Capacity Analysis for Gaussian and Discrete Memoryless Interference Networks

Interference is an important issue for wireless communication systems where multiple uncoordinated users try to access to a common medium. The problem is even more crucial for next-generation cellular networks where frequency reuse becomes ever more intense, leading to more closely placed co-channel cells. This thesis describes our attempt to understand the impact of interference on communication performance as well as optimal ways to handle interference. From the theoretical point of view, we examine how interference affects the fundamental performance limits, and provide insights on how interference should be treated for various channel models under different operating conditions. From the practical design point of view, we provide solutions to improve the system performance under unknown interference using multiple independent receptions of the same information. For the simple two-user Gaussian interference channel, we establish that the simple Frequency Division Multiplexing (FDM) technique suffices to provide the optimal sum- rate within the largest computable subregion of the general achievable rate region for a certain interference range. For the two-user discrete memoryless interference channels, we characterize different interference regimes as well as the corresponding capacity results. They include one- sided weak interference and mixed interference conditions. The sum-rate capacities are derived in both cases. The conditions, capacity expressions, as well as the capacity achieving schemes are analogous to those of the Gaussian channel model. The study also leads to new outer bounds that can be used to resolve the capacities of several new discrete memoryless interference channels. A three-user interference up-link transmission model is introduced. By examining how interference affects the behavior of the performance limits, we capture the differences and similarities between the traditional two-user channel model and the channel model with more than two users. If the interference is very strong, the capacity region is just a simple extension of the two-user case. For the strong interference case, a line segment on the boundary of the capacity region is attained. When there are links with weak interference, the performance limits behave very differently from that of the two-user case: there is no single case that is found of which treating interference as noise is optimal. In particular, for a subclass of Gaussian channels with mixed interference, a boundary point of the capacity region is determined. For the Gaussian channel with weak interference, sum capacities are obtained under various channel coefficients and power constraint conditions. The optimalities in all the cases are obtained by decoding part of the interference. Finally, we investigate a topic that has practical ramifications in real communication systems. We consider in particular a diversity reception system where independently copies of low density parity check (LDPC) coded signals are received. Relying only on non-coherent reception in a highly dynamic environment with unknown interference, soft-decision combining is achieved whose performance is shown to improve significantly over existing approaches that rely on hard decision combining

Riemann solution for a class of morphodynamic shallow water dam-break problems

This paper investigates a family of dam-break problems over an erodible bed. The hydrodynamics are described by the shallow water equations, and the bed change by a sediment conservation equation, coupled to the hydrodynamics by a sediment transport (bed load) law. When the initial states ~Ul and ~Ur are sufficiently close to each other the resulting solutions are consistent with the theory proposed by Lax (1973), that for a Riemann problem of n equations there are n waves associated with the n characteristic families. However, for wet-dry dam-break problems over a mobile bed, there are 3 governing equations, but only 2 waves. One wave vanishes because of the presence of the dry bed. When initial left and right bed levels (Bl and Br) are far apart, it is shown that a semi-characteristic shock may occur, which happens because, unlike in shallow water flow on a fixed bed, the flux function is non-convex. In these circumstances it is shown that it is necessary to reconsider the usual shock conditions. Instead, we propose an implied internal shock structure the concept of which originates from the fact that the stationary shock over fixed bed discontinuity can be regarded as a limiting case of flow over a sloping fixed bed. The Needham & Hey (1991) approximation for the ambiguous integral term RhdB in the shock condition is improved based on this internal shock structure, such that mathematically valid solutions that incorporate a morphodynamic semi-characteristic shock are arrived at

Swash zone morphodynamic modelling including sediment entrained by bore-generated turbulence

In this paper we introduce a mathematical model of sediment entrainment due to bore-generated turbulence in a shallow water context. In this model, the entrainment is assumed to be proportional to the energy decay rate across a bore on a mobile bed. The energy decay rate across a bore on a mobile bed is derived analytically. This model is incorporated into the one dimensional morphodynamic model developed by Zhu and Dodd (2015), which includes bed- and suspended load transport. This results in new shock conditions, which allow for sediment entrainment at a shock. With it we investigate the effects of sediment entrainment due to bore-generated turbulence on beachface evolution under a single swash event driven by a solitary wave. The simulation results imply that sediment entrainment by bore turbulence at the incoming bore dominates over sediment mobilisation by bed shear stress. In contrast, the backwash bore is dominated by bed shear stress related processes. The morphodynamic impact of bore turbulence on this swash event is primarily erosion of the sea bed seaward of the initial shoreline. Any sediment remaining in the water column seaward of this point is then available to be transported by subsequent events. It is shown that the bed step is primarily a bed load related feature, with sediment entrained as suspended load counteracting the bed step growth

