Recovery of a lattice generator matrix from its gram matrix for feedback and precoding in MIMO

Abstract

Either in communication or in control applications, multiple-input multiple-output systems often assume the knowledge of a matrix that relates the input and output vectors. For discrete inputs, this linear transformation generates a mu~tidi~ensional lattice. The same lattice may be described by an InfinIte number of generator matrixes, even if the rotated versions of a lattice are not considered. While obtaining the Gram matrix from a given generator matrix is a trivial operation, the converse is not obvious for non-square matrixes and is a research topic in algorithmic number theory. This paper proposes a method to execute such a conversion and applies it in a novel MIMO system implementation where most of complexity is taken from the receiver to the transmitter. Additionally, given the symmetry of the Gram matrix, the number of elements required in the feedback channel is nearly halved.

URLLC with Coded Massive MIMO via Random Linear Codes and GRAND

“…where T = H H H ∈ C N T ×N T is the Gram matrix [15]. As seen in ( 4), the correct detection of x is perturbed by the modified noise vector u.…”

Downlink MIMO-NOMA With and Without CSI: A Short Survey and Comparison

“…This is because the channel models of ( 11) and ( 16) are in fact equivalent in terms of end-to-end SNR per user. To understand why this happens one needs to revisit equations (11) and (24) and note that G 1,1 Λ 1 2…”

“…When MIMO-NOMA is considered, the natural approach is to spatially cluster users which, from a MU-MIMO precoding point of view, behave as one virtual-user [23,24]. Subsequently, the messages to each user in a cluster are separated by SIC.…”

Resource Allocation between Feedback and Forward MIMO Links and Energy Consumption

“…2) Quantization error: It has been shown in [7], [8] that the minimum necessary information for the design of the optimum linear precoder for the usual design criteria is contained in the channel Gram matrix defined as R i = H H i H i for user i; therefore, in the following, quantization and feedback of the Gram matrix will be assumed, as done in [9], [10], [11]. This means that only a quantized version of the estimated channel Gram matrix R ei , denoted by R eq i , is available at user i.…”