Area-Efficient Universal Code Generator for GPS L1C and BDS B1C Signals

Recently, multi-frequency multi-constellation receivers have been actively studied, which are single receivers that process multiple global navigation satellite system (GNSS) signals for high accuracy and reliability. However, in order for a single receiver to process multiple GNSS signals, it requires as many code generators as the number of supported GNSS signals, and this is one of the problems that must be solved in implementing an efficient multi-frequency multi-constellation receiver. This paper proposes an area-efficient universal code generator that can support both GPS L1C signals and BDS B1C signals. The proposed architecture alleviates the area problem by sharing common hardware in a time-multiplex mode without degrading the overall system performance. According to the result of the synthesis using the CMOS 65 nm process, the proposed universal code generator has an area reduced by 98%, 93%, and 60% compared to the previous memory-based universal code generator (MB UCG), the Legendre-generation universal code generator (LG UCG), and the Weil-generation universal code generator (WG UCG), respectively. Furthermore, the proposed generator is applicable to all Legendre sequence-based codes.

On the k-Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields

Let Fq be the finite field with q=pr elements, where p is an odd prime. For the ordered elements ξ0,ξ1,…,ξq-1∈Fq, the binary sequence σ=(σ0,σ1,…,σq-1) with period q is defined over the finite field F2={0,1} as follows: σn=0, if n=0, (1-χ(ξn))/2, if 1≤n<q, σn+q=σn, where χ is the quadratic character of Fq. Obviously, σ is the Legendre sequence if r=1. In this paper, our first contribution is to prove a lower bound on the linear complexity of σ for r≥2, which improves some results of Meidl and Winterhof. Our second contribution is to study the distribution of the k-error linear complexity of σ for r=2. Unfortunately, the method presented in this paper seems not suitable for the case r>2 and we leave it open.