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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| Veröffentlicht in: | IEEE transactions on signal processing Jg. 53; H. 8; S. 2819 - 2834 |
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IEEE
01.08.2005
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| 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. |
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| AbstractList | 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. 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. |
| Author | Vikalo, H. Hassibi, B. |
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| Cites_doi | 10.1002/bltj.2015 10.1109/ACSSC.2003.1291996 10.1109/18.771234 10.1109/18.651011 10.1109/78.726808 10.1109/18.333872 10.1109/TIT.2002.1013127 10.1007/BF01581144 10.1109/ISIT.2003.1228290 10.1109/TIT.2002.800499 10.1109/4234.846498 10.1007/978-1-4612-1872-2_12 |
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| Keywords | 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 |
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| Snippet | 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... Since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial, this suggests that maximum-likelihood... |
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| SubjectTerms | 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 |
| Title | On the sphere-decoding algorithm II. Generalizations, second-order statistics, and applications to communications |
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