The problem of sampling a 2D Poisson process is considered. Recently, such problems have been denoted as sampling of signals with finite rate of innovation. Therefore, a well-known sampling approach for the 1D approach is extended to the 2D case and the theoretic sampling bounds as well as the reconstruction approach are shown. By providing results from numerical simulations it can be demonstrated that reconstruction is exact up to numerical precision.Introduction: In [1 -5] sampling and reconstructing finite rate of innovation (FRI) signals have been analysed for periodic and aperiodic signals as well as for the noisy and the noiseless case. In general, FRI signals are not limited to a certain bandwidth and therefore, according to the Nyquist-Shannon sampling theorem, such signals would have to be captured with an infinite sampling rate. However, the number of parameters to be determined per unit of time is finite so that sampling at finite (low) rate should be possible. Two common approaches use ideal lowpass or Gaussian sampling kernels for the 1D [2, 5] and for the 2D [3, 4] case. However, these approaches suffer from different restrictions. On the one hand, the impulse response of the ideal lowpass sampling kernel is infinitely long and reconstruction will thus work only for periodic problems. On the other hand, the Gaussian sampling kernel requires a weighting of sampling values depending on the sampling position. Therefore, this method suffers from numerical instability even for small problem sizes [6,7].
This work analyses a multi-user relay network with orthogonal channel access using OFDMA. For the considered Multiple Access Relay Channel (MARC) the relay performs non adaptive Decode & Forward (DF) with repetition coding. The objective of this paper is to find a resource allocation (subcarrier and power) which maximises the sum rate. Within this context, different algorithms are proposed which are supposed to be near optimum. The algorithms will be derived and numerical results for their sum rate performance are presented.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.