Generalized robust shrinkage estimator and its application to STAP detection problem

Recently, in the context of covariance matrix estimation, in order to improve as well as to regularize the performance of the Tyler's estimator [1] also called the Fixed-Point Estimator (FPE) [2], a "shrinkage" fixed-point estimator has been introduced in [3]. First, this work extends the results of [3,4] by giving the general solution of the "shrinkage" fixed-point algorithm. Secondly, by analyzing this solution, called the generalized robust shrinkage estimator, we prove that this solution converges to a unique solution when the shrinkage parameter $\beta$ (losing factor) tends to 0. This solution is exactly the FPE with the trace of its inverse equal to the dimension of the problem. This general result allows one to give another interpretation of the FPE and more generally, on the Maximum Likelihood approach for covariance matrix estimation when constraints are added. Then, some simulations illustrate our theoretical results as well as the way to choose an optimal shrinkage factor. Finally, this work is applied to a Space-Time Adaptive Processing (STAP) detection problem on real STAP data

RF or THz signals generated from DC biased multimode lasers

Although self pulsating (SP) lasers are DC biased, they feature a modulation of the output power. For the results presented in this paper, the SP frequency corresponds to the frequency spacing between longitudinal modes or its second harmonic. The performances of both a 40 GHz self pulsating distributed Bragg reflector laser and of a 660 GHz slotted laser are presented. For the first laser, the radio frequency (RF) signal was analysed on electrical spectrum analyser and its linewidth was smaller that the sum of the main optical modes, proving a passive modelocking of the mode phases. For the slotted laser, a bolometer interfaced to a FT IR spectrometer is used for the terahertz (THz) detection. A signal 10 times larger than the noise level was measured with this set up. Both lasers have demonstrated to be an easy solution to produce RF or THz signal generator

Terahertz wave generation from a dc-biased multimode laser

We present results achieved in the generation of terahertz wave by a semiconductor laser. It is a Fabry–Pérot based device with shallow grooves implemented on its p-side to engineer the longitudinal mode spectrum. The laser is dc-biased and temperature controlled at 298 K. The main two modes are separated by 3 nm at 1550 nm with a side-mode-suppression ratio of 25 dB. Using a frequency resolved optical gating, evidence of mode beating at 373 GHz is observed. With a bolometer interfaced to a Fourier transform interferometer, the second harmonic signal is measured at 690 GHz

Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces

This paper is the third of a series on Hamiltonian stationary Lagrangian surfaces. We present here the most general theory, valid for any Hermitian symmetric target space. Using well-chosen moving frame formalism, we show that the equations are equivalent to an integrable system, generalizing the C^2 subcase analyzed in the first article (arXiv:math.DG/0009202). This system shares many features with the harmonic map equation of surfaces into symmetric spaces, allowing us to develop a theory close to Dorfmeister, Pedit and Wu's, including for instance a Weierstrass-type representation. Notice that this article encompasses the article mentioned above, although much fewer details will be given on that particular flat case

Passively mode-locked semiconductor lasers and their applications

In this paper we present some characterizations of passively mode-locked semiconductor lasers. These lasers are multimode and they exhibit a modulation of their output power even though they are DC-biased. The modulation frequency corresponds to their free-spectral range. We demonstrate their potential: for generation of ultra-fast modulation for THz wave generation at room temperature without any direct modulations applied, in the radio frequency range they synchronise their modulation to the bit-rate of an incoming signal used for clock extraction. Therefore these devices can be used for all-optical clock recovery