A light Higgs scalar in the NMSSM confronted with the latest LHC Higgs data

In the Next-to-Minimal Supersymemtric Standard Model (NMSSM), one of the neutral Higgs scalars (CP-even or CP-odd) may be lighter than half of the SM-like Higgs boson. In this case, the SM-like Higgs boson h can decay into such a light scalar pair and consequently the diphoton and ZZ signal rates at the LHC will be suppressed. In this work, we examine the constraints of the latest LHC Higgs data on such a possibility. We perform a comprehensive scan over the parameter space of the NMSSM by considering various experimental constraints and find that the LHC Higgs data can readily constrain the parameter space and the properties of the light scalar, e.g., at 3 $\sigma$ level this light scalar should be highly singlet dominant and the branching ratio of the SM-like Higgs boson decay into the scalar pair should be less than about 30%. Also we investigate the detection of this scalar at various colliders. Through a detailed Monte Carlo simulation we find that under the constraints of the current Higgs data this light scalar can be accessible at the LHC-14 with an integrated luminosity over 300 fb$^{-1}$.Comment: Accepted by JHE

Impact of a uniform bore on an erodible beach

AbstractThe impact of a uniform bore on an erodible beach is investigated using a shallow water description and a sediment conservation equation. The solution, which is obtained using the method of characteristics, employs a cubic bed-load formula and a crudely calibrated sediment transport coefficient. It is found that, as with the fixed bed case of Hibberd and Peregrine (1979), a backwash bore forms, which for the mobile bed also comprises a bed step. It is found that this bed step achieves a significant height. The volume of sand deposited above the final still water level is consistent with that observed under certain events on some sandy beaches

1D morphodynamical modelling of swash zone beachface evolution

The beachface evolution in the swash zone under different single swash events is investigated by fully coupled simulations. Two fully coupled models (bed-load-only and combined load models) comprising the one dimensional shallow water equations and bed evolution equation are developed. The two coupled systems are solved by the specified time interval method of characteristics (STI MOC) (Kelly and Dodd, 2009, 2010), which can resolve shocks very accurately. The fully coupled bed-load-only simulations with six different sediment transport formulae for a single Peregrine and Williams (2001) (PW01) swash over an erodible plane beach all yield net erosion all over the swash zone. Consistent with Kelly and Dodd (2010), however, full coupling yields significantly less erosion for all the q=q(u) (q instantaneous sediment flux and u water velocity) formulae compared to the equivalent uncoupled results. It is also shown that including a dependence on h (water depth) in q can result in net deposition in the upper swash, and that with such a formula q the shoreline motion over a plane mobile beach is ballistic in the uprush. Bed shear stress described by the Chezy law is further included in fully coupled simulations, and much reduced maximum inundation and net offshore sediment transport are predicted both for q=q(u) and q=q(h,u). Although the net sediment flux at x=0 under one PW01 event is still offshore, deposition in the middle or upper swash may be predicted when bed shear stress is included. The fully coupled bed-load-only simulation with q=q(u) for a single Hibberd and Peregrine (1979) (HP79) swash event predicts considerable deposition in the swash zone. A backwash bore develops, associated with which a bed step forms when the shoreline catches up with the backwash bore. The subsequent shoreline movement is obtained by the Riemann solution for a wet-dry dam-break problem with a bed step. A bed step also occurs under a solitary wave simulation; its height is much larger than that under the HP79 simulation. Bed step height is found to depend largely on the water depth on the seaward side of the step, which is related to the swash event and the step position. The PW01 and HP79 swash events are also examined by the combined load model. Results show that suspended load results in deposition in the upper swash and erosion in the lower swash. However, pre-suspended sediment results in deposition in the lower swash, implying that net bed change due to suspended load in the lower swash could be depositional. The inclusion of suspended load has much smaller effect on the maximum inundation and swash hydrodynamics than bed load. The inclusion of bed load reduces the maximum inundation significantly; importantly, bed load results in the formation of a bed step and dominates the beach change near the bed step even when suspended load is dominant in the overall beach change

Coastal morphodynamical modelling in nonlinear shallow water framework using a coordinate transformation method

A 1D numerical model of Nonlinear Shallow Water Equations (NSWEs) coupled to an advection equation for suspended sediment and a bed evolution equation is developed. The moving boundary at the shoreline is treated by a coordinate transformation method (CTM). An absorbing-generating seaward boundary condition in the transformed variables is also developed. The purely hydrodynamic component (NSWEs) is verifed against analytical results. The NSWEs plus advection equation is verifed quasi-analytical results. The fully-coupled model with bed change due to bed-load is verifed against a single swash event and long-term numerical simulation. Excellent agreement is observed in all verifcations