On Efficient and Low-Complexity Decoding of Binary LDPC-Coded CSK Signals for GNSS Links with Increased Data Rates

Abstract

GNSS with high data rate links are of interest to accommodate new needs and applications (e.g. precise positioning, authentication, reduction of TTFFD). In this context, a binary LDPC-coded CSK signal is an attractive candidate to increase data rates with a high data recovery robustness. However, such a proposal requires an increase of receiver's computational complexity with respect to receivers for current coded DSSS/BPSK GNSS links. The computational complexity required for data recovery is analysed in this article and insights on crucial technical choices are given for the reception of binary LDPC-coded CSK signals. CSK demodulation is shown to dominate the overall computational cost and the use of digital chip-matched filtering prior to demodulation is proposed to reduce this cost. In addition, iterative demapping, which is crucial to optimize the power efficiency of binary LDPC-coded CSK links is also shown to have high computational complexity. Therefore, low-complexity iterative demapping strategies are studied and simple yet efficient solutions are proposed.

Potential candidates for new SBAS signals

“…In the case of a BPSK modulation, the correlation is made with the signal fundamental PRN code and in the case of a CSK modulation, the correlation is made with all the shifted versions of the fundamental PRN code which represent a symbol (CSK symbols). In the CSK case, this correlation can be made in the time domain, bank of correlators, or in the frequency domain, FFT/IFFT block [6] [7].…”

“…However, for a non-binary modulation such as CSK, the demapping can have significant complexity. There are several demapping algorithms which can be used: Maximum a-Posteriori (MAP), MAP using *(•) and Look-Up Table (log-MAP-LUT), and the Max-log-MAP [7]. For clarification, note that *(•) is an operator defined as *(x1;x2) = max(x1;x2) + ln(1+exp(-|x1-x2|)).…”

“…4, and will also be analyzed in this work. For a more detailed explanation of the BICM-ID data recovery block, the reader is referred to [6] [7]. Note that since the LDPC decoding algorithm is iterative by definition, any moment this paper is going to refer to iterative decoding, it is going to refer to the iterative process between the demapper and the decoder (BICM-ID) and the iterations will be denoted as .…”

“…Nevertheless, note that the decoder can also iterate inside itself (between variable and check nodes); this means that for each iteration between the demapper and the decoder, the decoder can run is always equal to 1 and thus the total number of decoder internal iterations, , is always equal to the number of demapper iterations, . A more detailed explanation of the generic structure of the data recovery block can be found in [7].…”

“…This analysis consists in determining the number of real additions and multiplication required by the data recovery block. The mathematical formulas used to calculate these numbers can be found in [7]. In any case, the numbers presented in this section should only be used for relative comparison purposes.…”