IMPROVING THE DECODING OF M-SEQUENCES BY EXPLOITING THEIR DECIMATION PROPERTY Mathieu des Noes and Valentin Savin CEA, LETI, Minatec campusB 38054 Grenoble cedex9, France Email: mathieu.desnoes@cea.fr Laurent Ros and Jean Marc Brossier GIPSA-Lab BP46, 38402 Saint-Martin d’H` eres, France ABSTRACT M-sequences are widely used in communications and posi- tioning systems for synchronization purposes. In these sys- tems, the receiver does not know which sequence is used by the transmitter, this needs to be detected. This paper estab- lishes first a link between the conventional detection theory and the recently developed detection technique relying on it- erative message-passing algorithm. Then, a novel decoding strategy is proposed. It exploits the decimation property of m- sequences to improve significantly the detection performance compared to the existing decoding strategy. Index Terms— m-sequence, decoding, belief-propagation 1. INTRODUCTION A maximal length sequence (M-sequence) is a binary se- quence with excellent auto-correlation properties [1]. Hence, they are widely used for synchronization purpose in wire- less communications and positioning systems. They are for instance used for the cell search procedure in the WCDMA system or for the acquisition of GPS’s satellites [2][3]. The conventional method to synchronize with a m-sequence is to correlate the received signal with a replica of the searched m-sequence [4]. If a correlation peak is observed and is above a given threshold, the synchronization is declared. This cor- relation can be implemented either with a standard FIR filter whose coefficients are equal to the chips of the sequence, or with a FFT [5]. An alternative method consists in performing synchroniza- tion through a decoding of the received sequence. In fact, a m-sequence generator can be regarded as a linear code gener- ator. It is thus possible to detect a transmitted sequence with a suitable decoder. This solution was originally proposed in cryptography for fast correlation attacks on stream ciphers [6][7]. This has been applied more recently in wireless com- munications and localization [8][9]. Exploiting the unique properties of m-sequence, an iterative message-passing al- gorithm can be implemented to decode the received signal [10]. The main drawback of this decoding procedure is its sensitivity to the weight of the generator polynomial of the m-sequence. The weight is given by the number of non zero coefficients of the polynomial. In this paper, the link between conventional detection theory and sequence decoding is first established. Then, a novel de- coding strategy is proposed. It exploits the decimation prop- erty of m-sequences to decode any m-sequence of polynomial degree r, with the generator polynomial of the m-sequence having the smallest weight. This ensures to improve the de- coding performances. The paper is organized as follows. Section 2 establishes the relationship between the Generalized Likelihood Ratio Test technique (GLRT) and iterative decoding for the detection of m-sequences. Section 3 describes the main properties of m-sequences that will be exploited in this paper. Section 4 details the conventional message-passing algorithm used for decoding m-sequence. Section 5 presents the novel algorithm exploiting the decimation property of m-sequences. Section 6 presents simulation results and Section 7 concludes this paper. Notation: a sequence will be written in uppercase letters in its anti-modal representation (S(k) ∈ {−1, +1}) and in low- ercase in its binary representation (s(k) ∈{0, 1}). ‖S‖ 2 is the Euclidian norm of vector S. 2. RELATIONSHIP BETWEEN GLRT AND DECODING Many synchronization problems involving m-sequences can be modeled as a binary hypothesis testing problem [11]. At each sampling time, the receiver wants to decide for one of the 2 hypothesis : H 1 : Y = S + n H 0 : Y = n (1) When the receiver is synchronized, hypothesis H 1 is the cor- recte one, while H 0 is valid otherwise. However, the receiver can be synchronized with the transmitted sequence but with- out knowing which sequence was sent. This happens for in- stance in the cell search of UMTS and CDMA200 systems or for the acquisition of C/A code in the GPS system. The re- EUSIPCO 2013 1569743715 1