Channel Estimation for Massive MIMO: An Information Geometry Approach

Abstract

In this paper, we propose an information geometry approach (IGA) for signal detection (SD) in ultra-massive multiple-input multiple-output (MIMO) systems. We formulate the signal detection as obtaining the marginals of the a posteriori probability distribution of the transmitted symbol vector. Then, a maximization of the a posteriori marginals (MPM) for signal detection can be performed. With the information geometry theory, we calculate the approximations of the a posteriori marginals. It is formulated as an iterative m-projection process between submanifolds with different constraints. We then apply the central-limit-theorem (CLT) to simplify the calculation of the m-projection since the direct calculation of the m-projection is of exponential-complexity. With the CLT, we obtain an approximate solution of the m-projection, which is asymptotically accurate. Simulation results demonstrate that the proposed IGA-SD emerges as a promising and efficient method to implement the signal detector in ultra-massive MIMO systems.

Multi-User Symbol-Level Precoding for Downlink Reconfigurable MIMO Communication Systems

“…We use h k,n ∈ C N ×1 , n = 1, ..., N ds to represent the channel from the BS to the k-th UE at n-th downlink transmission symbols, which is considered to be described by the widely adopted jointly correlated channel model [35], [42], [43]. Define h u k,0 as the channel estimated at BS from the uplink training sequences in this slot by exploiting the channel reciprocity, and channel h k,n can be represented as the a posteriori channel model [38]:…”

“…In this formulation, V D ∈ C N ×F vh N is a matrix composed of (partial) discrete Fourier transform (DFT) matrix, where F vh ∈ N + is the fine factor utilized to improve the fineness of the model [42]; g k,n ∈ C F vh N ×1 is a complex Gaussian random vector whose elements follow CN (0, 1) independently; m k ∈ R F vh N ×1 is a sparse vector with nonnegative elements that remain constant for a relatively long period [35], [36]; The time variation of the channel is modeled by the first order Gauss-Markov process with the correlation coefficients α k,n and β k,n = 1 − α 2 k,n that are related to the UE speed [33], [34]. Specifically, α k,n is described by Jakes' autocorrelation model [32], [44], i.e., α k,n = J 0 (2πv k f c nT /c), where J 0 (•), v k , f c , T , and c represent the first kind of Bessel functions of zero order, the speed of k-th UE, carrier frequency, the duration of a symbol, and the speed of light, respectively.…”

“…where {h u k , m k , α k } K k=1 and σ 2 are assumed to be available at the BS [38], [39], [42], s c denotes the M -PSK (M > 2) symbols to be sent to UEs at this symbol duration, which is given by…”

“…Proposition 5: For NNLS problem (42) with certain Ψ and approximation matrix Υ, the R A of form (27) converges into the diagonal matrix κ Ψ 2 (I 2 ⊗ M)…”

“…APPENDIX F PROOF OF PROPOSITION 5 According to the definition in Appendix D, matrix R A for problem (42) is given by…”