Resource Allocation for Delay Differentiated Traffic in Multiuser OFDM Systems

Most existing work on adaptive allocation of subcarriers and power in multiuser orthogonal frequency division multiplexing (OFDM) systems has focused on homogeneous traffic consisting solely of either delay-constrained data (guaranteed service) or non-delay-constrained data (best-effort service). In this paper, we investigate the resource allocation problem in a heterogeneous multiuser OFDM system with both delay-constrained (DC) and non-delay-constrained (NDC) traffic. The objective is to maximize the sum-rate of all the users with NDC traffic while maintaining guaranteed rates for the users with DC traffic under a total transmit power constraint. Through our analysis we show that the optimal power allocation over subcarriers follows a multi-level water-filling principle; moreover, the valid candidates competing for each subcarrier include only one NDC user but all DC users. By converting this combinatorial problem with exponential complexity into a convex problem or showing that it can be solved in the dual domain, efficient iterative algorithms are proposed to find the optimal solutions. To further reduce the computational cost, a low-complexity suboptimal algorithm is also developed. Numerical studies are conducted to evaluate the performance the proposed algorithms in terms of service outage probability, achievable transmission rate pairs for DC and NDC traffic, and multiuser diversity.Comment: 29 pages, 8 figures, submitted to IEEE Transactions on Wireless Communication

Multi-photon Scattering Theory and Generalized Master Equations

We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time-evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S-matrix of the asymptotic in- and out- states. For the case of few incident photons in the waveguide, we also re-derive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the forth one, we show how a quantum emitter can generate entanglement of out-going photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.Comment: 21 pages,10 figure