Umberto Mengali

A comparison of pilot-aided channel estimation methods for OFDM systems

This paper deals with the estimation of the channel impulse response (CIR) in orthogonal frequency division multiplexed (OFDM) systems. In particular, we focus on two pilot-aided schemes: the maximum likelihood estimator (MLE) and the Bayesian minimum mean square error estimator (MMSEE). The advantage of the former is that it is simpler to implement as it needs no information on the channel statistics. On the other hand, the MMSEE is expected to have better performance as it exploits prior information about the channel. Theoretical analysis and computer simulations are used in the comparisons. At SNR values of practical interest, the two schemes are found to exhibit nearly equal performance, provided that the number of pilot tones is sufficiently greater than the CIRs length. Otherwise, the MMSEE is superior. In any case, the MMSEE is more complex to implement.

An improved frequency offset estimator for OFDM applications

An efficient algorithm has been proposed by Schmidl and Cox (see IEEE Trans. Commun., vol.45, p.1613-21, 1997) for carrier frequency estimation in orthogonal frequency-division multiplexing systems. The scheme is based on the transmission of a training symbol composed of two identical halves in the time domain. We extend this algorithm by considering a training symbol composed of L>2 identical parts. This makes it possible to achieve a better accuracy at the cost of some increase in computational load. The estimation range can be made as large as desired without the need of a second training symbol, as required by the Schmidl and Cox method.

Channel estimation for ultra-wideband communications

This paper deals with channel estimation in ultra-wideband communications operating in a multipath environment and in the presence of multiaccess interference. The channel parameters are the attenuations and delays incurred by the signal echoes along the propagation paths. Time-hopping modulation with binary symbols is assumed. The estimation method is based on the maximum-likelihood criterion and is applied to two different scenarios: either with known symbols (DA estimation) or with unknown symbols (NDA estimation). The effects of the estimation errors on the performance of a RAKE receiver are assessed by simulation by comparing the receiver bit-error rate with either perfect channel estimates or imperfect estimates as obtained from the proposed algorithms. The results show that the degradations are tolerable as long as the number of users is limited. They also show that the DA method has an edge over the NDA in that it can handle a larger number of users for a fixed degradation. The number of users that can be accommodated in practice is found for some values of the system parameters.

The modified Cramer-Rao bound and its application to synchronization problems

We introduce the modified Cramer-Rao bound (CRB) which, like the true CRB, is a lower bound to the error variance of any parameter estimator. The modified CRB proves useful when, in addition to the parameter to be estimated, the observed data also depend on other unwanted parameters. The relationship between the modified and true CRB is established and applications are discussed regarding the estimation of carrier-frequency offset, carrier phase, and timing epoch in linearly modulated signals. Modified CRBs for phase and timing estimation have been already discussed in previous works where it is shown that several practical carrier-phase and clock recovery circuits do attain such bounds. Frequency discrimination, instead, is not so well-represented in the literature and a significant contribution of this paper is the calculation of the modified CRB for frequency estimation. This bound is compared with the performance of some frequency detectors and it is concluded that further work is needed in search of more efficient frequency discrimination methods. >

Carrier-frequency estimation for transmissions over selective channels

This paper deals with carrier-frequency estimation for burst transmissions over frequency-selective channels. Three estimation schemes are proposed, all based on the use of known training sequences. The first scheme employs an arbitrary sequence and provides joint maximum-likelihood (ML) estimates of the carrier frequency and the channel response. Its implementation complexity is relatively high but its accuracy achieves the Cramer-Rao bound. The second scheme is still based on the ML criterion, but the training sequence is periodic, which helps to reduce the computational load. The third scheme also employs periodic sequences, but its structure comes from heuristic reasoning. Theoretical analysis and simulations are employed to assess the performance of the three schemes.

Data-aided frequency estimation for burst digital transmission

Burst transmission of digital data is employed in several applications such as satellite time-division multiple access (TDMA) systems and terrestrial mobile cellular radio. We propose a new algorithm for carrier frequency estimation in burst-mode phase shift keying (PSK) transmissions. The algorithm is data-aided and clock-aided and has a feedforward structure that is easy to implement in digital form. Its estimation range is large, about /spl plusmn/20% of the symbol rate and its accuracy is close to the Cramer-Rao bound (CRB) for a signal-to-noise ratio (SNR) as low as 0 dB. Comparisons with earlier methods are discussed.

Decomposition of M-ary CPM signals into PAM waveforms

It is widely known that minimum shift keying (MSK) may be seen as a PAM signaling scheme and that the same is true, albeit approximately, with MSK-like modulations. It is also known (perhaps not so widely) that any binary continuous phase-modulated (CPM) signal may be exactly decomposed into the sum of a few PAM waveforms. In this paper we show that this property extends to multilevel CPM signaling. Features of a PAM decomposition are discussed as a function of the alphabet size, the modulation index, and the frequency response of the system. It is found that, especially with signaling schemes with a long memory, the decomposition has so many terms that it becomes unmanageable. For these cases an approximation is proposed with a limited number of terms. >

Feedforward frequency estimation for PSK: A tutorial review

This paper considers feedforward carrier frequency estimation methods in burst-mode digital transmission, with tutorial objectives foremost. Assuming PSK modulation, two scenarios are envisaged in which frequency estimates are derived either from a preamble appended to the data block, or directly from the modulated signal. Several estimation algorithms are considered with different and somewhat contrasting characteristics. The characteristics we focus on are: estimation accuracy, estimation range, minimum operating signal-to-noise ratio (threshold), and implementation complexity. They provide a framework within which current estimation methods can be evaluated. The paper reviews and compares some prominent algorithms proposed in literature, trying to single out the best ones for a given application.

Frequency ambiguity resolution in OFDM systems

In orthogonal frequency division multiplexing systems, the carrier-frequency offset can be divided into two parts: (1) an integer one-multiple of the subcarrier spacing 1/T and (2) a fractional one-less than 1/2T in amplitude. Some schemes proposed in the literature can only recover the fractional part. We derive two algorithms for estimating the integer part. They are based on the observation of two consecutive OFDM symbols. The first algorithm exploits pilot symbols multiplexed with the data, the other is blind.

Synchronization algorithms for UWB signals

This paper is concerned with timing recovery for ultra-wideband communication systems operating in a dense multipath environment. Two timing algorithms are proposed that exploit the samples of the received signal to estimate the start of the individual frames with respect to the receivers clock (frame timing) and the location of the first frame in each symbol (symbol timing). Channel estimation comes out as a by-product and can be used for coherent matched filter detection. The proposed algorithms require sampling rates on the order of the inverse of the pulse duration. Their performance is assessed by simulating the operation of coherent and differential detectors. Their sensitivity to the sampling rate is discussed, and the effects of the multiple access interference are evaluated.