Modified Cramer-Rao Lower Bound Research Articles

Data-Aided SNR Estimation for Bandlimited Optical Intensity Channels.

Not only for radio frequency but also for optical communication systems, knowledge of the signal-to-noise ratio (SNR) is essential, e.g., for an adaptive network, where modulation schemes and/or error correction methods should be selected according to the varying channel states. In the current paper, this topic is discussed for a bandlimited optical intensity link under the assumption that the data symbols are known to the receiver unit in form of pilot sequences. This requires a unipolar signal design regarding the symbol constellation, but also a non-negative pulse shape satisfying the Nyquist criterion is necessary. Focusing on this kind of scenario, the modified Cramer-Rao lower bound is derived, representing the theoretical limit of the error performance of the data-aided SNR estimator developed in this context. Furthermore, we derive and analyze a maximum likelihood algorithm for SNR estimation, which turns out to be particularly simple for specific values of the excess bandwidth, among them the most attractive case of minimum bandwidth occupation. Numerical results confirming the analytical work conclude the paper.

Performance Analysis of a SAGE-Based Semi-Blind Channel Estimator for Pilot Contaminated MU Massive MIMO Systems

Massive multiple-input multiple-output (M-MIMO) is one of the key ingredients in the upcoming 5G technology. The benefits associated with M-MIMO rely largely on the accuracy of channel state information (CSI) available at the base station (BS). The existing literature mostly employs pilot-aided schemes which require additional pilots for improving their CSI accuracy; additionally, pilot contamination degrades their performance to a large extent. In this paper, we design a Space-Alternating Generalized Expectation-Maximization (SAGE) based semi-blind estimator for pilot contaminated multi-user (MU) M-MIMO systems. It utilizes both pilot and a few data symbols for CSI estimation through two stages, namely initialization and iterative SAGE (ISAGE). We obtain an initial channel estimate with the help of a pilot-aided linear minimum mean squared error (LMMSE) estimator in the initialization stage. The acquired initial estimate from the former stage is then iteratively updated by SAGE algorithm with the joint usage of pilot and a few data symbols in ISAGE stage. The inclusion of data information in ISAGE stages' estimation process aids in simultaneous improvement of CSI accuracy and spectral efficiency (SE) of a M-MIMO system; which is unlikely for a pilot based estimation scheme. Through simulations, we show that our estimator obtains a considerable improvement over the existing pilot-aided schemes in terms of mean squared error (MSE), bit error rate (BER), SE, and energy efficiency (EE) at a nominal increase in complexity. Besides, on average, it achieves convergence in almost two iterations. We also derive modified Cramer-Rao lower bound (MCRLB) to validate the estimation efficacy of our estimator. We evaluate a closed-form expression for lower bound on UL achievable rate of MU M-MIMO systems under both perfect and imperfect CSI scenario. We also discuss the trade-off between SE and EE.

Cramér–Rao lower bound for ATSC signal‐based passive radar systems

In multistatic passive radar systems, the Cramer–Rao lower bound (CRLB) can be used to select the optimal illuminator of opportunity so that it provides the best estimation accuracy for target parameters. In this Letter, the monostatic and bistatic modified Cramer–Rao lower bound (MCRLB) for the Advanced Television Systems Committee (ATSC) signal, which is the pervasive digital television signal of opportunity for North American passive radar systems, is derived using the relationship between the ambiguity function of a signal and its CRLB. It is shown that the derived bistatic MCRLB for the range and velocity measurements can be used to select the optimal illuminator that exhibits the lowest bounds at each region. Examples are provided in the Columbus, OH area where the Ohio State University passive radar is located.

Cramer‐Rao lower bound and parameter estimation for multibeam satellite links

SummaryData throughput and availability of multibeam satellite links are limited by interference problems, in particular when the design is determined by an aggressive reuse of frequency bands. Usually, this is mitigated by appropriately selected techniques like precoding or multi‐user detection. Before such methods are applicable, however, the most important transmission parameters have to be recovered successfully even under very challenging conditions caused by (full) frequency reuse. The detailed analysis of the log‐likelihood function characterizing the multibeam scenario shows that a beamwise decoupling of the estimation task is possible, if the following three conditions are met: (i) alignment of all frequency offsets; (ii) symbol synchronicity; (iii) orthogonal synchronization sequences. Based on these assumptions, it turns out that the modified Cramer‐Rao lower bound (MCRLB) for carrier frequency and phase, symbol timing and signal amplitude is the same, no matter whether we are dealing with a single or a multiple beam situation. Furthermore, because a maximum likelihood framework for parameter estimation is not available in closed form, we introduce a sub‐optimal concept of low‐complex algorithms. Finally, it is verified by simulation results that the jitter variance of each recovery scheme is close to the related MCRLB, when the decoupling conditions are satisfied. Copyright © 2016 John Wiley & Sons, Ltd.

Improved Code-Aided Symbol Timing Recovery with Large Estimation Range for LDPC-Coded Systems

We present an improved code-aided symbol timing recovery method for low-density parity-check (LDPC) coded systems, which comprises two supporting algorithms: 1) a coarse estimation by utilizing a cost function, the mean absolute value of soft output of the LDPC decoder and 2) a fine estimation based on the Expectation-Maximization (EM) algorithm with a simple maximization step. With low computational complexity, this proposed algorithm can achieve symbol timing recovery at low signal-to-noise ratio (SNR) with large estimation range, eliminating the biased results of many algorithms for large timing offset values. Simulation results for the case of 8-PSK system with (1944,972) LDPC code show that the root-mean-square-error (RMSE) performance of the proposed algorithm approaches the modified Cramer-Rao lower bound (MCRB) at Eb/No=4dB, and the bit-error-rate (BER) curve is very close to that of ideal synchronization.