On optimal dimension reduction for sensor array signal processing
Signal Processing
Geometry of the Cramer-Rao bound
Signal Processing
Matrix computations (3rd ed.)
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing
Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing
OFDM for Wireless Multimedia Communications
OFDM for Wireless Multimedia Communications
Beamforming and multiuser detection in CDMA systems with external interferences
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
Maximum likelihood array processing for stochastic coherent sources
IEEE Transactions on Signal Processing
Direction-of-arrival estimation for constant modulus signals
IEEE Transactions on Signal Processing
Maximum likelihood estimation for array processing in colored noise
IEEE Transactions on Signal Processing
Direction finding using noise covariance modeling
IEEE Transactions on Signal Processing
Optimal dimension reduction for array processing-generalized
IEEE Transactions on Signal Processing
Maximum likelihood DOA estimation and asymptotic Cramer-Rao boundsfor additive unknown colored noise
IEEE Transactions on Signal Processing
Multi-user detection for DS-CDMA communications
IEEE Communications Magazine
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The knowledge of the Cramer-Rao bound (CRB) for a given estimation problem not only gives a lower bound on the covariance matrix of any unbiased estimator applied to a set of observed data, but it can represent a mean for testing the suitability of given signal structures to provide the necessary information to the parameter estimation. An interesing problem is the evaluation of the CRB in the presence of pre-processing applied to the experimental data. It has been demonstrated that, in general, a linear pre-processing matrix multiplied "on the left-hand side" of the experimental data matrix (left pre-processing) can degrade the performance of any parameter estimator, unless the left pre-processing matrix fulfills proper constraints for the invariance of the pre-processors. This paper is aimed at discussing the performance degradation in parameter estimation due to pre-processing matrices applied "on the right-hand side" of the data matrix (right pre-processing), since this problem seems not to have received the due attention up to this moment, despite this kind of linear pre-processing often occurs in several application contexts in the field of the communications. The paper derives an expression of the deterministic CRB giving a very interesting insight on the structure of the processing matrices, providing the proof that a rank-deficient and/or not orthogonal matrix achieves the same CRB attainable through its full-rank and orthogonalized portion. Furthermore, the conditions upon which the formulation of the CRB for the pre-processed data corresponds to the CRB expression for the unprocessed data are expressed, giving the hypotheses that guarantee any linear pre-processor to be invariant. In order to give practical examples of the meaning and use of the pre-processing approach considered in the paper, some receiving techniques developed for direct sequence code division multiple access systems are briefly investigated and their performance in the context of the direction-of-arrival estimation are discussed on the basis of the CRB of the problem.