Non-data-aided Research Articles

Non-Data-Aided Approach to I/Q Mismatch Compensation in Low-IF Receivers

A digital signal processing (DSP) technique is presented that can compensate for the in-phase/quadrature-phase (I/Q) mismatch in low-intermediate frequency (IF) receivers. In particular, a non-data-aided (NDA) I/Q mismatch estimator is derived by exploiting the statistical independence between desired and image signals. The proposed technique obtains two baseband signals (uncompensated desired and image signals) from a digital IF signal and processes them to estimate and compensate for the I/Q mismatch. The mean-square error (MSE) of the estimate is analyzed. Computer simulation results indicate that the proposed technique can outperform existing adaptive DSP techniques that are based on the use of blind signal separation algorithms. It is observed that the image rejection ratio (IRR) of the proposed technique decreases monotonically with the number of observed samples for estimation, while that of conventional methods exhibits some floor.

SNR estimation in time-varying fading channels

Signal-to-noise ratio (SNR) estimation is considered for phase-shift keying communication systems in time-varying fading channels. Both data-aided (DA) estimation and nondata-aided (NDA) estimation are addressed. The time-varying fading channel is modeled as a polynomial-in-time. Inherent estimation accuracy limitations are examined via the Cramer-Rao lower bound, where it is shown that the effect of the channel's time variation on SNR estimation is negligible. A novel maximum-likelihood (ML) SNR estimator is derived for the time-varying channel model. In DA scenarios, where the estimator has a simple closed-form solution, the exact performance is evaluated both with correct and incorrect (i.e., mismatched) polynomial order. In NDA estimation, the unknown data symbols are modeled as random, and the marginal likelihood is used. The expectation-maximization algorithm is proposed to iteratively maximize this likelihood function. Simulation results show that the resulting estimator offers statistical efficiency over a wider range of scenarios than previously published methods.

Iterative APPA Symbol Timing Recovery for Turbo-coded Systems

This paper examines the problem of symbol timing recovery and decoding in turbo-coded systems. The large coding gain of Turbo-codes enables reliable communications at very low signal-to-noise ratio (SNR). However, the application of turbo coding exacerbates the problem of timing recovery due to its very low operating SNRs. Therefore we propose a new concept: ‘a-priori probability aided’ symbol timing recovery, which is suited to coding systems employing iterative soft-in/soft-out (SISO) decoding such as Turbo Codes, where the log-likelihood ratio obtained from a Maximum A Posteriori (MAP) decoder (as used in turbodecoding) is used to aid estimation in an iterative synchroniser/decoder. This method jointly solves the timing recovery and decoding problem and the synchroniser has effectively no acquisition period. We illustrate this in detail in a turbo-coded BPSK system on AWGN channel. We analyse the performance of the estimator in terms of the mean and the variance of the timing estimate, and demonstrate a substantial performance advantage over conventional non-data-aided (NDA) method. It is also shown that this method can approach the performance of Data-Aided (DA) method without using additional pilot symbols.

Carrier phase and frequency estimation for pilot-symbol assisted transmission: bounds and algorithms

In this paper we consider the Cramer-Rao lower bound (CRB) for the joint estimation of the carrier phase and the frequency offset from a noisy linearly modulated burst signal containing random data symbols (DSs) as well as known pilot symbols (PSs). We point out that the CRB depends on the location of the PSs in the burst, the number of PSs, the number of DSs, the signal-to-noise ratio (SNR), and the data modulation scheme. Distributing the PSs symmetrically about the center of the burst and estimating the carrier phase in the center of the burst interval decouples the frequency and phase estimation, making the CRB for phase estimation independent of the specific location of the PSs. At low and moderate SNR, the CRBs for both phase and frequency estimation decrease as the fraction of the PSs in the burst increases. In addition, the CRB for frequency estimation decreases as the PSs are separated with more DSs. Numerical evaluation of the CRB indicates that the carrier phase and frequency of a hybrid burst (i.e., containing PSs and DSs) can be estimated more accurately when exploiting both the presence of the DSs and the a priori knowledge about the PSs, instead of using only the knowledge about the PSs (and ignoring the DSs), or considering all the received symbols (PSs and DSs) as unknown (and ignoring the knowledge about the PSs). Comparison of the CRB with the performance of existing carrier synchronizers shows that the iterative soft-decision-directed (sDD) estimator with data-aided (DA) initialization performs very closely to the CRB and provides a large improvement over the classical non-data-aided (NDA) estimator at lower SNR.

