Unknown Carrier Phase Research Articles

Coherent detection of MPSK via efficient block estimation

A tree approach is proposed for efficient block estimation of MPSK sequences with unknown carrier phase. Its computational load increases with block length at a much lower rate than in previous algorithms. This enables coherent detection performance to be achieved through the use of large block lengths.

Approximate ML decoding of coded PSK with no explicit carrier phase reference

An approximate method is discussed for maximum likelihood estimation of coded PSK sequences in the presence of an unknown carrier phase. This method makes use of the Viterbi algorithm to find an optimum path in the encoder trellis diagram. Phase estimation is embedded into the structure of the detection algorithm and the branch metrics in the trellis are modified with respect to those employed with known carrier phase. Comparisons with traditional decoding schemes show that the proposed solution has better performance in terms of acquisition time and cycle slips.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimum symbol-by-symbol detection of uncoded digital data over the Gaussian channel with unknown carrier phase

A theory of optimum receiver design for symbol-by-symbol detection of an uncoded digital data sequence received over the Gaussian channel with unknown carrier phase is presented. Linear suppressed-carrier modulation is assumed. The work here aims at laying a conceptual foundation for optimum symbol-by-symbol detection, and rectifies existing approaches to the problem. The optimum receiver structure is obtained explicitly for an arbitrary carrier phase model, but its computational requirements are too heavy in general for any practical implementation. In one important special case, namely, the case in which the carrier phase can be treated as a constant over some K+1 symbol intervals, the optimum receiver can be approximated by a readily implementable decision-feedback structure at high SNR. Simulated error performance results are presented for this latter receiver for PSK modulations, with various carrier phase models. Since a decision-feedback receiver can encounter a runaway, a variation of this receiver is developed which uses feedforward of tentative decisions concerning future symbols. This modified receiver does not have any runaway problem, and has been shown to yield good error performance via simulations. >

Tight bounds on Rician-type error probabilities and some applications

Consider the classic problem of evaluating the probability that one Rician random variable exceeds another, possibly correlated, Rician random variable. This probability is given by Stein (1964) in terms of the Marcum's Q-function, which requires numerical integration on the computer for its evaluation. To facilitate application in many digital communication problems, we derive here tight upper and lower bounds on this probability. The bounds are motivated by a classic result in communication theory, namely, the error probability performance of binary orthogonal signaling over the Gaussian channel with unknown carrier phase. Various applications of the bounds are reported, including the evaluation of the bit error probabilities of MDPSK and MPSK with differential detection and generalized differential detection, respectively. The bounds prove to be tight in all cases. Further applications will be reported in the future.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Viterbi detection with simultaneous suboptimal maximum likelihood carrier phase estimation

The authors consider maximum-likelihood (ML) detection of convolutionally coded data over the AWGN channel with unknown carrier phase. A receiver is developed for simultaneous ML data decoding and suboptimal ML carrier-phase estimation. The receiver is readily implementable and, for a circular signal constellation, it is totally linear. Computer simulations using two different models of the time-varying carrier phase indicate that the receiver provides good bit error probability performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Maximum-Likelihood Digital Data Sequence Estimation Over the Gaussian Channel with Unknown Carrier Phase

We consider the problem of simultaneous ML estimation of data and carrier phase from a linear suppressed-carrier modulated signal received in the presence of additive white Gaussian noise. The ML detector of the data sequence is derived, and its error probability performance is analyzed. The result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length. A suboptimum decision-aided subsequence-by-subsequence detector whose complexity does not increase exponentially with sequence length is proposed, and its performance is analyzed.

Synchronization Problems in PAM Systems

In a PAM system with unknown carrier phase and timing phase the receiver has to estimate these parameters. The dataaided approach involves the joint estimation of the data symbols and the unknown parameters. This is in contrast with the nondataaided approach, where the carrier phase and timing phase are estimated independently of the data symbols. We first establish the equivalence of these two strategies for high signal-to-noise ratios. Then we demonstrate that several PAM systems (baseband, VSB, QAM) perform better when the data symbols are independent equiprobable bits, instead of independent identically distributed Gaussian random variables (a high signal-to-noise ratio is assumed). Finally, some generalizations of the previous conclusions are treated.

Optimal reception of digital data over the Gaussian channel with unknown delay and phase jitter

Asymptotically optimum (in the sense of minimum per-symbol error rate) receiver structures for data communication over the white Gaussian channel with unknown time delay and carrier phase jitter are developed. The receiver structures apply to the following suppressed-carrier modulation systems: double sideband (DSB), quadrature amplitude modulation (QAM) with an arbitrary constellation, vestigial sideband (VSB) and single sideband. The resulting minimum error probability receivers are asymptotically equivalent to maximum-likelihood digital {\em sequence}-estimating receivers. The optimum structures implicitly derive joint maximum-likelihood estimates of the unknown parameters and of the sequence of data symbols. It is shown that the parameter estimates can be obtained from two data-directed stochastic approximation algorithms. Unlike traditional theoretical treatments of this communication situation, which have separated the highly important carrier phase and timing recovery problem from the detection problem, a unified theory is presented from which the complete ideal receiver structure can be deduced.

Phase Measurement Accuracy with Modulated Sounding Signals

In this paper the problem of measuring an unknown carrier phase shift of a transmitted sounding signal in a Gaussian noise channel is considered. Receivers which minimize the probability that phase error is larger than some value are considered. In some cases, this criterion leads to simple phase measurement techniques. When it does not, suboptimum receivers are considered. The main objective is to determine the effectiveness of the various measurement techniques by finding the cumulative probability distribution of phase error. In this way, three sounding signals are compared: an unmodulated carrier, a binary phase shift keyed (PSK) carrier, and a Gaussian pulse amplitude modulated carrier.