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Design and implementation of variable radius sphere decoding

TL;DR: A Variable Radius Sphere Decoding (VR-SD) algorithm based on ZF algorithm is proposed in order to simplify the complex searching steps and the advantages of this algorithm are proved by analyzing from the derivation of mathematical formulas and the simulation of the BER performance between SD and VR-SD algorithm.
Abstract: Sphere Decoding (SD) algorithm is an implement decoding algorithm based on Zero Forcing (ZF) algorithm in the real number field. The classical SD algorithm is famous for its outstanding Bit Error Rate (BER) performance and decoding strategy. The algorithm gets its maximum likelihood solution by recursive shrinking the searching radius gradually. However, it is too complicated to use the method of shrinking the searching radius in ground communication system. This paper proposed a Variable Radius Sphere Decoding (VR-SD) algorithm based on ZF algorithm in order to simplify the complex searching steps. We prove the advantages of VR-SD algorithm by analyzing from the derivation of mathematical formulas and the simulation of the BER performance between SD and VR-SD algorithm.
References
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Journal ArticleDOI
TL;DR: A modification of the Fincke-Pohst (sphere decoding) algorithm to estimate the maximum a posteriori probability of the received symbol sequence is proposed and, over a wide range of rates and signal-to-noise ratios, has polynomial-time complexity.
Abstract: In recent years, soft iterative decoding techniques have been shown to greatly improve the bit error rate performance of various communication systems. For multiantenna systems employing space-time codes, however, it is not clear what is the best way to obtain the soft information required of the iterative scheme with low complexity. In this paper, we propose a modification of the Fincke-Pohst (sphere decoding) algorithm to estimate the maximum a posteriori probability of the received symbol sequence. The new algorithm solves a nonlinear integer least squares problem and, over a wide range of rates and signal-to-noise ratios, has polynomial-time complexity. Performance of the algorithm, combined with convolutional, turbo, and low-density parity check codes, is demonstrated on several multiantenna channels. The results for systems that employ space-time modulation schemes seem to indicate that the best performing schemes are those that support the highest mutual information between the transmitted and received signals, rather than the best diversity gain.

298 citations

Journal ArticleDOI
TL;DR: The resulting technique is referred to as multiple-symbol differential sphere decoding (MSDSD) by applying sphere decoding to ML-MSDD for time-varying Rayleigh fading channels.
Abstract: In multiple-symbol differential detection (MSDD) for power-efficient transmission over Rayleigh fading channels without channel state information, blocks of N received symbols are jointly processed to decide on N-1 data symbols. The search space for the maximum-likelihood (ML) estimate is therefore (complex) (N-1)-dimensional, and maximum-likelihood MSDD (ML-MSDD) quickly becomes computationally intractable as N grows. Mackenthun's low-complexity MSDD algorithm finds the ML estimate only for Rayleigh fading channels that are time-invariant over an N symbol period. For the general time-varying fading case, however, low-complexity ML-MSDD is an unsolved problem. In this letter, we solve this problem by applying sphere decoding (SD) to ML-MSDD for time-varying Rayleigh fading channels. The resulting technique is referred to as multiple-symbol differential sphere decoding (MSDSD).

110 citations

Journal ArticleDOI
TL;DR: A tight bound on the performance of maximum likelihood decoding of linear codes on q-ary symmetric channels is derived and this result is used to bound theperformance of q-ARY hard decision sphere decoders.
Abstract: A sphere decoder searches for the closest lattice point within a certain search radius. The search radius provides a tradeoff between performance and complexity. We focus on analyzing the performance of sphere decoding of linear block codes. We analyze the performance of soft-decision sphere decoding on AWGN channels and a variety of modulation schemes. A hard-decision sphere decoder is a bounded distance decoder with the corresponding decoding radius. We analyze the performance of hard-decision sphere decoding on binary and q-ary symmetric channels. An upper bound on the performance of maximum-likelihood decoding of linear codes defined over Fq (e.g. Reed- Solomon codes) and transmitted over q-ary symmetric channels is derived and used in the analysis.We then discuss sphere decoding of general block codes or lattices with arbitrary modulation schemes. The tradeoff between the performance and complexity of a sphere decoder is then discussed.

30 citations

Proceedings ArticleDOI
20 May 2014
TL;DR: A hybrid sphere decoding algorithm which contains the desired features of both DF SD and k-best sphere decoding is proposed in this paper and is able to reduce the computational complexity of sphere decoding remarkably.
Abstract: One effective way to reduce the complexity of receiver is the utilization of sphere decoding algorithm. Sphere decoding algorithms, particularly sphere decoding algorithms which search in the depth first known as depth first sphere decoding algorithm (DF SDA), have a similar performance to maximum likelihood with almost an acceptable complexity. However, depth first sphere decoding algorithm has a variable complexity. K-best sphere decoding algorithms have a fixed bitrate and complexity but their performances degrade compared to maximum likelihood detector (MLD). Therefore, we proposed a hybrid sphere decoding algorithm which contains the desired features of both DF SD and k-best sphere decoding in this paper. In order to reduce the complexity of DF SD, we proposed the utilization of the initial radius setting and radius updating strategy. Using this approach, we are able to reduce the computational complexity of sphere decoding remarkably. Simulation results confirm that the performance of our proposed method is at least equal to the performance of k-best sphere decoding algorithm but with a lower computational complexity.

7 citations

Proceedings ArticleDOI
23 May 2012
TL;DR: With the result of simulation, it shows that the novel algorithm not only keep the same performance as the traditional sphere decode algorithm, but also can efficiently decrease the calculation complexity of the sphere decoding algorithm.
Abstract: Among all of the signal detection algorithms in multiple-input multiple-output systems, the performance of sphere decoding algorithm is most closely to the performance of maximum-likelihood algorithm. But the calculation complexity of the sphere decoding algorithm is still very large. To solve this problem, we use the sorting algorithm in sphere decoding algorithm. To apply the sorting algorithm which comes from sorted QR decomposition algorithm to the sphere decoding algorithm, we can obtain the ordered sphere decoding detection algorithm. With the result of simulation, it shows that the novel algorithm not only keep the same performance as the traditional sphere decoding algorithm, but also can efficiently decrease the calculation complexity of the sphere decoding algorithm.

6 citations