrix of propagation coefficients of the channel. In this paper we propose a broader scope for the notion of block symmetry: block symmetries are the tensor product or direct sum of elementary symmetries (unitary, diagonal or signed permutation).…”

“…However, as we shall see, the symmetries of the matrix of propagation coefficients of the channel are the heart of the matter. In our context, these symmetries are unitary matrices that, under conjugation, leave invariant the distribution of the product of the matrix of propagation coefficients and its conjugate transpose, see equation (4). An analysis based on these symmetries does not depend on moment conditions, correlation assumptions, or distributional requirements for the propagation coefficients.…”

“…Let F be a finite multiset 1 with elements in U N . Motivated by [4,Lemma 1], we consider the average operator A F : M C N → M C N with respect to F ,…”