On the sphere-decoding algorithm II. Generalizations, second-order statistics, and applications to communications

Abstract

Abstract-In Part I, we found a closed-form expression for the expected complexity of the sphere-decoding algorithm, both for the infinite and finite lattice. We continue the discussion in this paper by generalizing the results to the complex version of the problem and using the expected complexity expressions to determine situations where sphere decoding is practically feasible. In particular, we consider applications of sphere decoding to detection in multiantenna systems. We show that, for a wide range of signal-to-noise ratios (SNRs), rates, and numbers of antennas, the expected complexity is polynomial, in fact, often roughly cubic. Since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial, this suggests that maximum-likelihood decoding, which was hitherto thought to be computationally intractable, can, in fact, be implemented in real-time-a result with many practical implications. To provide complexity information beyond the mean, we derive a closed-form expression for the variance of the complexity of sphere-decoding algorithm in a finite lattice. Furthermore, we consider the expected complexity of sphere decoding for channels with memory, where the lattice-generating matrix has a special Toeplitz structure. Results indicate that the expected complexity in this case is, too, polynomial over a wide range of SNRs, rates, data blocks, and channel impulse response lengths.

Capacity Maximizing ICI Canceling Windows for OFDM in Time-Varying Channels

“…At the receiver, s(u) in (5) can be detected using techniques such as the maximum likehood (ML) [8] and V-BLAST detectors [9]. Due to the fact that the complexity of MIMO detectors mainly depends on the number of simultaneously transmitted symbols, t is chosen to be a small number.…”

“…Due to the fact that the complexity of MIMO detectors mainly depends on the number of simultaneously transmitted symbols, t is chosen to be a small number. When t ≤ 4, an ML detector based on the sphere decoding algorithm has practical complexity [8]. Throughout this paper, the diagonal blocks {H(u, u)} is assumed to be perfectly known at the receiver, 2 while it is unknown at the transmitter.…”

Sphere-constrained ML detection for frequency-selective channels

“…It also allows for implementation of computationally more efficient versions of sphere constrained search, such as the Schnorr-Euchner (see [4], [5], and the references therein).…”

“…The derivation takes the approach originally proposed in [4] and [5], where it was used to find the expected complexity of the original SD algorithm of Fincke and Pohst [2]. Clearly, the expected complexity of the combined VA/SD is proportional to the expected number of the states that survive the pruning process # of states that survive in the state set # of flops per state…”

“…The sphere decoding (SD) algorithm [2] can also be used for detection on channels with memory [3], [4]. Permitting a guard interval, the SD algorithm provides ML performance.…”