MultiSphere: Massively Parallel Tree Search for Large Sphere Decoders

Abstract

Abstract-This work introduces MultiSphere, a method to massively parallelize the tree search of large sphere decoders in a nearly-independent manner, without compromising their maximum-likelihood performance, and by keeping the overall processing complexity at the levels of highly-optimized sequential sphere decoders. MultiSphere employs a novel sphere decoder tree partitioning which can adjust to the transmission channel with a small latency overhead. It also utilizes a new method to distribute nodes to parallel sphere decoders and a new tree traversal and enumeration strategy which minimize redundant computations despite the nearly-independent parallel processing of the subtrees. For an 8 × 8 MIMO spatially multiplexed system with 16-QAM modulation and 32 processing elements MultiSphere can achieve a latency reduction of more than an order of magnitude, approaching the processing latency of linear detection methods, while its overall complexity can be even smaller than the complexity of well-known sequential sphere decoders. For 8×8 MIMO systems, MultiSphere's sphere decoder tree partitioning method can achieve the processing latency of other partitioning schemes by using half of the processing elements. In addition, it is shown that for a multi-carrier system with 64 subcarriers, when performing sequential detection across subcarriers and using MultiSphere with 8 processing elements to parallelize detection, a smaller processing latency is achieved than when parallelizing the detection process by using a single processing element per subcarrier (64 in total).

Massively Parallel Tree Search for High-Dimensional Sphere Decoders

“…x or zz y , the d min values are sorted in an ascending order of their corresponding coordinates. We note that despite the fact that there are four possible squares where y l can lie, all d min values, predefined orders and corresponding zigzag coordinates exploit constellation symmetry, significantly reducing the architectural overhead compared to the preordering initially proposed in [1]. We note that this approximate ordering does not affect optimality since the union of all constructed sub-trees still forms the original SD tree.…”

“…is the non-negative cost assigned to each branch. The ML problem translates then into finding the leaf-node with the minimum d(s (1) ). In depth-first SDs with radius update and Schnorr-Euchner enumeration [5], [8], the initial squared radius r 2 = 1.…”

“…In depth-first SDs with radius update and Schnorr-Euchner enumeration [5], [8], the initial squared radius r 2 = 1. Any time a leaf node is reached for which d(s (1) ) < r 2 , r 2 is updated to d(s (1) ). Upon meeting a node s (l) , if d(s (l) ) r 2 then this node, its children nodes and its siblings with all their descendants are excluded from the tree search (i.e., they are pruned).…”

“…If the l th element of m equals k, then, for the corresponding path, its node at level l is the k th closest node to the received e y l . If, for example, m = [1,2,3] T the path consists of the node with the third smallest PD at the highest level of the tree (i.e., m(3) = 3), its child with the second smallest PD at the second level of the tree, and its child with the smallest PD at the lowest level of the SD tree.…”

“…s is an improved yet less complex version, of the heuristic MoP proposed in our original work in [1]. Since the MoPs are not a function of the actual received signal they can be pre-calculated before data detection (i.e., before sphere decoding).…”