Multipath Parameter Estimation from OFDM Signals in Mobile Channels

We study multipath parameter estimation from orthogonal frequency division multiplex signals transmitted over doubly dispersive mobile radio channels. We are interested in cases where the transmission is long enough to suffer time selectivity, but short enough such that the time variation can be accurately modeled as depending only on per-tap linear phase variations due to Doppler effects. We therefore concentrate on the estimation of the complex gain, delay and Doppler offset of each tap of the multipath channel impulse response. We show that the frequency domain channel coefficients for an entire packet can be expressed as the superimposition of two-dimensional complex sinusoids. The maximum likelihood estimate requires solution of a multidimensional non-linear least squares problem, which is computationally infeasible in practice. We therefore propose a low complexity suboptimal solution based on iterative successive and parallel cancellation. First, initial delay/Doppler estimates are obtained via successive cancellation. These estimates are then refined using an iterative parallel cancellation procedure. We demonstrate via Monte Carlo simulations that the root mean squared error statistics of our estimator are very close to the Cramer-Rao lower bound of a single two-dimensional sinusoid in Gaussian noise.Comment: Submitted to IEEE Transactions on Wireless Communications (26 pages, 9 figures and 3 tables

Improving Channel Estimation Performance for Uplink OTFS Transmissions: Pilot Design based on A Posteriori Cramer-Rao Bound

Orthogonal time frequency space (OTFS) has been widely acknowledged as a promising wireless technology for challenging transmission scenarios, including high-mobility channels. In this paper, we investigate the pilot design for the multi-user OTFS system based on the a priori statistical channel state information (CSI), where the practical threshold-based estimation scheme is adopted. Specifically, we first derive the a posteriori Cramer-Rao bound (PCRB) based on a priori channel information for each user. According to our derivation, the PCRB only relates to the user's pilot signal-to-noise ratio (SNR) and the range of delay and Doppler shifts under the practical power-delay and power-Doppler profiles. Then, a pilot scheme is proposed to minimize the average PCRB of different users, where a closed-form global optimal pilot power allocation is derived. Our numerical results verify the multi-user PCRB analysis. Also, we demonstrate an around 3 dB improvement in the average normalized-mean-square error (NMSE) by using the proposed pilot design in comparison to the conventional embedded pilot design under the same total pilot power

Cramer-Rao Bound for Target Localization for Widely Separated MIMO Radar

In this paper, we derive the Cramer-Rao Bounds (CRBs) for the 2-dimensional (2D) target localization and velocity estimations for widely separated Multiple-Input Multiple-Output (MIMO) radar. The transmitters emit signals with different frequencies and the receivers receive these signals with amplitude fluctuations and with Doppler shifts due to the target motion. The received signal model is constructed using the Swerling target fluctuations to take into account the undesired effects of target amplitude and phase fluctuations. Moreover, the time delays and the Doppler frequencies are included in the signal model to get a more realistic model. Then, the Cramer-Rao Bounds are derived for the proposed signal model for the target position and velocity estimations. Contrary to known models of CRBs, we derived the CRBs jointly and using the Swerling target fluctuations

Pulse-diverse radar waveform design for delay-doppler estimation.

