On Lattice-Based Broadcasting for Massive-User MIMO: Practical Algorithms and Optimization

This paper studies a lattice-based broadcasting (LBC) scheme for a single-cell downlink system. The base station (BS) has N antennas and the K user-equipments (UEs) have a single-antenna. The system is referred to as massive-user MIMO (mU-MIMO) when K is very large. At the transmitter side, the BS encodes the messages for the UEs with state-of-the-art channel codes and q-PAM modulation. We suggest a codeword-level precoding, which transforms the K UEs’ coded sequences by an invertible integer matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {A}^{-1}$ </tex-math></inline-formula> over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {Z}_{q}$ </tex-math></inline-formula>, resulting in K codeword-level precoded (CLP) streams. Then, the CLP streams undergo a linear signal-level precoding (SLP) with regularized integer-forcing, and the resultant signals are transmitted via the N antennas of BS. The operations of CLP and SLP are both linear. At the receiver side, each UE attempts to compute an integer-combination (ICB) of the K CLP streams w.r.t. the integer matrix A, which turns out to be its desired message thanks to the CLP. For computing the ICB, we put forth new soft detection algorithms, which efficiently calculate the a posteriori probability of ICB over the lattice. The complexity is shown to be (much) less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(Kq)$ </tex-math></inline-formula>, which is suited for large values of K. Further, we develop a particle swarm based approach that jointly optimizes A and the power allocation matrix. Numerical results demonstrate dramatically enhanced performance over baseline schemes including regularized zero-forcing and vector perturbation precoding, for both slow and fast fading channels.