A hkz reduction method and system for complex number fields
A complex number field and reduction technology, applied in the field of HKZ reduction method and system in the complex number field, can solve the problems of high uncertainty, increased complexity, and large amount of calculation in LLL reduction in the complex number field, so as to save the amount of calculation and save Iterative, low-complexity effects
Active Publication Date: 2019-04-05
HARBIN INST OF TECH SHENZHEN GRADUATE SCHOOL
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[0039] Defects of the HKZ reduction algorithm in the real number domain: Since the HKZ reduction algorithm in the real number domain cannot directly work in the complex number domain, if you need to apply the HKZ reduction algorithm in the real number domain to a MIMO wireless communication system, you must convert the complex baseband expression of the system becomes the equivalent real number expression
Since the construction of the HKZ reduction basis is carried out iteratively, the main problem brought about by this conversion is to convert the originally required N t Iterations increased to 2N t times, it brings a lot of extra computation and greatly increases the complexity
[0044] Defects of the HKZ reduction algorithm in the complex field: the main defect of the existing HKZ reduction algorithm in the complex field is that it adopts the method of LLL reduction in the complex field for the linearly independent vector group to expand the searched vector into a new basis
Although this method can achieve the purpose of building a new base, it requires a relatively large amount of calculation, and the complexity of LLL reduction in the complex field also has high uncertainty
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[0078] The present invention discloses a HKZ reduction method working in the field of complex numbers. The main contents of the present invention include three aspects: first, we give a lemma for complex number lattices and prove it; then according to the proof of this lemma, we give An algorithm for constructing unimodal matrices in the complex field is proposed, and it is named as the sub-algorithm UNIH; finally, a HKZ reduction algorithm that directly works on the complex field and has lower complexity than the existing algorithms is constructed, and it is named the algorithm CHKZ.
[0079] 1. Lemma and proof
[0080] Lemma: For an m-dimensional complex lattice a lattice vector of it The necessary and sufficient condition for expanding into a new base is: gcd(z 1 ,...,z m )=1. For a Gaussian integer z 1 ,...,z m , gcd(z 1 ,...,z m ) represents their greatest common divisor, that is, their greatest common divisor with a positive real part (ie the one with the large...
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The invention provides a complex number field HKZ reduction method and a complex number field HKZ reduction system. The beneficial effects are as follows: there is no need to convert a baseband system model of a complex number into an equivalent real number system model when the method and the system are applied to a MIMO wireless communication system; compared with the existing real number field HKZ reduction method, the method of the invention can save half of iteration and save a large amount of computation; and compared with the only existing complex number field HKZ reduction method, the method of the invention is lower in complexity and has greater robustness by constructing a complex number field single-mode matrix to extend a lattice vector into a new base.
Description
technical field [0001] The present invention relates to the technical field of communication, in particular to a HKZ protocol method and system for a complex number field. Background technique [0002] Lattice theory is a classic research field in geometric number theory, and lattice-based reduction is an important problem in lattice theory. A lattice reduction criterion proposed by Hermite, Korkine and Zolotareff, namely the Hermite-Korkine-Zolotareff (HKZ) criterion, is a well-recognized reduction criterion with better performance. In recent years, lattice theory has been applied more and more in Multiple-Input Multiple-Output (MIMO) wireless communication systems. The application of the HKZ protocol in MIMO systems includes: improving the receiving performance of traditional low-complexity linear and nonlinear receivers, including zero-forcing (ZF) linear receivers, zero-forcing continuous interference cancellation receivers, minimum average Square error (minimum mean s...
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IPC IPC(8): H04L25/03
Inventor 汪洋丁丽琴张继良
Owner HARBIN INST OF TECH SHENZHEN GRADUATE SCHOOL