Beamforming and interference cancellation in D2D communication underlaying cellular networks

This paper presents an analytical performance investigation of both beamforming (BF) and interference cancellation (IC) strategies for a device-to-device (D2D) communication system underlaying a cellular network with an M-antenna base station (BS). We first derive new closed-form expressions for the ergodic achievable rate for BF and IC precoding strategies with quantized channel state information (CSI), as well as, perfect CSI. Then, novel lower and upper bounds are derived which apply for an arbitrary number of antennas and are shown to be sufficiently tight to the Monte-Carlo results. Based on these results, we examine in detail three important special cases including: high signal-to-noise ratio (SNR), weak interference between cellular link and D2D link, and BS equipped with a large number of antennas. We also derive asymptotic expressions for the ergodic achievable rate for these scenarios. Based on these results, we obtain valuable insights into the impact of the system parameters, such as the number of antennas, SNR and the interference for each link. In particular, we show that an irreducible saturation point exists in the high SNR regime, while the ergodic rate under IC strategy is verified to be always better than that under BF strategy. We also reveal that the ergodic achievable rate under perfect CSI scales as log2M, whilst it reaches a ceiling with quantized CSI.

Combined Conduction-Convection-Radiation Heat Transfer of Slip Flow inside a Micro-channel Filled with a Cellular Porous Material

Combined conduction–convection–radiation heat transfer is investigated numerically in a micro-channel filled with a saturated cellular porous medium, with the channel walls held at a constant heat flux. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous–fluid system are studied by considering hydrodynamically fully developed flow and applying the Darcy–Brinkman flow model. One energy equation model based on the local thermal equilibrium condition is adopted to evaluate the temperature field within the porous medium. Combined conduction and radiation heat transfer is treated as an effective conduction process with a temperature-dependent effective thermal conductivity. Results are reported in terms of the average Nusselt number and dimensionless temperature distribution, as a function of velocity slip coefficient, temperature jump coefficient, porous medium shape parameter and radiation parameters. Results show that increasing the radiation parameter (Tr)(Tr) and the temperature jump coefficient flattens the dimensionless temperature profile. The Nusselt numbers are more sensitive to the variation in the temperature jump coefficient rather than to the velocity slip coefficient. Such that for high porous medium shape parameter, the Nusselt number is found to be independent of velocity slip. Furthermore, it is found that as the temperature jump coefficient increases, the Nusselt number decrease. In addition, for high temperature jump coefficients, the Nusselt number is found to be insensitive to the radiation parameters and porous medium shape parameter. It is also concluded that compared with the conventional macro-channels, wherein using a porous material enhances the rate of heat transfer (up to about 40 % compared to the clear channel), insertion of a porous material inside a micro-channel in slip regime does not effectively enhance the rate of heat transfer that is about 2 %.