Carrier recovery systems in high performance digital modem receivers must remove carrier phase jitter as well as track carrier phase and frequency offsets. A popular approach to removing periodic phase jitter is to use an adaptive LMS FIR linear predictor with baud spaced taps to predict the jitter angle one baud in the future. Experimentally, the convergence rates for such predictors were found to depend heavily on the jitter frequency. It is well known in adaptive filter theory that the predictor convergence rate depends on the eigenvalues of the correlation matrix of the input signal. By allowing jitter predictors with a given number of taps to have tap spacings greater than one baud and by deriving a general formula for the eigenvalues of the appropriate correlation matrix, it is shown how to design predictors exhibiting optimal convergence rates over a range of commonly observed jitter frequencies.>

A scheme for the optimal shaping of multidimensional constellations is proposed. This scheme is motivated by a type of structured vector quantizer for memoryless sources, and results in N-sphere shaping of N-dimensional cubic lattice-based constellations. Because N-sphere shaping is optimal in N dimensions, shaping gains higher than those of N-dimensional Voronoi constellations can be realized. While optimal shaping for a large N can realize most of the 1.53 dB total shaping gain, it has the undesirable effect of increasing the size and the peak-to-average power ratio of the constituent 2D constellation. This limits its usefulness for many real world channels which have nonlinearities. The proposed scheme alleviates this problem by achieving optimal constellation shapes for a given limit on the constellation expansion ratio or the peak-to-average power ratio of the constituent 2D constellation. Results of Calderbank and Ozarow (1990) on nonequiprobable signaling are used to reduce the complexity of this scheme and make it independent of the data rate with essentially no effect on the shaping gain. Comparisons with Forney's (1989) trellis shaping scheme are also provided.>

A precoding scheme for noise whitening on intersymbol interference (ISI) channels is presented. This scheme is compatible with trellis-coded modulation and, unlike Tomlinson precoding, allows constellation shaping. It can be used with almost any shaping scheme, including the optimal SVQ shaping, as opposed to trellis precoding, which can only be used with trellis shaping. The implementation complexity of this scheme is minimal-only three times that of the noise prediction filter, hence effective noise whitening can be achieved by using a high-order predictor.>

The Householder transformation outperforms the Givens rotation in numerical stability under finite-precision implementation, and requires fewer arithmetic operations than the modified Gram-Schmidt. As a result, the QR decomposition using the Householder transformation is promising for VLSI implementation and real-time throughput signal processing. A recursive complex Householder transformation with a fast initializing algorithm is presented, and its associated parallel/pipelined architecture is discussed.>

An eight-dimensional, 64-state, 90 degrees rotationally invariant trellis code for transmitting 4 bits/baud over a bandlimited channel is described. The 2-D constellation contains 20 points. The code achieves a 5.23-dB coding gain over the uncoded 4*4 QAM (quadrature amplitude modulation) constellation and a 1.23-dB gain over the standard CCITT V32 trellis code. Simulation results are presented that verify these coding gains. Simulation results showing symbol error probability versus signal/noise ratio and trellis depth are also presented.>

The estimation of the parameters of a sinusoid from observations of signal samples corrupted by additive noise is investigated. At high signal-to-noise ratios the additive noise is viewed as an equivalent phase noise, suggesting frequency and phase estimation by linear regression on the signal phase. The variances of the regression estimates are shown to achieve the Cramer-Rao bounds. A formula for the variance of the regression frequency estimator is derived in terms of the noise power spectrum. A simple formula for the variance with1/f^{2}phase noise is presented.

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (D) are derived. The approach used is based on the {\em a posteriori} probability of a nonobservable event expressed in terms of the {\em a priori} probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed is considered. It is shown that the MMSE estimates ale linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

A method for generating sequences that approximate binary random sequences with the probability of a 1 equal to 1/4 is described. These are calledPN^2sequences.PN^2sequences are generated by clocking aPNsequence generator at the l's of aPNsequence. ThePN^2sequence is 1 when the generator output makes a transition and is 0 otherwise. It is shown thatPN^2sequences have periodN^2if thePNsequence generators have periodN. The density of l's is shown to approach 1/4 for largeN. It is shown that the normalized out-of-phase pulse-coincidence autocorrelation function can never exceed 1/2 or be less than 1/4 and is 1/4 most of the time for largeN.

For the purpose of localizing a distant noisy target, or, conversely, calibrating a receiving array, the time delays defined by the propagation across the array of the target-generated signal wavefronts are estimated in the presence of sensor-to-sensor-independent array self-noise. The Cramér-Rao matrix bound for the vector delay estimate is derived, and used to show that either properly filtered beamformers or properly filtered systems of multiplier-correlators can be used to provide efficient estimates. The effect of suboptimally filtering the array outputs is discussed.