Performance Evaluation of Decision-Directed Carrier Synchronization for SC-FDE Schemes Pedro Pedrosa †1 , Rui Dinis †2 , Fernando Nunes ‡3 † ISR, ‡ IT - Instituto Superior Técnico, 1049-001 Lisboa, Portugal 1 ppedrosa@isr.ist.utl.pt 2 rdinis@isr.ist.utl.pt 3 nunes@lx.it.pt Abstract—In this paper we consider a decision-directed Carrier Frequency Offset (CFO) estimation technique employed in joint equalization and synchronization schemes for broadband wireless systems using Single Carrier (SC) modulations combined with Frequency Domain Equalization (FDE). We build a model for the estimates, explain the reason for their biased behavior and validate the theoretical results through simulations. The model applies to ideal Additive White Gaussian Noise (AWGN) channels. The use of the AWGN channel is justified because, although SC-FDE is usually applied to frequency selective fading channels, the signal at the output of the FDE presents no time dispersion effects. The performance analysis conducted on the CFO estimator suggests that the model describes conveniently the behavior of the system for the Signal-to-Noise Ratio (SNR) operating range. I. I NTRODUCTION Future wireless systems are planned to support ever in- creasing data rates. However, for such high transfer rates the channels dispersive characteristics tend to manifest. Block transmission techniques, with the appropriate cyclic exten- sions and employing Frequency Domain Equalization (FDE), proved to be adequate for high rate data transfer over highly time-dispersive channels without requiring complex receivers. Presently, two generally accepted solutions are Orthogonal Frequency Division Multiplexing (OFDM) and Single Car- rier Frequency-Domain Equalization (SC-FDE) transmission schemes, since they can cope with highly dispersive channels without requiring complex receiver structures [1], [2]. The implementation complexity for both schemes is similar: SC- FDE requires an Inverse Discrete Fourier Transform/Discrete Fourier Transform (IDFT/DFT) pair on the receiver; OFDM requires one IDFT operation at the transmitter and one DFT operation at the receiver. This difference in the transmit- ter/receiver implementation and the SC amplification advan- tage leads to a mixed solution [3], [4]: an OFDM scheme for the downlink, i.e., from the Base Station (BS) to the Mobile Terminal (MT) and a SC-FDE scheme to the uplink, i.e., from the MT to the BS. This way, the implementation cost becomes concentrated on the BS where increased power consumption and cost are not so critical. In [5] an Iterative Block Decision Feedback Equalization (IB-DFE) receiver structure was presented and later extended to diversity scenarios in [6]. The IB-DFE receivers can be regarded as iterative DFE receivers with the feedforward and This work was supported by the FCT plurianual funding and project U- BOAT PTDC/EEA-TEL/67066/2006 feedback operations implemented in the frequency domain. Since the feedback loop takes into account not just the hard decisions for each block, but also the overall block reliability, it is expected to have little error propagation. Consequently, the IB-DFE techniques seem to offer much better performance than the non-iterative methods [5], [6]. These IB-DFE tech- niques can be regarded as low complexity turbo equalization schemes [7]. Associated with multipath channels is the occurrence of Inter-Symbol Interference (ISI). In order to prevent this, a guard interval is added to the block by extending the signal with a cyclic prefix. The guard interval has to be larger than the overall Channel Impulse Response (CIR) and, in order to maintain bandwidth efficiency, it is expected to be a small fraction of the total symbol duration. This results in longer symbols and consequently, as frequency errors can not exceed a small fraction of the inverse total symbol duration, block transmission tend to be very sensitive to Carrier Frequency Offset (CFO). One source of CFO is the frequency mismatch between the local oscillators at the transmitter and receiver. Another possible source of CFO is the Doppler frequency caused by relative motion between the transmitter and the receiver. There are two basic approaches for dealing with CFO estimation ( see [8] and references within): using pilot symbols to extract the carrier frequency and phase of the received signal; or deriving the carrier frequency directly from the modulated signal, usually called a blind scheme. The first option will always require additional bandwidth consumption. Alternatively, in SC-FDE schemes differentially encoded transmission proved to be robust to the presence of CFO. For Time Division Mul- tiple Access (TDMA) schemes the CFO estimation becomes more challenging as a result of the non-continuity of the users time-slots. In [9], [10] receiver structures for joint fine carrier syn- chronization and equalization which combines iterative FDE and post-equalization carrier synchronization schemes were proposed. The receiver proposed in [9] can be regarded as a modified IB-DFE where a decision-directed CFO estimation is performed within each iteration of the equalizer. For SC mod- ulations, the CFO produces a progressive constellation rotation and the equalized signal resembles the received signal for an ideal Gaussian channel, resulting that the carrier synchroniza- tion can be performed after the equalization procedure. For the ideal case where the receiver knows the transmitted data