Low-complexity ML timing acquisition for UWB communications in dense multipath channels

Timing acquisition for ultrawideband (UWB) communication systems operating in dense multipath environments faces major challenges due to the stringent requirements to resolve and capture ultrashort transmitted pulses. This paper develops low-complexity maximum-likelihood (LC-ML) acquisition methods that offer explicit design options to trade off acquisition accuracy and complexity. The proposed schemes are based on a tapped delay line (TDL) model whose tap spacing is set in accordance with a low frame-level rate. By avoiding subpulse rate sampling, the LC-ML methods achieve low complexity and fast acquisition speed and at the same time retain good estimation accuracy due to the underlying ML principle. Both the data-aided (DA) and nondata-aided (NDA) versions are derived. It is also demonstrated by simulations that the proposed synchronizers are markedly robust with respect to the effects of both multipath channel and multiple access interference.

Symbol timing estimation in MIMO correlated flat‐fading channels

AbstractIn this paper, the data aided (DA) and non‐data aided (NDA) maximum likelihood (ML) symbol timing estimators and their corresponding conditional Cramer–Rao bound (CCRB) and modified Cramer–Rao bound (MCRB) in multiple‐input‐multiple‐output (MIMO) correlated flat‐fading channels are derived. It is shown that the approximated ML algorithm in References [4,13] is just a special case of the DA ML estimator; while the extended squaring algorithm in Reference [14] is just a special case of the NDA ML estimator. For the DA case, the optimal orthogonal training sequences are also derived. It is found that the optimal orthogonal sequences resemble the Walsh sequences, but present different envelopes. Simulation results under different operating conditions (e.g. number of antennas and correlation between antennas) are given to assess and compare the performances of the DA and NDA ML estimators with respect to their corresponding CCRBs and MCRBs. It is found that (i) the mean square error (MSE) of the DA ML estimator is close to the CCRB and MCRB, (ii) the MSE of the NDA ML estimator is close to the CCRB but not to the MCRB, (iii) the MSEs of both DA and NDA ML estimators are approximately independent of the number of transmit antennas and are inversely proportional to the number of receive antennas, (iv) correlation between antennas has little effect on the MSEs of DA and NDA ML estimators and (v) DA ML estimator performs better than NDA ML estimator at the cost of lower transmission efficiency and higher implementation complexity. Copyright © 2004 John Wiley & Sons, Ltd.

On the Miller–Chang Lower Bound for NDA Carrier Phase Estimation

In this letter, we derive a new Miller-Chang lower bound (MCB) for the variance of unbiased non-data-aided (NDA) carrier phase estimates obtained from a block of N samples of a linearly modulated pulse-amplitude modulation or quadrature-amplitude modulation information signal, transmitted through an additive white Gaussian noise channel. This bound is tighter than the corresponding Crame/spl acute/r-Rao lower bound (CRB) for data-aided or continuous-wave carrier phase estimation (CW-CRB), particularly when N is small. For some given N and sufficiently high signal-to-noise ratios, the MCB is tighter than the corresponding true NDA CRB. The main limitation of this new MCB is that its application is restricted to carrier phase estimators which are unbiased for all possible values of the received symbol sequence.

A Performance Lower Bound for Quadratic Timing Recovery Accounting for the Symbol Transition Density

The symbol transition density in a digitally modulated signal affects the performance of practical synchronization schemes designed for timing recovery. This paper focuses on the derivation of simple performance limits for the estimation of the time delay of a noisy linearly modulated signal in the presence of various degrees of symbol correlation produced by the various transition densities in the symbol streams. The paper develops high- and low-signal-to-noise ratio (SNR) approximations of the so-called (Gaussian) unconditional Crame/spl acute/r-Rao bound (UCRB), as well as general expressions that are applicable in all ranges of SNR. The derived bounds are valid only for the class of quadratic, non-data-aided (NDA) timing recovery schemes. To illustrate the validity of the derived bounds, they are compared with the actual performance achieved by some well-known quadratic NDA timing recovery schemes. The impact of the symbol transition density on the classical threshold effect present in NDA timing recovery schemes is also analyzed. Previous work on performance bounds for timing recovery from various authors is generalized and unified in this contribution.

