Heidi Steendam

Log-domain decoding of LDPC codes over GF(q)

This paper introduces a log-domain decoding scheme for LDPC codes over GF(q). While this scheme is mathematically equivalent to the conventional sum-product decoder, log-domain decoding has advantages in terms of implementation, computational complexity and numerical stability. Further, a suboptimal variant of the log-domain decoding algorithm is proposed, yielding a lower computational complexity. The proposed algorithms and the sum-product algorithm are compared both in terms of simulated BER performance and computational complexity.

Analysis and optimization of the performance of OFDM on frequency-selective time-selective fading channels

In mobile radio communication, the fading channels generally exhibit both time-selectivity and frequency-selectivity. Orthogonal frequency-division multiplexing has been proposed to combat the frequency-selectivity, but its performance is also affected by the time-selectivity. We investigate how various parameters, such as the number of carriers, the guard time length, and the sampling offset between receiver and transmitter, affect the system performance. Further, we determine the optimum values of the above parameters, which minimize the degradation of the signal to-noise ratio at the input of the decision device.

Turbo synchronization: an EM algorithm interpretation

This paper is devoted to turbo synchronization, that is to say the use of soft information to estimate parameters like carrier phase, frequency offset or timing within a turbo receiver. It is shown how maximum-likelihood estimation of those synchronization parameters can be implemented by means of the iterative expectation-maximization (EM) algorithm [A.P. Dempster, et al., 1977]. Then we show that the EM algorithm iterations can be combined with those of a turbo receiver. This leads to a general theoretical framework for turbo synchronization. The soft decision-directed ad-hoc algorithm proposed in V. Lottici and M. Luise, [2002] for carrier phase recovery turns out to be a particular instance of this implementation. The proposed mathematical framework is illustrated by simulations reported for the particular case of carrier phase estimation combined with iterative demodulation and decoding [S. ten Brink, et al., 1998].

The effect of carrier frequency offsets on downlink and uplink MC-DS-CDMA

In this paper, we study the sensitivity of uplink and downlink MC-DS-CDMA to carrier frequency offsets, assuming orthogonal spreading sequences. For both uplink and downlink MC-DS-CDMA, we show that the performance rapidly degrades for an increasing ratio of maximum frequency offset to carrier spacing. We point out that the degradation in the uplink is larger than in the downlink because only the former is affected by multiuser interference. For a given (small) ratio of maximum frequency offset to carrier spacing, enlarging the spreading factor in a fully loaded system does not affect the downlink degradation but strongly increases the uplink degradation. Finally, we show that the downlink degradations of MC-DS-CDMA and fully loaded MC-CDMA are the same, provided that for both systems the ratio of frequency offset to carrier spacing is the same.

Sensitivity of orthogonal frequency-division multiplexed systems to carrier and clock synchronization errors

Abstract In this contribution, we present an overview of research results pertaining to the sensitivity of orthogonal frequency-division multiplexed (OFDM) systems to synchronization errors. We show that OFDM systems are quite sensitive to carrier frequency offset and clock frequency offset : in the presence of these impairments, the signal-to-noise ratio (SNR) at the input of the decision device is a decreasing function of the number of carriers. On the other hand, carrier phase jitter and timing jitter give rise to a degradation of the SNR at the input of the decision device which does not depend on the number of carriers; as compared to traditional single-carrier systems, OFDM systems have the same sensitivity to carrier phase jitter and a somewhat larger sensitivity to timing jitter.

The Cramer-Rao bound for phase estimation from coded linearly modulated signals

In this letter, we express the Cramer-Rao bound (CRB) for carrier phase estimation from a noisy linearly modulated signal with encoded data symbols, in terms of the marginal a posteriori probabilities (APPs) of the coded symbols. For a wide range of classical codes (block codes, convolutional codes, and trellis-coded modulation), these marginal APPs can be computed efficiently by means of the Bahl-Cocke-Jelinke-Raviv (BCJR) algorithm, whereas for codes that involve interleaving (turbo codes and bit interleaved coded modulation), iterated application of the BCJR algorithm is required. Our numerical results show that when the BER of the coded system is less than about 10/sup -3/, the resulting CRB is essentially the same as when transmitting a training sequence.

True Cramer-Rao bound for timing recovery from a bandlimited linearly Modulated waveform with unknown carrier phase and frequency

This paper derives the Cramer-Rao bound (CRB) related to the estimation of the time delay of a linearly modulated bandpass signal with unknown carrier phase and frequency. We consider the following two scenarios: joint estimation of the time delay, the carrier phase, and the carrier frequency; and joint estimation of the time delay and the carrier frequency irrespective of the carrier phase. The transmit pulse is a bandlimited square-root Nyquist pulse. For each scenario, the transmitted symbols constitute either an a priori known training sequence or an unknown random data sequence. In spite of the presence of random data symbols and/or a random carrier phase, we obtain a relatively simple expression of the CRB, from which the effect of the constellation and the transmit pulse are easily derived. We show that the penalty resulting from estimating the time delay irrespective of the carrier phase decreases with increasing observation interval. However, the penalty, caused by not knowing the data symbols a priori, cannot be reduced by increasing the observation interval. Comparison of the true CRB to existing symbol synchronizer performance reveals that decision-directed timing recovery is close to optimum for moderate-to-large signal-to-noise ratios.

Effectiveness Study of Code-Aided and Non-Code-Aided ML-Based Feedback Phase Synchronizers

This paper investigates the effectiveness of a (non-)code-aided ML-based FB phase synchronizer at the low operating signal-to-noise ratio of capacity-approaching codes. We show that the performance of the code-aided synchronizer is very close to that of a data-aided synchronizer that knows all data symbols in advance. This illustrates the optimality of the code-aided synchronizer. For the non-code-aided and the data-aided synchronizer, the linearized mean square phase error (MSPE) is evaluated analytically in the case of a first order loop. We demonstrate that, the MSPE of the non-code-aided synchronizer equals that of the data-aided synchronizer when the carrier phase is essentially constant and the loop filter gain is the same for both synchronizers, but that the non-code-aided synchronizer (as compared to the data-aided synchronizer) yields a larger MSPE due to phase fluctuations. This proves that code-aided FB phase estimation outperforms non-code-aided FB phase estimation when that the phase to be estimated is time-varying.

The effect of carrier phase jitter on the performance of orthogonal frequency-division multiple-access systems

We investigate the sensitivity to carrier phase jitter of an orthogonal frequency-division multiple-access (OFDMA) system. When all OFDMA carriers have the same power level and jitter spectrum, the degradation caused by the jitter is shown to be equal to the degradation of an OFDM system. Also, traditional FDMA is found to be slightly more robust than OFDMA.

The true Cramer-Rao bound for carrier frequency estimation from a PSK signal

This paper considers the Cramer-Rao bound (CRB) related to estimating the carrier frequency of a noisy phase-shift keying signal. The following scenarios are discussed: 1) carrier frequency estimation irrespective of the carrier phase, based on either known or random data and 2) joint carrier phase and frequency estimation, based on either known or random data. Ideal symbol timing is assumed. We compare the results obtained from a (commonly used) simplified observation model against those resulting from the correct model. Because of the presence of nuisance parameters (random data and/or random carrier phase), the analytical computation of the corresponding CRBs is often not feasible. Here we present results that are based upon a combined analytical/numerical approach. Our results show that the choice of the observation model has essentially no effect on the CRBs at moderate and high signal-to-noise ratios. We also show that of the two scenarios considered, joint frequency and phase estimation yields the smaller CRB; the penalty resulting from frequency estimation, irrespective of the carrier phase, decreases with increasing observation interval.