Optimised Golay correlator

Abstract

Golay complementary sequences are widely used to detect digital signals immersed in noise. Previous works have dealt not only with the application of sequences but also with their generation and correlation. An optimised Golay correlator which significantly improves calculation efficiency is presented.Introduction: Golay sequences are a particular case of complementary sequences [1], defined as a pair of binary sequences of length L ¼ 2 N elements (where N is a natural number) termed a N [k] and b N [k], respectively. The particular property of these sequences is that the addition of their aperiodic autocorrelation functions is a Krönecker delta of amplitude 2L for t ¼ 0, and is null for t = 0. This can be expressed as follows:

Software and Hardware Solutions for Channel Estimation based on Cyclic Golay Sequences

“…The following algorithm is used for generating the corresponding Golay sequences with a length of N, where N is a power of 2 [2]:…”

“…The FGC [2] is the conventional solution to calculate the correlations with the sequences g A and g B . This correlator has the same description and structure as the generator in Fig.…”

“…The focus of the paper is the application of the complementary Golay sequences [1], [2] in digital transmission using complex baseband signals. Based on their advantageous correlation properties, powerful algorithms can be developed for the receivers to estimate and compensate imperfections [3], [4] or channel impulse response (CIR) [5].…”

Effects of quantization on Golay sequence based channel estimation

“…To estimate the CIR from the received complimentary Golay sequences, a special lattice filter, a Golay correlator can be be applied [4]. It calculates the correlation of the incoming signal with the ideal Golay sequences, and the sum of these correlations will result in the CIR [2], [5].…”

“…The following efficient algorithm can be used for generating the corresponding Golay sequences with a length of N , where N is a power of 2 [4]:…”