Conception d'une forme d'onde IR-UWB optimisée et analyse de ses performances dans le canal IEEE 802.15.3a

National audienceIn this paper, an optimal approach based on B-splines functions is presented for the design of ultra wideband (UWB) pulses which satisfy simultaneously the following 3 criteria : compatibility with the spectral mask authorised in USA or in Europe, spectral efficiency and orthogonality of generated pulses. The first property allows UWB systems to coexist with other applications without disturbing their operation. The second property enables the efficient utilization of power spectrum allowed by mask while third permits to reduce inter-symbol interference. Afterwards, a general architecture of transmitter/receiver adapted to these types of signals is described using TH-PSM (Time Hopping - Pulse Shape Modulation). The performance of proposed UWB structure is firstly assessed in ideal channel i.e. in the presence of additive white Gaussian noise only and then in second step the performance is evaluated in a more realistic channel, i.e. the indoor multipath channel defined by the standard IEEE 802.15.3a

Cardinal Exponential Splines: Part II—Think Analog, Act Digital

By interpreting the Green-function reproduction property of exponential splines in signal processing terms, we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts. The link is that the latter are the B-spline coefficients of the former (which happen to be exponential splines). Motivated by this observation, we introduce an extended family of cardinal splines—the generalized E-splines—to generalize the concept for all convolution operators with rational transfer functions. We construct the corresponding compactly-supported B-spline basis functions, which are characterized by their poles and zeros, thereby establishing an interesting connection with analog filter design techniques. We investigate the properties of these new B-splines and present the corresponding signal processing calculus, which allows us to perform continuous-time operations, such as convolution, differential operators, and modulation, by simple application of the discrete version of these operators in the B-spline domain. In particular, we show how the formalism can be used to obtain exact, discrete implementations of analog filters. Finally, we apply our results to the design of hybrid signal processing systems that rely on digital filtering to compensate for the nonideal characteristics of real-world analog-to-digital (A-to-D) and D-to-A conversion systems