SNR Adaptive Limited Constellation Sphere Decoding

Abstract

Sphere Decoding algorithm has been shown to achieve near Maximum Likelihood (ML) performance with low complexity for MIMO communication systems, but still has higher complexity than other suboptimum detectors. Especially at low SNR, the complexity of sphere decoding algorithm gets much higher. In this paper, sphere decoding algorithms combined with other suboptimum detectors are proposed. Pre-estimated vectors by suboptimum detectors such as MMSE V-BLAST are used to assist sphere decoding algorithm. The number of search points in the tree search lattice area can be restricted, and the complexity can be reduced significantly. The number of limited constellation points can be changed by considering the trade-off between bit-error-rate (BER) performance and complexity. If we adjust the number of limited points according to SNR, we can achieve the BER performance close to that of an optimal sphere decoding algorithm, and lower complexity than the Schnorr- Euchner algorithm. I. INTRODUCTION Many detectors which are used for MIMO communication system have been investigated in the literature. Among them, maximum likelihood (ML) decoder has good performance but it is not practical since its complexity increases exponentially with the number of transmitted symbols and the size of mod- ulation constellation. Suboptimum detectors like zero forcing (ZF),minimum mean square error (MMSE), MMSE V-BLAST can be implemented easily because of the low complexity but their bit-error-rate (BER) performance is not optimal. Sphere decoding algorithm can have the BER performance of ML decoder with moderate complexity. However the complexity of a sphere decoder is still much higher than other suboptimum detectors, so we may still have difficulty implementing a sphere decoder. The complexity of sphere decoding is depen- dent on the choice of the initial radius, because it determines the number of vectors inside the hypersphere. The complexity is dependent on the constellation size. The tree search order is related to the complexity if the algorithm updates a radius like Schnorr-Euchner algorithm. SNR affects the complexity especially at low SNR because low SNR enlarges hypersphere size to be searched over. Many sphere decoding algorithms are proposed to address the above issues. The Fincke-Pohst algorithm uses a fixed and small initial radius but decoding can be a failure if there is no lattice vector in the hypersphere (1). The Schnorr- Euchner algorithm updates the radius adaptively with little BER degradation, and reduce the complexity (2). In order to use small initial radius without decoding failure, some sphere decoding algorithms use other suboptimum detectors (3). The K-best algorithm restricts the number of child nodes at each dimension so its BER performance is not optimal (4). This paper proposes a modified sphere decoding algorithm to reduce the complexity and to maintain the BER performance (close to that of an ML detector) using predetection of other suboptimum detectors. A suboptimum detector solution such as MMSE V-BLAST is first calculated, we can use that solution to determine the initial radius and the tree traversal order. The number of lattice vectors to be searched over is restricted to the neighborhood of the solution to decrease the complexity. We will also adjust the number of lattice vectors according to SNR. This paper is organized as follows. We provide an overview of the existing sphere decoding algorithms, and the compu- tational complexity in Section II. Section III proposes the limited constellation sphere decoding algorithm using pre- estimated vector by suboptimum detectors. SNR adaptive limited constellation sphere decoding algorithm is proposed in Section IV. Performance and complexity comparisons with other sphere decoding algorithms are simulated in Section V. Finally, we conclude the paper in Section VI.