Abstract-Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Cramér-Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions.

Abstract-A linear prediction based method is proposed for real harmonic sinusoidal frequency estimation. The estimator basically involves two steps. An initial fundamental frequency estimate is first obtained by solving a standard least-squares equation with exploitation of the harmonic structure of the sinusoidal signal or by using the MUSIC approach. Based on the initial estimate, an optimally weighted least squares cost function is then constructed from which the final estimate is acquired. Computer simulations show that the performance of the estimator approaches Cramér-Rao lower bound for sufficiently high signal-to-noise ratios and/or data lengths.Index Terms-Frequency estimation, harmonic sinusoidal signals, weighted least squares.

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Carcino-embryonic antigen-related cell adhesion molecule 6 (CEACAM6), one of the members of human carcino-embryonic antigens, is a multifunctional regulatory protein involved in various cellular processes in cancers. Its role in malignant transformation and the clinical significance has been extensively studied in colonic and pancreatic cancers. However, relatively few studies have been done on breast cancers. In the current study, CEACAM6 expression in two independent cohorts of invasive breast cancers were evaluated immunohistochemically and correlated with clinico-pathological features, biomarker profiles and patient survival. In the primary cohort, CEACAM6 expression was detected in 37.1 % (312/840) of primary invasive cancers. It was positively correlated with HER2 (p < 0.001). Concordantly, HER2-OE subtype showed the highest CEACAM6 expression (62.7 %) among all molecular subtypes; whereas, other subtypes also showed substantial CEACAM6 expression (21.8-37.5 %). Interestingly, a significantly worse overall survival was found in high pN stage HER2 positive cancers with CEACAM6 positivity (log-rank = 4.452, p = 0.035) and this could be validated in an independent cohort. Additionally, HER2 signaling was found to induce SMAD3 phosphorylation and CEACAM6 expression in a cell line model. Likewise, in the primary tumors, a positive association was found between HER2 and SMAD3 phosphorylation in CEACAM6 positive cancers (p = 0.012). Overall, CEACAM6 was widely expressed in different molecular subtypes, but highest and significantly in HER2-OE breast cancer. Within this group, CEACAM6 was associated with adverse high nodal stage patient outcome. Given the wide expression of CEACAM6 in all breast cancers, its roles as prognostic marker and therapeutic target warrant further evaluation.

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Based on linear prediction and weighted least squares, an iterative procedure for frequency estimation of a complex sinusoid in white noise is devised. The proposed approach, which utilizes the first-order as well as higher-order linear prediction terms simultaneously but does not require phase unwrapping, can be considered as a generalized version of the weighted linear predictor frequency estimator. Computer simulations are included to contrast the performance of the proposed algorithms with Cramér-Rao lower bound in one-dimensional and two-dimensional frequency estimation.

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