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

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 expression...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 53; no. 8; pp. 2819 - 2834
Main Authors: Vikalo, H., Hassibi, B.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.2005
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Channels
Closed-form solution
Coding, codes
Complexity
Decoding
Exact sciences and technology
Exact solutions
Expected complexity
Frequency
frequency-selective channels
Impulse response
Information, signal and communications theory
Lattices
Mathematical analysis
Maximum likelihood decoding
Maximum likelihood detection
multiple-antenna systems
polynomial-time complexity
Polynomials
Signal and communications theory
Signal processing algorithms
Signal to noise ratio
sphere decoding
Statistics
Studies
Telecommunications and information theory
Wireless communication
wireless communications
Channel with memory
wireless communications
Second order
Wireless telecommunication
Information rate
Implementation
Noise level
sphere decoding
Frequency selection
Pulse response
Algorithm complexity
polynomial-time complexity
Antenna array
Fading channels
frequency-selective channels
multiple-antenna systems
Order statistic
Algorithm
Information transmission
Maximum likelihood decoding
Polynomial time
Statistical method
Telecommunication system
Expected complexity
Time complexity
Signal to noise ratio
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2005.850350