CARRIER PHASE TRACKING AT LOW SIGNAL-TO-NOISE RATIO: A PERFORMANCE COMPARISON OF A PARITY-CODE-AIDED AND A PILOT- SYMBOL-ASSISTED APPROACH Nele Noels (1) , Mathieu Dervin (2) , Marc Moeneclaey (1) and Marie-Laure Boucheret (3) 1 TELIN Department, Ghent University, St-Pietersnieuwstraat 41 B-9000 GENT, BELGIUM {nnoels, mm} @telin.UGent.be 2 DRT Department, Alcatel Alenia Space, 26 av. J.F. Champollion, BP 1187 F-31037 Toulouse, FRANCE Mathieu.Dervin@support-externe.alcatelaleniaspace.com 3 IRIT-ENSEEIHT-TéSA, 2 rue Charles Camichel, BP 7122 F-31071 Toulouse Cedex 7, FRANCE marie-laure.boucheret@enseeiht.fr INTRODUCTION The last decade has seen the development of powerful channel codes such as turbo codes and low-density parity-check (LDPC) codes. The impressive bit error rate (BER) performance of the associated decoding processes implicitly assumes coherent detection, meaning that the carrier phase must be recovered accurately before the data is decoded. However, since the receiver usually operates at extremely low signal-to-noise ratio (SNR) values, conventional carrier synchronizers often fail to provide sufficiently accurate phase estimates. Numerous efforts to improve the carrier synchronization at low SNR have resulted in a myriad of different transceiver schemes; all based on the exploitation of some form of a priori information regarding the conveyed data during the phase estimation process. The resulting synchronization algorithms may be distinguished into two categories: category-I and category-II. Category-I algorithms take advantage of the structure that the channel code enforces upon the data stream, and which can be considered as a kind of a priori information that is available at the receiver. Assuming that the carrier phase (after possible frequency correction) is essentially constant over a codeword, synchronizers that accept soft information from the channel decoder have been presented [1,2], which yield a mean square estimation error (MSEE) that is close to the Cramer-Rao lower bound at the normal operating SNR of the code. However, in the presence of phase variations due to phase noise, the carrier phase estimate must be updated at regular intervals during the codeword; when the channel decoder needs a long observation interval before decoding can start (as is the case with turbo codes and LDPC codes), obtaining soft information to aid the synchronizer is rather cumbersome. A practical solution to this problem was proposed in [3] for a classical turbo code: the synchronizer based on soft information from only one of the concatenated convolutional decoders (operating on a reduced number of observations) has shown to yield satisfactory performance. However, as the approach from [3] cannot be extended to more general codes (such as LDPC codes), researchers have investigated a second category of algorithms. Category-II algorithms completely ignore the underlying channel code, and use only additional redundancy that is introduced into the transmission scheme for the sake of synchronization. This approach permits to control the complexity and the update period of the synchronizer, but brings about a reduction in the power and bandwidth efficiency of the overall system. In this paper we present a general formulation for maximum likelihood (ML) based feedback phase synchronizers. The category-I feedback phase synchronizer considered in [2,3] and the category-II feedback phase synchronizers considered in [2,4] can be derived as special cases of the proposed general approach. This gives new insights into the relation between the different strategies. A comparison of two category-II feedback phase synchronizers, causing the same reduction of power and bandwidth efficiency, is then considered. The first scheme [4] adds a short single-parity- check (SPC) code to aid synchronization; the second scheme [2] is based on the insertion of known pilot bits. Both schemes have recently been developed to track a time-varying carrier phase at very low SNR. In order to test the algorithms in realistic conditions, we base our study on the transmission system defined by the recently published DVB-S2 standard [5]. The feedback synchronizer is a second-order phase-locked loop (PLL) with damping factor equal to 0.707. We evaluate the synchronizer performance in the case of a constant carrier phase and in the presence of phase