Kasami Sequence Generation for LTE Secondary Synchronization
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Solution Overview
Problem
The 3GPP LTE system faces challenges in generating a sufficient number of secondary synchronization signal sequences to distinguish between 504 base stations, as existing sequences with lengths equal to or shorter than 72 do not meet the required 168 or more sequences needed for reliable performance, leading to performance degradation due to increased overhead and collisions.
Innovation Solution
A method and apparatus for generating sequences using Kasami sequences, which involve determining sequences from an mth order primitive polynomial, cyclically shifting and performing modulo 2 arithmetic on these sequences to produce a fourth sequence, thereby increasing the number of sequences while maintaining cross-correlation characteristics similar to conventional sequences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If conventional sequences (GCL, Zadoff-Chu, Hadamard, m-sequence) with length ≤72 are used for secondary synchronization signal, then the sequence length fits within the 72 sub-carrier limit, but the number of sequences is limited to ≤72 which is insufficient for discriminating 168 cell groups
Solution Approach 1:
The patent divides the sequence generation into two independent components: a base sequence of length 72 and a shift value. By segmenting the sequence identification into (base_sequence_index, shift_value) pairs, the system generates 168 sequences from a single base sequence, overcoming the limitation of having only 72 sequences available.
Solution Approach 2:
The patent changes the parameter space by introducing cyclic shift values as an additional degree of freedom. Instead of relying solely on different base sequences, the system varies the cyclic shift parameter to generate diverse sequences, effectively increasing the number of available sequences from 72 to 168 while maintaining the same base sequence length.
2Quantity of substance
If the number of sequences is increased to 168 or more for secondary synchronization signal, then sufficient sequences are available for cell group discrimination, but the cross-correlation performance between sequences deteriorates
Solution Approach 1:
The patent applies local quality by ensuring that each cyclically shifted version of the base sequence maintains the optimal auto-correlation and cross-correlation properties of the original sequence. The local structure (base sequence) is preserved while only the position (cyclic shift) is changed, thereby maintaining reliability across all 168 sequences.
Solution Approach 2:
The patent creates a composite sequence structure by combining a base sequence with cyclic shift operations. This composite approach generates 168 distinct sequences from one base sequence, achieving both the quantity requirement (168 sequences) and the quality requirement (maintained cross-correlation performance) simultaneously.
3Quantity of substance
If multiple different base sequences are used to generate 168 sequences, then the number of sequences increases, but the system complexity and overhead increase exponentially
Solution Approach 1:
The patent makes a single base sequence universal by using it to generate all 168 sequences through cyclic shifts. This multi-functional approach eliminates the need to store and manage multiple different base sequences, reducing system overhead and complexity while still providing sufficient sequence diversity for cell group discrimination.
Solution Approach 2:
Instead of generating multiple base sequences and selecting among them, the patent inverts the approach by generating multiple sequences from a single base sequence through cyclic shifts. This inversion simplifies the system by reducing the number of base sequences from 168 to 1, thereby reducing overhead and complexity.
Data Source
AI summary
Disclosed is a method for generating a sequence and an apparatus for the same which can satisfy the number M′ of sequences sufficiently larger than a length N of a sequence required in a wireless communication system. When the generation of a sequence of the wireless communication system is intended, a first sequence is generated from an mth order primitive polynomial determined according to the length of a required sequence. Then, a second sequence and a third sequence are generated from the first sequence, and a remainder and a quotient is obtained by dividing a particular reference parameter by a number equal to or smaller than 2m+1. Next, a fourth sequence having a desired length N is generated by using the remainder and the quotient. Therefore, it is possible to generate sequences satisfying that the number M′ of sequences is sufficiently larger than a length N of the sequence.