Pedro Pedrosa

Joint turbo equalisation and carrier synchronisation for SC-FDE schemes

In this paper we consider the use of single carrier (SC) modulations combined with frequency-domain equalisation (FDE) in future broadband wireless systems. We propose iterative receiver structures with joint equalisation and carrier synchronisation. The proposed receivers can be regarded as modified frequency-domain turbo equalisers where we perform a decision-directed frequency offset estimation within each iteration of the turbo equaliser. Our performance results show that the proposed receiver structure has good bit error rate (BER), even with moderate frequency offsets and in severely time-dispersive channels. Moreover, our receiver has a relatively low implementation complexity, due to its fast Fourier transform (FFT)-based frequency-domain implementation. Copyright

Iterative Frequency Domain Equalization and Carrier Synchronization for Multi-Resolution Constellations

Broadband broadcast and multicast wireless systems usually employ OFDM modulations (Orthogonal Frequency Division Multiplexing) combined with non-uniform hierarchical constellations. However, these schemes are very prone to nonlinear distortion effects and have high carrier synchronization requirements. SC-FDE (Single-Carrier with Frequency-Domain Equalization) is an attractive alternative for OFDM, especially when an efficient power amplification is intended. In this paper we consider the use of SC-FDE schemes combined with non-uniform hierarchical constellations in broadband broadcast and multicast wireless systems. We study the impact of residual CFO (Carrier Frequency Offset) on the performance of multi-resolution schemes and we propose iterative frequency domain receivers with joint detection and carrier synchronization to cope with residual CFO estimation errors (a coarse CFO estimation and compensation is assumed before the equalization procedure). Our results show that while a very high carrier synchronization accuracy is required for the least protected bits, the most protected bits are relatively robust to the CFO. By employing the proposed receiver we increase significantly the robustness to residual CFO estimation errors.

Bayesian Approach for the Estimation of Phase Noise in SC-FDE Schemes

A solution for the problem of estimating the PN (Phase Noise) from the observation of the channel output in burst communications is to establish a state-model for the PN and determine the a posteriori probability density function (pdf) of the state conditioned on all measurement data, thus providing the means to compute an optimal estimate with respect to any criterion, e.g., Minimum Mean-Squared Error (MMSE). However, except in the Gaussian case, it is extremely difficult to determine and propagate this density function. As a result,and since the observation model of the PN is non-linear, the a posteriori pdf becomes non-Gaussian, and a sub-optimal solution for the problem must be found. In this paper we approximate the non-Gaussian pdf by a weighted sum of Gaussians. Additionally, we compare the performance results obtained when modeling the density function by a weighted sum of Gaussians with those obtained with a single Gaussian using a SC-FDE (Single Carrier-Frequency Domain Equalizer) scheme.

Performance evaluation of decision-directed carrier synchronization for SC-FDE schemes

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.

Joint Equalization and Phase Noise Tracking for Doubly Selective Channels

In this paper we consider the use of single carrier modulations combined with frequency-domain equalization schemes (SC-FDE) in doubly selective channels where the channel variations are due to both phase noise and carrier frequency offset (CFO). Since carrier phase variations within the block duration can compromise significantly the performance of block transmission techniques. We propose an iterative receiver with joint symbol detection and phase-noise decision-directed estimation where we approximate the a posteriori phase noise probability density function by a weighted sum of Gaussian functions.

Joint Detection and CFO Estimation for QAM Constellations

In this paper we propose the use of QAM constellations, specifically 4, 16, and 64-QAM, in severely time-dispersive channels and with moderate CFOs (Carrier Frequency Offsets). We consider an SC-FDE (Single Carrier Frequency-Domain Equalization) and assume that previously to the equalization procedure a coarse CFO estimation and compensation is performed. Since the coarse CFO estimate can have a significant error leading to a residual CFO we present and evaluate a receiver with joint detection and carrier synchronization in order to guarantee a good BER. We employ frequency-domain iterative DFE (Decision Feedback Equalization) receivers denoted by IB-DFE (Iterative Block-Decision Feedback Equalization), which are combined with a DD (Decision-Directed) CFO estimator. Our aim is to determine the synchronization requirements for 4, 16, and 64-QAM and compare several methods for the DD CFO estimators when using these QAM constellations.

A Model of an Iterative Estimator of the Carrier Frequency Offset

In this paper we consider a digital transmission affected by carrier frequency offset (CFO). We consider an iterative receiver where we perform a decision-directed (DD) estimation of the CFO which is then employed for its compensation. It is shown that the DD CFO estimates are biased and our receiver is able to cope with this bias. We propose an analytical method to study the performance of this iterative receiver with DD CFO estimation and compensation, namely the computation of the residual CFO bias after each iteration and the corresponding bit error rate (BER) performance, for different initial CFO values. Performance results show that our analytical method is very accurate, both in terms of CFO bias estimation and BER performance.

State-space estimation for OFDM and SC-FDE schemes with strongly varying carrier frequency offset

Block transmission in wireless communications systems is very sensitive to Carrier Frequency Offset (CFO). In order to reduce the number of pilot symbols used in the estimation of rapidly-varying CFO it was proposed to use a truncated Taylors series to predict the CFO, where the derivatives up to order d -1 of the series terms are recursively estimated with a d-order Kalman filter (KF). We propose to compare the performance of fourth-order KF predictor in the most popular block transmission systems: OFDM and SC-FDE systems.

Analytical performance evaluation of a class of receivers with joint equalisation and residual carrier frequency offset estimation

In this paper, we consider a single-carrier modulation combined with frequency-domain equalisation block transmission with residual frequency errors. We employ a frequency-domain iterative decision feedback equalisation (DFE) denoted iterative block-decision feedback equalisation (IB-DFE), which is combined with a decision-directed carrier frequency offset (CFO) estimator. This estimator produces a CFO estimate within each iteration of the equaliser, which is used to compensate for the CFO. As the analytical study of the IB-DFE is very hard because of the feedback chain, IB-DFE receivers with joint symbol detection and carrier frequency synchronisation are also very difficult to tackle. To address this problem, we propose three new models. One models the decision-directed CFO estimator, another models the IB-DFE and finally one makes use of the previous two models to jointly characterise equalisation and carrier frequency synchronisation. In addition, a novel graphical tool for the convergence evaluation of the iterative receiver is included. Finally, we validate our models using Monte Carlo simulations and conclude that they are accurate for small and moderate residual CFO values. Copyright

Phase Drift Estimation and Symbol Detection in Digital Communications: A Stochastic Recursive Filtering Approach

This paper proposes a novel Bayesian stochastic filtering approach for the simultaneous phase drift estimation and symbol detection in digital communications. The posterior density of the phase drift is propagated in a recursive fashion by implementing a prediction and a filtering step in each iteration. The prediction step is supported on a random walk model playing the role of prior for the phase drift process; the filtering step is supported on a Gaussian sum approximation for the probability density of the current observation, i.e., the so-called sensor factor. The Gaussian sum approximation turns out to be the key element allowing to derive a fast and efficient stochastic filter, which otherwise would be very hard to compute. The detection of the digital symbols is then carried out based on the inferred statistics of the phase drift. The effectiveness of the proposed method is illustrated for BPSK signals in the presence of strong phase drift.