by Wing-Kit Chung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 123-127).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Application of Time Delay and Doppler Shift Estimation in Active Radar --- p.1Chapter 1.2 --- Joint Time delay and Doppler Shift Estimation Algorithm based on Correlation --- p.4Chapter 1.3 --- A Brief Review of Radar Signal Design --- p.6Chapter 1.3.1 --- Suppression of Range Sidelobes Level --- p.6Chapter 1.3.2 --- Reduction of Ambiguity of Delay-Doppler Plane --- p.8Chapter 1.4 --- Goal and Outline of the Thesis --- p.9Chapter 2 --- CAF and Pulse Diversity for Radar Signals --- p.11Chapter 2.1 --- Radar Ambiguity Function --- p.12Chapter 2.1.1 --- Properties of Radar Ambiguity Function --- p.12Chapter 2.1.2 --- Ideal Ambiguity Function --- p.13Chapter 2.2 --- Composite Ambiguity Function (CAF) --- p.14Chapter 2.2.1 --- Properties of Composite Ambiguity Function --- p.15Chapter 2.3 --- CAF of Joint Phase and Frequency Shift Keying (PSK-FSK) Mod- ulated Signal --- p.17Chapter 2.4 --- Summary --- p.21Chapter 3 --- CAF Algorithm and Its Performance Analysis --- p.22Chapter 3.1 --- CAF Algorithm for Time Delay and Doppler Shift Estimation --- p.23Chapter 3.2 --- The Cramer-Rao Lower Bound of the CAF Algorithm --- p.24Chapter 3.3 --- Performance Analysis of the CAF Algorithm --- p.28Chapter 3.4 --- Global Accuracy --- p.31Chapter 3.5 --- Numerical Results for Derivation of CAF Algorithm --- p.35Chapter 3.5.1 --- Simulation Results of CRLB for Various Multi-pulse Signals --- p.35Chapter 3.5.2 --- Simulation Results of Global Accuracy for Various Multi- pulse Signals --- p.36Chapter 3.5.3 --- Simulation on Global Accuracy with Different Parameters --- p.37Chapter 3.6 --- Summary --- p.39Chapter 4 --- Optimum Pulse-Diverse Waveforms Design --- p.46Chapter 4.1 --- Criteria for Optimum Waveforms --- p.46Chapter 4.2 --- Optimum Signals Based on Joint Phase and Frequency Shift Key- ing (PSK-FSK) Modulated Signal --- p.48Chapter 4.3 --- Genetic Algorithm (GA) --- p.50Chapter 4.4 --- Numerical Results --- p.54Chapter 4.4.1 --- "Comparison of Optimized PSK, FSK and PSK-FSK Signals" --- p.55Chapter 4.4.2 --- Simulation on Large Number of Pulses for Pulse-diverse Waveform Set --- p.59Chapter 4.4.3 --- Simulation Results of CAF algorithm for Time Delay and Doppler Shift Estimation --- p.63Chapter 4.4.4 --- Various Distribution of Ambiguity Volume on the Delay- Doppler Plane --- p.70Chapter 4.5 --- Summary --- p.74Chapter 5 --- Wideband CAF (WCAF) and Its Analysis --- p.75Chapter 5.1 --- WCAF Algorithm for Time Delay and Doppler Stretch Estimation --- p.76Chapter 5.2 --- Theory of Wavelet Packets --- p.77Chapter 5.3 --- Design of Wideband Optimum Waveforms for WCAF Algorithm --- p.80Chapter 5.4 --- Performance Evaluation --- p.82Chapter 5.4.1 --- The Cramer-Rao Lower Bound of WCAF Algorithm --- p.83Chapter 5.4.2 --- The Global Accuracy of WCAF Algorithm --- p.84Chapter 5.4.3 --- Numerical Results --- p.86Chapter 5.5 --- Summary --- p.89Chapter 6 --- Conclusion and Suggestion for Future Research --- p.90Chapter 6.1 --- Conclusion --- p.90Chapter 6.2 --- Suggestion for Future Research --- p.93Chapter A --- Derivation of Ambiguity Function and CAF --- p.94Chapter A.1 --- Properties of Radar Ambiguity Function --- p.94Chapter A.2 --- Properties of Composite Ambiguity Function --- p.96Chapter B --- Derivation of Fisher Information Matrix of CAF Algorithm --- p.98Chapter C --- Derivation of Performance Analysis of CAF Algorithm --- p.103Chapter C.1 --- Derivation of TD and DS Estimate by Proposed Estimator --- p.103Chapter C.2 --- Derivation the Asymptotic Variance of The Estimates --- p.106Chapter D --- Derivation of Probability of Decision Error --- p.113Chapter E --- PSK-FSK Modulating Code of Various Multi-pulse Signals --- p.116Chapter F --- Derivation of Wavelet-Based Wideband CAF --- p.120Chapter F.1 --- Volume of Wideband Ambiguity Function --- p.120Chapter F.2 --- Volume of Wideband Composite Ambiguity Function --- p.121Bibliography --- p.12

Cramer-Rao bounds in the estimation of time of arrival in fading channels

This paper computes the Cramer-Rao bounds for the time of arrival estimation in a multipath Rice and Rayleigh fading scenario, conditioned to the previous estimation of a set of propagation channels, since these channel estimates (correlation between received signal and the pilot sequence) are sufficient statistics in the estimation of delays. Furthermore, channel estimation is a constitutive block in receivers, so we can take advantage of this information to improve timing estimation by using time and space diversity. The received signal is modeled as coming from a scattering environment that disperses the signal both in space and time. Spatial scattering is modeled with a Gaussian distribution and temporal dispersion as an exponential random variable. The impact of the sampling rate, the roll-off factor, the spatial and temporal correlation among channel estimates, the number of channel estimates, and the use of multiple sensors in the antenna at the receiver is studied and related to the mobile subscriber positioning issue. To our knowledge, this model is the only one of its kind as a result of the relationship between the space-time diversity and the accuracy of the timing estimation.Peer ReviewedPostprint (published version