Jerome Lebrun

Gröbner bases and wavelet design

Abstract In this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example to construct the well-known Daubechies filters) is not applicable. In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Grobner algorithms offer an effective way to obtain solutions in some of these cases.

L2 orthogonal space time code for Continuous Phase Modulation

To combine the high power efficiency of Continuous Phase Modulation (CPM) with either high spectral efficiency or enhanced performance in low signal to noise conditions, some authors have proposed to introduce CPM in a MIMO frame, by using Space Time Codes (STC). In this paper, we address the code design problem of Space Time Block Codes combined with CPM and introduce a new design criterion based on L2 orthogonality. This L2 orthogonality condition, with the help of simplifying assumption, leads, in the 2times2 case, to a new family of codes. These codes generalize the Wang and Xia code, which was based on pointwise orthogonality. Simulations indicate that the new codes achieve full diversity and a slightly better coding gain. Moreover, one of the codes can be interpreted as two antennas fed by two conventional CPMs using the same data but with different alphabet sets. Inspection of these alphabet sets lead also to a simple explanation of the (small) spectrum broadening of Space Time Coded CPM.

Full Rate L2-Orthogonal Space-Time CPM for Three Antennas

To combine the power efficiency of continuous phase modulation (CPM) with enhanced performance in fading environments, some authors have suggested to use CPM in combination with space-time codes (STC). Recently, we have proposed a CPM ST-coding scheme based on L2-orthogonality for two transmitting antennas. In this paper we extend this approach to the three antennas case. We analytically derive a family of coding schemes which we call parallel code (PC). This code family has full rate and we prove that the proposed coding scheme achieves full diversity as confirmed by accompanying simulations. We detail an example of the proposed ST codes that can be interpreted as a conventional CPM scheme with different alphabet sets for the different transmit antennas which results in a simplified implementation. Thanks to L2-orthogonality, the decoding complexity, usually exponentially proportional to the number of transmitting antennas, is reduced to linear complexity.

Separable Implementation of L2-Orthogonal STC CPM with Fast Decoding

In this paper we present an alternative separable implementation of L2-orthogonal space-time codes (STC) for continuous phase modulation (CPM). In this approach, we split the STC CPM transmitter into a single conventional CPM modulator and a correction filter bank. While the CPM modulator is common to all transmit antennas, the correction filter bank applies different correction units to each antenna. Thereby desirable code properties as orthogonality and full diversity are achievable with just a slightly larger bandwidth demand. This new representation has three main advantages. First, it allows to easily generalize the orthogonality condition to any arbitrary number of transmit antennas. Second, for a quite general set of correction functions that we detail, it can be proved that full diversity is achieved. Third, by separating the modulation and correction steps inside the receiver, a simpler receiver can be designed as a bank of data independent inverse correction filters followed by a single CPM demodulator. Therefore, in this implementation, only one correlation filter bank for the detection of all transmitted signals is necessary. The decoding effort grows only linearly with the number of transmit antennas.

An algebraic approach to blind identification of communication channels

In this paper, a new algorithm for the blind identification of SISO communication channels is introduced. Based on methods from computational algebraic geometry, the approach achieves a full description of the solution space and thus avoids the local minima issue of adaptive algorithms. Furthermore, unlike most symbolic methods, the computational cost is kept low by a split of the problem into two stages. First, a symbolic pre-computation is done offline, once for all, to get a more convenient parametric representation of the problem. The solutions of the problem are then easily obtained from this representation by solving a single univariate polynomial equation.

Wireless Robotics: Generalization of an Efficient Approach with Multi-h CPM Signaling and L2-Orthogonal Space-Time Coding

Wireless Robotics has become an important research topic in the last two decades. The need of controlling a robot to perform tasks remotely has significantly increased with the number of applications in fields like medicine and military, among many others. Taking advantage of current standards like Bluetooth and Wifi, Wireless Robotics calls for low power consumption components, robustness and high data rate through the wireless channel. This call can be fulfilled with a reliable signaling format, satisfying the needs of low power consumption and high spectral efficiency. Besides, continuous phase modulation (CPM) has gained increasing attention due to its favorable trade-off between power and bandwidth efficiency. Multi-h CPM recently appeared as a generalization of single-h schemes so as to further decrease the need for bandwidth expansion over the wireless channel. Despite the interesting characteristics of CPM, the decoding of the received signal is particularly difficult in a multi-path wireless environment with no diversity. To provide some level of diversity, several authors have proposed to combine CPM with space-time block coding. A new family of codes for CPM, based on

Optimized L2-orthogonal STC CPM for 3 antennas

L^2

Zero-Forcing approach for L2-Orthogonal ST-Codes with CPM-OFDM schemes and frequency selective Rayleigh fading channels

-orthogonality was recently introduced in Hesse et al. (IEEE Trans Commun 59(11): 3158–3166, 2011). These full rate codes achieve full diversity and a low decoding complexity. In this paper, we detail a non trivial extension of these