Approximate Expressions for Cramer-Rao Bounds of Code Aided QAM Dynamical Phase Estimation

IEEE Trans. Signal Process.

Bay

2011

In this paper, we study Bayesian and hybrid Cramé r-Rao bounds (BCRB and HCRB) for the code-aided (CA), the data-aided (DA) and the non-data-aided (NDA) dynamical phase estimation of QAM modulated signals. We address the bounds derivation for both the off-line scenario, for which the whole observation frame is used, and the on-line which only takes into account the current and the previous observations. For the CA scenario we show that the computation of the Bayesian information matrix (BIM) and of the hybrid information matrix (HIM) is NP hard. We then resort to the belief-propagation (BP) algorithm or to the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to obtain some approximate values. Moreover, in order to avoid the calculus of the inverse of the BIM and of the HIM, we present some closed form expressions for the various CRBs, which greatly reduces the computation complexity. Finally, some simulations allow us to compare the possible improvements enabled by the off-line and the CA scenarios.

Section: Introductionmentioning

confidence: 99%

Bayesian and Hybrid Cramér–Rao Bounds for the Carrier Recovery Under Dynamic Phase Uncertain Channels

IEEE Trans. Signal Process.

Bay

2011

“…"Forward / Backward" (Sim)) with the on-line BCRB (resp. the off-line BCRB) X [3], [5], [6], on Fig. 1 to Fig.…”

Section: Amentioning

confidence: 99%

“…However, generally, the performance gain using a data-aided scenario is relatively low compared to the performance difference between the off-line and the on-line scenarios, and logically, when comparing with the forward recursion, there is still an appreciable gain in favor of the F/B recursion. [6] for different constellations on Fig. 4 to Fig.…”

Section: Amentioning

confidence: 99%

Smoothing PLLs for QAM Dynamical Phase Estimation

2009 IEEE International Conference on Communications

Herzet

et al. 2009

Self Cite

International audienceThis paper presents a near-optimum, low-complexity, fixed-interval smoothing algorithm that approaches the performance of an optimal smoother for the price of two low-complexity sequential estimators (two PLLs). The proposed Smoothing PLL (S-PLL) algorithm is easy to implement and fits the Cramer-Rao bounds over a wide range of signal-to-noise ratios. Moreover we show that, compared to the conventional forward loop, the proposed scheme allows to have a large gain of several dBs and is able to track frequency offsets. Due to the increasing requirements of modern communication systems to face the physical channel (low signal-to-noise ratio, high data rates), phase estimation is more challenging than ever before. Since phase errors rapidly degrade the overall performance of communication systems, synchronization has recently become one of the most challenging tasks that a digital receiver has to cope with. Noels et al [1],[2]X derived a maximum likelihood (ML) algorithm for the problem of constant phase estimation, and then applied a first-order and a second order phase-locked loop (PLL) based algorithm for the coded BPSK and QPSK dynamical phase estimation. The corresponding performances are limited both by the on-line bound and by a non-zero phase MSE floor. On the contrary, this paper deals with the non data aided (NDA) estimation of a time-varying phase and proposes an off-line Smoothing PLL (S-PLL) algorithm. To assess the performance of such algorithms, Bayesian and hybrid Cramér-Rao Bounds (BCRB and HCRB) associated to this dynamical phase synchronization problem have already been considered in some recent contributions X[3]XX-[6]X and clearly show the superiority of the off-line scenario [7]

“…Second we want to provide benchmarks for the QAM dynamical phase estimation, since we present a generalization of the off-line synchronizing scheme [16] to QAM modulated signals in [17] whose performance can exactly reach the bounds derived in this paper. For lack of space reasons, this study is extended to the code-aided case in [18]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

“…Using the i.i.d condition among data, the FIM can be written as: (18) where L I is the L L × identity matrix and D J is defined as:…”

mentioning

confidence: 99%

Bayesian and hybrid Cramer-Rao bounds for QAM dynamical phase estimation

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

Wei

2009

Self Cite

Abstract-In this paper, we study Bayesian and hybrid Cramer-Rao bounds for the dynamical phase estimation of QAM modulated signals. We present the analytical expressions for the various CRBs. This avoids the calculation of any matrix inversion and thus greatly reduces the computation complexity. Through simulations, we also illustrate the behaviors of the BCRB and of the HCRB with the signal-to-noise ratio.