Conditional maximum likelihood timing recovery: estimators and bounds

This paper is concerned with the derivation of new estimators and performance bounds for the problem of timing estimation of (linearly) digitally modulated signals. The conditional maximum likelihood (CML) method is adopted, in contrast to the classical low-SNR unconditional ML (UML) formulation that is systematically applied in the literature for the derivation of non-data-aided (NDA) timing-error-detectors (TEDs). A new CML TED is derived and proved to be self-noise free, in contrast to the conventional low-SNR-UML TED. In addition, the paper provides a derivation of the conditional Cramer-Rao bound (CRB/sub c/), which is higher (less optimistic) than the modified CRB (MCRB) [which is only reached by decision-directed (DD) methods]. It is shown that the CRB, is a lower bound on the asymptotic statistical accuracy of the set of consistent estimators that are quadratic with respect to the received signal. Although the obtained bound is not general, it applies to most NDA synchronizers proposed in the literature. A closed-form expression of the conditional CRB is obtained, and numerical results confirm that the CML TED attains the new bound for moderate to high E/sub s//N/sub o/.

Non—data—aided ML carrier frequency and phase synchronization in OFDM systems

AbstractIn this paper non—data—aided(NDA), maximum likelihood(ML) algorithms are derived for the carrier frequency and phase offset, separately, for OFDM systems employing M—PSK modulation scheme. NDA ML estimation algorithm for frequency offset estimation exploits the redundant information contained in the cyclic prefix proceeding the OFDM symbols, thus reducing the need for pilots. Its mean—squared performance is obtained analytically and compared with simulation results. It is observed that the resulting algorithm generates very accurate estimation even when the offset is high. It is also shown that the frequency estimator may be used in a tracking mode. The ML algorithm derived for the carrier phase estimation is also a non—data—aided(NDA) and maximizes the low SNR limit of the likelihood function averaged over M—PSK signal constellation. It is shown that for sufficiently small SNR the ML phase estimator obtained reduces to the familiar M/th order power synchronizer which belongs to the class of NDA feedforward carrier synchronizers introduced earlier in the literature. Its mean—squared performance is obtained analytically and compared with simulation results. We observe that the resulting algorithm generates very accurate estimation even when the phase offset is high, that the self noise is absent and the performance of the algorithm is basically the same as die Cramer—Rao bound for moderate to high SNR. Finally we note mat me error variance derived for the mean—squared performance of this NDA ML synchronizer is an extension of the approximate variance formula appeared in Reference 20,equation(14) for M—PSK.

Two-stage nondata-aided adaptive linear receivers for DS/CDMA

Closed-form steady-state performance analysis of the signal-to-interference plus noise ratio (SINR) at the output of well-known adaptive implementations of the linear minimum mean-square error (MSE) receiver for direct-sequence code-division multiple access show that nondata-aided (NDA) schemes may suffer from a considerable performance degradation with respect to their data-aided counterparts. Motivated by this fact, we propose a new two-stage NDA scheme where symbol-by-symbol predecisions at the output of a first adaptive stage are used to train a second stage. We derive closed-form steady-state performance analysis for both the two-stage and classical decision-directed schemes, taking into account detection errors in decision-directed adaptation. Our analysis shows that the SINR of the two-stage algorithm is close to optimal over a large range of values, while the SINR of the decision-directed scheme is far from optimal when the optimal SINR is small. Finally, we consider the case of time-varying fading channels. We derive modified recursive least square and least mean square adaptation schemes by considering SINR maximization rather than MSE minimization (that is useless under the assumption of zero-mean random channels). The resulting two-stage receiver shows good tracking properties in heavy near-far conditions (at least for moderate normalized Doppler bandwidth), while the decision-directed receiver may easily loose tracking after deep fades.

Hangup in asynchronous timing recovery loops

The effects of hangup in digital asynchronous timing recovery loops are investigated. It is demonstrated that delay quantisation in the interpolation filter exacerbates the problem of hangup. It is also noted that the effects of hangup are worse for the non-data aided (NDA) loops than they are for the decision-directed (DD) loops. This may preclude the use of the former in TDMA applications.