A 0.18nJ/Matrix QR decomposition and lattice reduction processor for 8×8 MIMO preprocessing

Abstract

This study presents a joint QR decomposition and lattice reduction processor for 8 × 8 multiple-input multipleoutput (MIMO) systems. The proposed algorithm enhances the BER performance by lattice reduction and reduces the hardware cost by sharing computation units and removing redundant operations. This processor can be reconfigured as three different modes, including joint QR decomposition and lattice reduction, lattice reduction, and QR decomposition. The proposed processor was implemented in TSMC 90nm 1P9M CMOS technology. The maximum throughput is 1.1 M matrix/s for QR decomposition, and 0.5 M matrix/s for the lattice reduction, and 0.33 M matrix/s for the joint QR decomposition and lattice reduction at a power consumption of 31.2 mW. The energy efficiency achieves 0.18nJ/matrix for the 8 × 8 MIMO preprocessing including both QR decomposition and lattice reduction.

Low-Latency Lattice-Reduction-Aided One-Bit Precoding Processor for 64-QAM 4×64 MU–MIMO Systems

“…We adopted a joint QR decomposition and constantthroughput Lenstra, Lenstra, and Lovasz (CTLLL) algorithm [15], [24] to realize ( 20) and ( 22) together for parallel processing as shown in Algorithm 3. In the first part, the Givens rotation-based QR decomposition and the size reduction of the LLL algorithm were combined in a column-wise iteration loop.…”

“…the same joint QR decomposition and lattice reduction algorithm as [24], the processed matrix dimension (68 × 64) of this work is much larger than that in the 8 × 8 MIMO detector. The major circuit design consideration will be discussed in the following section.…”

“…In the preprocessing part, we used three dual-port SRAMs for the storage of R (or H), Q , and T matrices; we designed the GR block, condition check block, and size reduction block to perform the joint QR decomposition and E-CTLLL algorithm in Algorithm 3. The Gram-Schmidt (GS) [25] and GR algorithms [24] are two primary schemes to perform QR decomposition in the literature, but the GS requires a large number of division operations, which cause the numeric instability and significantly increase signal word-lengths and hardware cost. The GR-based scheme primarily consists of numerically stable vector rotation operations, which can also be shared with the size reduction operations for lattice reduction.…”

“…The designed joint QR decomposition and LR preprocessor was designed based on the algorithm in [24] but the processed channel matrix dimension (68 × 64) was much larger than that (8 × 8) in [24], in which data register files of Q, R, and T could be used for the parallel row-wise LR processing. However, when matrix dimension increases up to 64, the storage of Q, R, and T should be implemented with SRAMs for hardware efficiency.…”