Geosphere: An Exact Depth-First Sphere Decoder Architecture Scalable to Very Dense Constellations

Abstract

This paper presents the algorithmic design, experimental evaluation, and very large scale of integration (VLSI) implementation of Geosphere, a depth-first sphere decoder able to provide the exact maximum-likelihood solution in dense (e.g., 64) and very dense (e.g., 256, 1024) quadrature amplitude modulation (QAM) constellations by means of a geometrically inspired enumeration. In general, linear detection methods can be highly effective when the multiple input, multiple output (MIMO) channel is well-conditioned. However, this is not the case when the size of the MIMO system increases and the number of transmit antennas approaches the number of the receive antennas. Via our wireless open access research platform (WARP) testbed implementation, we gather indoor channel traces in order to evaluate the performance gains of sphere detection against zero-forcing and minimum mean-square errors (MMSE) in an actual indoor environment. We show that Geosphere can nearly linearly scale performance with the number of user antennas; in $4\times 4$ multi-user MIMO for 256-QAM modulation at 30-dB SNR, there is a $1.7\times $ gain over MMSE and $2.4\times $ over zero-forcing and a 14% and 22% respective gain in $2\times 2$ systems. In addition, by using a new node labeling-based enumeration technique, low-complexity integer arithmetic, and fine-grained clock gating, we implement for up to 1024-QAM constellations and compare in terms of area, delay, power characteristics, the Geosphere VLSI architecture, and the best-known best-scalable exact ML sphere decoder. Results show that Geosphere is twice as area-efficient and 70% more energy efficient in 1024-QAM. Even for 16-QAM, Geosphere is 13% more area-efficient than the best-known implementation for 16-QAM, and it is at least 80% more area-efficient than the state-of-the-art $K$ -best detectors for 64-QAM.